Add post about sidenotes

.gitignore

@@ -0,0 +1 @@
+**/build/*

assets/scss/gmachine.scss

@@ -0,0 +1,44 @@
+@import "style.scss";
+
+.gmachine-instruction {
+    display: flex;
+    @include bordered-block;
+}
+
+.gmachine-instruction-name {
+    padding: 10px;
+    border-right: $standard-border;
+    flex-grow: 1;
+    flex-basis: 20%;
+    text-align: center;
+}
+
+.gmachine-instruction-sem {
+    width: 100%;
+    flex-grow: 4;
+}
+
+.gmachine-inner {
+    border-bottom: $standard-border;
+    width: 100%;
+
+    &:last-child {
+        border-bottom: none;
+    }
+}
+
+.gmachine-inner-label {
+    padding: 10px;
+    font-weight: bold;
+}
+
+.gmachine-inner-text {
+    padding: 10px;
+    text-align: right;
+    flex-grow: 1;
+}
+
+.gmachine-instruction-name, .gmachine-inner-label, .gmachine-inner {
+    display: flex;
+    align-items: center;
+}

code/compiler/04/CMakeLists.txt

@@ -16,6 +16,7 @@ add_executable(compiler
     ast.cpp ast.hpp definition.cpp
     env.cpp env.hpp
     type.cpp type.hpp
+    error.cpp error.hpp
     ${BISON_parser_OUTPUTS}
     ${FLEX_scanner_OUTPUTS}
     main.cpp

code/compiler/04/ast.cpp

@@ -1,5 +1,6 @@
 #include "ast.hpp"
 #include <ostream>
+#include "error.hpp"
 
 std::string op_name(binop op) {
     switch(op) {
@@ -8,7 +9,7 @@ std::string op_name(binop op) {
         case TIMES: return "*";
         case DIVIDE: return "/";
     }
-    throw 0;
+    return "??";
 }
 
 void print_indent(int n, std::ostream& to) {
@@ -53,7 +54,7 @@ type_ptr ast_binop::typecheck(type_mgr& mgr, const type_env& env) const {
     type_ptr ltype = left->typecheck(mgr, env);
     type_ptr rtype = right->typecheck(mgr, env);
     type_ptr ftype = env.lookup(op_name(op));
-    if(!ftype) throw 0;
+    if(!ftype) throw type_error(std::string("unknown binary operator ") + op_name(op));
 
     type_ptr return_type = mgr.new_type();
     type_ptr arrow_one = type_ptr(new type_arr(rtype, return_type));
@@ -92,7 +93,8 @@ void ast_case::print(int indent, std::ostream& to) const {
 }
 
 type_ptr ast_case::typecheck(type_mgr& mgr, const type_env& env) const {
-    type_ptr case_type = of->typecheck(mgr, env);
+    type_var* var;
+    type_ptr case_type = mgr.resolve(of->typecheck(mgr, env), var);
     type_ptr branch_type = mgr.new_type();
 
     for(auto& branch : branches) {
@@ -102,6 +104,11 @@ type_ptr ast_case::typecheck(type_mgr& mgr, const type_env& env) const {
         mgr.unify(branch_type, curr_branch_type);
     }
 
+    case_type = mgr.resolve(case_type, var);
+    if(!dynamic_cast<type_base*>(case_type.get())) {
+        throw type_error("attempting case analysis of non-data type");
+    }
+
     return branch_type;
 }
 
@@ -122,17 +129,17 @@ void pattern_constr::print(std::ostream& to) const {
 
 void pattern_constr::match(type_ptr t, type_mgr& mgr, type_env& env) const {
     type_ptr constructor_type = env.lookup(constr);
-    if(!constructor_type) throw 0;
+    if(!constructor_type) {
+        throw type_error(std::string("pattern using unknown constructor ") + constr);
+    }
 
     for(int i = 0; i < params.size(); i++) {
         type_arr* arr = dynamic_cast<type_arr*>(constructor_type.get());
-        if(!arr) throw 0;
+        if(!arr) throw type_error("too many parameters in constructor pattern");
 
         env.bind(params[i], arr->left);
         constructor_type = arr->right;
     }
 
     mgr.unify(t, constructor_type);
-    type_base* result_type = dynamic_cast<type_base*>(constructor_type.get());
-    if(!result_type) throw 0;
 }

code/compiler/04/error.cpp

@@ -0,0 +1,5 @@
+#include "error.hpp"
+
+const char* type_error::what() const noexcept {
+    return "an error occured while checking the types of the program";
+}

code/compiler/04/error.hpp

@@ -0,0 +1,21 @@
+#pragma once
+#include <exception>
+#include "type.hpp"
+
+struct type_error : std::exception {
+    std::string description;
+
+    type_error(std::string d)
+        : description(std::move(d)) {}
+
+    const char* what() const noexcept override;
+};
+
+struct unification_error : public type_error {
+    type_ptr left;
+    type_ptr right;
+
+    unification_error(type_ptr l, type_ptr r)
+        : left(std::move(l)), right(std::move(r)), 
+            type_error("failed to unify types") {}
+};

code/compiler/04/main.cpp

@@ -1,7 +1,8 @@
 #include "ast.hpp"
-#include "parser.hpp"
-#include "type.hpp"
 #include <iostream>
+#include "parser.hpp"
+#include "error.hpp"
+#include "type.hpp"
 
 void yy::parser::error(const std::string& msg) {
     std::cout << "An error occured: " << msg << std::endl;
@@ -9,10 +10,9 @@ void yy::parser::error(const std::string& msg) {
 
 extern std::vector<definition_ptr> program;
 
-void typecheck_program(const std::vector<definition_ptr>& prog) {
+void typecheck_program(
-    type_mgr mgr;
+        const std::vector<definition_ptr>& prog,
-    type_env env;
+        type_mgr& mgr, type_env& env) {
-
     type_ptr int_type = type_ptr(new type_base("Int")); 
     type_ptr binop_type = type_ptr(new type_arr(
                 int_type,
@@ -40,6 +40,9 @@ void typecheck_program(const std::vector<definition_ptr>& prog) {
 
 int main() {
     yy::parser parser;
+    type_mgr mgr;
+    type_env env;
+
     parser.parse();
     for(auto& definition : program) {
         definition_defn* def = dynamic_cast<definition_defn*>(definition.get());
@@ -51,6 +54,17 @@ int main() {
 
         def->body->print(1, std::cout);
     }
-    typecheck_program(program);
+    try {
-    std::cout << program.size() << std::endl;
+        typecheck_program(program, mgr, env);
+    } catch(unification_error& err) {
+        std::cout << "failed to unify types: " << std::endl;
+        std::cout << "  (1) \033[34m";
+        err.left->print(mgr, std::cout);
+        std::cout << "\033[0m" << std::endl;
+        std::cout << "  (2) \033[32m";
+        err.right->print(mgr, std::cout);
+        std::cout << "\033[0m" << std::endl;
+    } catch(type_error& err) {
+        std::cout << "failed to type check program: " << err.description << std::endl;
+    }
 }

code/compiler/04/type.cpp

@@ -1,6 +1,7 @@
 #include "type.hpp"
 #include <sstream>
 #include <algorithm>
+#include "error.hpp"
 
 void type_var::print(const type_mgr& mgr, std::ostream& to) const {
     auto it = mgr.types.find(name);
@@ -87,7 +88,7 @@ void type_mgr::unify(type_ptr l, type_ptr r) {
         if(lid->name == rid->name) return;
     }
 
-    throw 0;
+    throw unification_error(l, r);
 }
 
 void type_mgr::bind(const std::string& s, type_ptr t) {

code/compiler/06/CMakeLists.txt

@@ -0,0 +1,28 @@
+cmake_minimum_required(VERSION 3.1)
+project(compiler)
+
+find_package(BISON)
+find_package(FLEX)
+bison_target(parser
+    ${CMAKE_CURRENT_SOURCE_DIR}/parser.y
+    ${CMAKE_CURRENT_BINARY_DIR}/parser.cpp
+    COMPILE_FLAGS "-d")
+flex_target(scanner
+    ${CMAKE_CURRENT_SOURCE_DIR}/scanner.l
+    ${CMAKE_CURRENT_BINARY_DIR}/scanner.cpp)
+add_flex_bison_dependency(scanner parser)
+
+add_executable(compiler
+    ast.cpp ast.hpp definition.cpp
+    type_env.cpp type_env.hpp
+    env.cpp env.hpp
+    type.cpp type.hpp
+    error.cpp error.hpp
+    binop.cpp binop.hpp
+    instruction.cpp instruction.hpp
+    ${BISON_parser_OUTPUTS}
+    ${FLEX_scanner_OUTPUTS}
+    main.cpp
+)
+target_include_directories(compiler PUBLIC ${CMAKE_CURRENT_SOURCE_DIR})
+target_include_directories(compiler PUBLIC ${CMAKE_CURRENT_BINARY_DIR})

code/compiler/06/ast.cpp

@@ -0,0 +1,262 @@
+#include "ast.hpp"
+#include <ostream>
+#include "error.hpp"
+
+static void print_indent(int n, std::ostream& to) {
+    while(n--) to << "  ";
+}
+
+type_ptr ast::typecheck_common(type_mgr& mgr, const type_env& env) {
+    node_type = typecheck(mgr, env);
+    return node_type;
+}
+
+void ast::resolve_common(const type_mgr& mgr) {
+    type_var* var;
+    type_ptr resolved_type = mgr.resolve(node_type, var);
+    if(var) throw type_error("ambiguously typed program");
+
+    resolve(mgr);
+    node_type = std::move(resolved_type);
+}
+
+void ast_int::print(int indent, std::ostream& to) const {
+    print_indent(indent, to);
+    to << "INT: " << value << std::endl;
+}
+
+type_ptr ast_int::typecheck(type_mgr& mgr, const type_env& env) const {
+    return type_ptr(new type_base("Int"));
+}
+
+void ast_int::resolve(const type_mgr& mgr) const {
+    
+}
+
+void ast_int::compile(const env_ptr& env, std::vector<instruction_ptr>& into) const {
+    into.push_back(instruction_ptr(new instruction_pushint(value)));
+}
+
+void ast_lid::print(int indent, std::ostream& to) const {
+    print_indent(indent, to);
+    to << "LID: " << id << std::endl;
+}
+
+type_ptr ast_lid::typecheck(type_mgr& mgr, const type_env& env) const {
+    return env.lookup(id);
+}
+
+void ast_lid::resolve(const type_mgr& mgr) const {
+
+}
+
+void ast_lid::compile(const env_ptr& env, std::vector<instruction_ptr>& into) const {
+    into.push_back(instruction_ptr(
+        env->has_variable(id) ?
+            (instruction*) new instruction_push(env->get_offset(id)) :
+            (instruction*) new instruction_pushglobal(id)));
+}
+
+void ast_uid::print(int indent, std::ostream& to) const {
+    print_indent(indent, to);
+    to << "UID: " << id << std::endl;
+}
+
+type_ptr ast_uid::typecheck(type_mgr& mgr, const type_env& env) const {
+    return env.lookup(id);
+}
+
+void ast_uid::resolve(const type_mgr& mgr) const {
+
+}
+
+void ast_uid::compile(const env_ptr& env, std::vector<instruction_ptr>& into) const {
+    into.push_back(instruction_ptr(new instruction_pushglobal(id)));
+}
+
+void ast_binop::print(int indent, std::ostream& to) const {
+    print_indent(indent, to);
+    to << "BINOP: " << op_name(op) << std::endl;
+    left->print(indent + 1, to);
+    right->print(indent + 1, to);
+}
+
+type_ptr ast_binop::typecheck(type_mgr& mgr, const type_env& env) const {
+    type_ptr ltype = left->typecheck_common(mgr, env);
+    type_ptr rtype = right->typecheck_common(mgr, env);
+    type_ptr ftype = env.lookup(op_name(op));
+    if(!ftype) throw type_error(std::string("unknown binary operator ") + op_name(op));
+
+    type_ptr return_type = mgr.new_type();
+    type_ptr arrow_one = type_ptr(new type_arr(rtype, return_type));
+    type_ptr arrow_two = type_ptr(new type_arr(ltype, arrow_one));
+
+    mgr.unify(arrow_two, ftype);
+    return return_type;
+}
+
+void ast_binop::resolve(const type_mgr& mgr) const {
+    left->resolve_common(mgr);
+    right->resolve_common(mgr);
+}
+
+void ast_binop::compile(const env_ptr& env, std::vector<instruction_ptr>& into) const {
+    right->compile(env, into);
+    left->compile(env_ptr(new env_offset(1, env)), into);
+
+    into.push_back(instruction_ptr(new instruction_pushglobal(op_action(op))));
+    into.push_back(instruction_ptr(new instruction_mkapp()));
+    into.push_back(instruction_ptr(new instruction_mkapp()));
+}
+
+void ast_app::print(int indent, std::ostream& to) const {
+    print_indent(indent, to);
+    to << "APP:" << std::endl;
+    left->print(indent + 1, to);
+    right->print(indent + 1, to);
+}
+
+type_ptr ast_app::typecheck(type_mgr& mgr, const type_env& env) const {
+    type_ptr ltype = left->typecheck_common(mgr, env);
+    type_ptr rtype = right->typecheck_common(mgr, env);
+
+    type_ptr return_type = mgr.new_type();
+    type_ptr arrow = type_ptr(new type_arr(rtype, return_type));
+    mgr.unify(arrow, ltype);
+    return return_type;
+}
+
+void ast_app::resolve(const type_mgr& mgr) const {
+    left->resolve_common(mgr);
+    right->resolve_common(mgr);
+}
+
+void ast_app::compile(const env_ptr& env, std::vector<instruction_ptr>& into) const {
+    right->compile(env, into);
+    left->compile(env_ptr(new env_offset(1, env)), into);
+    into.push_back(instruction_ptr(new instruction_mkapp()));
+}
+
+void ast_case::print(int indent, std::ostream& to) const {
+    print_indent(indent, to);
+    to << "CASE: " << std::endl;
+    for(auto& branch : branches) {
+        print_indent(indent + 1, to);
+        branch->pat->print(to);
+        to << std::endl;
+        branch->expr->print(indent + 2, to);
+    }
+}
+
+type_ptr ast_case::typecheck(type_mgr& mgr, const type_env& env) const {
+    type_var* var;
+    type_ptr case_type = mgr.resolve(of->typecheck_common(mgr, env), var);
+    type_ptr branch_type = mgr.new_type();
+
+    for(auto& branch : branches) {
+        type_env new_env = env.scope();
+        branch->pat->match(case_type, mgr, new_env);
+        type_ptr curr_branch_type = branch->expr->typecheck_common(mgr, new_env);
+        mgr.unify(branch_type, curr_branch_type);
+    }
+
+    case_type = mgr.resolve(case_type, var);
+    if(!dynamic_cast<type_data*>(case_type.get())) {
+        throw type_error("attempting case analysis of non-data type");
+    }
+
+    return branch_type;
+}
+
+void ast_case::resolve(const type_mgr& mgr) const {
+    of->resolve_common(mgr);
+    for(auto& branch : branches) {
+        branch->expr->resolve_common(mgr);
+    }
+}
+
+void ast_case::compile(const env_ptr& env, std::vector<instruction_ptr>& into) const {
+    type_data* type = dynamic_cast<type_data*>(of->node_type.get());
+
+    of->compile(env, into);
+    into.push_back(instruction_ptr(new instruction_eval()));
+
+    instruction_jump* jump_instruction = new instruction_jump();
+    into.push_back(instruction_ptr(jump_instruction));
+    for(auto& branch : branches) {
+        std::vector<instruction_ptr> branch_instructions;
+        pattern_var* vpat;
+        pattern_constr* cpat;
+
+        if((vpat = dynamic_cast<pattern_var*>(branch->pat.get()))) {
+            branch->expr->compile(env_ptr(new env_offset(1, env)), branch_instructions);
+
+            for(auto& constr_pair : type->constructors) {
+                if(jump_instruction->tag_mappings.find(constr_pair.second.tag) !=
+                        jump_instruction->tag_mappings.end())
+                    break;
+
+                jump_instruction->tag_mappings[constr_pair.second.tag] =
+                    jump_instruction->branches.size();
+            }
+            jump_instruction->branches.push_back(std::move(branch_instructions));
+        } else if((cpat = dynamic_cast<pattern_constr*>(branch->pat.get()))) {
+            env_ptr new_env = env;
+            for(auto it = cpat->params.rbegin(); it != cpat->params.rend(); it++) {
+                new_env = env_ptr(new env_var(*it, new_env));
+            }
+
+            branch_instructions.push_back(instruction_ptr(new instruction_split()));
+            branch->expr->compile(new_env, branch_instructions);
+            branch_instructions.push_back(instruction_ptr(new instruction_slide(
+                            cpat->params.size())));
+
+            int new_tag = type->constructors[cpat->constr].tag;
+            if(jump_instruction->tag_mappings.find(new_tag) !=
+                    jump_instruction->tag_mappings.end())
+                throw type_error("technically not a type error: duplicate pattern");
+
+            jump_instruction->tag_mappings[new_tag] =
+                jump_instruction->branches.size();
+            jump_instruction->branches.push_back(std::move(branch_instructions));
+        }
+    }
+
+    for(auto& constr_pair : type->constructors) {
+        if(jump_instruction->tag_mappings.find(constr_pair.second.tag) ==
+                jump_instruction->tag_mappings.end())
+            throw type_error("non-total pattern");
+    }
+}
+
+void pattern_var::print(std::ostream& to) const {
+    to << var;
+}
+
+void pattern_var::match(type_ptr t, type_mgr& mgr, type_env& env) const {
+    env.bind(var, t);
+}
+
+void pattern_constr::print(std::ostream& to) const {
+    to << constr;
+    for(auto& param : params) {
+        to << " " << param;
+    }
+}
+
+void pattern_constr::match(type_ptr t, type_mgr& mgr, type_env& env) const {
+    type_ptr constructor_type = env.lookup(constr);
+    if(!constructor_type) {
+        throw type_error(std::string("pattern using unknown constructor ") + constr);
+    }
+
+    for(int i = 0; i < params.size(); i++) {
+        type_arr* arr = dynamic_cast<type_arr*>(constructor_type.get());
+        if(!arr) throw type_error("too many parameters in constructor pattern");
+
+        env.bind(params[i], arr->left);
+        constructor_type = arr->right;
+    }
+
+    mgr.unify(t, constructor_type);
+}

code/compiler/06/ast.hpp

@@ -0,0 +1,197 @@
+#pragma once
+#include <memory>
+#include <vector>
+#include "type.hpp"
+#include "type_env.hpp"
+#include "binop.hpp"
+#include "instruction.hpp"
+#include "env.hpp"
+
+struct ast {
+    type_ptr node_type;
+
+    virtual ~ast() = default;
+
+    virtual void print(int indent, std::ostream& to) const = 0;
+    virtual type_ptr typecheck(type_mgr& mgr, const type_env& env) const = 0;
+    virtual void resolve(const type_mgr& mgr) const = 0;
+    virtual void compile(const env_ptr& env,
+        std::vector<instruction_ptr>& into) const = 0;
+
+    type_ptr typecheck_common(type_mgr& mgr, const type_env& env);
+    void resolve_common(const type_mgr& mgr);
+};
+
+using ast_ptr = std::unique_ptr<ast>;
+
+struct pattern {
+    virtual ~pattern() = default;
+
+    virtual void print(std::ostream& to) const = 0;
+    virtual void match(type_ptr t, type_mgr& mgr, type_env& env) const = 0;
+};
+
+using pattern_ptr = std::unique_ptr<pattern>;
+
+struct branch {
+    pattern_ptr pat;
+    ast_ptr expr;
+
+    branch(pattern_ptr p, ast_ptr a)
+        : pat(std::move(p)), expr(std::move(a)) {}
+};
+
+using branch_ptr = std::unique_ptr<branch>;
+
+struct constructor {
+    std::string name;
+    std::vector<std::string> types;
+    int8_t tag;
+
+    constructor(std::string n, std::vector<std::string> ts)
+        : name(std::move(n)), types(std::move(ts)) {}
+};
+
+using constructor_ptr = std::unique_ptr<constructor>;
+
+struct definition {
+    virtual ~definition() = default;
+    
+    virtual void typecheck_first(type_mgr& mgr, type_env& env) = 0;
+    virtual void typecheck_second(type_mgr& mgr, const type_env& env) const = 0;
+    virtual void resolve(const type_mgr& mgr) = 0;
+    virtual void compile() = 0;
+};
+
+using definition_ptr = std::unique_ptr<definition>;
+
+struct ast_int : public ast {
+    int value;
+
+    explicit ast_int(int v)
+        : value(v) {}
+
+    void print(int indent, std::ostream& to) const;
+    type_ptr typecheck(type_mgr& mgr, const type_env& env) const;
+    void resolve(const type_mgr& mgr) const;
+    void compile(const env_ptr& env, std::vector<instruction_ptr>& into) const;
+};
+
+struct ast_lid : public ast {
+    std::string id;
+
+    explicit ast_lid(std::string i)
+        : id(std::move(i)) {}
+
+    void print(int indent, std::ostream& to) const;
+    type_ptr typecheck(type_mgr& mgr, const type_env& env) const;
+    void resolve(const type_mgr& mgr) const;
+    void compile(const env_ptr& env, std::vector<instruction_ptr>& into) const;
+};
+
+struct ast_uid : public ast {
+    std::string id;
+
+    explicit ast_uid(std::string i)
+        : id(std::move(i)) {}
+
+    void print(int indent, std::ostream& to) const;
+    type_ptr typecheck(type_mgr& mgr, const type_env& env) const;
+    void resolve(const type_mgr& mgr) const;
+    void compile(const env_ptr& env, std::vector<instruction_ptr>& into) const;
+};
+
+struct ast_binop : public ast {
+    binop op;  
+    ast_ptr left;
+    ast_ptr right;
+
+    ast_binop(binop o, ast_ptr l, ast_ptr r)
+        : op(o), left(std::move(l)), right(std::move(r)) {}
+
+    void print(int indent, std::ostream& to) const;
+    type_ptr typecheck(type_mgr& mgr, const type_env& env) const;
+    void resolve(const type_mgr& mgr) const;
+    void compile(const env_ptr& env, std::vector<instruction_ptr>& into) const;
+};
+
+struct ast_app : public ast {
+    ast_ptr left;
+    ast_ptr right;
+
+    ast_app(ast_ptr l, ast_ptr r)
+        : left(std::move(l)), right(std::move(r)) {}
+
+    void print(int indent, std::ostream& to) const;
+    type_ptr typecheck(type_mgr& mgr, const type_env& env) const;
+    void resolve(const type_mgr& mgr) const;
+    void compile(const env_ptr& env, std::vector<instruction_ptr>& into) const;
+};
+
+struct ast_case : public ast {
+    ast_ptr of;
+    std::vector<branch_ptr> branches;
+
+    ast_case(ast_ptr o, std::vector<branch_ptr> b)
+        : of(std::move(o)), branches(std::move(b)) {}
+
+    void print(int indent, std::ostream& to) const;
+    type_ptr typecheck(type_mgr& mgr, const type_env& env) const;
+    void resolve(const type_mgr& mgr) const;
+    void compile(const env_ptr& env, std::vector<instruction_ptr>& into) const;
+};
+
+struct pattern_var : public pattern {
+    std::string var;
+
+    pattern_var(std::string v)
+        : var(std::move(v)) {}
+
+    void print(std::ostream &to) const;
+    void match(type_ptr t, type_mgr& mgr, type_env& env) const;
+};
+
+struct pattern_constr : public pattern {
+    std::string constr;
+    std::vector<std::string> params;
+
+    pattern_constr(std::string c, std::vector<std::string> p)
+        : constr(std::move(c)), params(std::move(p)) {}
+
+    void print(std::ostream &to) const;
+    void match(type_ptr t, type_mgr&, type_env& env) const;
+};
+
+struct definition_defn : public definition {
+    std::string name;
+    std::vector<std::string> params;
+    ast_ptr body;
+
+    type_ptr return_type;
+    std::vector<type_ptr> param_types;
+
+    std::vector<instruction_ptr> instructions;
+
+    definition_defn(std::string n, std::vector<std::string> p, ast_ptr b)
+        : name(std::move(n)), params(std::move(p)), body(std::move(b)) {
+
+    }
+
+    void typecheck_first(type_mgr& mgr, type_env& env);
+    void typecheck_second(type_mgr& mgr, const type_env& env) const;
+    void resolve(const type_mgr& mgr);
+    void compile();
+};
+
+struct definition_data : public definition {
+    std::string name;
+    std::vector<constructor_ptr> constructors;
+
+    definition_data(std::string n, std::vector<constructor_ptr> cs)
+        : name(std::move(n)), constructors(std::move(cs)) {}
+
+    void typecheck_first(type_mgr& mgr, type_env& env);
+    void typecheck_second(type_mgr& mgr, const type_env& env) const;
+    void resolve(const type_mgr& mgr);
+    void compile();
+};

code/compiler/06/binop.cpp

@@ -0,0 +1,21 @@
+#include "binop.hpp"
+
+std::string op_name(binop op) {
+    switch(op) {
+        case PLUS: return "+";
+        case MINUS: return "-";
+        case TIMES: return "*";
+        case DIVIDE: return "/";
+    }
+    return "??";
+}
+
+std::string op_action(binop op) {
+    switch(op) {
+        case PLUS: return "plus";
+        case MINUS: return "minus";
+        case TIMES: return "times";
+        case DIVIDE: return "divide";
+    }
+    return "??";
+}

code/compiler/06/binop.hpp

@@ -0,0 +1,12 @@
+#pragma once
+#include <string>
+
+enum binop {
+    PLUS,
+    MINUS,
+    TIMES,
+    DIVIDE
+};
+
+std::string op_name(binop op);
+std::string op_action(binop op);

code/compiler/06/definition.cpp

@@ -0,0 +1,83 @@
+#include "ast.hpp"
+#include "error.hpp"
+
+void definition_defn::typecheck_first(type_mgr& mgr, type_env& env) {
+    return_type = mgr.new_type();
+    type_ptr full_type = return_type;
+
+    for(auto it = params.rbegin(); it != params.rend(); it++) {
+        type_ptr param_type = mgr.new_type();
+        full_type = type_ptr(new type_arr(param_type, full_type));
+        param_types.push_back(param_type);
+    }
+
+    env.bind(name, full_type);
+}
+
+void definition_defn::typecheck_second(type_mgr& mgr, const type_env& env) const {
+    type_env new_env = env.scope();
+    auto param_it = params.begin();
+    auto type_it = param_types.rbegin();
+
+    while(param_it != params.end() && type_it != param_types.rend()) {
+        new_env.bind(*param_it, *type_it);
+        param_it++;
+        type_it++;
+    }
+
+    type_ptr body_type = body->typecheck_common(mgr, new_env);
+    mgr.unify(return_type, body_type);
+}
+
+void definition_defn::resolve(const type_mgr& mgr) {
+    type_var* var;
+    body->resolve_common(mgr);
+
+    return_type = mgr.resolve(return_type, var);
+    if(var) throw type_error("ambiguously typed program");
+    for(auto& param_type : param_types) {
+        param_type = mgr.resolve(param_type, var);
+        if(var) throw type_error("ambiguously typed program");
+    }
+}
+
+void definition_defn::compile() {
+    env_ptr new_env = env_ptr(new env_offset(0, nullptr));
+    for(auto it = params.rbegin(); it != params.rend(); it++) {
+        new_env = env_ptr(new env_var(*it, new_env));
+    }
+    body->compile(new_env, instructions);
+    instructions.push_back(instruction_ptr(new instruction_update(params.size())));
+    instructions.push_back(instruction_ptr(new instruction_pop(params.size())));
+}
+
+void definition_data::typecheck_first(type_mgr& mgr, type_env& env) {
+    type_data* this_type = new type_data(name);
+    type_ptr return_type = type_ptr(this_type);
+    int next_tag = 0;
+
+    for(auto& constructor : constructors) {
+        constructor->tag = next_tag;
+        this_type->constructors[constructor->name] = { next_tag++ };
+
+        type_ptr full_type = return_type;
+        for(auto it = constructor->types.rbegin(); it != constructor->types.rend(); it++) {
+            type_ptr type = type_ptr(new type_base(*it));
+            full_type = type_ptr(new type_arr(type, full_type));
+        }
+
+        env.bind(constructor->name, full_type);
+    }
+}
+
+void definition_data::typecheck_second(type_mgr& mgr, const type_env& env) const {
+    // Nothing
+}
+
+void definition_data::resolve(const type_mgr& mgr) {
+    // Nothing
+}
+
+void definition_data::compile() {
+
+}

code/compiler/06/env.cpp

@@ -0,0 +1,23 @@
+#include "env.hpp"
+
+int env_var::get_offset(const std::string& name) const {
+    if(name == this->name) return 0;
+    if(parent) return parent->get_offset(name) + 1;
+    throw 0;
+}
+
+bool env_var::has_variable(const std::string& name) const {
+    if(name == this->name) return true;
+    if(parent) return parent->has_variable(name);
+    return false;
+}
+
+int env_offset::get_offset(const std::string& name) const {
+    if(parent) return parent->get_offset(name) + offset;
+    throw 0;
+}
+
+bool env_offset::has_variable(const std::string& name) const {
+    if(parent) return parent->has_variable(name);
+    return false;
+}

code/compiler/06/env.hpp

@@ -0,0 +1,34 @@
+#pragma once
+#include <memory>
+#include <string>
+
+struct env {
+    virtual ~env() = default;
+
+    virtual int get_offset(const std::string& name) const = 0;
+    virtual bool has_variable(const std::string& name) const = 0;
+};
+
+using env_ptr = std::shared_ptr<env>;
+
+struct env_var : public env {
+    std::string name;
+    env_ptr parent;
+
+    env_var(std::string& n, env_ptr p)
+        : name(std::move(n)), parent(std::move(p)) {}
+
+    int get_offset(const std::string& name) const;
+    bool has_variable(const std::string& name) const;
+};
+
+struct env_offset : public env {
+    int offset;
+    env_ptr parent;
+
+    env_offset(int o, env_ptr p)
+        : offset(o), parent(std::move(p)) {}
+
+    int get_offset(const std::string& name) const;
+    bool has_variable(const std::string& name) const;
+};

code/compiler/06/error.cpp

@@ -0,0 +1,5 @@
+#include "error.hpp"
+
+const char* type_error::what() const noexcept {
+    return "an error occured while checking the types of the program";
+}

code/compiler/06/error.hpp

@@ -0,0 +1,21 @@
+#pragma once
+#include <exception>
+#include "type.hpp"
+
+struct type_error : std::exception {
+    std::string description;
+
+    type_error(std::string d)
+        : description(std::move(d)) {}
+
+    const char* what() const noexcept override;
+};
+
+struct unification_error : public type_error {
+    type_ptr left;
+    type_ptr right;
+
+    unification_error(type_ptr l, type_ptr r)
+        : left(std::move(l)), right(std::move(r)), 
+            type_error("failed to unify types") {}
+};

code/compiler/06/examples/bad1.txt

@@ -0,0 +1,2 @@
+data Bool = { True, False }
+defn main = { 3 + True }

code/compiler/06/examples/bad2.txt

@@ -0,0 +1 @@
+defn main = { 1 2 3 4 5 }

code/compiler/06/examples/bad3.txt

@@ -0,0 +1,8 @@
+data List = { Nil, Cons Int List }
+
+defn head l = {
+    case l of {
+        Nil -> { 0 }
+        Cons x y z -> { x }
+    }
+}

code/compiler/06/examples/works1.txt

@@ -0,0 +1,2 @@
+defn main = { plus 320 6 }
+defn plus x y = { x + y }

code/compiler/06/examples/works2.txt

@@ -0,0 +1,3 @@
+defn add x y = { x + y }
+defn double x = { add x x }
+defn main = { double 163 }

code/compiler/06/examples/works3.txt

@@ -0,0 +1,7 @@
+data List = { Nil, Cons Int List }
+defn length l = {
+    case l of {
+        Nil -> { 0 }
+        Cons x xs -> { 1 + length xs }
+    }
+}

code/compiler/06/instruction.cpp

@@ -0,0 +1,83 @@
+#include "instruction.hpp"
+
+static void print_indent(int n, std::ostream& to) {
+    while(n--) to << "  ";
+}
+
+void instruction_pushint::print(int indent, std::ostream& to) const {
+    print_indent(indent, to);
+    to << "PushInt(" << value << ")" << std::endl;
+}
+
+void instruction_pushglobal::print(int indent, std::ostream& to) const {
+    print_indent(indent, to);
+    to << "PushGlobal(" << name << ")" << std::endl;
+}
+
+void instruction_push::print(int indent, std::ostream& to) const {
+    print_indent(indent, to);
+    to << "Push(" << offset << ")" << std::endl;
+}
+
+void instruction_pop::print(int indent, std::ostream& to) const {
+    print_indent(indent, to);
+    to << "Pop(" << count << ")" << std::endl;
+}
+
+void instruction_mkapp::print(int indent, std::ostream& to) const {
+    print_indent(indent, to);
+    to << "MkApp()" << std::endl;
+}
+
+void instruction_update::print(int indent, std::ostream& to) const {
+    print_indent(indent, to);
+    to << "Update(" << offset << ")" << std::endl;
+}
+
+void instruction_pack::print(int indent, std::ostream& to) const {
+    print_indent(indent, to);
+    to << "Pack(" << tag << ", " << size << ")" << std::endl;
+}
+
+void instruction_split::print(int indent, std::ostream& to) const {
+    print_indent(indent, to);
+    to << "Split()" << std::endl;
+}
+
+void instruction_jump::print(int indent, std::ostream& to) const {
+    print_indent(indent, to);
+    to << "Jump(" << std::endl;
+    for(auto& instruction_set : branches) {
+        for(auto& instruction : instruction_set) {
+            instruction->print(indent + 2, to);
+        }
+        to << std::endl;
+    }
+    print_indent(indent, to);
+    to << ")" << std::endl;
+}
+
+void instruction_slide::print(int indent, std::ostream& to) const {
+    print_indent(indent, to);
+    to << "Slide(" << offset << ")" << std::endl;
+}
+
+void instruction_binop::print(int indent, std::ostream& to) const {
+    print_indent(indent, to);
+    to << "BinOp(" << op_action(op) << ")" << std::endl;
+}
+
+void instruction_eval::print(int indent, std::ostream& to) const {
+    print_indent(indent, to);
+    to << "Eval()" << std::endl;
+}
+
+void instruction_alloc::print(int indent, std::ostream& to) const {
+    print_indent(indent, to);
+    to << "Alloc(" << amount << ")" << std::endl;
+}
+
+void instruction_unwind::print(int indent, std::ostream& to) const {
+    print_indent(indent, to);
+    to << "Unwind()" << std::endl;
+}

code/compiler/06/instruction.hpp

@@ -0,0 +1,120 @@
+#pragma once
+#include <string>
+#include <memory>
+#include <vector>
+#include <map>
+#include <ostream>
+#include "binop.hpp"
+
+struct instruction {
+    virtual ~instruction() = default;
+
+    virtual void print(int indent, std::ostream& to) const = 0;
+};
+
+using instruction_ptr = std::unique_ptr<instruction>;
+
+struct instruction_pushint : public instruction {
+    int value;
+
+    instruction_pushint(int v)
+        : value(v) {}
+
+    void print(int indent, std::ostream& to) const;
+};
+
+struct instruction_pushglobal : public instruction {
+    std::string name;
+
+    instruction_pushglobal(std::string n)
+        : name(std::move(n)) {}
+
+    void print(int indent, std::ostream& to) const;
+};
+
+struct instruction_push : public instruction {
+    int offset;
+
+    instruction_push(int o)
+        : offset(o) {}
+
+    void print(int indent, std::ostream& to) const;
+};
+
+struct instruction_pop : public instruction {
+    int count;
+
+    instruction_pop(int c)
+        : count(c) {}
+
+    void print(int indent, std::ostream& to) const;
+};
+
+struct instruction_mkapp : public instruction {
+    void print(int indent, std::ostream& to) const;
+};
+
+struct instruction_update : public instruction {
+    int offset;
+
+    instruction_update(int o)
+        : offset(o) {}
+
+    void print(int indent, std::ostream& to) const;
+};
+
+struct instruction_pack : public instruction {
+    int tag;
+    int size;
+
+    instruction_pack(int t, int s)
+        : tag(t), size(s) {}
+
+    void print(int indent, std::ostream& to) const;
+};
+
+struct instruction_split : public instruction {
+    void print(int indent, std::ostream& to) const;
+};
+
+struct instruction_jump : public instruction {
+    std::vector<std::vector<instruction_ptr>> branches;
+    std::map<int, int> tag_mappings;
+
+    void print(int indent, std::ostream& to) const;
+};
+
+struct instruction_slide : public instruction {
+    int offset;
+
+    instruction_slide(int o)
+        : offset(o) {}
+
+    void print(int indent, std::ostream& to) const;
+};
+
+struct instruction_binop : public instruction {
+    binop op;
+
+    instruction_binop(binop o)
+        : op(o) {}
+
+    void print(int indent, std::ostream& to) const;
+};
+
+struct instruction_eval : public instruction {
+    void print(int indent, std::ostream& to) const;
+};
+
+struct instruction_alloc : public instruction {
+    int amount;
+
+    instruction_alloc(int a)
+        : amount(a) {}
+
+    void print(int indent, std::ostream& to) const;
+};
+
+struct instruction_unwind : public instruction {
+    void print(int indent, std::ostream& to) const;
+};

code/compiler/06/main.cpp

@@ -0,0 +1,88 @@
+#include "ast.hpp"
+#include <iostream>
+#include "parser.hpp"
+#include "error.hpp"
+#include "type.hpp"
+
+void yy::parser::error(const std::string& msg) {
+    std::cout << "An error occured: " << msg << std::endl;
+}
+
+extern std::vector<definition_ptr> program;
+
+void typecheck_program(
+        const std::vector<definition_ptr>& prog,
+        type_mgr& mgr, type_env& env) {
+    type_ptr int_type = type_ptr(new type_base("Int")); 
+    type_ptr binop_type = type_ptr(new type_arr(
+                int_type,
+                type_ptr(new type_arr(int_type, int_type))));
+
+    env.bind("+", binop_type);
+    env.bind("-", binop_type);
+    env.bind("*", binop_type);
+    env.bind("/", binop_type);
+
+    for(auto& def : prog) {
+        def->typecheck_first(mgr, env);
+    }
+
+    for(auto& def : prog) {
+        def->typecheck_second(mgr, env);
+    }
+
+    for(auto& pair : env.names) {
+        std::cout << pair.first << ": ";
+        pair.second->print(mgr, std::cout);
+        std::cout << std::endl;
+    }
+
+    for(auto& def : prog) {
+        def->resolve(mgr);
+    }
+}
+
+void compile_program(const std::vector<definition_ptr>& prog) {
+    for(auto& def : prog) {
+        def->compile();
+
+        definition_defn* defn = dynamic_cast<definition_defn*>(def.get());
+        if(!defn) continue;
+        for(auto& instruction : defn->instructions) {
+            instruction->print(0, std::cout);
+        }
+        std::cout << std::endl;
+    }
+}
+
+int main() {
+    yy::parser parser;
+    type_mgr mgr;
+    type_env env;
+
+    parser.parse();
+    for(auto& definition : program) {
+        definition_defn* def = dynamic_cast<definition_defn*>(definition.get());
+        if(!def) continue;
+
+        std::cout << def->name;
+        for(auto& param : def->params) std::cout << " " << param;
+        std::cout << ":" << std::endl;
+
+        def->body->print(1, std::cout);
+    }
+    try {
+        typecheck_program(program, mgr, env);
+        compile_program(program);
+    } catch(unification_error& err) {
+        std::cout << "failed to unify types: " << std::endl;
+        std::cout << "  (1) \033[34m";
+        err.left->print(mgr, std::cout);
+        std::cout << "\033[0m" << std::endl;
+        std::cout << "  (2) \033[32m";
+        err.right->print(mgr, std::cout);
+        std::cout << "\033[0m" << std::endl;
+    } catch(type_error& err) {
+        std::cout << "failed to type check program: " << err.description << std::endl;
+    }
+}

code/compiler/06/parser.y

@@ -0,0 +1,140 @@
+%{
+#include <string>
+#include <iostream>
+#include "ast.hpp"
+#include "parser.hpp"
+
+std::vector<definition_ptr> program;
+extern yy::parser::symbol_type yylex();
+
+%}
+
+%token PLUS
+%token TIMES
+%token MINUS
+%token DIVIDE
+%token <int> INT
+%token DEFN
+%token DATA
+%token CASE
+%token OF
+%token OCURLY
+%token CCURLY
+%token OPAREN
+%token CPAREN
+%token COMMA
+%token ARROW
+%token EQUAL
+%token <std::string> LID
+%token <std::string> UID
+
+%language "c++"
+%define api.value.type variant
+%define api.token.constructor
+
+%type <std::vector<std::string>> lowercaseParams uppercaseParams
+%type <std::vector<definition_ptr>> program definitions
+%type <std::vector<branch_ptr>> branches
+%type <std::vector<constructor_ptr>> constructors
+%type <ast_ptr> aAdd aMul case app appBase
+%type <definition_ptr> definition defn data 
+%type <branch_ptr> branch
+%type <pattern_ptr> pattern
+%type <constructor_ptr> constructor
+
+%start program
+
+%%
+
+program
+    : definitions { program = std::move($1); }
+    ;
+
+definitions
+    : definitions definition { $$ = std::move($1); $$.push_back(std::move($2)); }
+    | definition { $$ = std::vector<definition_ptr>(); $$.push_back(std::move($1)); }
+    ;
+
+definition
+    : defn { $$ = std::move($1); }
+    | data { $$ = std::move($1); }
+    ;
+
+defn
+    : DEFN LID lowercaseParams EQUAL OCURLY aAdd CCURLY
+        { $$ = definition_ptr(
+            new definition_defn(std::move($2), std::move($3), std::move($6))); }
+    ;
+
+lowercaseParams
+    : %empty { $$ = std::vector<std::string>(); }
+    | lowercaseParams LID { $$ = std::move($1); $$.push_back(std::move($2)); }
+    ;
+
+uppercaseParams
+    : %empty { $$ = std::vector<std::string>(); }
+    | uppercaseParams UID { $$ = std::move($1); $$.push_back(std::move($2)); }
+    ;
+
+aAdd
+    : aAdd PLUS aMul { $$ = ast_ptr(new ast_binop(PLUS, std::move($1), std::move($3))); }
+    | aAdd MINUS aMul { $$ = ast_ptr(new ast_binop(MINUS, std::move($1), std::move($3))); }
+    | aMul { $$ = std::move($1); }
+    ;
+
+aMul
+    : aMul TIMES app { $$ = ast_ptr(new ast_binop(TIMES, std::move($1), std::move($3))); }
+    | aMul DIVIDE app { $$ = ast_ptr(new ast_binop(DIVIDE, std::move($1), std::move($3))); }
+    | app { $$ = std::move($1); }
+    ;
+
+app
+    : app appBase { $$ = ast_ptr(new ast_app(std::move($1), std::move($2))); }
+    | appBase { $$ = std::move($1); }
+    ;
+
+appBase
+    : INT { $$ = ast_ptr(new ast_int($1)); }
+    | LID { $$ = ast_ptr(new ast_lid(std::move($1))); }
+    | UID { $$ = ast_ptr(new ast_uid(std::move($1))); }
+    | OPAREN aAdd CPAREN { $$ = std::move($2); }
+    | case { $$ = std::move($1); }
+    ;
+
+case
+    : CASE aAdd OF OCURLY branches CCURLY 
+        { $$ = ast_ptr(new ast_case(std::move($2), std::move($5))); }
+    ;
+
+branches
+    : branches branch { $$ = std::move($1); $$.push_back(std::move($2)); }
+    | branch { $$ = std::vector<branch_ptr>(); $$.push_back(std::move($1));}
+    ;
+
+branch
+    : pattern ARROW OCURLY aAdd CCURLY
+        { $$ = branch_ptr(new branch(std::move($1), std::move($4))); }
+    ;
+
+pattern
+    : LID { $$ = pattern_ptr(new pattern_var(std::move($1))); }
+    | UID lowercaseParams
+        { $$ = pattern_ptr(new pattern_constr(std::move($1), std::move($2))); }
+    ;
+
+data
+    : DATA UID EQUAL OCURLY constructors CCURLY
+        { $$ = definition_ptr(new definition_data(std::move($2), std::move($5))); }
+    ;
+
+constructors
+    : constructors COMMA constructor { $$ = std::move($1); $$.push_back(std::move($3)); }
+    | constructor
+        { $$ = std::vector<constructor_ptr>(); $$.push_back(std::move($1)); }
+    ;
+
+constructor
+    : UID uppercaseParams
+        { $$ = constructor_ptr(new constructor(std::move($1), std::move($2))); }
+    ;
+

code/compiler/06/scanner.l

@@ -0,0 +1,34 @@
+%option noyywrap
+
+%{
+#include <iostream>
+#include "ast.hpp"
+#include "parser.hpp"
+
+#define YY_DECL yy::parser::symbol_type yylex()
+
+%}
+
+%%
+
+[ \n]+ {}
+\+ { return yy::parser::make_PLUS(); }
+\* { return yy::parser::make_TIMES(); }
+- { return yy::parser::make_MINUS(); }
+\/ { return yy::parser::make_DIVIDE(); }
+[0-9]+ { return yy::parser::make_INT(atoi(yytext)); }
+defn { return yy::parser::make_DEFN(); }
+data { return yy::parser::make_DATA(); }
+case { return yy::parser::make_CASE(); }
+of { return yy::parser::make_OF(); }
+\{ { return yy::parser::make_OCURLY(); }
+\} { return yy::parser::make_CCURLY(); }
+\( { return yy::parser::make_OPAREN(); }
+\) { return yy::parser::make_CPAREN(); }
+,  { return yy::parser::make_COMMA(); }
+-> { return yy::parser::make_ARROW(); }
+= { return yy::parser::make_EQUAL(); }
+[a-z][a-zA-Z]* { return yy::parser::make_LID(std::string(yytext)); }
+[A-Z][a-zA-Z]* { return yy::parser::make_UID(std::string(yytext)); }
+
+%%

code/compiler/06/type.cpp

@@ -0,0 +1,99 @@
+#include "type.hpp"
+#include <sstream>
+#include <algorithm>
+#include "error.hpp"
+
+void type_var::print(const type_mgr& mgr, std::ostream& to) const {
+    auto it = mgr.types.find(name);
+    if(it != mgr.types.end()) {
+        it->second->print(mgr, to);
+    } else {
+        to << name;
+    }
+}
+
+void type_base::print(const type_mgr& mgr, std::ostream& to) const {
+    to << name;
+}
+
+void type_arr::print(const type_mgr& mgr, std::ostream& to) const {
+    left->print(mgr, to);
+    to << " -> (";
+    right->print(mgr, to);
+    to << ")";
+}
+
+std::string type_mgr::new_type_name() {
+    int temp = last_id++;
+    std::string str = "";
+
+    while(temp != -1) {
+        str += (char) ('a' + (temp % 26));
+        temp = temp / 26 - 1;
+    }
+
+    std::reverse(str.begin(), str.end());
+    return str;
+}
+
+type_ptr type_mgr::new_type() {
+    return type_ptr(new type_var(new_type_name()));
+}
+
+type_ptr type_mgr::new_arrow_type() {
+    return type_ptr(new type_arr(new_type(), new_type()));
+}
+
+type_ptr type_mgr::resolve(type_ptr t, type_var*& var) const {
+    type_var* cast;
+
+    var = nullptr;
+    while((cast = dynamic_cast<type_var*>(t.get()))) {
+        auto it = types.find(cast->name);
+
+        if(it == types.end()) {
+            var = cast;
+            break;
+        }
+        t = it->second;
+    }
+
+    return t;
+}
+
+void type_mgr::unify(type_ptr l, type_ptr r) {
+    type_var* lvar;
+    type_var* rvar;
+    type_arr* larr;
+    type_arr* rarr;
+    type_base* lid;
+    type_base* rid;
+
+    l = resolve(l, lvar);
+    r = resolve(r, rvar);
+
+    if(lvar) {
+        bind(lvar->name, r);
+        return;
+    } else if(rvar) {
+        bind(rvar->name, l);
+        return;
+    } else if((larr = dynamic_cast<type_arr*>(l.get())) &&
+            (rarr = dynamic_cast<type_arr*>(r.get()))) {
+        unify(larr->left, rarr->left);
+        unify(larr->right, rarr->right);
+        return;
+    } else if((lid = dynamic_cast<type_base*>(l.get())) &&
+            (rid = dynamic_cast<type_base*>(r.get()))) {
+        if(lid->name == rid->name) return;
+    }
+
+    throw unification_error(l, r);
+}
+
+void type_mgr::bind(const std::string& s, type_ptr t) {
+    type_var* other = dynamic_cast<type_var*>(t.get());
+    
+    if(other && other->name == s) return;
+    types[s] = t;
+}

code/compiler/06/type.hpp

@@ -0,0 +1,65 @@
+#pragma once
+#include <memory>
+#include <map>
+
+struct type_mgr;
+
+struct type {
+    virtual ~type() = default;
+
+    virtual void print(const type_mgr& mgr, std::ostream& to) const = 0;
+};
+
+using type_ptr = std::shared_ptr<type>;
+
+struct type_var : public type {
+    std::string name;
+
+    type_var(std::string n)
+        : name(std::move(n)) {}
+
+    void print(const type_mgr& mgr, std::ostream& to) const;
+};
+
+struct type_base : public type {
+    std::string name;
+
+    type_base(std::string n) 
+        : name(std::move(n)) {}
+
+    void print(const type_mgr& mgr, std::ostream& to) const;
+};
+
+struct type_data : public type_base {
+    struct constructor {
+        int tag;
+    };
+
+    std::map<std::string, constructor> constructors;
+
+    type_data(std::string n)
+        : type_base(std::move(n)) {}
+};
+
+struct type_arr : public type {
+    type_ptr left;
+    type_ptr right;
+
+    type_arr(type_ptr l, type_ptr r)
+        : left(std::move(l)), right(std::move(r)) {}
+
+    void print(const type_mgr& mgr, std::ostream& to) const;
+};
+
+struct type_mgr {
+    int last_id = 0;
+    std::map<std::string, type_ptr> types;
+
+    std::string new_type_name();
+    type_ptr new_type();
+    type_ptr new_arrow_type();
+
+    void unify(type_ptr l, type_ptr r);
+    type_ptr resolve(type_ptr t, type_var*& var) const;
+    void bind(const std::string& s, type_ptr t);
+};

code/compiler/06/type_env.cpp

@@ -0,0 +1,16 @@
+#include "type_env.hpp"
+
+type_ptr type_env::lookup(const std::string& name) const {
+    auto it = names.find(name);
+    if(it != names.end()) return it->second;
+    if(parent) return parent->lookup(name);
+    return nullptr;
+}
+
+void type_env::bind(const std::string& name, type_ptr t) {
+    names[name] = t;
+}
+
+type_env type_env::scope() const {
+    return type_env(this);
+}

code/compiler/06/type_env.hpp

@@ -0,0 +1,16 @@
+#pragma once
+#include <map>
+#include "type.hpp"
+
+struct type_env {
+    std::map<std::string, type_ptr> names;
+    type_env const* parent = nullptr;
+
+    type_env(type_env const* p)
+        : parent(p) {}
+    type_env() : type_env(nullptr) {}
+
+    type_ptr lookup(const std::string& name) const;
+    void bind(const std::string& name, type_ptr t);
+    type_env scope() const;
+};

code/compiler/07/CMakeLists.txt

@@ -0,0 +1,28 @@
+cmake_minimum_required(VERSION 3.1)
+project(compiler)
+
+find_package(BISON)
+find_package(FLEX)
+bison_target(parser
+    ${CMAKE_CURRENT_SOURCE_DIR}/parser.y
+    ${CMAKE_CURRENT_BINARY_DIR}/parser.cpp
+    COMPILE_FLAGS "-d")
+flex_target(scanner
+    ${CMAKE_CURRENT_SOURCE_DIR}/scanner.l
+    ${CMAKE_CURRENT_BINARY_DIR}/scanner.cpp)
+add_flex_bison_dependency(scanner parser)
+
+add_executable(compiler
+    ast.cpp ast.hpp definition.cpp
+    type_env.cpp type_env.hpp
+    env.cpp env.hpp
+    type.cpp type.hpp
+    error.cpp error.hpp
+    binop.cpp binop.hpp
+    instruction.cpp instruction.hpp
+    ${BISON_parser_OUTPUTS}
+    ${FLEX_scanner_OUTPUTS}
+    main.cpp
+)
+target_include_directories(compiler PUBLIC ${CMAKE_CURRENT_SOURCE_DIR})
+target_include_directories(compiler PUBLIC ${CMAKE_CURRENT_BINARY_DIR})

code/compiler/07/ast.cpp

@@ -0,0 +1,262 @@
+#include "ast.hpp"
+#include <ostream>
+#include "error.hpp"
+
+static void print_indent(int n, std::ostream& to) {
+    while(n--) to << "  ";
+}
+
+type_ptr ast::typecheck_common(type_mgr& mgr, const type_env& env) {
+    node_type = typecheck(mgr, env);
+    return node_type;
+}
+
+void ast::resolve_common(const type_mgr& mgr) {
+    type_var* var;
+    type_ptr resolved_type = mgr.resolve(node_type, var);
+    if(var) throw type_error("ambiguously typed program");
+
+    resolve(mgr);
+    node_type = std::move(resolved_type);
+}
+
+void ast_int::print(int indent, std::ostream& to) const {
+    print_indent(indent, to);
+    to << "INT: " << value << std::endl;
+}
+
+type_ptr ast_int::typecheck(type_mgr& mgr, const type_env& env) const {
+    return type_ptr(new type_base("Int"));
+}
+
+void ast_int::resolve(const type_mgr& mgr) const {
+    
+}
+
+void ast_int::compile(const env_ptr& env, std::vector<instruction_ptr>& into) const {
+    into.push_back(instruction_ptr(new instruction_pushint(value)));
+}
+
+void ast_lid::print(int indent, std::ostream& to) const {
+    print_indent(indent, to);
+    to << "LID: " << id << std::endl;
+}
+
+type_ptr ast_lid::typecheck(type_mgr& mgr, const type_env& env) const {
+    return env.lookup(id);
+}
+
+void ast_lid::resolve(const type_mgr& mgr) const {
+
+}
+
+void ast_lid::compile(const env_ptr& env, std::vector<instruction_ptr>& into) const {
+    into.push_back(instruction_ptr(
+        env->has_variable(id) ?
+            (instruction*) new instruction_push(env->get_offset(id)) :
+            (instruction*) new instruction_pushglobal(id)));
+}
+
+void ast_uid::print(int indent, std::ostream& to) const {
+    print_indent(indent, to);
+    to << "UID: " << id << std::endl;
+}
+
+type_ptr ast_uid::typecheck(type_mgr& mgr, const type_env& env) const {
+    return env.lookup(id);
+}
+
+void ast_uid::resolve(const type_mgr& mgr) const {
+
+}
+
+void ast_uid::compile(const env_ptr& env, std::vector<instruction_ptr>& into) const {
+    into.push_back(instruction_ptr(new instruction_pushglobal(id)));
+}
+
+void ast_binop::print(int indent, std::ostream& to) const {
+    print_indent(indent, to);
+    to << "BINOP: " << op_name(op) << std::endl;
+    left->print(indent + 1, to);
+    right->print(indent + 1, to);
+}
+
+type_ptr ast_binop::typecheck(type_mgr& mgr, const type_env& env) const {
+    type_ptr ltype = left->typecheck_common(mgr, env);
+    type_ptr rtype = right->typecheck_common(mgr, env);
+    type_ptr ftype = env.lookup(op_name(op));
+    if(!ftype) throw type_error(std::string("unknown binary operator ") + op_name(op));
+
+    type_ptr return_type = mgr.new_type();
+    type_ptr arrow_one = type_ptr(new type_arr(rtype, return_type));
+    type_ptr arrow_two = type_ptr(new type_arr(ltype, arrow_one));
+
+    mgr.unify(arrow_two, ftype);
+    return return_type;
+}
+
+void ast_binop::resolve(const type_mgr& mgr) const {
+    left->resolve_common(mgr);
+    right->resolve_common(mgr);
+}
+
+void ast_binop::compile(const env_ptr& env, std::vector<instruction_ptr>& into) const {
+    right->compile(env, into);
+    left->compile(env_ptr(new env_offset(1, env)), into);
+
+    into.push_back(instruction_ptr(new instruction_pushglobal(op_action(op))));
+    into.push_back(instruction_ptr(new instruction_mkapp()));
+    into.push_back(instruction_ptr(new instruction_mkapp()));
+}
+
+void ast_app::print(int indent, std::ostream& to) const {
+    print_indent(indent, to);
+    to << "APP:" << std::endl;
+    left->print(indent + 1, to);
+    right->print(indent + 1, to);
+}
+
+type_ptr ast_app::typecheck(type_mgr& mgr, const type_env& env) const {
+    type_ptr ltype = left->typecheck_common(mgr, env);
+    type_ptr rtype = right->typecheck_common(mgr, env);
+
+    type_ptr return_type = mgr.new_type();
+    type_ptr arrow = type_ptr(new type_arr(rtype, return_type));
+    mgr.unify(arrow, ltype);
+    return return_type;
+}
+
+void ast_app::resolve(const type_mgr& mgr) const {
+    left->resolve_common(mgr);
+    right->resolve_common(mgr);
+}
+
+void ast_app::compile(const env_ptr& env, std::vector<instruction_ptr>& into) const {
+    right->compile(env, into);
+    left->compile(env_ptr(new env_offset(1, env)), into);
+    into.push_back(instruction_ptr(new instruction_mkapp()));
+}
+
+void ast_case::print(int indent, std::ostream& to) const {
+    print_indent(indent, to);
+    to << "CASE: " << std::endl;
+    for(auto& branch : branches) {
+        print_indent(indent + 1, to);
+        branch->pat->print(to);
+        to << std::endl;
+        branch->expr->print(indent + 2, to);
+    }
+}
+
+type_ptr ast_case::typecheck(type_mgr& mgr, const type_env& env) const {
+    type_var* var;
+    type_ptr case_type = mgr.resolve(of->typecheck_common(mgr, env), var);
+    type_ptr branch_type = mgr.new_type();
+
+    for(auto& branch : branches) {
+        type_env new_env = env.scope();
+        branch->pat->match(case_type, mgr, new_env);
+        type_ptr curr_branch_type = branch->expr->typecheck_common(mgr, new_env);
+        mgr.unify(branch_type, curr_branch_type);
+    }
+
+    case_type = mgr.resolve(case_type, var);
+    if(!dynamic_cast<type_data*>(case_type.get())) {
+        throw type_error("attempting case analysis of non-data type");
+    }
+
+    return branch_type;
+}
+
+void ast_case::resolve(const type_mgr& mgr) const {
+    of->resolve_common(mgr);
+    for(auto& branch : branches) {
+        branch->expr->resolve_common(mgr);
+    }
+}
+
+void ast_case::compile(const env_ptr& env, std::vector<instruction_ptr>& into) const {
+    type_data* type = dynamic_cast<type_data*>(of->node_type.get());
+
+    of->compile(env, into);
+    into.push_back(instruction_ptr(new instruction_eval()));
+
+    instruction_jump* jump_instruction = new instruction_jump();
+    into.push_back(instruction_ptr(jump_instruction));
+    for(auto& branch : branches) {
+        std::vector<instruction_ptr> branch_instructions;
+        pattern_var* vpat;
+        pattern_constr* cpat;
+
+        if((vpat = dynamic_cast<pattern_var*>(branch->pat.get()))) {
+            branch->expr->compile(env_ptr(new env_offset(1, env)), branch_instructions);
+
+            for(auto& constr_pair : type->constructors) {
+                if(jump_instruction->tag_mappings.find(constr_pair.second.tag) !=
+                        jump_instruction->tag_mappings.end())
+                    break;
+
+                jump_instruction->tag_mappings[constr_pair.second.tag] =
+                    jump_instruction->branches.size();
+            }
+            jump_instruction->branches.push_back(std::move(branch_instructions));
+        } else if((cpat = dynamic_cast<pattern_constr*>(branch->pat.get()))) {
+            env_ptr new_env = env;
+            for(auto it = cpat->params.rbegin(); it != cpat->params.rend(); it++) {
+                new_env = env_ptr(new env_var(*it, new_env));
+            }
+
+            branch_instructions.push_back(instruction_ptr(new instruction_split()));
+            branch->expr->compile(new_env, branch_instructions);
+            branch_instructions.push_back(instruction_ptr(new instruction_slide(
+                            cpat->params.size())));
+
+            int new_tag = type->constructors[cpat->constr].tag;
+            if(jump_instruction->tag_mappings.find(new_tag) !=
+                    jump_instruction->tag_mappings.end())
+                throw type_error("technically not a type error: duplicate pattern");
+
+            jump_instruction->tag_mappings[new_tag] =
+                jump_instruction->branches.size();
+            jump_instruction->branches.push_back(std::move(branch_instructions));
+        }
+    }
+
+    for(auto& constr_pair : type->constructors) {
+        if(jump_instruction->tag_mappings.find(constr_pair.second.tag) ==
+                jump_instruction->tag_mappings.end())
+            throw type_error("non-total pattern");
+    }
+}
+
+void pattern_var::print(std::ostream& to) const {
+    to << var;
+}
+
+void pattern_var::match(type_ptr t, type_mgr& mgr, type_env& env) const {
+    env.bind(var, t);
+}
+
+void pattern_constr::print(std::ostream& to) const {
+    to << constr;
+    for(auto& param : params) {
+        to << " " << param;
+    }
+}
+
+void pattern_constr::match(type_ptr t, type_mgr& mgr, type_env& env) const {
+    type_ptr constructor_type = env.lookup(constr);
+    if(!constructor_type) {
+        throw type_error(std::string("pattern using unknown constructor ") + constr);
+    }
+
+    for(int i = 0; i < params.size(); i++) {
+        type_arr* arr = dynamic_cast<type_arr*>(constructor_type.get());
+        if(!arr) throw type_error("too many parameters in constructor pattern");
+
+        env.bind(params[i], arr->left);
+        constructor_type = arr->right;
+    }
+
+    mgr.unify(t, constructor_type);
+}

code/compiler/07/ast.hpp

@@ -0,0 +1,197 @@
+#pragma once
+#include <memory>
+#include <vector>
+#include "type.hpp"
+#include "type_env.hpp"
+#include "binop.hpp"
+#include "instruction.hpp"
+#include "env.hpp"
+
+struct ast {
+    type_ptr node_type;
+
+    virtual ~ast() = default;
+
+    virtual void print(int indent, std::ostream& to) const = 0;
+    virtual type_ptr typecheck(type_mgr& mgr, const type_env& env) const = 0;
+    virtual void resolve(const type_mgr& mgr) const = 0;
+    virtual void compile(const env_ptr& env,
+        std::vector<instruction_ptr>& into) const = 0;
+
+    type_ptr typecheck_common(type_mgr& mgr, const type_env& env);
+    void resolve_common(const type_mgr& mgr);
+};
+
+using ast_ptr = std::unique_ptr<ast>;
+
+struct pattern {
+    virtual ~pattern() = default;
+
+    virtual void print(std::ostream& to) const = 0;
+    virtual void match(type_ptr t, type_mgr& mgr, type_env& env) const = 0;
+};
+
+using pattern_ptr = std::unique_ptr<pattern>;
+
+struct branch {
+    pattern_ptr pat;
+    ast_ptr expr;
+
+    branch(pattern_ptr p, ast_ptr a)
+        : pat(std::move(p)), expr(std::move(a)) {}
+};
+
+using branch_ptr = std::unique_ptr<branch>;
+
+struct constructor {
+    std::string name;
+    std::vector<std::string> types;
+    int8_t tag;
+
+    constructor(std::string n, std::vector<std::string> ts)
+        : name(std::move(n)), types(std::move(ts)) {}
+};
+
+using constructor_ptr = std::unique_ptr<constructor>;
+
+struct definition {
+    virtual ~definition() = default;
+    
+    virtual void typecheck_first(type_mgr& mgr, type_env& env) = 0;
+    virtual void typecheck_second(type_mgr& mgr, const type_env& env) const = 0;
+    virtual void resolve(const type_mgr& mgr) = 0;
+    virtual void compile() = 0;
+};
+
+using definition_ptr = std::unique_ptr<definition>;
+
+struct ast_int : public ast {
+    int value;
+
+    explicit ast_int(int v)
+        : value(v) {}
+
+    void print(int indent, std::ostream& to) const;
+    type_ptr typecheck(type_mgr& mgr, const type_env& env) const;
+    void resolve(const type_mgr& mgr) const;
+    void compile(const env_ptr& env, std::vector<instruction_ptr>& into) const;
+};
+
+struct ast_lid : public ast {
+    std::string id;
+
+    explicit ast_lid(std::string i)
+        : id(std::move(i)) {}
+
+    void print(int indent, std::ostream& to) const;
+    type_ptr typecheck(type_mgr& mgr, const type_env& env) const;
+    void resolve(const type_mgr& mgr) const;
+    void compile(const env_ptr& env, std::vector<instruction_ptr>& into) const;
+};
+
+struct ast_uid : public ast {
+    std::string id;
+
+    explicit ast_uid(std::string i)
+        : id(std::move(i)) {}
+
+    void print(int indent, std::ostream& to) const;
+    type_ptr typecheck(type_mgr& mgr, const type_env& env) const;
+    void resolve(const type_mgr& mgr) const;
+    void compile(const env_ptr& env, std::vector<instruction_ptr>& into) const;
+};
+
+struct ast_binop : public ast {
+    binop op;  
+    ast_ptr left;
+    ast_ptr right;
+
+    ast_binop(binop o, ast_ptr l, ast_ptr r)
+        : op(o), left(std::move(l)), right(std::move(r)) {}
+
+    void print(int indent, std::ostream& to) const;
+    type_ptr typecheck(type_mgr& mgr, const type_env& env) const;
+    void resolve(const type_mgr& mgr) const;
+    void compile(const env_ptr& env, std::vector<instruction_ptr>& into) const;
+};
+
+struct ast_app : public ast {
+    ast_ptr left;
+    ast_ptr right;
+
+    ast_app(ast_ptr l, ast_ptr r)
+        : left(std::move(l)), right(std::move(r)) {}
+
+    void print(int indent, std::ostream& to) const;
+    type_ptr typecheck(type_mgr& mgr, const type_env& env) const;
+    void resolve(const type_mgr& mgr) const;
+    void compile(const env_ptr& env, std::vector<instruction_ptr>& into) const;
+};
+
+struct ast_case : public ast {
+    ast_ptr of;
+    std::vector<branch_ptr> branches;
+
+    ast_case(ast_ptr o, std::vector<branch_ptr> b)
+        : of(std::move(o)), branches(std::move(b)) {}
+
+    void print(int indent, std::ostream& to) const;
+    type_ptr typecheck(type_mgr& mgr, const type_env& env) const;
+    void resolve(const type_mgr& mgr) const;
+    void compile(const env_ptr& env, std::vector<instruction_ptr>& into) const;
+};
+
+struct pattern_var : public pattern {
+    std::string var;
+
+    pattern_var(std::string v)
+        : var(std::move(v)) {}
+
+    void print(std::ostream &to) const;
+    void match(type_ptr t, type_mgr& mgr, type_env& env) const;
+};
+
+struct pattern_constr : public pattern {
+    std::string constr;
+    std::vector<std::string> params;
+
+    pattern_constr(std::string c, std::vector<std::string> p)
+        : constr(std::move(c)), params(std::move(p)) {}
+
+    void print(std::ostream &to) const;
+    void match(type_ptr t, type_mgr&, type_env& env) const;
+};
+
+struct definition_defn : public definition {
+    std::string name;
+    std::vector<std::string> params;
+    ast_ptr body;
+
+    type_ptr return_type;
+    std::vector<type_ptr> param_types;
+
+    std::vector<instruction_ptr> instructions;
+
+    definition_defn(std::string n, std::vector<std::string> p, ast_ptr b)
+        : name(std::move(n)), params(std::move(p)), body(std::move(b)) {
+
+    }
+
+    void typecheck_first(type_mgr& mgr, type_env& env);
+    void typecheck_second(type_mgr& mgr, const type_env& env) const;
+    void resolve(const type_mgr& mgr);
+    void compile();
+};
+
+struct definition_data : public definition {
+    std::string name;
+    std::vector<constructor_ptr> constructors;
+
+    definition_data(std::string n, std::vector<constructor_ptr> cs)
+        : name(std::move(n)), constructors(std::move(cs)) {}
+
+    void typecheck_first(type_mgr& mgr, type_env& env);
+    void typecheck_second(type_mgr& mgr, const type_env& env) const;
+    void resolve(const type_mgr& mgr);
+    void compile();
+};

code/compiler/07/binop.cpp

@@ -0,0 +1,21 @@
+#include "binop.hpp"
+
+std::string op_name(binop op) {
+    switch(op) {
+        case PLUS: return "+";
+        case MINUS: return "-";
+        case TIMES: return "*";
+        case DIVIDE: return "/";
+    }
+    return "??";
+}
+
+std::string op_action(binop op) {
+    switch(op) {
+        case PLUS: return "plus";
+        case MINUS: return "minus";
+        case TIMES: return "times";
+        case DIVIDE: return "divide";
+    }
+    return "??";
+}

code/compiler/07/binop.hpp

@@ -0,0 +1,12 @@
+#pragma once
+#include <string>
+
+enum binop {
+    PLUS,
+    MINUS,
+    TIMES,
+    DIVIDE
+};
+
+std::string op_name(binop op);
+std::string op_action(binop op);

code/compiler/07/definition.cpp

@@ -0,0 +1,83 @@
+#include "ast.hpp"
+#include "error.hpp"
+
+void definition_defn::typecheck_first(type_mgr& mgr, type_env& env) {
+    return_type = mgr.new_type();
+    type_ptr full_type = return_type;
+
+    for(auto it = params.rbegin(); it != params.rend(); it++) {
+        type_ptr param_type = mgr.new_type();
+        full_type = type_ptr(new type_arr(param_type, full_type));
+        param_types.push_back(param_type);
+    }
+
+    env.bind(name, full_type);
+}
+
+void definition_defn::typecheck_second(type_mgr& mgr, const type_env& env) const {
+    type_env new_env = env.scope();
+    auto param_it = params.begin();
+    auto type_it = param_types.rbegin();
+
+    while(param_it != params.end() && type_it != param_types.rend()) {
+        new_env.bind(*param_it, *type_it);
+        param_it++;
+        type_it++;
+    }
+
+    type_ptr body_type = body->typecheck_common(mgr, new_env);
+    mgr.unify(return_type, body_type);
+}
+
+void definition_defn::resolve(const type_mgr& mgr) {
+    type_var* var;
+    body->resolve_common(mgr);
+
+    return_type = mgr.resolve(return_type, var);
+    if(var) throw type_error("ambiguously typed program");
+    for(auto& param_type : param_types) {
+        param_type = mgr.resolve(param_type, var);
+        if(var) throw type_error("ambiguously typed program");
+    }
+}
+
+void definition_defn::compile() {
+    env_ptr new_env = env_ptr(new env_offset(0, nullptr));
+    for(auto it = params.rbegin(); it != params.rend(); it++) {
+        new_env = env_ptr(new env_var(*it, new_env));
+    }
+    body->compile(new_env, instructions);
+    instructions.push_back(instruction_ptr(new instruction_update(params.size())));
+    instructions.push_back(instruction_ptr(new instruction_pop(params.size())));
+}
+
+void definition_data::typecheck_first(type_mgr& mgr, type_env& env) {
+    type_data* this_type = new type_data(name);
+    type_ptr return_type = type_ptr(this_type);
+    int next_tag = 0;
+
+    for(auto& constructor : constructors) {
+        constructor->tag = next_tag;
+        this_type->constructors[constructor->name] = { next_tag++ };
+
+        type_ptr full_type = return_type;
+        for(auto it = constructor->types.rbegin(); it != constructor->types.rend(); it++) {
+            type_ptr type = type_ptr(new type_base(*it));
+            full_type = type_ptr(new type_arr(type, full_type));
+        }
+
+        env.bind(constructor->name, full_type);
+    }
+}
+
+void definition_data::typecheck_second(type_mgr& mgr, const type_env& env) const {
+    // Nothing
+}
+
+void definition_data::resolve(const type_mgr& mgr) {
+    // Nothing
+}
+
+void definition_data::compile() {
+
+}

code/compiler/07/env.cpp

@@ -0,0 +1,23 @@
+#include "env.hpp"
+
+int env_var::get_offset(const std::string& name) const {
+    if(name == this->name) return 0;
+    if(parent) return parent->get_offset(name) + 1;
+    throw 0;
+}
+
+bool env_var::has_variable(const std::string& name) const {
+    if(name == this->name) return true;
+    if(parent) return parent->has_variable(name);
+    return false;
+}
+
+int env_offset::get_offset(const std::string& name) const {
+    if(parent) return parent->get_offset(name) + offset;
+    throw 0;
+}
+
+bool env_offset::has_variable(const std::string& name) const {
+    if(parent) return parent->has_variable(name);
+    return false;
+}

code/compiler/07/env.hpp

@@ -0,0 +1,34 @@
+#pragma once
+#include <memory>
+#include <string>
+
+struct env {
+    virtual ~env() = default;
+
+    virtual int get_offset(const std::string& name) const = 0;
+    virtual bool has_variable(const std::string& name) const = 0;
+};
+
+using env_ptr = std::shared_ptr<env>;
+
+struct env_var : public env {
+    std::string name;
+    env_ptr parent;
+
+    env_var(std::string& n, env_ptr p)
+        : name(std::move(n)), parent(std::move(p)) {}
+
+    int get_offset(const std::string& name) const;
+    bool has_variable(const std::string& name) const;
+};
+
+struct env_offset : public env {
+    int offset;
+    env_ptr parent;
+
+    env_offset(int o, env_ptr p)
+        : offset(o), parent(std::move(p)) {}
+
+    int get_offset(const std::string& name) const;
+    bool has_variable(const std::string& name) const;
+};

code/compiler/07/error.cpp

@@ -0,0 +1,5 @@
+#include "error.hpp"
+
+const char* type_error::what() const noexcept {
+    return "an error occured while checking the types of the program";
+}

code/compiler/07/error.hpp

@@ -0,0 +1,21 @@
+#pragma once
+#include <exception>
+#include "type.hpp"
+
+struct type_error : std::exception {
+    std::string description;
+
+    type_error(std::string d)
+        : description(std::move(d)) {}
+
+    const char* what() const noexcept override;
+};
+
+struct unification_error : public type_error {
+    type_ptr left;
+    type_ptr right;
+
+    unification_error(type_ptr l, type_ptr r)
+        : left(std::move(l)), right(std::move(r)), 
+            type_error("failed to unify types") {}
+};

code/compiler/07/examples/bad1.txt

@@ -0,0 +1,2 @@
+data Bool = { True, False }
+defn main = { 3 + True }

code/compiler/07/examples/bad2.txt

@@ -0,0 +1 @@
+defn main = { 1 2 3 4 5 }

code/compiler/07/examples/bad3.txt

@@ -0,0 +1,8 @@
+data List = { Nil, Cons Int List }
+
+defn head l = {
+    case l of {
+        Nil -> { 0 }
+        Cons x y z -> { x }
+    }
+}

code/compiler/07/examples/runtime1.c

@@ -0,0 +1,31 @@
+#include "../runtime.h"
+
+void f_add(struct stack* s) {
+    struct node_num* left = (struct node_num*) eval(stack_peek(s, 0));
+    struct node_num* right = (struct node_num*) eval(stack_peek(s, 1));
+    stack_push(s, (struct node_base*) alloc_num(left->value + right->value));
+}
+
+void f_main(struct stack* s) {
+    // PushInt 320
+    stack_push(s, (struct node_base*) alloc_num(320));
+
+    // PushInt 6
+    stack_push(s, (struct node_base*) alloc_num(6));
+
+    // PushGlobal f_add (the function for +)
+    stack_push(s, (struct node_base*) alloc_global(f_add, 2));
+
+    struct node_base* left;
+    struct node_base* right;
+    
+    // MkApp
+    left = stack_pop(s);
+    right = stack_pop(s);
+    stack_push(s, (struct node_base*) alloc_app(left, right));
+    
+    // MkApp
+    left = stack_pop(s);
+    right = stack_pop(s);
+    stack_push(s, (struct node_base*) alloc_app(left, right));
+}

code/compiler/07/examples/works1.txt

@@ -0,0 +1,2 @@
+defn main = { plus 320 6 }
+defn plus x y = { x + y }

code/compiler/07/examples/works2.txt

@@ -0,0 +1,3 @@
+defn add x y = { x + y }
+defn double x = { add x x }
+defn main = { double 163 }

code/compiler/07/examples/works3.txt

@@ -0,0 +1,7 @@
+data List = { Nil, Cons Int List }
+defn length l = {
+    case l of {
+        Nil -> { 0 }
+        Cons x xs -> { 1 + length xs }
+    }
+}

code/compiler/07/instruction.cpp

@@ -0,0 +1,83 @@
+#include "instruction.hpp"
+
+static void print_indent(int n, std::ostream& to) {
+    while(n--) to << "  ";
+}
+
+void instruction_pushint::print(int indent, std::ostream& to) const {
+    print_indent(indent, to);
+    to << "PushInt(" << value << ")" << std::endl;
+}
+
+void instruction_pushglobal::print(int indent, std::ostream& to) const {
+    print_indent(indent, to);
+    to << "PushGlobal(" << name << ")" << std::endl;
+}
+
+void instruction_push::print(int indent, std::ostream& to) const {
+    print_indent(indent, to);
+    to << "Push(" << offset << ")" << std::endl;
+}
+
+void instruction_pop::print(int indent, std::ostream& to) const {
+    print_indent(indent, to);
+    to << "Pop(" << count << ")" << std::endl;
+}
+
+void instruction_mkapp::print(int indent, std::ostream& to) const {
+    print_indent(indent, to);
+    to << "MkApp()" << std::endl;
+}
+
+void instruction_update::print(int indent, std::ostream& to) const {
+    print_indent(indent, to);
+    to << "Update(" << offset << ")" << std::endl;
+}
+
+void instruction_pack::print(int indent, std::ostream& to) const {
+    print_indent(indent, to);
+    to << "Pack(" << tag << ", " << size << ")" << std::endl;
+}
+
+void instruction_split::print(int indent, std::ostream& to) const {
+    print_indent(indent, to);
+    to << "Split()" << std::endl;
+}
+
+void instruction_jump::print(int indent, std::ostream& to) const {
+    print_indent(indent, to);
+    to << "Jump(" << std::endl;
+    for(auto& instruction_set : branches) {
+        for(auto& instruction : instruction_set) {
+            instruction->print(indent + 2, to);
+        }
+        to << std::endl;
+    }
+    print_indent(indent, to);
+    to << ")" << std::endl;
+}
+
+void instruction_slide::print(int indent, std::ostream& to) const {
+    print_indent(indent, to);
+    to << "Slide(" << offset << ")" << std::endl;
+}
+
+void instruction_binop::print(int indent, std::ostream& to) const {
+    print_indent(indent, to);
+    to << "BinOp(" << op_action(op) << ")" << std::endl;
+}
+
+void instruction_eval::print(int indent, std::ostream& to) const {
+    print_indent(indent, to);
+    to << "Eval()" << std::endl;
+}
+
+void instruction_alloc::print(int indent, std::ostream& to) const {
+    print_indent(indent, to);
+    to << "Alloc(" << amount << ")" << std::endl;
+}
+
+void instruction_unwind::print(int indent, std::ostream& to) const {
+    print_indent(indent, to);
+    to << "Unwind()" << std::endl;
+}

code/compiler/07/instruction.hpp

@@ -0,0 +1,120 @@
+#pragma once
+#include <string>
+#include <memory>
+#include <vector>
+#include <map>
+#include <ostream>
+#include "binop.hpp"
+
+struct instruction {
+    virtual ~instruction() = default;
+
+    virtual void print(int indent, std::ostream& to) const = 0;
+};
+
+using instruction_ptr = std::unique_ptr<instruction>;
+
+struct instruction_pushint : public instruction {
+    int value;
+
+    instruction_pushint(int v)
+        : value(v) {}
+
+    void print(int indent, std::ostream& to) const;
+};
+
+struct instruction_pushglobal : public instruction {
+    std::string name;
+
+    instruction_pushglobal(std::string n)
+        : name(std::move(n)) {}
+
+    void print(int indent, std::ostream& to) const;
+};
+
+struct instruction_push : public instruction {
+    int offset;
+
+    instruction_push(int o)
+        : offset(o) {}
+
+    void print(int indent, std::ostream& to) const;
+};
+
+struct instruction_pop : public instruction {
+    int count;
+
+    instruction_pop(int c)
+        : count(c) {}
+
+    void print(int indent, std::ostream& to) const;
+};
+
+struct instruction_mkapp : public instruction {
+    void print(int indent, std::ostream& to) const;
+};
+
+struct instruction_update : public instruction {
+    int offset;
+
+    instruction_update(int o)
+        : offset(o) {}
+
+    void print(int indent, std::ostream& to) const;
+};
+
+struct instruction_pack : public instruction {
+    int tag;
+    int size;
+
+    instruction_pack(int t, int s)
+        : tag(t), size(s) {}
+
+    void print(int indent, std::ostream& to) const;
+};
+
+struct instruction_split : public instruction {
+    void print(int indent, std::ostream& to) const;
+};
+
+struct instruction_jump : public instruction {
+    std::vector<std::vector<instruction_ptr>> branches;
+    std::map<int, int> tag_mappings;
+
+    void print(int indent, std::ostream& to) const;
+};
+
+struct instruction_slide : public instruction {
+    int offset;
+
+    instruction_slide(int o)
+        : offset(o) {}
+
+    void print(int indent, std::ostream& to) const;
+};
+
+struct instruction_binop : public instruction {
+    binop op;
+
+    instruction_binop(binop o)
+        : op(o) {}
+
+    void print(int indent, std::ostream& to) const;
+};
+
+struct instruction_eval : public instruction {
+    void print(int indent, std::ostream& to) const;
+};
+
+struct instruction_alloc : public instruction {
+    int amount;
+
+    instruction_alloc(int a)
+        : amount(a) {}
+
+    void print(int indent, std::ostream& to) const;
+};
+
+struct instruction_unwind : public instruction {
+    void print(int indent, std::ostream& to) const;
+};

code/compiler/07/main.cpp

@@ -0,0 +1,88 @@
+#include "ast.hpp"
+#include <iostream>
+#include "parser.hpp"
+#include "error.hpp"
+#include "type.hpp"
+
+void yy::parser::error(const std::string& msg) {
+    std::cout << "An error occured: " << msg << std::endl;
+}
+
+extern std::vector<definition_ptr> program;
+
+void typecheck_program(
+        const std::vector<definition_ptr>& prog,
+        type_mgr& mgr, type_env& env) {
+    type_ptr int_type = type_ptr(new type_base("Int")); 
+    type_ptr binop_type = type_ptr(new type_arr(
+                int_type,
+                type_ptr(new type_arr(int_type, int_type))));
+
+    env.bind("+", binop_type);
+    env.bind("-", binop_type);
+    env.bind("*", binop_type);
+    env.bind("/", binop_type);
+
+    for(auto& def : prog) {
+        def->typecheck_first(mgr, env);
+    }
+
+    for(auto& def : prog) {
+        def->typecheck_second(mgr, env);
+    }
+
+    for(auto& pair : env.names) {
+        std::cout << pair.first << ": ";
+        pair.second->print(mgr, std::cout);
+        std::cout << std::endl;
+    }
+
+    for(auto& def : prog) {
+        def->resolve(mgr);
+    }
+}
+
+void compile_program(const std::vector<definition_ptr>& prog) {
+    for(auto& def : prog) {
+        def->compile();
+
+        definition_defn* defn = dynamic_cast<definition_defn*>(def.get());
+        if(!defn) continue;
+        for(auto& instruction : defn->instructions) {
+            instruction->print(0, std::cout);
+        }
+        std::cout << std::endl;
+    }
+}
+
+int main() {
+    yy::parser parser;
+    type_mgr mgr;
+    type_env env;
+
+    parser.parse();
+    for(auto& definition : program) {
+        definition_defn* def = dynamic_cast<definition_defn*>(definition.get());
+        if(!def) continue;
+
+        std::cout << def->name;
+        for(auto& param : def->params) std::cout << " " << param;
+        std::cout << ":" << std::endl;
+
+        def->body->print(1, std::cout);
+    }
+    try {
+        typecheck_program(program, mgr, env);
+        compile_program(program);
+    } catch(unification_error& err) {
+        std::cout << "failed to unify types: " << std::endl;
+        std::cout << "  (1) \033[34m";
+        err.left->print(mgr, std::cout);
+        std::cout << "\033[0m" << std::endl;
+        std::cout << "  (2) \033[32m";
+        err.right->print(mgr, std::cout);
+        std::cout << "\033[0m" << std::endl;
+    } catch(type_error& err) {
+        std::cout << "failed to type check program: " << err.description << std::endl;
+    }
+}

code/compiler/07/parser.y

@@ -0,0 +1,140 @@
+%{
+#include <string>
+#include <iostream>
+#include "ast.hpp"
+#include "parser.hpp"
+
+std::vector<definition_ptr> program;
+extern yy::parser::symbol_type yylex();
+
+%}
+
+%token PLUS
+%token TIMES
+%token MINUS
+%token DIVIDE
+%token <int> INT
+%token DEFN
+%token DATA
+%token CASE
+%token OF
+%token OCURLY
+%token CCURLY
+%token OPAREN
+%token CPAREN
+%token COMMA
+%token ARROW
+%token EQUAL
+%token <std::string> LID
+%token <std::string> UID
+
+%language "c++"
+%define api.value.type variant
+%define api.token.constructor
+
+%type <std::vector<std::string>> lowercaseParams uppercaseParams
+%type <std::vector<definition_ptr>> program definitions
+%type <std::vector<branch_ptr>> branches
+%type <std::vector<constructor_ptr>> constructors
+%type <ast_ptr> aAdd aMul case app appBase
+%type <definition_ptr> definition defn data 
+%type <branch_ptr> branch
+%type <pattern_ptr> pattern
+%type <constructor_ptr> constructor
+
+%start program
+
+%%
+
+program
+    : definitions { program = std::move($1); }
+    ;
+
+definitions
+    : definitions definition { $$ = std::move($1); $$.push_back(std::move($2)); }
+    | definition { $$ = std::vector<definition_ptr>(); $$.push_back(std::move($1)); }
+    ;
+
+definition
+    : defn { $$ = std::move($1); }
+    | data { $$ = std::move($1); }
+    ;
+
+defn
+    : DEFN LID lowercaseParams EQUAL OCURLY aAdd CCURLY
+        { $$ = definition_ptr(
+            new definition_defn(std::move($2), std::move($3), std::move($6))); }
+    ;
+
+lowercaseParams
+    : %empty { $$ = std::vector<std::string>(); }
+    | lowercaseParams LID { $$ = std::move($1); $$.push_back(std::move($2)); }
+    ;
+
+uppercaseParams
+    : %empty { $$ = std::vector<std::string>(); }
+    | uppercaseParams UID { $$ = std::move($1); $$.push_back(std::move($2)); }
+    ;
+
+aAdd
+    : aAdd PLUS aMul { $$ = ast_ptr(new ast_binop(PLUS, std::move($1), std::move($3))); }
+    | aAdd MINUS aMul { $$ = ast_ptr(new ast_binop(MINUS, std::move($1), std::move($3))); }
+    | aMul { $$ = std::move($1); }
+    ;
+
+aMul
+    : aMul TIMES app { $$ = ast_ptr(new ast_binop(TIMES, std::move($1), std::move($3))); }
+    | aMul DIVIDE app { $$ = ast_ptr(new ast_binop(DIVIDE, std::move($1), std::move($3))); }
+    | app { $$ = std::move($1); }
+    ;
+
+app
+    : app appBase { $$ = ast_ptr(new ast_app(std::move($1), std::move($2))); }
+    | appBase { $$ = std::move($1); }
+    ;
+
+appBase
+    : INT { $$ = ast_ptr(new ast_int($1)); }
+    | LID { $$ = ast_ptr(new ast_lid(std::move($1))); }
+    | UID { $$ = ast_ptr(new ast_uid(std::move($1))); }
+    | OPAREN aAdd CPAREN { $$ = std::move($2); }
+    | case { $$ = std::move($1); }
+    ;
+
+case
+    : CASE aAdd OF OCURLY branches CCURLY 
+        { $$ = ast_ptr(new ast_case(std::move($2), std::move($5))); }
+    ;
+
+branches
+    : branches branch { $$ = std::move($1); $$.push_back(std::move($2)); }
+    | branch { $$ = std::vector<branch_ptr>(); $$.push_back(std::move($1));}
+    ;
+
+branch
+    : pattern ARROW OCURLY aAdd CCURLY
+        { $$ = branch_ptr(new branch(std::move($1), std::move($4))); }
+    ;
+
+pattern
+    : LID { $$ = pattern_ptr(new pattern_var(std::move($1))); }
+    | UID lowercaseParams
+        { $$ = pattern_ptr(new pattern_constr(std::move($1), std::move($2))); }
+    ;
+
+data
+    : DATA UID EQUAL OCURLY constructors CCURLY
+        { $$ = definition_ptr(new definition_data(std::move($2), std::move($5))); }
+    ;
+
+constructors
+    : constructors COMMA constructor { $$ = std::move($1); $$.push_back(std::move($3)); }
+    | constructor
+        { $$ = std::vector<constructor_ptr>(); $$.push_back(std::move($1)); }
+    ;
+
+constructor
+    : UID uppercaseParams
+        { $$ = constructor_ptr(new constructor(std::move($1), std::move($2))); }
+    ;
+

code/compiler/07/runtime.c

@@ -0,0 +1,159 @@
+#include <stdint.h>
+#include <assert.h>
+#include <memory.h>
+#include "runtime.h"
+
+struct node_base* alloc_node() {
+    struct node_base* new_node = malloc(sizeof(struct node_app));
+    assert(new_node != NULL);
+    return new_node;
+}
+
+struct node_app* alloc_app(struct node_base* l, struct node_base* r) {
+    struct node_app* node = (struct node_app*) alloc_node();
+    node->base.tag = NODE_APP;
+    node->left = l;
+    node->right = r;
+    return node;
+}
+
+struct node_num* alloc_num(int32_t n) {
+    struct node_num* node = (struct node_num*) alloc_node();
+    node->base.tag = NODE_NUM;
+    node->value = n;
+    return node;
+}
+
+struct node_global* alloc_global(void (*f)(struct stack*), int32_t a) {
+    struct node_global* node = (struct node_global*) alloc_node();
+    node->base.tag = NODE_GLOBAL;
+    node->arity = a;
+    node->function = f;
+    return node;
+}
+
+struct node_ind* alloc_ind(struct node_base* n) {
+    struct node_ind* node = (struct node_ind*) alloc_node();
+    node->base.tag = NODE_IND;
+    node->next = n;
+    return node;
+}
+
+void stack_init(struct stack* s) {
+    s->size = 4;
+    s->count = 0;
+    s->data = malloc(sizeof(*s->data) * s->size);
+    assert(s->data != NULL);
+}
+
+void stack_free(struct stack* s) {
+    free(s->data);
+}
+
+void stack_push(struct stack* s, struct node_base* n) {
+    while(s->count >= s->size) {
+        s->data = realloc(s->data, sizeof(*s->data) * (s->size *= 2));
+        assert(s->data != NULL);
+    }
+    s->data[s->count++] = n;
+}
+
+struct node_base* stack_pop(struct stack* s) {
+    assert(s->count > 0);
+    return s->data[--s->count];
+}
+
+struct node_base* stack_peek(struct stack* s, size_t o) {
+    assert(s->count > o);
+    return s->data[s->count - o - 1];
+}
+
+void stack_popn(struct stack* s, size_t n) {
+    assert(s->count >= n);
+    s->count -= n;
+}
+
+void stack_slide(struct stack* s, size_t n) {
+    assert(s->count > n);
+    s->data[s->count - n - 1] = s->data[s->count - 1];
+    s->count -= n;
+}
+
+void stack_update(struct stack* s, size_t o) {
+    assert(s->count > o + 1);
+    struct node_ind* ind = (struct node_ind*) s->data[s->count - o - 2];
+    ind->base.tag = NODE_IND;
+    ind->next = s->data[s->count -= 1];
+}
+
+void stack_alloc(struct stack* s, size_t o) {
+    while(o--) {
+        stack_push(s, (struct node_base*) alloc_ind(NULL));
+    }
+}
+
+void stack_pack(struct stack* s, size_t n, int8_t t) {
+    assert(s->count >= n);
+
+    struct node_base** data = malloc(sizeof(*data) * n);
+    assert(data != NULL);
+    memcpy(data, &s->data[s->count - 1 - n], n * sizeof(*data));
+
+    struct node_data* new_node = (struct node_data*) alloc_node();
+    new_node->array = data;
+    new_node->base.tag = NODE_DATA;
+    new_node->tag = t;
+
+    stack_popn(s, n);
+    stack_push(s, (struct node_base*) new_node);
+}
+
+void stack_split(struct stack* s, size_t n) {
+    struct node_data* node = (struct node_data*) stack_pop(s);
+    for(size_t i = 0; i < n; i++) {
+        stack_push(s, node->array[i]);
+    }
+}
+
+void unwind(struct stack* s) {
+    while(1) {
+        struct node_base* peek = stack_peek(s, 0);
+        if(peek->tag == NODE_APP) {
+            struct node_app* n = (struct node_app*) peek;
+            stack_push(s, n->left);
+        } else if(peek->tag == NODE_GLOBAL) {
+            struct node_global* n = (struct node_global*) peek;
+            assert(s->count > n->arity);
+
+            for(size_t i = 1; i <= n->arity; i++) {
+                s->data[s->count - i]
+                    = ((struct node_app*) s->data[s->count - i - 1])->right;
+            }
+
+            n->function(s);
+        } else if(peek->tag == NODE_IND) {
+            struct node_ind* n = (struct node_ind*) peek;
+            stack_pop(s);
+            stack_push(s, n->next);
+        } else {
+            break;
+        }
+    }
+}
+
+struct node_base* eval(struct node_base* n) {
+    struct stack program_stack;
+    stack_init(&program_stack);
+    stack_push(&program_stack, n);
+    unwind(&program_stack);
+    struct node_base* result = stack_pop(&program_stack);
+    stack_free(&program_stack);
+    return result;
+}
+
+extern void f_main(struct stack* s);
+
+int main(int argc, char** argv) {
+    struct node_global* first_node = alloc_global(f_main, 0);
+    struct node_base* result = eval((struct node_base*) first_node);
+}

code/compiler/07/runtime.h

@@ -0,0 +1,70 @@
+#pragma once
+#include <stdlib.h>
+
+struct stack;
+
+enum node_tag {
+    NODE_APP,
+    NODE_NUM,
+    NODE_GLOBAL,
+    NODE_IND,
+    NODE_DATA
+};
+
+struct node_base {
+    enum node_tag tag;
+};
+
+struct node_app {
+    struct node_base base;
+    struct node_base* left;
+    struct node_base* right;
+};
+
+struct node_num {
+    struct node_base base;
+    int32_t value;
+};
+
+struct node_global {
+    struct node_base base;
+    int32_t arity;
+    void (*function)(struct stack*);
+};
+
+struct node_ind {
+    struct node_base base;
+    struct node_base* next;
+};
+
+struct node_data {
+    struct node_base base;
+    int8_t tag;
+    struct node_base** array;
+};
+
+struct node_base* alloc_node();
+struct node_app* alloc_app(struct node_base* l, struct node_base* r);
+struct node_num* alloc_num(int32_t n);
+struct node_global* alloc_global(void (*f)(struct stack*), int32_t a);
+struct node_ind* alloc_ind(struct node_base* n);
+
+struct stack {
+    size_t size;
+    size_t count;
+    struct node_base** data;
+};
+
+void stack_init(struct stack* s);
+void stack_free(struct stack* s);
+void stack_push(struct stack* s, struct node_base* n);
+struct node_base* stack_pop(struct stack* s);
+struct node_base* stack_peek(struct stack* s, size_t o);
+void stack_popn(struct stack* s, size_t n);
+void stack_slide(struct stack* s, size_t n);
+void stack_update(struct stack* s, size_t o);
+void stack_alloc(struct stack* s, size_t o);
+void stack_pack(struct stack* s, size_t n, int8_t t);
+void stack_split(struct stack* s, size_t n);
+
+struct node_base* eval(struct node_base* n);

code/compiler/07/scanner.l

@@ -0,0 +1,34 @@
+%option noyywrap
+
+%{
+#include <iostream>
+#include "ast.hpp"
+#include "parser.hpp"
+
+#define YY_DECL yy::parser::symbol_type yylex()
+
+%}
+
+%%
+
+[ \n]+ {}
+\+ { return yy::parser::make_PLUS(); }
+\* { return yy::parser::make_TIMES(); }
+- { return yy::parser::make_MINUS(); }
+\/ { return yy::parser::make_DIVIDE(); }
+[0-9]+ { return yy::parser::make_INT(atoi(yytext)); }
+defn { return yy::parser::make_DEFN(); }
+data { return yy::parser::make_DATA(); }
+case { return yy::parser::make_CASE(); }
+of { return yy::parser::make_OF(); }
+\{ { return yy::parser::make_OCURLY(); }
+\} { return yy::parser::make_CCURLY(); }
+\( { return yy::parser::make_OPAREN(); }
+\) { return yy::parser::make_CPAREN(); }
+,  { return yy::parser::make_COMMA(); }
+-> { return yy::parser::make_ARROW(); }
+= { return yy::parser::make_EQUAL(); }
+[a-z][a-zA-Z]* { return yy::parser::make_LID(std::string(yytext)); }
+[A-Z][a-zA-Z]* { return yy::parser::make_UID(std::string(yytext)); }
+
+%%

code/compiler/07/type.cpp

@@ -0,0 +1,99 @@
+#include "type.hpp"
+#include <sstream>
+#include <algorithm>
+#include "error.hpp"
+
+void type_var::print(const type_mgr& mgr, std::ostream& to) const {
+    auto it = mgr.types.find(name);
+    if(it != mgr.types.end()) {
+        it->second->print(mgr, to);
+    } else {
+        to << name;
+    }
+}
+
+void type_base::print(const type_mgr& mgr, std::ostream& to) const {
+    to << name;
+}
+
+void type_arr::print(const type_mgr& mgr, std::ostream& to) const {
+    left->print(mgr, to);
+    to << " -> (";
+    right->print(mgr, to);
+    to << ")";
+}
+
+std::string type_mgr::new_type_name() {
+    int temp = last_id++;
+    std::string str = "";
+
+    while(temp != -1) {
+        str += (char) ('a' + (temp % 26));
+        temp = temp / 26 - 1;
+    }
+
+    std::reverse(str.begin(), str.end());
+    return str;
+}
+
+type_ptr type_mgr::new_type() {
+    return type_ptr(new type_var(new_type_name()));
+}
+
+type_ptr type_mgr::new_arrow_type() {
+    return type_ptr(new type_arr(new_type(), new_type()));
+}
+
+type_ptr type_mgr::resolve(type_ptr t, type_var*& var) const {
+    type_var* cast;
+
+    var = nullptr;
+    while((cast = dynamic_cast<type_var*>(t.get()))) {
+        auto it = types.find(cast->name);
+
+        if(it == types.end()) {
+            var = cast;
+            break;
+        }
+        t = it->second;
+    }
+
+    return t;
+}
+
+void type_mgr::unify(type_ptr l, type_ptr r) {
+    type_var* lvar;
+    type_var* rvar;
+    type_arr* larr;
+    type_arr* rarr;
+    type_base* lid;
+    type_base* rid;
+
+    l = resolve(l, lvar);
+    r = resolve(r, rvar);
+
+    if(lvar) {
+        bind(lvar->name, r);
+        return;
+    } else if(rvar) {
+        bind(rvar->name, l);
+        return;
+    } else if((larr = dynamic_cast<type_arr*>(l.get())) &&
+            (rarr = dynamic_cast<type_arr*>(r.get()))) {
+        unify(larr->left, rarr->left);
+        unify(larr->right, rarr->right);
+        return;
+    } else if((lid = dynamic_cast<type_base*>(l.get())) &&
+            (rid = dynamic_cast<type_base*>(r.get()))) {
+        if(lid->name == rid->name) return;
+    }
+
+    throw unification_error(l, r);
+}
+
+void type_mgr::bind(const std::string& s, type_ptr t) {
+    type_var* other = dynamic_cast<type_var*>(t.get());
+    
+    if(other && other->name == s) return;
+    types[s] = t;
+}

code/compiler/07/type.hpp

@@ -0,0 +1,65 @@
+#pragma once
+#include <memory>
+#include <map>
+
+struct type_mgr;
+
+struct type {
+    virtual ~type() = default;
+
+    virtual void print(const type_mgr& mgr, std::ostream& to) const = 0;
+};
+
+using type_ptr = std::shared_ptr<type>;
+
+struct type_var : public type {
+    std::string name;
+
+    type_var(std::string n)
+        : name(std::move(n)) {}
+
+    void print(const type_mgr& mgr, std::ostream& to) const;
+};
+
+struct type_base : public type {
+    std::string name;
+
+    type_base(std::string n) 
+        : name(std::move(n)) {}
+
+    void print(const type_mgr& mgr, std::ostream& to) const;
+};
+
+struct type_data : public type_base {
+    struct constructor {
+        int tag;
+    };
+
+    std::map<std::string, constructor> constructors;
+
+    type_data(std::string n)
+        : type_base(std::move(n)) {}
+};
+
+struct type_arr : public type {
+    type_ptr left;
+    type_ptr right;
+
+    type_arr(type_ptr l, type_ptr r)
+        : left(std::move(l)), right(std::move(r)) {}
+
+    void print(const type_mgr& mgr, std::ostream& to) const;
+};
+
+struct type_mgr {
+    int last_id = 0;
+    std::map<std::string, type_ptr> types;
+
+    std::string new_type_name();
+    type_ptr new_type();
+    type_ptr new_arrow_type();
+
+    void unify(type_ptr l, type_ptr r);
+    type_ptr resolve(type_ptr t, type_var*& var) const;
+    void bind(const std::string& s, type_ptr t);
+};

code/compiler/07/type_env.cpp

@@ -0,0 +1,16 @@
+#include "type_env.hpp"
+
+type_ptr type_env::lookup(const std::string& name) const {
+    auto it = names.find(name);
+    if(it != names.end()) return it->second;
+    if(parent) return parent->lookup(name);
+    return nullptr;
+}
+
+void type_env::bind(const std::string& name, type_ptr t) {
+    names[name] = t;
+}
+
+type_env type_env::scope() const {
+    return type_env(this);
+}

code/compiler/07/type_env.hpp

@@ -0,0 +1,16 @@
+#pragma once
+#include <map>
+#include "type.hpp"
+
+struct type_env {
+    std::map<std::string, type_ptr> names;
+    type_env const* parent = nullptr;
+
+    type_env(type_env const* p)
+        : parent(p) {}
+    type_env() : type_env(nullptr) {}
+
+    type_ptr lookup(const std::string& name) const;
+    void bind(const std::string& name, type_ptr t);
+    type_env scope() const;
+};

code/compiler/08/CMakeLists.txt

@@ -0,0 +1,42 @@
+cmake_minimum_required(VERSION 3.1)
+project(compiler)
+
+# Find all the required packages
+find_package(BISON)
+find_package(FLEX)
+find_package(LLVM REQUIRED CONFIG)
+
+# Set up the flex and bison targets
+bison_target(parser
+    ${CMAKE_CURRENT_SOURCE_DIR}/parser.y
+    ${CMAKE_CURRENT_BINARY_DIR}/parser.cpp
+    COMPILE_FLAGS "-d")
+flex_target(scanner
+    ${CMAKE_CURRENT_SOURCE_DIR}/scanner.l
+    ${CMAKE_CURRENT_BINARY_DIR}/scanner.cpp)
+add_flex_bison_dependency(scanner parser)
+
+# Find all the relevant LLVM components
+llvm_map_components_to_libnames(LLVM_LIBS core x86asmparser x86codegen)
+
+# Create compiler executable
+add_executable(compiler
+    ast.cpp ast.hpp definition.cpp
+    llvm_context.cpp llvm_context.hpp
+    type_env.cpp type_env.hpp
+    env.cpp env.hpp
+    type.cpp type.hpp
+    error.cpp error.hpp
+    binop.cpp binop.hpp
+    instruction.cpp instruction.hpp
+    ${BISON_parser_OUTPUTS}
+    ${FLEX_scanner_OUTPUTS}
+    main.cpp
+)
+
+# Configure compiler executable
+target_include_directories(compiler PUBLIC ${CMAKE_CURRENT_SOURCE_DIR})
+target_include_directories(compiler PUBLIC ${CMAKE_CURRENT_BINARY_DIR})
+target_include_directories(compiler PUBLIC ${LLVM_INCLUDE_DIRS})
+target_compile_definitions(compiler PUBLIC ${LLVM_DEFINITIONS})
+target_link_libraries(compiler ${LLVM_LIBS})

code/compiler/08/ast.cpp

@@ -0,0 +1,264 @@
+#include "ast.hpp"
+#include <ostream>
+#include "binop.hpp"
+#include "error.hpp"
+
+static void print_indent(int n, std::ostream& to) {
+    while(n--) to << "  ";
+}
+
+type_ptr ast::typecheck_common(type_mgr& mgr, const type_env& env) {
+    node_type = typecheck(mgr, env);
+    return node_type;
+}
+
+void ast::resolve_common(const type_mgr& mgr) {
+    type_var* var;
+    type_ptr resolved_type = mgr.resolve(node_type, var);
+    if(var) throw type_error("ambiguously typed program");
+
+    resolve(mgr);
+    node_type = std::move(resolved_type);
+}
+
+void ast_int::print(int indent, std::ostream& to) const {
+    print_indent(indent, to);
+    to << "INT: " << value << std::endl;
+}
+
+type_ptr ast_int::typecheck(type_mgr& mgr, const type_env& env) const {
+    return type_ptr(new type_base("Int"));
+}
+
+void ast_int::resolve(const type_mgr& mgr) const {
+    
+}
+
+void ast_int::compile(const env_ptr& env, std::vector<instruction_ptr>& into) const {
+    into.push_back(instruction_ptr(new instruction_pushint(value)));
+}
+
+void ast_lid::print(int indent, std::ostream& to) const {
+    print_indent(indent, to);
+    to << "LID: " << id << std::endl;
+}
+
+type_ptr ast_lid::typecheck(type_mgr& mgr, const type_env& env) const {
+    return env.lookup(id);
+}
+
+void ast_lid::resolve(const type_mgr& mgr) const {
+
+}
+
+void ast_lid::compile(const env_ptr& env, std::vector<instruction_ptr>& into) const {
+    into.push_back(instruction_ptr(
+        env->has_variable(id) ?
+            (instruction*) new instruction_push(env->get_offset(id)) :
+            (instruction*) new instruction_pushglobal(id)));
+}
+
+void ast_uid::print(int indent, std::ostream& to) const {
+    print_indent(indent, to);
+    to << "UID: " << id << std::endl;
+}
+
+type_ptr ast_uid::typecheck(type_mgr& mgr, const type_env& env) const {
+    return env.lookup(id);
+}
+
+void ast_uid::resolve(const type_mgr& mgr) const {
+
+}
+
+void ast_uid::compile(const env_ptr& env, std::vector<instruction_ptr>& into) const {
+    into.push_back(instruction_ptr(new instruction_pushglobal(id)));
+}
+
+void ast_binop::print(int indent, std::ostream& to) const {
+    print_indent(indent, to);
+    to << "BINOP: " << op_name(op) << std::endl;
+    left->print(indent + 1, to);
+    right->print(indent + 1, to);
+}
+
+type_ptr ast_binop::typecheck(type_mgr& mgr, const type_env& env) const {
+    type_ptr ltype = left->typecheck_common(mgr, env);
+    type_ptr rtype = right->typecheck_common(mgr, env);
+    type_ptr ftype = env.lookup(op_name(op));
+    if(!ftype) throw type_error(std::string("unknown binary operator ") + op_name(op));
+
+    type_ptr return_type = mgr.new_type();
+    type_ptr arrow_one = type_ptr(new type_arr(rtype, return_type));
+    type_ptr arrow_two = type_ptr(new type_arr(ltype, arrow_one));
+
+    mgr.unify(arrow_two, ftype);
+    return return_type;
+}
+
+void ast_binop::resolve(const type_mgr& mgr) const {
+    left->resolve_common(mgr);
+    right->resolve_common(mgr);
+}
+
+void ast_binop::compile(const env_ptr& env, std::vector<instruction_ptr>& into) const {
+    right->compile(env, into);
+    left->compile(env_ptr(new env_offset(1, env)), into);
+
+    into.push_back(instruction_ptr(new instruction_pushglobal(op_action(op))));
+    into.push_back(instruction_ptr(new instruction_mkapp()));
+    into.push_back(instruction_ptr(new instruction_mkapp()));
+}
+
+void ast_app::print(int indent, std::ostream& to) const {
+    print_indent(indent, to);
+    to << "APP:" << std::endl;
+    left->print(indent + 1, to);
+    right->print(indent + 1, to);
+}
+
+type_ptr ast_app::typecheck(type_mgr& mgr, const type_env& env) const {
+    type_ptr ltype = left->typecheck_common(mgr, env);
+    type_ptr rtype = right->typecheck_common(mgr, env);
+
+    type_ptr return_type = mgr.new_type();
+    type_ptr arrow = type_ptr(new type_arr(rtype, return_type));
+    mgr.unify(arrow, ltype);
+    return return_type;
+}
+
+void ast_app::resolve(const type_mgr& mgr) const {
+    left->resolve_common(mgr);
+    right->resolve_common(mgr);
+}
+
+void ast_app::compile(const env_ptr& env, std::vector<instruction_ptr>& into) const {
+    right->compile(env, into);
+    left->compile(env_ptr(new env_offset(1, env)), into);
+    into.push_back(instruction_ptr(new instruction_mkapp()));
+}
+
+void ast_case::print(int indent, std::ostream& to) const {
+    print_indent(indent, to);
+    to << "CASE: " << std::endl;
+    for(auto& branch : branches) {
+        print_indent(indent + 1, to);
+        branch->pat->print(to);
+        to << std::endl;
+        branch->expr->print(indent + 2, to);
+    }
+}
+
+type_ptr ast_case::typecheck(type_mgr& mgr, const type_env& env) const {
+    type_var* var;
+    type_ptr case_type = mgr.resolve(of->typecheck_common(mgr, env), var);
+    type_ptr branch_type = mgr.new_type();
+
+    for(auto& branch : branches) {
+        type_env new_env = env.scope();
+        branch->pat->match(case_type, mgr, new_env);
+        type_ptr curr_branch_type = branch->expr->typecheck_common(mgr, new_env);
+        mgr.unify(branch_type, curr_branch_type);
+    }
+
+    case_type = mgr.resolve(case_type, var);
+    if(!dynamic_cast<type_data*>(case_type.get())) {
+        throw type_error("attempting case analysis of non-data type");
+    }
+
+    return branch_type;
+}
+
+void ast_case::resolve(const type_mgr& mgr) const {
+    of->resolve_common(mgr);
+    for(auto& branch : branches) {
+        branch->expr->resolve_common(mgr);
+    }
+}
+
+void ast_case::compile(const env_ptr& env, std::vector<instruction_ptr>& into) const {
+    type_data* type = dynamic_cast<type_data*>(of->node_type.get());
+
+    of->compile(env, into);
+    into.push_back(instruction_ptr(new instruction_eval()));
+
+    instruction_jump* jump_instruction = new instruction_jump();
+    into.push_back(instruction_ptr(jump_instruction));
+    for(auto& branch : branches) {
+        std::vector<instruction_ptr> branch_instructions;
+        pattern_var* vpat;
+        pattern_constr* cpat;
+
+        if((vpat = dynamic_cast<pattern_var*>(branch->pat.get()))) {
+            branch->expr->compile(env_ptr(new env_offset(1, env)), branch_instructions);
+
+            for(auto& constr_pair : type->constructors) {
+                if(jump_instruction->tag_mappings.find(constr_pair.second.tag) !=
+                        jump_instruction->tag_mappings.end())
+                    break;
+
+                jump_instruction->tag_mappings[constr_pair.second.tag] =
+                    jump_instruction->branches.size();
+            }
+            jump_instruction->branches.push_back(std::move(branch_instructions));
+        } else if((cpat = dynamic_cast<pattern_constr*>(branch->pat.get()))) {
+            env_ptr new_env = env;
+            for(auto it = cpat->params.rbegin(); it != cpat->params.rend(); it++) {
+                new_env = env_ptr(new env_var(*it, new_env));
+            }
+
+            branch_instructions.push_back(instruction_ptr(new instruction_split(
+                            cpat->params.size())));
+            branch->expr->compile(new_env, branch_instructions);
+            branch_instructions.push_back(instruction_ptr(new instruction_slide(
+                            cpat->params.size())));
+
+            int new_tag = type->constructors[cpat->constr].tag;
+            if(jump_instruction->tag_mappings.find(new_tag) !=
+                    jump_instruction->tag_mappings.end())
+                throw type_error("technically not a type error: duplicate pattern");
+
+            jump_instruction->tag_mappings[new_tag] =
+                jump_instruction->branches.size();
+            jump_instruction->branches.push_back(std::move(branch_instructions));
+        }
+    }
+
+    for(auto& constr_pair : type->constructors) {
+        if(jump_instruction->tag_mappings.find(constr_pair.second.tag) ==
+                jump_instruction->tag_mappings.end())
+            throw type_error("non-total pattern");
+    }
+}
+
+void pattern_var::print(std::ostream& to) const {
+    to << var;
+}
+
+void pattern_var::match(type_ptr t, type_mgr& mgr, type_env& env) const {
+    env.bind(var, t);
+}
+
+void pattern_constr::print(std::ostream& to) const {
+    to << constr;
+    for(auto& param : params) {
+        to << " " << param;
+    }
+}
+
+void pattern_constr::match(type_ptr t, type_mgr& mgr, type_env& env) const {
+    type_ptr constructor_type = env.lookup(constr);
+    if(!constructor_type) {
+        throw type_error(std::string("pattern using unknown constructor ") + constr);
+    }
+
+    for(int i = 0; i < params.size(); i++) {
+        type_arr* arr = dynamic_cast<type_arr*>(constructor_type.get());
+        if(!arr) throw type_error("too many parameters in constructor pattern");
+
+        env.bind(params[i], arr->left);
+        constructor_type = arr->right;
+    }
+
+    mgr.unify(t, constructor_type);
+}

code/compiler/08/ast.hpp

@@ -0,0 +1,141 @@
+#pragma once
+#include <memory>
+#include <vector>
+#include "type.hpp"
+#include "type_env.hpp"
+#include "binop.hpp"
+#include "instruction.hpp"
+#include "env.hpp"
+
+struct ast {
+    type_ptr node_type;
+
+    virtual ~ast() = default;
+
+    virtual void print(int indent, std::ostream& to) const = 0;
+    virtual type_ptr typecheck(type_mgr& mgr, const type_env& env) const = 0;
+    virtual void resolve(const type_mgr& mgr) const = 0;
+    virtual void compile(const env_ptr& env,
+        std::vector<instruction_ptr>& into) const = 0;
+
+    type_ptr typecheck_common(type_mgr& mgr, const type_env& env);
+    void resolve_common(const type_mgr& mgr);
+};
+
+using ast_ptr = std::unique_ptr<ast>;
+
+struct pattern {
+    virtual ~pattern() = default;
+
+    virtual void print(std::ostream& to) const = 0;
+    virtual void match(type_ptr t, type_mgr& mgr, type_env& env) const = 0;
+};
+
+using pattern_ptr = std::unique_ptr<pattern>;
+
+struct branch {
+    pattern_ptr pat;
+    ast_ptr expr;
+
+    branch(pattern_ptr p, ast_ptr a)
+        : pat(std::move(p)), expr(std::move(a)) {}
+};
+
+using branch_ptr = std::unique_ptr<branch>;
+
+struct ast_int : public ast {
+    int value;
+
+    explicit ast_int(int v)
+        : value(v) {}
+
+    void print(int indent, std::ostream& to) const;
+    type_ptr typecheck(type_mgr& mgr, const type_env& env) const;
+    void resolve(const type_mgr& mgr) const;
+    void compile(const env_ptr& env, std::vector<instruction_ptr>& into) const;
+};
+
+struct ast_lid : public ast {
+    std::string id;
+
+    explicit ast_lid(std::string i)
+        : id(std::move(i)) {}
+
+    void print(int indent, std::ostream& to) const;
+    type_ptr typecheck(type_mgr& mgr, const type_env& env) const;
+    void resolve(const type_mgr& mgr) const;
+    void compile(const env_ptr& env, std::vector<instruction_ptr>& into) const;
+};
+
+struct ast_uid : public ast {
+    std::string id;
+
+    explicit ast_uid(std::string i)
+        : id(std::move(i)) {}
+
+    void print(int indent, std::ostream& to) const;
+    type_ptr typecheck(type_mgr& mgr, const type_env& env) const;
+    void resolve(const type_mgr& mgr) const;
+    void compile(const env_ptr& env, std::vector<instruction_ptr>& into) const;
+};
+
+struct ast_binop : public ast {
+    binop op;  
+    ast_ptr left;
+    ast_ptr right;
+
+    ast_binop(binop o, ast_ptr l, ast_ptr r)
+        : op(o), left(std::move(l)), right(std::move(r)) {}
+
+    void print(int indent, std::ostream& to) const;
+    type_ptr typecheck(type_mgr& mgr, const type_env& env) const;
+    void resolve(const type_mgr& mgr) const;
+    void compile(const env_ptr& env, std::vector<instruction_ptr>& into) const;
+};
+
+struct ast_app : public ast {
+    ast_ptr left;
+    ast_ptr right;
+
+    ast_app(ast_ptr l, ast_ptr r)
+        : left(std::move(l)), right(std::move(r)) {}
+
+    void print(int indent, std::ostream& to) const;
+    type_ptr typecheck(type_mgr& mgr, const type_env& env) const;
+    void resolve(const type_mgr& mgr) const;
+    void compile(const env_ptr& env, std::vector<instruction_ptr>& into) const;
+};
+
+struct ast_case : public ast {
+    ast_ptr of;
+    std::vector<branch_ptr> branches;
+
+    ast_case(ast_ptr o, std::vector<branch_ptr> b)
+        : of(std::move(o)), branches(std::move(b)) {}
+
+    void print(int indent, std::ostream& to) const;
+    type_ptr typecheck(type_mgr& mgr, const type_env& env) const;
+    void resolve(const type_mgr& mgr) const;
+    void compile(const env_ptr& env, std::vector<instruction_ptr>& into) const;
+};
+
+struct pattern_var : public pattern {
+    std::string var;
+
+    pattern_var(std::string v)
+        : var(std::move(v)) {}
+
+    void print(std::ostream &to) const;
+    void match(type_ptr t, type_mgr& mgr, type_env& env) const;
+};
+
+struct pattern_constr : public pattern {
+    std::string constr;
+    std::vector<std::string> params;
+
+    pattern_constr(std::string c, std::vector<std::string> p)
+        : constr(std::move(c)), params(std::move(p)) {}
+
+    void print(std::ostream &to) const;
+    void match(type_ptr t, type_mgr&, type_env& env) const;
+};

code/compiler/08/binop.cpp

@@ -0,0 +1,21 @@
+#include "binop.hpp"
+
+std::string op_name(binop op) {
+    switch(op) {
+        case PLUS: return "+";
+        case MINUS: return "-";
+        case TIMES: return "*";
+        case DIVIDE: return "/";
+    }
+    return "??";
+}
+
+std::string op_action(binop op) {
+    switch(op) {
+        case PLUS: return "plus";
+        case MINUS: return "minus";
+        case TIMES: return "times";
+        case DIVIDE: return "divide";
+    }
+    return "??";
+}

code/compiler/08/binop.hpp

@@ -0,0 +1,12 @@
+#pragma once
+#include <string>
+
+enum binop {
+    PLUS,
+    MINUS,
+    TIMES,
+    DIVIDE
+};
+
+std::string op_name(binop op);
+std::string op_action(binop op);

code/compiler/08/definition.cpp

@@ -0,0 +1,116 @@
+#include "definition.hpp"
+#include "error.hpp"
+#include "ast.hpp"
+#include "llvm_context.hpp"
+#include <llvm/IR/DerivedTypes.h>
+#include <llvm/IR/Function.h>
+#include <llvm/IR/Type.h>
+
+void definition_defn::typecheck_first(type_mgr& mgr, type_env& env) {
+    return_type = mgr.new_type();
+    type_ptr full_type = return_type;
+
+    for(auto it = params.rbegin(); it != params.rend(); it++) {
+        type_ptr param_type = mgr.new_type();
+        full_type = type_ptr(new type_arr(param_type, full_type));
+        param_types.push_back(param_type);
+    }
+
+    env.bind(name, full_type);
+}
+
+void definition_defn::typecheck_second(type_mgr& mgr, const type_env& env) const {
+    type_env new_env = env.scope();
+    auto param_it = params.begin();
+    auto type_it = param_types.rbegin();
+
+    while(param_it != params.end() && type_it != param_types.rend()) {
+        new_env.bind(*param_it, *type_it);
+        param_it++;
+        type_it++;
+    }
+
+    type_ptr body_type = body->typecheck_common(mgr, new_env);
+    mgr.unify(return_type, body_type);
+}
+
+void definition_defn::resolve(const type_mgr& mgr) {
+    type_var* var;
+    body->resolve_common(mgr);
+
+    return_type = mgr.resolve(return_type, var);
+    if(var) throw type_error("ambiguously typed program");
+    for(auto& param_type : param_types) {
+        param_type = mgr.resolve(param_type, var);
+        if(var) throw type_error("ambiguously typed program");
+    }
+}
+
+void definition_defn::compile() {
+    env_ptr new_env = env_ptr(new env_offset(0, nullptr));
+    for(auto it = params.rbegin(); it != params.rend(); it++) {
+        new_env = env_ptr(new env_var(*it, new_env));
+    }
+    body->compile(new_env, instructions);
+    instructions.push_back(instruction_ptr(new instruction_update(params.size())));
+    instructions.push_back(instruction_ptr(new instruction_pop(params.size())));
+}
+void definition_defn::gen_llvm_first(llvm_context& ctx) {
+    generated_function = ctx.create_custom_function(name, params.size());
+}
+
+void definition_defn::gen_llvm_second(llvm_context& ctx) {
+    ctx.builder.SetInsertPoint(&generated_function->getEntryBlock());
+    for(auto& instruction : instructions) {
+        instruction->gen_llvm(ctx, generated_function);
+    }
+    ctx.builder.CreateRetVoid();
+}
+
+void definition_data::typecheck_first(type_mgr& mgr, type_env& env) {
+    type_data* this_type = new type_data(name);
+    type_ptr return_type = type_ptr(this_type);
+    int next_tag = 0;
+
+    for(auto& constructor : constructors) {
+        constructor->tag = next_tag;
+        this_type->constructors[constructor->name] = { next_tag++ };
+
+        type_ptr full_type = return_type;
+        for(auto it = constructor->types.rbegin(); it != constructor->types.rend(); it++) {
+            type_ptr type = type_ptr(new type_base(*it));
+            full_type = type_ptr(new type_arr(type, full_type));
+        }
+
+        env.bind(constructor->name, full_type);
+    }
+}
+
+void definition_data::typecheck_second(type_mgr& mgr, const type_env& env) const {
+    // Nothing
+}
+
+void definition_data::resolve(const type_mgr& mgr) {
+    // Nothing
+}
+
+void definition_data::compile() {
+
+}
+
+void definition_data::gen_llvm_first(llvm_context& ctx) {
+    for(auto& constructor : constructors) {
+        auto new_function =
+            ctx.create_custom_function(constructor->name, constructor->types.size());
+        ctx.builder.SetInsertPoint(&new_function->getEntryBlock());
+        ctx.create_pack(new_function,
+                ctx.create_size(constructor->types.size()),
+                ctx.create_i8(constructor->tag)
+        );
+        ctx.builder.CreateRetVoid();
+    }
+}
+
+void definition_data::gen_llvm_second(llvm_context& ctx) {
+    // Nothing
+}

code/compiler/08/definition.hpp

@@ -0,0 +1,73 @@
+#pragma once
+#include <memory>
+#include <vector>
+#include "instruction.hpp"
+#include "llvm_context.hpp"
+#include "type_env.hpp"
+
+struct ast;
+using ast_ptr = std::unique_ptr<ast>;
+
+struct definition {
+    virtual ~definition() = default;
+    
+    virtual void typecheck_first(type_mgr& mgr, type_env& env) = 0;
+    virtual void typecheck_second(type_mgr& mgr, const type_env& env) const = 0;
+    virtual void resolve(const type_mgr& mgr) = 0;
+    virtual void compile() = 0;
+    virtual void gen_llvm_first(llvm_context& ctx) = 0;
+    virtual void gen_llvm_second(llvm_context& ctx) = 0;
+};
+
+using definition_ptr = std::unique_ptr<definition>;
+
+struct constructor {
+    std::string name;
+    std::vector<std::string> types;
+    int8_t tag;
+
+    constructor(std::string n, std::vector<std::string> ts)
+        : name(std::move(n)), types(std::move(ts)) {}
+};
+
+using constructor_ptr = std::unique_ptr<constructor>;
+
+struct definition_defn : public definition {
+    std::string name;
+    std::vector<std::string> params;
+    ast_ptr body;
+
+    type_ptr return_type;
+    std::vector<type_ptr> param_types;
+
+    std::vector<instruction_ptr> instructions;
+
+    llvm::Function* generated_function;
+
+    definition_defn(std::string n, std::vector<std::string> p, ast_ptr b)
+        : name(std::move(n)), params(std::move(p)), body(std::move(b)) {
+
+    }
+
+    void typecheck_first(type_mgr& mgr, type_env& env);
+    void typecheck_second(type_mgr& mgr, const type_env& env) const;
+    void resolve(const type_mgr& mgr);
+    void compile();
+    void gen_llvm_first(llvm_context& ctx);
+    void gen_llvm_second(llvm_context& ctx);
+};
+
+struct definition_data : public definition {
+    std::string name;
+    std::vector<constructor_ptr> constructors;
+
+    definition_data(std::string n, std::vector<constructor_ptr> cs)
+        : name(std::move(n)), constructors(std::move(cs)) {}
+
+    void typecheck_first(type_mgr& mgr, type_env& env);
+    void typecheck_second(type_mgr& mgr, const type_env& env) const;
+    void resolve(const type_mgr& mgr);
+    void compile();
+    void gen_llvm_first(llvm_context& ctx);
+    void gen_llvm_second(llvm_context& ctx);
+};

code/compiler/08/env.cpp

@@ -0,0 +1,23 @@
+#include "env.hpp"
+
+int env_var::get_offset(const std::string& name) const {
+    if(name == this->name) return 0;
+    if(parent) return parent->get_offset(name) + 1;
+    throw 0;
+}
+
+bool env_var::has_variable(const std::string& name) const {
+    if(name == this->name) return true;
+    if(parent) return parent->has_variable(name);
+    return false;
+}
+
+int env_offset::get_offset(const std::string& name) const {
+    if(parent) return parent->get_offset(name) + offset;
+    throw 0;
+}
+
+bool env_offset::has_variable(const std::string& name) const {
+    if(parent) return parent->has_variable(name);
+    return false;
+}

code/compiler/08/env.hpp

@@ -0,0 +1,34 @@
+#pragma once
+#include <memory>
+#include <string>
+
+struct env {
+    virtual ~env() = default;
+
+    virtual int get_offset(const std::string& name) const = 0;
+    virtual bool has_variable(const std::string& name) const = 0;
+};
+
+using env_ptr = std::shared_ptr<env>;
+
+struct env_var : public env {
+    std::string name;
+    env_ptr parent;
+
+    env_var(std::string& n, env_ptr p)
+        : name(std::move(n)), parent(std::move(p)) {}
+
+    int get_offset(const std::string& name) const;
+    bool has_variable(const std::string& name) const;
+};
+
+struct env_offset : public env {
+    int offset;
+    env_ptr parent;
+
+    env_offset(int o, env_ptr p)
+        : offset(o), parent(std::move(p)) {}
+
+    int get_offset(const std::string& name) const;
+    bool has_variable(const std::string& name) const;
+};

code/compiler/08/error.cpp

@@ -0,0 +1,5 @@
+#include "error.hpp"
+
+const char* type_error::what() const noexcept {
+    return "an error occured while checking the types of the program";
+}

code/compiler/08/error.hpp

@@ -0,0 +1,21 @@
+#pragma once
+#include <exception>
+#include "type.hpp"
+
+struct type_error : std::exception {
+    std::string description;
+
+    type_error(std::string d)
+        : description(std::move(d)) {}
+
+    const char* what() const noexcept override;
+};
+
+struct unification_error : public type_error {
+    type_ptr left;
+    type_ptr right;
+
+    unification_error(type_ptr l, type_ptr r)
+        : left(std::move(l)), right(std::move(r)), 
+            type_error("failed to unify types") {}
+};

code/compiler/08/examples/bad1.txt

@@ -0,0 +1,2 @@
+data Bool = { True, False }
+defn main = { 3 + True }

code/compiler/08/examples/bad2.txt

@@ -0,0 +1 @@
+defn main = { 1 2 3 4 5 }

code/compiler/08/examples/bad3.txt

@@ -0,0 +1,8 @@
+data List = { Nil, Cons Int List }
+
+defn head l = {
+    case l of {
+        Nil -> { 0 }
+        Cons x y z -> { x }
+    }
+}

code/compiler/08/examples/runtime1.c

@@ -0,0 +1,31 @@
+#include "../runtime.h"
+
+void f_add(struct stack* s) {
+    struct node_num* left = (struct node_num*) eval(stack_peek(s, 0));
+    struct node_num* right = (struct node_num*) eval(stack_peek(s, 1));
+    stack_push(s, (struct node_base*) alloc_num(left->value + right->value));
+}
+
+void f_main(struct stack* s) {
+    // PushInt 320
+    stack_push(s, (struct node_base*) alloc_num(320));
+
+    // PushInt 6
+    stack_push(s, (struct node_base*) alloc_num(6));
+
+    // PushGlobal f_add (the function for +)
+    stack_push(s, (struct node_base*) alloc_global(f_add, 2));
+
+    struct node_base* left;
+    struct node_base* right;
+    
+    // MkApp
+    left = stack_pop(s);
+    right = stack_pop(s);
+    stack_push(s, (struct node_base*) alloc_app(left, right));
+    
+    // MkApp
+    left = stack_pop(s);
+    right = stack_pop(s);
+    stack_push(s, (struct node_base*) alloc_app(left, right));
+}

code/compiler/08/examples/works1.txt

@@ -0,0 +1,3 @@
+defn main = { sum 320 6 }
+defn sum x y = { x + y }
+

code/compiler/08/examples/works2.txt

@@ -0,0 +1,3 @@
+defn add x y = { x + y }
+defn double x = { add x x }
+defn main = { double 163 }

code/compiler/08/examples/works3.txt

@@ -0,0 +1,8 @@
+data List = { Nil, Cons Int List }
+defn length l = {
+    case l of {
+        Nil -> { 0 }
+        Cons x xs -> { 1 + length xs }
+    }
+}
+defn main = { length (Cons 1 (Cons 2 (Cons 3 Nil))) }

code/compiler/08/examples/works4.txt

@@ -0,0 +1,16 @@
+data List = { Nil, Cons Int List }
+
+defn add x y = { x + y }
+defn mul x y = { x * y }
+
+defn foldr f b l = {
+    case l of {
+        Nil -> { b }
+        Cons x xs -> { f x (foldr f b xs) }
+    }
+}
+
+defn main = {
+    foldr add 0 (Cons 1 (Cons 2 (Cons 3 (Cons 4 Nil)))) +
+    foldr mul 1 (Cons 1 (Cons 2 (Cons 3 (Cons 4 Nil))))
+}

code/compiler/08/examples/works5.txt

@@ -0,0 +1,17 @@
+data List = { Nil, Cons Int List }
+
+defn sumZip l m = {
+    case l of {
+        Nil -> { 0 }
+        Cons x xs -> {
+            case m of {
+                Nil -> { 0 }
+                Cons y ys -> { x + y + sumZip xs ys }
+            }
+        }
+    }
+}
+
+defn ones = { Cons 1 ones }
+
+defn main = { sumZip ones (Cons 1 (Cons 2 (Cons 3 Nil))) }

code/compiler/08/instruction.cpp

@@ -0,0 +1,177 @@
+#include "instruction.hpp"
+#include "llvm_context.hpp"
+#include <llvm/IR/BasicBlock.h>
+#include <llvm/IR/Function.h>
+
+using namespace llvm;
+
+static void print_indent(int n, std::ostream& to) {
+    while(n--) to << "  ";
+}
+
+void instruction_pushint::print(int indent, std::ostream& to) const {
+    print_indent(indent, to);
+    to << "PushInt(" << value << ")" << std::endl;
+}
+
+void instruction_pushint::gen_llvm(llvm_context& ctx, Function* f) const {
+    ctx.create_push(f, ctx.create_num(ctx.create_i32(value)));
+}
+
+void instruction_pushglobal::print(int indent, std::ostream& to) const {
+    print_indent(indent, to);
+    to << "PushGlobal(" << name << ")" << std::endl;
+}
+
+void instruction_pushglobal::gen_llvm(llvm_context& ctx, Function* f) const {
+    auto& global_f = ctx.custom_functions.at("f_" + name);
+    auto arity = ctx.create_i32(global_f->arity);
+    ctx.create_push(f, ctx.create_global(global_f->function, arity));
+}
+
+void instruction_push::print(int indent, std::ostream& to) const {
+    print_indent(indent, to);
+    to << "Push(" << offset << ")" << std::endl;
+}
+
+void instruction_push::gen_llvm(llvm_context& ctx, Function* f) const {
+    ctx.create_push(f, ctx.create_peek(f, ctx.create_size(offset)));
+}
+
+void instruction_pop::print(int indent, std::ostream& to) const {
+    print_indent(indent, to);
+    to << "Pop(" << count << ")" << std::endl;
+}
+
+void instruction_pop::gen_llvm(llvm_context& ctx, Function* f) const {
+    ctx.create_popn(f, ctx.create_size(count));
+}
+
+void instruction_mkapp::print(int indent, std::ostream& to) const {
+    print_indent(indent, to);
+    to << "MkApp()" << std::endl;
+}
+
+void instruction_mkapp::gen_llvm(llvm_context& ctx, Function* f) const {
+    auto left = ctx.create_pop(f);
+    auto right = ctx.create_pop(f);
+    ctx.create_push(f, ctx.create_app(left, right));
+}
+
+void instruction_update::print(int indent, std::ostream& to) const {
+    print_indent(indent, to);
+    to << "Update(" << offset << ")" << std::endl;
+}
+
+void instruction_update::gen_llvm(llvm_context& ctx, Function* f) const {
+    ctx.create_update(f, ctx.create_size(offset));
+}
+
+void instruction_pack::print(int indent, std::ostream& to) const {
+    print_indent(indent, to);
+    to << "Pack(" << tag << ", " << size << ")" << std::endl;
+}
+
+void instruction_pack::gen_llvm(llvm_context& ctx, Function* f) const {
+    ctx.create_pack(f, ctx.create_size(size), ctx.create_i8(tag));
+}
+
+void instruction_split::print(int indent, std::ostream& to) const {
+    print_indent(indent, to);
+    to << "Split()" << std::endl;
+}
+
+void instruction_split::gen_llvm(llvm_context& ctx, Function* f) const {
+    ctx.create_split(f, ctx.create_size(size));
+}
+
+void instruction_jump::print(int indent, std::ostream& to) const {
+    print_indent(indent, to);
+    to << "Jump(" << std::endl;
+    for(auto& instruction_set : branches) {
+        for(auto& instruction : instruction_set) {
+            instruction->print(indent + 2, to);
+        }
+        to << std::endl;
+    }
+    print_indent(indent, to);
+    to << ")" << std::endl;
+}
+
+void instruction_jump::gen_llvm(llvm_context& ctx, Function* f) const {
+    auto top_node = ctx.create_peek(f, ctx.create_size(0));
+    auto tag = ctx.unwrap_data_tag(top_node);
+    auto safety_block = BasicBlock::Create(ctx.ctx, "safety", f);
+    auto switch_op = ctx.builder.CreateSwitch(tag, safety_block, tag_mappings.size());
+    std::vector<BasicBlock*> blocks;
+
+    for(auto& branch : branches) {
+        auto branch_block = BasicBlock::Create(ctx.ctx, "branch", f);
+        ctx.builder.SetInsertPoint(branch_block);
+        for(auto& instruction : branch) {
+            instruction->gen_llvm(ctx, f);
+        }
+        ctx.builder.CreateBr(safety_block);
+        blocks.push_back(branch_block);
+    }
+
+    for(auto& mapping : tag_mappings) {
+        switch_op->addCase(ctx.create_i8(mapping.first), blocks[mapping.second]);
+    }
+
+    ctx.builder.SetInsertPoint(safety_block);
+}
+
+void instruction_slide::print(int indent, std::ostream& to) const {
+    print_indent(indent, to);
+    to << "Slide(" << offset << ")" << std::endl;
+}
+
+void instruction_slide::gen_llvm(llvm_context& ctx, Function* f) const {
+    ctx.create_slide(f, ctx.create_size(offset));
+}
+
+void instruction_binop::print(int indent, std::ostream& to) const {
+    print_indent(indent, to);
+    to << "BinOp(" << op_action(op) << ")" << std::endl;
+}
+
+void instruction_binop::gen_llvm(llvm_context& ctx, Function* f) const {
+    auto left_int = ctx.unwrap_num(ctx.create_pop(f));
+    auto right_int = ctx.unwrap_num(ctx.create_pop(f));
+    llvm::Value* result;
+    switch(op) {
+        case PLUS: result = ctx.builder.CreateAdd(left_int, right_int); break;
+        case MINUS: result = ctx.builder.CreateSub(left_int, right_int); break;
+        case TIMES: result = ctx.builder.CreateMul(left_int, right_int); break;
+        case DIVIDE: result = ctx.builder.CreateSDiv(left_int, right_int); break;
+    }
+    ctx.create_push(f, ctx.create_num(result));
+}
+
+void instruction_eval::print(int indent, std::ostream& to) const {
+    print_indent(indent, to);
+    to << "Eval()" << std::endl;
+}
+
+void instruction_eval::gen_llvm(llvm_context& ctx, Function* f) const {
+    ctx.create_push(f, ctx.create_eval(ctx.create_pop(f)));
+}
+
+void instruction_alloc::print(int indent, std::ostream& to) const {
+    print_indent(indent, to);
+    to << "Alloc(" << amount << ")" << std::endl;
+}
+
+void instruction_alloc::gen_llvm(llvm_context& ctx, Function* f) const {
+    ctx.create_alloc(f, ctx.create_size(amount));
+}
+
+void instruction_unwind::print(int indent, std::ostream& to) const {
+    print_indent(indent, to);
+    to << "Unwind()" << std::endl;
+}
+
+void instruction_unwind::gen_llvm(llvm_context& ctx, Function* f) const {
+    // Nothing
+}

code/compiler/08/instruction.hpp

@@ -0,0 +1,142 @@
+#pragma once
+#include <llvm/IR/Function.h>
+#include <string>
+#include <memory>
+#include <vector>
+#include <map>
+#include <ostream>
+#include "binop.hpp"
+#include "llvm_context.hpp"
+
+struct instruction {
+    virtual ~instruction() = default;
+
+    virtual void print(int indent, std::ostream& to) const = 0;
+    virtual void gen_llvm(llvm_context& ctx, llvm::Function* f) const = 0;
+};
+
+using instruction_ptr = std::unique_ptr<instruction>;
+
+struct instruction_pushint : public instruction {
+    int value;
+
+    instruction_pushint(int v)
+        : value(v) {}
+
+    void print(int indent, std::ostream& to) const;
+    void gen_llvm(llvm_context& ctx, llvm::Function* f) const;
+};
+
+struct instruction_pushglobal : public instruction {
+    std::string name;
+
+    instruction_pushglobal(std::string n)
+        : name(std::move(n)) {}
+
+    void print(int indent, std::ostream& to) const;
+    void gen_llvm(llvm_context& ctx, llvm::Function* f) const;
+};
+
+struct instruction_push : public instruction {
+    int offset;
+
+    instruction_push(int o)
+        : offset(o) {}
+
+    void print(int indent, std::ostream& to) const;
+    void gen_llvm(llvm_context& ctx, llvm::Function* f) const;
+};
+
+struct instruction_pop : public instruction {
+    int count;
+
+    instruction_pop(int c)
+        : count(c) {}
+
+    void print(int indent, std::ostream& to) const;
+    void gen_llvm(llvm_context& ctx, llvm::Function* f) const;
+};
+
+struct instruction_mkapp : public instruction {
+    void print(int indent, std::ostream& to) const;
+    void gen_llvm(llvm_context& ctx, llvm::Function* f) const;
+};
+
+struct instruction_update : public instruction {
+    int offset;
+
+    instruction_update(int o)
+        : offset(o) {}
+
+    void print(int indent, std::ostream& to) const;
+    void gen_llvm(llvm_context& ctx, llvm::Function* f) const;
+};
+
+struct instruction_pack : public instruction {
+    int tag;
+    int size;
+
+    instruction_pack(int t, int s)
+        : tag(t), size(s) {}
+
+    void print(int indent, std::ostream& to) const;
+    void gen_llvm(llvm_context& ctx, llvm::Function* f) const;
+};
+
+struct instruction_split : public instruction {
+    int size;
+
+    instruction_split(int s)
+        : size(s) {}
+
+    void print(int indent, std::ostream& to) const;
+    void gen_llvm(llvm_context& ctx, llvm::Function* f) const;
+};
+
+struct instruction_jump : public instruction {
+    std::vector<std::vector<instruction_ptr>> branches;
+    std::map<int, int> tag_mappings;
+
+    void print(int indent, std::ostream& to) const;
+    void gen_llvm(llvm_context& ctx, llvm::Function* f) const;
+};
+
+struct instruction_slide : public instruction {
+    int offset;
+
+    instruction_slide(int o)
+        : offset(o) {}
+
+    void print(int indent, std::ostream& to) const;
+    void gen_llvm(llvm_context& ctx, llvm::Function* f) const;
+};
+
+struct instruction_binop : public instruction {
+    binop op;
+
+    instruction_binop(binop o)
+        : op(o) {}
+
+    void print(int indent, std::ostream& to) const;
+    void gen_llvm(llvm_context& ctx, llvm::Function* f) const;
+};
+
+struct instruction_eval : public instruction {
+    void print(int indent, std::ostream& to) const;
+    void gen_llvm(llvm_context& ctx, llvm::Function* f) const;
+};
+
+struct instruction_alloc : public instruction {
+    int amount;
+
+    instruction_alloc(int a)
+        : amount(a) {}
+
+    void print(int indent, std::ostream& to) const;
+    void gen_llvm(llvm_context& ctx, llvm::Function* f) const;
+};
+
+struct instruction_unwind : public instruction {
+    void print(int indent, std::ostream& to) const;
+    void gen_llvm(llvm_context& ctx, llvm::Function* f) const;
+};

code/compiler/08/llvm_context.cpp

@@ -0,0 +1,252 @@
+#include "llvm_context.hpp"
+#include <llvm/IR/DerivedTypes.h>
+
+using namespace llvm;
+
+void llvm_context::create_types() {
+    stack_type = StructType::create(ctx, "stack");
+    stack_ptr_type = PointerType::getUnqual(stack_type);
+    tag_type = IntegerType::getInt8Ty(ctx);
+    struct_types["node_base"] = StructType::create(ctx, "node_base");
+    struct_types["node_app"] = StructType::create(ctx, "node_app");
+    struct_types["node_num"] = StructType::create(ctx, "node_num");
+    struct_types["node_global"] = StructType::create(ctx, "node_global");
+    struct_types["node_ind"] = StructType::create(ctx, "node_ind");
+    struct_types["node_data"] = StructType::create(ctx, "node_data");
+    node_ptr_type = PointerType::getUnqual(struct_types.at("node_base"));
+    function_type = FunctionType::get(Type::getVoidTy(ctx), { stack_ptr_type }, false);
+
+    struct_types.at("node_base")->setBody(
+            IntegerType::getInt32Ty(ctx)
+    );
+    struct_types.at("node_app")->setBody(
+            struct_types.at("node_base"),
+            node_ptr_type,
+            node_ptr_type
+    );
+    struct_types.at("node_num")->setBody(
+            struct_types.at("node_base"),
+            IntegerType::getInt32Ty(ctx)
+    );
+    struct_types.at("node_global")->setBody(
+            struct_types.at("node_base"),
+            FunctionType::get(Type::getVoidTy(ctx), { stack_ptr_type }, false)
+    );
+    struct_types.at("node_ind")->setBody(
+            struct_types.at("node_base"),
+            node_ptr_type
+    );
+    struct_types.at("node_data")->setBody(
+            struct_types.at("node_base"),
+            IntegerType::getInt8Ty(ctx),
+            PointerType::getUnqual(node_ptr_type)
+    );
+}
+
+void llvm_context::create_functions() {
+    auto void_type = Type::getVoidTy(ctx);
+    auto sizet_type = IntegerType::get(ctx, sizeof(size_t) * 8);
+    functions["stack_init"] = Function::Create(
+            FunctionType::get(void_type, { stack_ptr_type }, false),
+            Function::LinkageTypes::ExternalLinkage,
+            "stack_init",
+            &module
+    );
+    functions["stack_free"] = Function::Create(
+            FunctionType::get(void_type, { stack_ptr_type }, false),
+            Function::LinkageTypes::ExternalLinkage,
+            "stack_free",
+            &module
+    );
+    functions["stack_push"] = Function::Create(
+            FunctionType::get(void_type, { stack_ptr_type, node_ptr_type }, false),
+            Function::LinkageTypes::ExternalLinkage,
+            "stack_push",
+            &module
+    );
+    functions["stack_pop"] = Function::Create(
+            FunctionType::get(node_ptr_type, { stack_ptr_type }, false),
+            Function::LinkageTypes::ExternalLinkage,
+            "stack_pop",
+            &module
+    );
+    functions["stack_peek"] = Function::Create(
+            FunctionType::get(node_ptr_type, { stack_ptr_type, sizet_type }, false),
+            Function::LinkageTypes::ExternalLinkage,
+            "stack_peek",
+            &module
+    );
+    functions["stack_popn"] = Function::Create(
+            FunctionType::get(void_type, { stack_ptr_type, sizet_type }, false),
+            Function::LinkageTypes::ExternalLinkage,
+            "stack_popn",
+            &module
+    );
+    functions["stack_slide"] = Function::Create(
+            FunctionType::get(void_type, { stack_ptr_type, sizet_type }, false),
+            Function::LinkageTypes::ExternalLinkage,
+            "stack_slide",
+            &module
+    );
+    functions["stack_update"] = Function::Create(
+            FunctionType::get(void_type, { stack_ptr_type, sizet_type }, false),
+            Function::LinkageTypes::ExternalLinkage,
+            "stack_update",
+            &module
+    );
+    functions["stack_alloc"] = Function::Create(
+            FunctionType::get(void_type, { stack_ptr_type, sizet_type }, false),
+            Function::LinkageTypes::ExternalLinkage,
+            "stack_alloc",
+            &module
+    );
+    functions["stack_pack"] = Function::Create(
+            FunctionType::get(void_type, { stack_ptr_type, sizet_type, tag_type }, false),
+            Function::LinkageTypes::ExternalLinkage,
+            "stack_pack",
+            &module
+    );
+    functions["stack_split"] = Function::Create(
+            FunctionType::get(node_ptr_type, { stack_ptr_type, sizet_type }, false),
+            Function::LinkageTypes::ExternalLinkage,
+            "stack_split",
+            &module
+    );
+
+    auto int32_type = IntegerType::getInt32Ty(ctx);
+    functions["alloc_app"] = Function::Create(
+            FunctionType::get(node_ptr_type, { node_ptr_type, node_ptr_type }, false),
+            Function::LinkageTypes::ExternalLinkage,
+            "alloc_app",
+            &module
+    );
+    functions["alloc_num"] = Function::Create(
+            FunctionType::get(node_ptr_type, { int32_type }, false),
+            Function::LinkageTypes::ExternalLinkage,
+            "alloc_num",
+            &module
+    );
+    functions["alloc_global"] = Function::Create(
+            FunctionType::get(node_ptr_type, { function_type, int32_type }, false),
+            Function::LinkageTypes::ExternalLinkage,
+            "alloc_global",
+            &module
+    );
+    functions["alloc_ind"] = Function::Create(
+            FunctionType::get(node_ptr_type, { node_ptr_type }, false),
+            Function::LinkageTypes::ExternalLinkage,
+            "alloc_ind",
+            &module
+    );
+
+    functions["eval"] = Function::Create(
+            FunctionType::get(node_ptr_type, { node_ptr_type }, false),
+            Function::LinkageTypes::ExternalLinkage,
+            "eval",
+            &module
+    );
+}
+
+ConstantInt* llvm_context::create_i8(int8_t i) {
+    return ConstantInt::get(ctx, APInt(8, i));
+}
+ConstantInt* llvm_context::create_i32(int32_t i) {
+    return ConstantInt::get(ctx, APInt(32, i));
+}
+ConstantInt* llvm_context::create_size(size_t i) {
+    return ConstantInt::get(ctx, APInt(sizeof(size_t) * 8, i));
+}
+
+Value* llvm_context::create_pop(Function* f) {
+    auto pop_f = functions.at("stack_pop");
+    return builder.CreateCall(pop_f, { f->arg_begin() });
+}
+Value* llvm_context::create_peek(Function* f, Value* off) {
+    auto peek_f = functions.at("stack_peek");
+    return builder.CreateCall(peek_f, { f->arg_begin(), off });
+}
+void llvm_context::create_push(Function* f, Value* v) {
+    auto push_f = functions.at("stack_push");
+    builder.CreateCall(push_f, { f->arg_begin(), v });
+}
+void llvm_context::create_popn(Function* f, Value* off) {
+    auto popn_f = functions.at("stack_popn");
+    builder.CreateCall(popn_f, { f->arg_begin(), off });
+}
+void llvm_context::create_update(Function* f, Value* off) {
+    auto update_f = functions.at("stack_update");
+    builder.CreateCall(update_f, { f->arg_begin(), off });
+}
+void llvm_context::create_pack(Function* f, Value* c, Value* t) {
+    auto pack_f = functions.at("stack_pack");
+    builder.CreateCall(pack_f, { f->arg_begin(), c, t });
+}
+void llvm_context::create_split(Function* f, Value* c) {
+    auto split_f = functions.at("stack_split");
+    builder.CreateCall(split_f, { f->arg_begin(), c });
+}
+void llvm_context::create_slide(Function* f, Value* off) {
+    auto slide_f = functions.at("stack_slide");
+    builder.CreateCall(slide_f, { f->arg_begin(), off });
+}
+void llvm_context::create_alloc(Function* f, Value* n) {
+    auto alloc_f = functions.at("stack_alloc");
+    builder.CreateCall(alloc_f, { f->arg_begin(), n });
+}
+
+Value* llvm_context::create_eval(Value* e) {
+    auto eval_f = functions.at("eval");
+    return builder.CreateCall(eval_f, { e });
+}
+
+Value* llvm_context::unwrap_num(Value* v) {
+    auto num_ptr_type = PointerType::getUnqual(struct_types.at("node_num"));
+    auto cast = builder.CreatePointerCast(v, num_ptr_type);
+    auto offset_0 = create_i32(0);
+    auto offset_1 = create_i32(1);
+    auto int_ptr = builder.CreateGEP(cast, { offset_0, offset_1 });
+    return builder.CreateLoad(int_ptr);
+}
+Value* llvm_context::create_num(Value* v) {
+    auto alloc_num_f = functions.at("alloc_num");
+    return builder.CreateCall(alloc_num_f, { v });
+}
+
+Value* llvm_context::unwrap_data_tag(Value* v) {
+    auto data_ptr_type = PointerType::getUnqual(struct_types.at("node_data"));
+    auto cast = builder.CreatePointerCast(v, data_ptr_type);
+    auto offset_0 = create_i32(0);
+    auto offset_1 = create_i32(1);
+    auto tag_ptr = builder.CreateGEP(cast, { offset_0, offset_1 });
+    return builder.CreateLoad(tag_ptr);
+}
+
+Value* llvm_context::create_global(Value* f, Value* a) {
+    auto alloc_global_f = functions.at("alloc_global");
+    return builder.CreateCall(alloc_global_f, { f, a });
+}
+
+Value* llvm_context::create_app(Value* l, Value* r) {
+    auto alloc_app_f = functions.at("alloc_app");
+    return builder.CreateCall(alloc_app_f, { l, r });
+}
+
+llvm::Function* llvm_context::create_custom_function(std::string name, int32_t arity) {
+    auto void_type = llvm::Type::getVoidTy(ctx);
+    auto function_type =
+        llvm::FunctionType::get(void_type, { stack_ptr_type }, false);
+    auto new_function = llvm::Function::Create(
+            function_type,
+            llvm::Function::LinkageTypes::ExternalLinkage,
+            "f_" + name,
+            &module
+    );
+    auto start_block = llvm::BasicBlock::Create(ctx, "entry", new_function);
+
+    auto new_custom_f = custom_function_ptr(new custom_function());
+    new_custom_f->arity = arity;
+    new_custom_f->function = new_function;
+    custom_functions["f_" + name] = std::move(new_custom_f);
+
+    return new_function;
+}

code/compiler/08/llvm_context.hpp

@@ -0,0 +1,66 @@
+#pragma once
+#include <llvm/IR/DerivedTypes.h>
+#include <llvm/IR/Function.h>
+#include <llvm/IR/LLVMContext.h>
+#include <llvm/IR/IRBuilder.h>
+#include <llvm/IR/Module.h>
+#include <map>
+
+struct llvm_context {
+    struct custom_function {
+        llvm::Function* function;
+        int32_t arity;
+    };
+
+    using custom_function_ptr = std::unique_ptr<custom_function>;
+
+    llvm::LLVMContext ctx;
+    llvm::IRBuilder<> builder;
+    llvm::Module module;
+
+    std::map<std::string, custom_function_ptr> custom_functions;
+    std::map<std::string, llvm::Function*> functions;
+    std::map<std::string, llvm::StructType*> struct_types;
+
+    llvm::StructType* stack_type;
+    llvm::PointerType* stack_ptr_type;
+    llvm::PointerType* node_ptr_type;
+    llvm::IntegerType* tag_type;
+    llvm::FunctionType* function_type;
+
+    llvm_context()
+        : builder(ctx), module("bloglang", ctx) {
+        create_types();
+        create_functions();
+    }
+
+    void create_types();
+    void create_functions();
+
+    llvm::ConstantInt* create_i8(int8_t);
+    llvm::ConstantInt* create_i32(int32_t);
+    llvm::ConstantInt* create_size(size_t);
+
+    llvm::Value* create_pop(llvm::Function*);
+    llvm::Value* create_peek(llvm::Function*, llvm::Value*);
+    void create_push(llvm::Function*, llvm::Value*);
+    void create_popn(llvm::Function*, llvm::Value*);
+    void create_update(llvm::Function*, llvm::Value*);
+    void create_pack(llvm::Function*, llvm::Value*, llvm::Value*);
+    void create_split(llvm::Function*, llvm::Value*);
+    void create_slide(llvm::Function*, llvm::Value*);
+    void create_alloc(llvm::Function*, llvm::Value*);
+
+    llvm::Value* create_eval(llvm::Value*);
+
+    llvm::Value* unwrap_num(llvm::Value*);
+    llvm::Value* create_num(llvm::Value*);
+
+    llvm::Value* unwrap_data_tag(llvm::Value*);
+
+    llvm::Value* create_global(llvm::Value*, llvm::Value*);
+
+    llvm::Value* create_app(llvm::Value*, llvm::Value*);
+
+    llvm::Function* create_custom_function(std::string name, int32_t arity);
+};

code/compiler/08/main.cpp

@@ -0,0 +1,174 @@
+#include "ast.hpp"
+#include <iostream>
+#include "binop.hpp"
+#include "definition.hpp"
+#include "instruction.hpp"
+#include "llvm_context.hpp"
+#include "parser.hpp"
+#include "error.hpp"
+#include "type.hpp"
+#include "llvm/IR/LegacyPassManager.h"
+#include "llvm/IR/Verifier.h"
+#include "llvm/Support/TargetSelect.h"
+#include "llvm/Support/TargetRegistry.h"
+#include "llvm/Support/raw_ostream.h"
+#include "llvm/Support/FileSystem.h"
+#include "llvm/Target/TargetOptions.h"
+#include "llvm/Target/TargetMachine.h"
+
+void yy::parser::error(const std::string& msg) {
+    std::cout << "An error occured: " << msg << std::endl;
+}
+
+extern std::vector<definition_ptr> program;
+
+void typecheck_program(
+        const std::vector<definition_ptr>& prog,
+        type_mgr& mgr, type_env& env) {
+    type_ptr int_type = type_ptr(new type_base("Int")); 
+    type_ptr binop_type = type_ptr(new type_arr(
+                int_type,
+                type_ptr(new type_arr(int_type, int_type))));
+
+    env.bind("+", binop_type);
+    env.bind("-", binop_type);
+    env.bind("*", binop_type);
+    env.bind("/", binop_type);
+
+    for(auto& def : prog) {
+        def->typecheck_first(mgr, env);
+    }
+
+    for(auto& def : prog) {
+        def->typecheck_second(mgr, env);
+    }
+
+    for(auto& pair : env.names) {
+        std::cout << pair.first << ": ";
+        pair.second->print(mgr, std::cout);
+        std::cout << std::endl;
+    }
+
+    for(auto& def : prog) {
+        def->resolve(mgr);
+    }
+}
+
+void compile_program(const std::vector<definition_ptr>& prog) {
+    for(auto& def : prog) {
+        def->compile();
+
+        definition_defn* defn = dynamic_cast<definition_defn*>(def.get());
+        if(!defn) continue;
+        for(auto& instruction : defn->instructions) {
+            instruction->print(0, std::cout);
+        }
+        std::cout << std::endl;
+    }
+}
+
+void gen_llvm_internal_op(llvm_context& ctx, binop op) {
+    auto new_function = ctx.create_custom_function(op_action(op), 2);
+    std::vector<instruction_ptr> instructions;
+    instructions.push_back(instruction_ptr(new instruction_push(1)));
+    instructions.push_back(instruction_ptr(new instruction_eval()));
+    instructions.push_back(instruction_ptr(new instruction_push(1)));
+    instructions.push_back(instruction_ptr(new instruction_eval()));
+    instructions.push_back(instruction_ptr(new instruction_binop(op)));
+    ctx.builder.SetInsertPoint(&new_function->getEntryBlock());
+    for(auto& instruction : instructions) {
+        instruction->gen_llvm(ctx, new_function);
+    }
+    ctx.builder.CreateRetVoid();
+}
+
+void output_llvm(llvm_context& ctx, const std::string& filename) {
+    std::string targetTriple = llvm::sys::getDefaultTargetTriple();
+
+    llvm::InitializeNativeTarget();
+    llvm::InitializeNativeTargetAsmParser();
+    llvm::InitializeNativeTargetAsmPrinter();
+
+    std::string error;
+    const llvm::Target* target =
+        llvm::TargetRegistry::lookupTarget(targetTriple, error);
+    if (!target) {
+        std::cerr << error << std::endl;
+    } else {
+        std::string cpu = "generic";
+        std::string features = "";
+        llvm::TargetOptions options;
+        llvm::TargetMachine* targetMachine =
+            target->createTargetMachine(targetTriple, cpu, features,
+                    options, llvm::Optional<llvm::Reloc::Model>());
+
+        ctx.module.setDataLayout(targetMachine->createDataLayout());
+        ctx.module.setTargetTriple(targetTriple);
+
+        std::error_code ec;
+        llvm::raw_fd_ostream file(filename, ec, llvm::sys::fs::F_None);
+        if (ec) {
+            throw 0;
+        } else {
+            llvm::TargetMachine::CodeGenFileType type = llvm::TargetMachine::CGFT_ObjectFile;
+            llvm::legacy::PassManager pm;
+            if (targetMachine->addPassesToEmitFile(pm, file, NULL, type)) {
+                throw 0;
+            } else {
+                pm.run(ctx.module);
+                file.close();
+            }
+        }
+    }
+}
+
+void gen_llvm(const std::vector<definition_ptr>& prog) {
+    llvm_context ctx;
+    gen_llvm_internal_op(ctx, PLUS);
+    gen_llvm_internal_op(ctx, MINUS);
+    gen_llvm_internal_op(ctx, TIMES);
+    gen_llvm_internal_op(ctx, DIVIDE);
+
+    for(auto& definition : prog) {
+        definition->gen_llvm_first(ctx);
+    }
+
+    for(auto& definition : prog) {
+        definition->gen_llvm_second(ctx);
+    }
+    ctx.module.print(llvm::outs(), nullptr);
+    output_llvm(ctx, "program.o");
+}
+
+int main() {
+    yy::parser parser;
+    type_mgr mgr;
+    type_env env;
+
+    parser.parse();
+    for(auto& definition : program) {
+        definition_defn* def = dynamic_cast<definition_defn*>(definition.get());
+        if(!def) continue;
+
+        std::cout << def->name;
+        for(auto& param : def->params) std::cout << " " << param;
+        std::cout << ":" << std::endl;
+
+        def->body->print(1, std::cout);
+    }
+    try {
+        typecheck_program(program, mgr, env);
+        compile_program(program);
+        gen_llvm(program);
+    } catch(unification_error& err) {
+        std::cout << "failed to unify types: " << std::endl;
+        std::cout << "  (1) \033[34m";
+        err.left->print(mgr, std::cout);
+        std::cout << "\033[0m" << std::endl;
+        std::cout << "  (2) \033[32m";
+        err.right->print(mgr, std::cout);
+        std::cout << "\033[0m" << std::endl;
+    } catch(type_error& err) {
+        std::cout << "failed to type check program: " << err.description << std::endl;
+    }
+}

code/compiler/08/parser.y

@@ -0,0 +1,141 @@
+%{
+#include <string>
+#include <iostream>
+#include "ast.hpp"
+#include "definition.hpp"
+#include "parser.hpp"
+
+std::vector<definition_ptr> program;
+extern yy::parser::symbol_type yylex();
+
+%}
+
+%token PLUS
+%token TIMES
+%token MINUS
+%token DIVIDE
+%token <int> INT
+%token DEFN
+%token DATA
+%token CASE
+%token OF
+%token OCURLY
+%token CCURLY
+%token OPAREN
+%token CPAREN
+%token COMMA
+%token ARROW
+%token EQUAL
+%token <std::string> LID
+%token <std::string> UID
+
+%language "c++"
+%define api.value.type variant
+%define api.token.constructor
+
+%type <std::vector<std::string>> lowercaseParams uppercaseParams
+%type <std::vector<definition_ptr>> program definitions
+%type <std::vector<branch_ptr>> branches
+%type <std::vector<constructor_ptr>> constructors
+%type <ast_ptr> aAdd aMul case app appBase
+%type <definition_ptr> definition defn data 
+%type <branch_ptr> branch
+%type <pattern_ptr> pattern
+%type <constructor_ptr> constructor
+
+%start program
+
+%%
+
+program
+    : definitions { program = std::move($1); }
+    ;
+
+definitions
+    : definitions definition { $$ = std::move($1); $$.push_back(std::move($2)); }
+    | definition { $$ = std::vector<definition_ptr>(); $$.push_back(std::move($1)); }
+    ;
+
+definition
+    : defn { $$ = std::move($1); }
+    | data { $$ = std::move($1); }
+    ;
+
+defn
+    : DEFN LID lowercaseParams EQUAL OCURLY aAdd CCURLY
+        { $$ = definition_ptr(
+            new definition_defn(std::move($2), std::move($3), std::move($6))); }
+    ;
+
+lowercaseParams
+    : %empty { $$ = std::vector<std::string>(); }
+    | lowercaseParams LID { $$ = std::move($1); $$.push_back(std::move($2)); }
+    ;
+
+uppercaseParams
+    : %empty { $$ = std::vector<std::string>(); }
+    | uppercaseParams UID { $$ = std::move($1); $$.push_back(std::move($2)); }
+    ;
+
+aAdd
+    : aAdd PLUS aMul { $$ = ast_ptr(new ast_binop(PLUS, std::move($1), std::move($3))); }
+    | aAdd MINUS aMul { $$ = ast_ptr(new ast_binop(MINUS, std::move($1), std::move($3))); }
+    | aMul { $$ = std::move($1); }
+    ;
+
+aMul
+    : aMul TIMES app { $$ = ast_ptr(new ast_binop(TIMES, std::move($1), std::move($3))); }
+    | aMul DIVIDE app { $$ = ast_ptr(new ast_binop(DIVIDE, std::move($1), std::move($3))); }
+    | app { $$ = std::move($1); }
+    ;
+
+app
+    : app appBase { $$ = ast_ptr(new ast_app(std::move($1), std::move($2))); }
+    | appBase { $$ = std::move($1); }
+    ;
+
+appBase
+    : INT { $$ = ast_ptr(new ast_int($1)); }
+    | LID { $$ = ast_ptr(new ast_lid(std::move($1))); }
+    | UID { $$ = ast_ptr(new ast_uid(std::move($1))); }
+    | OPAREN aAdd CPAREN { $$ = std::move($2); }
+    | case { $$ = std::move($1); }
+    ;
+
+case
+    : CASE aAdd OF OCURLY branches CCURLY 
+        { $$ = ast_ptr(new ast_case(std::move($2), std::move($5))); }
+    ;
+
+branches
+    : branches branch { $$ = std::move($1); $$.push_back(std::move($2)); }
+    | branch { $$ = std::vector<branch_ptr>(); $$.push_back(std::move($1));}
+    ;
+
+branch
+    : pattern ARROW OCURLY aAdd CCURLY
+        { $$ = branch_ptr(new branch(std::move($1), std::move($4))); }
+    ;
+
+pattern
+    : LID { $$ = pattern_ptr(new pattern_var(std::move($1))); }
+    | UID lowercaseParams
+        { $$ = pattern_ptr(new pattern_constr(std::move($1), std::move($2))); }
+    ;
+
+data
+    : DATA UID EQUAL OCURLY constructors CCURLY
+        { $$ = definition_ptr(new definition_data(std::move($2), std::move($5))); }
+    ;
+
+constructors
+    : constructors COMMA constructor { $$ = std::move($1); $$.push_back(std::move($3)); }
+    | constructor
+        { $$ = std::vector<constructor_ptr>(); $$.push_back(std::move($1)); }
+    ;
+
+constructor
+    : UID uppercaseParams
+        { $$ = constructor_ptr(new constructor(std::move($1), std::move($2))); }
+    ;
+

code/compiler/08/runtime.c

@@ -0,0 +1,183 @@
+#include <stdint.h>
+#include <assert.h>
+#include <memory.h>
+#include <stdio.h>
+#include "runtime.h"
+
+struct node_base* alloc_node() {
+    struct node_base* new_node = malloc(sizeof(struct node_app));
+    assert(new_node != NULL);
+    return new_node;
+}
+
+struct node_app* alloc_app(struct node_base* l, struct node_base* r) {
+    struct node_app* node = (struct node_app*) alloc_node();
+    node->base.tag = NODE_APP;
+    node->left = l;
+    node->right = r;
+    return node;
+}
+
+struct node_num* alloc_num(int32_t n) {
+    struct node_num* node = (struct node_num*) alloc_node();
+    node->base.tag = NODE_NUM;
+    node->value = n;
+    return node;
+}
+
+struct node_global* alloc_global(void (*f)(struct stack*), int32_t a) {
+    struct node_global* node = (struct node_global*) alloc_node();
+    node->base.tag = NODE_GLOBAL;
+    node->arity = a;
+    node->function = f;
+    return node;
+}
+
+struct node_ind* alloc_ind(struct node_base* n) {
+    struct node_ind* node = (struct node_ind*) alloc_node();
+    node->base.tag = NODE_IND;
+    node->next = n;
+    return node;
+}
+
+void stack_init(struct stack* s) {
+    s->size = 4;
+    s->count = 0;
+    s->data = malloc(sizeof(*s->data) * s->size);
+    assert(s->data != NULL);
+}
+
+void stack_free(struct stack* s) {
+    free(s->data);
+}
+
+void stack_push(struct stack* s, struct node_base* n) {
+    while(s->count >= s->size) {
+        s->data = realloc(s->data, sizeof(*s->data) * (s->size *= 2));
+        assert(s->data != NULL);
+    }
+    s->data[s->count++] = n;
+}
+
+struct node_base* stack_pop(struct stack* s) {
+    assert(s->count > 0);
+    return s->data[--s->count];
+}
+
+struct node_base* stack_peek(struct stack* s, size_t o) {
+    assert(s->count > o);
+    return s->data[s->count - o - 1];
+}
+
+void stack_popn(struct stack* s, size_t n) {
+    assert(s->count >= n);
+    s->count -= n;
+}
+
+void stack_slide(struct stack* s, size_t n) {
+    assert(s->count > n);
+    s->data[s->count - n - 1] = s->data[s->count - 1];
+    s->count -= n;
+}
+
+void stack_update(struct stack* s, size_t o) {
+    assert(s->count > o + 1);
+    struct node_ind* ind = (struct node_ind*) s->data[s->count - o - 2];
+    ind->base.tag = NODE_IND;
+    ind->next = s->data[s->count -= 1];
+}
+
+void stack_alloc(struct stack* s, size_t o) {
+    while(o--) {
+        stack_push(s, (struct node_base*) alloc_ind(NULL));
+    }
+}
+
+void stack_pack(struct stack* s, size_t n, int8_t t) {
+    assert(s->count >= n);
+
+    struct node_base** data = malloc(sizeof(*data) * n);
+    assert(data != NULL);
+    memcpy(data, &s->data[s->count - n], n * sizeof(*data));
+
+    struct node_data* new_node = (struct node_data*) alloc_node();
+    new_node->array = data;
+    new_node->base.tag = NODE_DATA;
+    new_node->tag = t;
+
+    stack_popn(s, n);
+    stack_push(s, (struct node_base*) new_node);
+}
+
+void stack_split(struct stack* s, size_t n) {
+    struct node_data* node = (struct node_data*) stack_pop(s);
+    for(size_t i = 0; i < n; i++) {
+        stack_push(s, node->array[i]);
+    }
+}
+
+void unwind(struct stack* s) {
+    while(1) {
+        struct node_base* peek = stack_peek(s, 0);
+        if(peek->tag == NODE_APP) {
+            struct node_app* n = (struct node_app*) peek;
+            stack_push(s, n->left);
+        } else if(peek->tag == NODE_GLOBAL) {
+            struct node_global* n = (struct node_global*) peek;
+            assert(s->count > n->arity);
+
+            for(size_t i = 1; i <= n->arity; i++) {
+                s->data[s->count - i]
+                    = ((struct node_app*) s->data[s->count - i - 1])->right;
+            }
+
+            n->function(s);
+        } else if(peek->tag == NODE_IND) {
+            struct node_ind* n = (struct node_ind*) peek;
+            stack_pop(s);
+            stack_push(s, n->next);
+        } else {
+            break;
+        }
+    }
+}
+
+struct node_base* eval(struct node_base* n) {
+    struct stack program_stack;
+    stack_init(&program_stack);
+    stack_push(&program_stack, n);
+    unwind(&program_stack);
+    struct node_base* result = stack_pop(&program_stack);
+    stack_free(&program_stack);
+    return result;
+}
+
+extern void f_main(struct stack* s);
+
+void print_node(struct node_base* n) {
+    if(n->tag == NODE_APP) {
+        struct node_app* app = (struct node_app*) n;
+        print_node(app->left);
+        putchar(' ');
+        print_node(app->right);
+    } else if(n->tag == NODE_DATA) {
+        printf("(Packed)");
+    } else if(n->tag == NODE_GLOBAL) {
+        struct node_global* global = (struct node_global*) n;
+        printf("(Global: %p)", global->function);
+    } else if(n->tag == NODE_IND) {
+        print_node(((struct node_ind*) n)->next);
+    } else if(n->tag == NODE_NUM) {
+        struct node_num* num = (struct node_num*) n;
+        printf("%d", num->value);
+    }
+}
+
+int main(int argc, char** argv) {
+    struct node_global* first_node = alloc_global(f_main, 0);
+    struct node_base* result = eval((struct node_base*) first_node);
+
+    printf("Result: ");
+    print_node(result);
+    putchar('\n');
+}

code/compiler/08/runtime.h

@@ -0,0 +1,70 @@
+#pragma once
+#include <stdlib.h>
+
+struct stack;
+
+enum node_tag {
+    NODE_APP,
+    NODE_NUM,
+    NODE_GLOBAL,
+    NODE_IND,
+    NODE_DATA
+};
+
+struct node_base {
+    enum node_tag tag;
+};
+
+struct node_app {
+    struct node_base base;
+    struct node_base* left;
+    struct node_base* right;
+};
+
+struct node_num {
+    struct node_base base;
+    int32_t value;
+};
+
+struct node_global {
+    struct node_base base;
+    int32_t arity;
+    void (*function)(struct stack*);
+};
+
+struct node_ind {
+    struct node_base base;
+    struct node_base* next;
+};
+
+struct node_data {
+    struct node_base base;
+    int8_t tag;
+    struct node_base** array;
+};
+
+struct node_base* alloc_node();
+struct node_app* alloc_app(struct node_base* l, struct node_base* r);
+struct node_num* alloc_num(int32_t n);
+struct node_global* alloc_global(void (*f)(struct stack*), int32_t a);
+struct node_ind* alloc_ind(struct node_base* n);
+
+struct stack {
+    size_t size;
+    size_t count;
+    struct node_base** data;
+};
+
+void stack_init(struct stack* s);
+void stack_free(struct stack* s);
+void stack_push(struct stack* s, struct node_base* n);
+struct node_base* stack_pop(struct stack* s);
+struct node_base* stack_peek(struct stack* s, size_t o);
+void stack_popn(struct stack* s, size_t n);
+void stack_slide(struct stack* s, size_t n);
+void stack_update(struct stack* s, size_t o);
+void stack_alloc(struct stack* s, size_t o);
+void stack_pack(struct stack* s, size_t n, int8_t t);
+void stack_split(struct stack* s, size_t n);
+
+struct node_base* eval(struct node_base* n);

code/compiler/08/scanner.l

@@ -0,0 +1,35 @@
+%option noyywrap
+
+%{
+#include <iostream>
+#include "ast.hpp"
+#include "definition.hpp"
+#include "parser.hpp"
+
+#define YY_DECL yy::parser::symbol_type yylex()
+
+%}
+
+%%
+
+[ \n]+ {}
+\+ { return yy::parser::make_PLUS(); }
+\* { return yy::parser::make_TIMES(); }
+- { return yy::parser::make_MINUS(); }
+\/ { return yy::parser::make_DIVIDE(); }
+[0-9]+ { return yy::parser::make_INT(atoi(yytext)); }
+defn { return yy::parser::make_DEFN(); }
+data { return yy::parser::make_DATA(); }
+case { return yy::parser::make_CASE(); }
+of { return yy::parser::make_OF(); }
+\{ { return yy::parser::make_OCURLY(); }
+\} { return yy::parser::make_CCURLY(); }
+\( { return yy::parser::make_OPAREN(); }
+\) { return yy::parser::make_CPAREN(); }
+,  { return yy::parser::make_COMMA(); }
+-> { return yy::parser::make_ARROW(); }
+= { return yy::parser::make_EQUAL(); }
+[a-z][a-zA-Z]* { return yy::parser::make_LID(std::string(yytext)); }
+[A-Z][a-zA-Z]* { return yy::parser::make_UID(std::string(yytext)); }
+
+%%

code/compiler/08/type.cpp

@@ -0,0 +1,99 @@
+#include "type.hpp"
+#include <sstream>
+#include <algorithm>
+#include "error.hpp"
+
+void type_var::print(const type_mgr& mgr, std::ostream& to) const {
+    auto it = mgr.types.find(name);
+    if(it != mgr.types.end()) {
+        it->second->print(mgr, to);
+    } else {
+        to << name;
+    }
+}
+
+void type_base::print(const type_mgr& mgr, std::ostream& to) const {
+    to << name;
+}
+
+void type_arr::print(const type_mgr& mgr, std::ostream& to) const {
+    left->print(mgr, to);
+    to << " -> (";
+    right->print(mgr, to);
+    to << ")";
+}
+
+std::string type_mgr::new_type_name() {
+    int temp = last_id++;
+    std::string str = "";
+
+    while(temp != -1) {
+        str += (char) ('a' + (temp % 26));
+        temp = temp / 26 - 1;
+    }
+
+    std::reverse(str.begin(), str.end());
+    return str;
+}
+
+type_ptr type_mgr::new_type() {
+    return type_ptr(new type_var(new_type_name()));
+}
+
+type_ptr type_mgr::new_arrow_type() {
+    return type_ptr(new type_arr(new_type(), new_type()));
+}
+
+type_ptr type_mgr::resolve(type_ptr t, type_var*& var) const {
+    type_var* cast;
+
+    var = nullptr;
+    while((cast = dynamic_cast<type_var*>(t.get()))) {
+        auto it = types.find(cast->name);
+
+        if(it == types.end()) {
+            var = cast;
+            break;
+        }
+        t = it->second;
+    }
+
+    return t;
+}
+
+void type_mgr::unify(type_ptr l, type_ptr r) {
+    type_var* lvar;
+    type_var* rvar;
+    type_arr* larr;
+    type_arr* rarr;
+    type_base* lid;
+    type_base* rid;
+
+    l = resolve(l, lvar);
+    r = resolve(r, rvar);
+
+    if(lvar) {
+        bind(lvar->name, r);
+        return;
+    } else if(rvar) {
+        bind(rvar->name, l);
+        return;
+    } else if((larr = dynamic_cast<type_arr*>(l.get())) &&
+            (rarr = dynamic_cast<type_arr*>(r.get()))) {
+        unify(larr->left, rarr->left);
+        unify(larr->right, rarr->right);
+        return;
+    } else if((lid = dynamic_cast<type_base*>(l.get())) &&
+            (rid = dynamic_cast<type_base*>(r.get()))) {
+        if(lid->name == rid->name) return;
+    }
+
+    throw unification_error(l, r);
+}
+
+void type_mgr::bind(const std::string& s, type_ptr t) {
+    type_var* other = dynamic_cast<type_var*>(t.get());
+    
+    if(other && other->name == s) return;
+    types[s] = t;
+}

code/compiler/08/type.hpp

@@ -0,0 +1,65 @@
+#pragma once
+#include <memory>
+#include <map>
+
+struct type_mgr;
+
+struct type {
+    virtual ~type() = default;
+
+    virtual void print(const type_mgr& mgr, std::ostream& to) const = 0;
+};
+
+using type_ptr = std::shared_ptr<type>;
+
+struct type_var : public type {
+    std::string name;
+
+    type_var(std::string n)
+        : name(std::move(n)) {}
+
+    void print(const type_mgr& mgr, std::ostream& to) const;
+};
+
+struct type_base : public type {
+    std::string name;
+
+    type_base(std::string n) 
+        : name(std::move(n)) {}
+
+    void print(const type_mgr& mgr, std::ostream& to) const;
+};
+
+struct type_data : public type_base {
+    struct constructor {
+        int tag;
+    };
+
+    std::map<std::string, constructor> constructors;
+
+    type_data(std::string n)
+        : type_base(std::move(n)) {}
+};
+
+struct type_arr : public type {
+    type_ptr left;
+    type_ptr right;
+
+    type_arr(type_ptr l, type_ptr r)
+        : left(std::move(l)), right(std::move(r)) {}
+
+    void print(const type_mgr& mgr, std::ostream& to) const;
+};
+
+struct type_mgr {
+    int last_id = 0;
+    std::map<std::string, type_ptr> types;
+
+    std::string new_type_name();
+    type_ptr new_type();
+    type_ptr new_arrow_type();
+
+    void unify(type_ptr l, type_ptr r);
+    type_ptr resolve(type_ptr t, type_var*& var) const;
+    void bind(const std::string& s, type_ptr t);
+};

code/compiler/08/type_env.cpp

@@ -0,0 +1,16 @@
+#include "type_env.hpp"
+
+type_ptr type_env::lookup(const std::string& name) const {
+    auto it = names.find(name);
+    if(it != names.end()) return it->second;
+    if(parent) return parent->lookup(name);
+    return nullptr;
+}
+
+void type_env::bind(const std::string& name, type_ptr t) {
+    names[name] = t;
+}
+
+type_env type_env::scope() const {
+    return type_env(this);
+}

code/compiler/08/type_env.hpp

@@ -0,0 +1,16 @@
+#pragma once
+#include <map>
+#include "type.hpp"
+
+struct type_env {
+    std::map<std::string, type_ptr> names;
+    type_env const* parent = nullptr;
+
+    type_env(type_env const* p)
+        : parent(p) {}
+    type_env() : type_env(nullptr) {}
+
+    type_ptr lookup(const std::string& name) const;
+    void bind(const std::string& name, type_ptr t);
+    type_env scope() const;
+};

content/blog/00_compiler_intro.md

@@ -2,12 +2,11 @@
 title: Compiling a Functional Language Using C++, Part 0 - Intro
 date: 2019-08-03T01:02:30-07:00
 tags: ["C and C++", "Functional Languages", "Compilers"]
-draft: true
 ---
 During my last academic term, I was enrolled in a compilers course.
 We had a final project - develop a compiler for a basic Python subset,
 using LLVM. It was a little boring - virtually nothing about the compiler
-was __not__ covered in class, and it felt more like putting two puzzles
+was __not__ covered in class, and it felt more like putting two puzzle
 pieces together than building a real project.
 
 Instead, I chose to implement a compiler for a functional programming language,
@@ -54,7 +53,7 @@ an alternative way of representing the program that isn't machine code.
 In some compilers, the stages of parsing and analysis can overlap.
 In short, just like the pirate's code, it's more of a guideline than a rule.
 
-#### What we'll cover
+#### What we will cover
 We'll go through the stages of a compiler, starting from scratch
 and building up our project. We'll cover:
 
@@ -128,7 +127,7 @@ constructed from an integer and another list (as defined in our `data` example),
 return the integer".
 
 That's it for the introduction! In the next post, we'll cover tokenizng, which is
-the first step in coverting source code into an executable program.
+the first step in converting source code into an executable program.
 
 ### Navigation
 Here are the posts that I've written so far for this series:
@@ -136,3 +135,8 @@ Here are the posts that I've written so far for this series:
 * [Tokenizing]({{< relref "01_compiler_tokenizing.md" >}})
 * [Parsing]({{< relref "02_compiler_parsing.md" >}})
 * [Typechecking]({{< relref "03_compiler_typechecking.md" >}})
+* [Small Improvements]({{< relref "04_compiler_improvements.md" >}})
+* [Execution]({{< relref "05_compiler_execution.md" >}})
+* [Compilation]({{< relref "06_compiler_compilation.md" >}})
+* [Runtime]({{< relref "07_compiler_runtime.md" >}})
+* [LLVM]({{< relref "08_compiler_llvm.md" >}})

content/blog/01_compiler_tokenizing.md

@@ -2,7 +2,6 @@
 title: Compiling a Functional Language Using C++, Part 1 - Tokenizing
 date: 2019-08-03T01:02:30-07:00
 tags: ["C and C++", "Functional Languages", "Compilers"]
-draft: true
 ---
 It makes sense to build a compiler bit by bit, following the stages we outlined in
 the first post of the series. This is because these stages are essentially a pipeline,
@@ -48,7 +47,7 @@ are fairly simple - one or more digits is an integer, a few letters together
 are a variable name. In order to be able to efficiently break text up into
 such tokens, we restrict ourselves to __regular languages__. A language
 is defined as a set of strings (potentially infinite), and a regular
-language for which we can write a __regular expression__ to check if
+language is one for which we can write a __regular expression__ to check if
 a string is in the set. Regular expressions are a way of representing
 patterns that a string has to match. We define regular expressions
 as follows:
@@ -77,7 +76,7 @@ Let's see some examples. An integer, such as 326, can be represented with \\([0-
 This means, one or more characters between 0 or 9. Some (most) regex implementations
 have a special symbol for \\([0-9]\\), written as \\(\\setminus d\\). A variable,
 starting with a lowercase letter and containing lowercase or uppercase letters after it,
-can be written as \\(\[a-z\]([a-z]+)?\\). Again, most regex implementations provide
+can be written as \\(\[a-z\]([a-zA-Z]+)?\\). Again, most regex implementations provide
 a special operator for \\((r_1+)?\\), written as \\(r_1*\\).
 
 So how does one go about checking if a regular expression matches a string? An efficient way is to
@@ -115,8 +114,8 @@ represent numbers directly into numbers, and do other small tasks.
 
 So, what tokens do we have? From our arithmetic definition, we see that we have integers.
 Let's use the regex `[0-9]+` for those. We also have the operators `+`, `-`, `*`, and `/`.
-`-` is simple enough: the corresponding regex is `-`. We need to
+The regex for `-` is simple enough: it's just `-`. However, we need to
-preface our `/`, `+` and `*` with a backslash, though, since they happen to also be modifiers
+preface our `/`, `+` and `*` with a backslash, since they happen to also be modifiers
 in flex's regular expressions: `\/`, `\+`, `\*`.
 
 Let's also represent some reserved keywords. We'll say that `defn`, `data`, `case`, and `of`
@@ -142,7 +141,7 @@ C++ code that should be executed when the regular expression is matched.
 The first token: whitespace. This includes the space character,
 and the newline character. We ignore it, so its rule is empty. After that,
 we have the regular expressions for the tokens we've talked about. For each, I just
-print a description of the token that matched. This will change we we hook this up to
+print a description of the token that matched. This will change when we hook this up to
 a parser, but for now, this works fine. Notice that the variable `yytext` contains
 the string matched by our regular expression. This variable is set by the code flex
 generates, and we can use it to get the extract text that matched a regex. This is
@@ -170,3 +169,6 @@ TIMES
 NUMBER: 6
 ```
 Hooray! We have tokenizing.
+
+With our text neatly divided into meaningful chunks, we
+can continue on to [Part 2 - Parsing]({{< relref "02_compiler_parsing.md" >}}).

content/blog/02_compiler_parsing.md

@@ -2,7 +2,6 @@
 title: Compiling a Functional Language Using C++, Part 2 - Parsing
 date: 2019-08-03T01:02:30-07:00
 tags: ["C and C++", "Functional Languages", "Compilers"]
-draft: true
 ---
 In the previous post, we covered tokenizing. We learned how to convert an input string into logical segments, and even wrote up a tokenizer to do it according to the rules of our language. Now, it's time to make sense of the tokens, and parse our language.
 
@@ -38,7 +37,7 @@ $$
 In practice, there are many ways of using a CFG to parse a programming language. Various parsing algorithms support various subsets
 of context free languages. For instance, top down parsers follow nearly exactly the structure that we had. They try to parse
 a nonterminal by trying to match each symbol in its body. In the rule \\(S \\rightarrow \\alpha \\beta \\gamma\\), it will
-first try to match \\(alpha\\), then \\(beta\\), and so on. If one of the three contains a nonterminal, it will attempt to parse
+first try to match \\(\\alpha\\), then \\(\\beta\\), and so on. If one of the three contains a nonterminal, it will attempt to parse
 that nonterminal following the same strategy. However, this leaves a flaw - For instance, consider the grammar
 $$
 \\begin{align}
@@ -105,7 +104,7 @@ A\_{add} & \\rightarrow A\_{add}-A\_{mult} \\\\\\
 A\_{add} & \\rightarrow A\_{mult}
 \\end{align}
 $$
-The first rule matches another addition, added to the result of another addition. We use the addition in the body
+The first rule matches another addition, added to the result of a multiplication. Similarly, the second rule matches another addition, from which the result of a multiplication is then subtracted. We use the \\(A\_{add}\\) on the left side of \\(+\\) and \\(-\\) in the body
 because we want to be able to parse strings like `1+2+3+4`, which we want to view as `((1+2)+3)+4` (mostly because
 subtraction is [left-associative](https://en.wikipedia.org/wiki/Operator_associativity)). So, we want the top level
 of the tree to be the rightmost `+` or `-`, since that means it will be the "last" operation. You may be asking,
@@ -150,7 +149,7 @@ What's the last \\(C\\)? We also want a "thing" to be a case expression. Here ar
 $$
 \\begin{align}
 C & \\rightarrow \\text{case} \\; A\_{add} \\; \\text{of} \\; \\{ L\_B\\} \\\\\\
-L\_B & \\rightarrow R \\; , \\; L\_B \\\\\\
+L\_B & \\rightarrow R \\; L\_B \\\\\\
 L\_B & \\rightarrow R \\\\\\
 R & \\rightarrow N \\; \\text{arrow} \\; \\{ A\_{add} \\} \\\\\\
 N & \\rightarrow \\text{lowerVar} \\\\\\
@@ -289,5 +288,6 @@ wrong:
 }{
 ```
 We are told an error occured. Excellent! We're not really sure what our tree looks like, though.
-We just know there's __stuff__ in the list of definitions. We will revisit our trees
+We just know there's __stuff__ in the list of definitions. Having read our source code into
-in the next post, adding code to print them and to verify that our programs make some sense.
+a structure we're more equipped to handle, we can now try to verify that the code
+makes sense in [Part 3 - Type Checking]({{< relref "03_compiler_typechecking.md" >}}).

content/blog/03_compiler_typechecking.md

@@ -1,7 +1,6 @@
 ---
 title: Compiling a Functional Language Using C++, Part 3 - Type Checking
 date: 2019-08-06T14:26:38-07:00
-draft: true
 tags: ["C and C++", "Functional Languages", "Compilers"]
 ---
 I think tokenizing and parsing are boring. The thing is, looking at syntax
@@ -604,3 +603,6 @@ as well as these two:
 
 All of our examples print the number of declarations in the program,
 which means they don't throw 0. And so, we have typechecking!
+Before we look at how we will execute our source code,
+we will slow down and make quality of life improvements
+in our codebase in [Part 4 - Small Improvements]({{< relref "04_compiler_improvements.md" >}}).

content/blog/04_compiler_improvements.md

@@ -1,7 +1,6 @@
 ---
 title: Compiling a Functional Language Using C++, Part 4 - Small Improvements
 date: 2019-08-06T14:26:38-07:00
-draft: true
 tags: ["C and C++", "Functional Languages", "Compilers"]
 ---
 We've done quite a big push in the previous post. We defined
@@ -47,29 +46,29 @@ virtual void print(std::ostream& to) const;
 
 Let's take a look at the implementation. For `ast_int`,
 `ast_lid`, and `ast_uid`:
-{{< codelines "C++" "compiler/04/ast.cpp" 18 21 >}}
+{{< codelines "C++" "compiler/04/ast.cpp" 19 22 >}}
-{{< codelines "C++" "compiler/04/ast.cpp" 27 30 >}}
+{{< codelines "C++" "compiler/04/ast.cpp" 28 31 >}}
-{{< codelines "C++" "compiler/04/ast.cpp" 36 39 >}}
+{{< codelines "C++" "compiler/04/ast.cpp" 37 40 >}}
 
 With `ast_binop` things get a bit more interesting.
 We call `print` recursively on the children of the
 `binop` node:
-{{< codelines "C++" "compiler/04/ast.cpp" 45 50 >}}
+{{< codelines "C++" "compiler/04/ast.cpp" 46 51 >}}
 
 The same idea for `ast_app`:
-{{< codelines "C++" "compiler/04/ast.cpp" 66 71 >}}
+{{< codelines "C++" "compiler/04/ast.cpp" 67 72 >}}
 
 Finally, just like `ast_case::typecheck` called 
 `pattern::match`, `ast_case::print` calls `pattern::print`:
-{{< codelines "C++" "compiler/04/ast.cpp" 83 92 >}}
+{{< codelines "C++" "compiler/04/ast.cpp" 84 93 >}}
 
 We follow the same implementation strategy for patterns,
 but we don't need indentation, or recursion:
-{{< codelines "C++" "compiler/04/ast.cpp" 108 110 >}}
+{{< codelines "C++" "compiler/04/ast.cpp" 115 117 >}}
-{{< codelines "C++" "compiler/04/ast.cpp" 116 121 >}}
+{{< codelines "C++" "compiler/04/ast.cpp" 123 128 >}}
 
-Let's print the bodies of each function we receive from the parser:
+In `main`, let's print the bodies of each function we receive from the parser:
-{{< codelines "C++" "compiler/04/main.cpp" 41 56 >}}
+{{< codelines "C++" "compiler/04/main.cpp" 47 56 >}}
 
 ### Printing Types
 Types are another thing that we want to be able to inspect, so let's
@@ -79,7 +78,7 @@ virtual void print(const type_mgr& mgr, std::ostream& to) const;
 ```
 We need the type manager so we can follow substitutions.
 The implementation is simple enough:
-{{< codelines "C++" "compiler/04/type.cpp" 5 24 >}}
+{{< codelines "C++" "compiler/04/type.cpp" 6 24 >}}
 
 Let's also print out the types we infer. We'll make it a separate loop
 at the bottom of the `typecheck_program` function, because it's mostly just
@@ -127,6 +126,72 @@ Remember how we build the function type backwards in Part 3? We have to do the s
 We replace the fragment with the proper reverse iteration:
 {{< codelines "C++" "compiler/04/definition.cpp" 37 40 >}}
 
+### Throwing Exceptions
+Throwing 0 is never a good idea. Such an exception doesn't contain any information
+that we may find useful in debugging, nor any information that would benefit
+the users of the compiler. Instead, let's define our own exception classes,
+and throw them instead. We'll make two:
+{{< codeblock "C++" "compiler/04/error.hpp" >}}
+
+Only one function needs to be implemented, and it's pretty boring:
+{{< codeblock "C++" "compiler/04/error.cpp" >}}
+
+It's time to throw these instead of 0. Let's take a look at the places
+we do so.
+
+First, we throw 0 in `type.cpp`, in the `type_mgr::unify` method. This is
+where our `unification_error` comes in. The error will
+contain the two types that we failed to unify, which we will
+later report to the user:
+{{< codelines "C++" "compiler/04/type.cpp" 91 91 >}}
+
+Next up, we have a few throws in `ast.cpp`. The first is in `op_string`, but
+we will simply replace it with `return "??"`, which will be caught later on
+(either way, the case expression falling through would be a compiler bug,
+since the user has no way of providing an invalid binary operator). The
+first throw we need to address is in `ast_binop::typecheck`, in the case
+that we don't find a type for a binary operator. We report this
+directly:
+{{< codelines "C++" "compiler/04/ast.cpp" 57 57 >}}
+
+We will introduce a new exception into `ast_case::typecheck`. Previously,
+we simply pass the type of the expression to be case analyzed into
+the pattern matching method. However, since we don't want
+case analysis on functions, we ensure that the type of the expression
+is `type_base`. If not, we report this:
+{{< codelines "C++" "compiler/04/ast.cpp" 107 110 >}}
+
+The next exception is in `pattern_constr::match`. It occurs
+when the pattern has a constructor we don't recognize, and
+that's exactly what we report:
+{{< codelines "C++" "compiler/04/ast.cpp" 132 134 >}}
+
+The next exception occurs in a loop, when we bind
+types for each of the constructor pattern's variables.
+We throw when we are unable to cast the remaining
+constructor type to a `type_arr`. Conceptually,
+this means that the pattern wants to apply the
+constructor to more parameters than it actually
+takes:
+{{< codelines "C++" "compiler/04/ast.cpp" 138 138 >}}
+
+We remove the last throw at the bottom of `pattern_constr::match`.
+This is because once unification succeeds, we know
+that the return type of the pattern is a base type since
+we know the type of the case expression is a base type
+(we know this because we added that check to `ast_case::typecheck`).
+
+Finally, let's catch and report these exceptions. We could do it
+in `typecheck_program`, but I think doing so in `main` is neater.
+Since printing types requires a `type_mgr`, we'll move the
+declarations of both `type_mgr` and `type_env` to the top of
+main, and pass them to `typecheck_program` as parameters. Then,
+we can surround the call to `typecheck_program` with
+try/catch:
+{{< codelines "C++" "compiler/04/main.cpp" 57 69 >}}
+
+We use some [ANSI escape codes](https://en.wikipedia.org/wiki/ANSI_escape_code)
+to color the types in the case of a unification error.
 
 ### Setting up CMake
 We will set up CMake as our build system. This would be extremely easy
@@ -147,16 +212,16 @@ in order to compile. We add this dependency:
 Finally, we add our source code to a CMake target. We use
 the `BISON_parser_OUTPUTS` and `FLEX_scanner_OUTPUTS` to
 pass in the source files generated by Flex and Bison.
-{{< codelines "CMake" "compiler/04/CMakeLists.txt" 15 22 >}}
+{{< codelines "CMake" "compiler/04/CMakeLists.txt" 15 23 >}}
 
 Almost there! `parser.cpp` will be generated in the `build` directory
 during an out-of-source build, and so will `parser.hpp`. When building,
 `parser.cpp` will try to look for `ast.hpp`, and `main.cpp` will look for
 `parser.hpp`. We want them to be able to find each other, so we
 add both the source directory and the build (binary) directory to
-the list of includes directories:
+the list of include directories:
 
-{{< codelines "CMake" "compiler/04/CMakeLists.txt" 23 24 >}}
+{{< codelines "CMake" "compiler/04/CMakeLists.txt" 24 25 >}}
 
 That's it for CMake! Let's try our build:
 ```
@@ -164,5 +229,10 @@ cmake -S . -B build
 cd build && make -j8
 ```
 
-We get an executable called `compiler`. Excellent! Here's the whole file:
+### Updated Code
-{{< codeblock "CMake" "compiler/04/CMakeLists.txt" >}}
+We've made a lot of changes to the codebase, and I've only shown snippets of the code
+so far. If you'de like to see the whole codebase, you can go to my site's git repository
+and check out [the code so far](https://dev.danilafe.com/Web-Projects/blog-static/src/branch/master/code/compiler/04).
+
+Having taken this little break, it's time for our next push. We will define
+how our programs will be evaluated in [Part 5 - Execution]({{< relref "05_compiler_execution.md" >}}).

content/blog/05_compiler_execution.md

@@ -0,0 +1,614 @@
+---
+title: Compiling a Functional Language Using C++, Part 5 - Execution
+date: 2019-08-06T14:26:38-07:00
+tags: ["C and C++", "Functional Languages", "Compilers"]
+---
+{{< gmachine_css >}}
+We now have trees representing valid programs in our language,
+and it's time to think about how to compile them into machine code,
+to be executed on hardware. But __how should we execute programs__?
+
+The programs we define are actually lists of definitions. But
+you can't evaluate definitions - they just tell you, well,
+how things are defined. Expressions, on the other hand,
+can be simplified. So, let's start by evaluating
+the body of the function called `main`, similarly
+to how C/C++ programs start.
+
+Alright, we've made it past that hurdle. Next,
+to figure out how to evaluate expressions. It's easy
+enough with binary operators: `3+2*6` becomes `3+12`,
+and `3+12` becomes `15`. Functions are when things
+get interesting. Consider:
+```
+double (160+3)
+```
+There's many perfectly valid ways to evaluate the program.
+When we get to a function application, we can first evaluate
+the arguments, and then expand the function definition:
+```
+double (160+3)
+double 163
+163+163
+326
+```
+Let's come up with a more interesting program to illustrate
+execution. How about:
+```
+data Pair = { P Int Int }
+defn fst p = {
+    case p of {
+        P x y -> { x }
+    }
+}
+defn snd p = {
+    case p of {
+        P x y -> { y }
+    }
+}
+defn slow x = { returns x after waiting for 1 second }
+defn main = { fst (P (slow 320) (slow 6)) }
+```
+
+If we follow our rules for evaluating functions,
+the execution will follow the following steps:
+```
+fst (P (slow 320) (slow 6))
+fst (P 320 (slow 6)) <- after 1 second
+fst (P 320 6) <- after 1 second
+320
+```
+We waited for two seconds, even though we really only
+needed to wait one. To avoid this, we could instead
+define our function application to substitute in 
+the parameters of a function before evaluating them:
+```
+fst (P (slow 320) (slow 6))
+(slow 320)
+320 <- after 1 second
+```
+This seems good, until we try doubling an expression again:
+```
+double (slow 163)
+(slow 163) + (slow 163)
+163 + (slow 163) <- after 1 second
+163 + 163 <- after 1 second
+326
+```
+With ony one argument, we've actually spent two seconds on the
+evaluation! If we instead tried to triple using addition,
+we'd spend three seconds. 
+
+Observe that with these new rules (called "call by name" in programming language theory),
+we only waste time because we evaluate an expression that was passed in more than 1 time.
+What if we didn't have to do that? Since we have a functional language, there's no way
+that two expressions that are the same evaluate to a different value. Thus,
+once we know the result of an expression, we can replace all occurences of that expression
+with the result:
+```
+double (slow 163)
+(slow 163) + (slow 163)
+163 + 163 <- after 1 second
+326
+```
+We're back down to one second, and since we're still substituting parameters
+before we evaluate them, we still only take one second. 
+
+Alright, this all sounds good. How do we go about implementing this?
+Since we're substituting variables for whole expressions, we can't
+just use values. Instead, because expressions are represented with trees,
+we might as well consider operating on trees. When we evaluate a tree,
+we can substitute it in-place with what it evaluates to. We'll do this
+depth-first, replacing the children of a node with their reduced trees,
+and then moving on to the parent.
+
+There's only one problem with this: if we substitute a variable that occurs many times
+with the same expression tree, we no longer have a tree! Trees, by definition,
+have only one path from the root to any other node. Since we now have
+many ways to reach that expression we substituted, we instead have a __graph__.
+Indeed, the way we will be executing our functional code is called __graph reduction__.
+
+### Building Graphs
+Naively, we might consider creating a tree for each function at the beginning of our
+program, and then, when that function is called, substituting the variables
+in it with the parameters of the application. But that approach quickly goes out
+the window when we realize that we could be applying a function
+multiple times - in fact, an arbitrary number of times. This means we can't
+have a single tree, and we must build a new tree every time we call a function.
+
+The question, then, is: how do we construct a new graph? We could
+reach into Plato's [Theory of Forms](https://en.wikipedia.org/wiki/Theory_of_forms) and
+have a "reference" tree which we then copy every time we apply the function.
+But how do you copy a tree? Copying a tree is usually a recursive function,
+and __every__ time that we copy a tree, we'll have to look at each node
+and decide whether or not to visit its children (or if it has any at all).
+If we copy a tree 100 times, we will have to look at each "reference"
+node 100 times. Since the reference tree doesn't change, __we'd
+be following the exact same sequence of decisions 100 times__. That's
+no good!
+
+An alternative approach, one that we'll use from now on, is to instead
+convert each function's expression tree into a sequence of instructions
+that you can follow to build an identical tree. Every time we have
+to apply a function, we'll follow the corresponding recipe for
+that function, and end up with a new tree that we continue evaluating.
+
+### G-machine
+"Instructions" is a very generic term. Specifically, we will be creating instructions
+for a [G-machine](https://link.springer.com/chapter/10.1007/3-540-15975-4_50),
+an abstract architecture which we will use to reduce our graphs. The G-machine
+is stack-based - all operations push and pop items from a stack. The machine
+will also have a "dump", which is a stack of stacks; this will help with
+separating evaluation of various graphs.
+
+We will follow the same notation as Simon Peyton Jones in
+[his book](https://www.microsoft.com/en-us/research/wp-content/uploads/1992/01/student.pdf)
+, which was my source of truth when implementing my compiler. The machine
+will be executing instructions that we give it, and as such, it must have
+an instruction queue, which we will reference as \\(i\\). We will write
+\\(x:i\\) to mean "an instruction queue that starts with
+an instruction x and ends with instructions \\(i\\)". A stack machine
+obviously needs to have a stack - we will call it \\(s\\), and will
+adopt a similar notation to the instruction queue: \\(a\_1, a\_2, a\_3 : s\\)
+will mean "a stack with the top values \\(a\_1\\), \\(a\_2\\), and \\(a\_3\\),
+and remaining instructions \\(s\\)". Finally, as we said, our stack
+machine has a dump, which we will write as \\(d\\). On this dump,
+we will push not only the current stack, but also the current
+instructions that we are executing, so we may resume execution
+later. We will write \\(\\langle i, s \\rangle : d\\) to mean
+"a dump with instructions \\(i\\) and stack \\(s\\) on top,
+followed by instructions and stacks in \\(d\\)".
+
+There's one more thing the G-machine will have that we've not yet discussed at all,
+and it's needed because of the following quip earlier in the post:
+
+> When we evaluate a tree, we can substitute it in-place with what it evaluates to. 
+
+How can we substitute a value in place? Surely we won't iterate over the entire
+tree and look for an occurence of the tree we evaluted. Rather, wouldn't it be
+nice if we could update all references to a tree to be something else? Indeed,
+we can achieve this effect by using __pointers__. I don't mean specifically
+C/C++ pointers - I mean the more general concept of "an address in memory".
+The G-machine has a __heap__, much like the heap of a C/C++ process. We
+can create a tree node on the heap, and then get an __address__ of the node.
+We then have trees use these addresses to link their child nodes.
+If we want to replace a tree node with its reduced form, we keep
+its address the same, but change the value on the heap.
+This way, all trees that reference the node we change become updated,
+without us having to change them - their child address remains the same,
+but the child has now been updated. We represent the heap
+using \\(h\\). We write \\(h[a : v]\\) to say "the address \\(a\\) points
+to value \\(v\\) in the heap \\(h\\)". Now you also know why we used
+the letter \\(a\\) when describing values on the stack - the stack contains
+addresses of (or pointers to) tree nodes.
+
+_Compiling Functional Languages: a tutorial_ also keeps another component
+of the G-machine, the __global map__, which maps function names to addresses of nodes
+that represent them. We'll stick with this, and call this global map \\(m\\).
+
+Finally, let's talk about what kind of nodes our trees will be made of.
+We don't have to include every node that we've defined as a subclass of
+`ast` - some nodes we can compile to instructions, without having to build
+them. We will also include nodes that we didn't need for to represent expressions.
+Here's the list of nodes types we'll have:
+
+* `NInt` - represents an integer.
+* `NApp` - represents an application (has two children).
+* `NGlobal` - represents a global function (like the `f` in `f x`).
+* `NInd` - an "indrection" node that points to another node. This will help with "replacing" a node.
+* `NData` - a "packed" node that will represent a constructor with all the arguments.
+
+With these nodes in mind, let's try defining some instructions for the G-machine.
+We start with instructions we'll use to assemble new version of function body trees as we discussed above.
+First up is __PushInt__:
+
+{{< gmachine "PushInt" >}}
+    {{< gmachine_inner "Before">}}
+    \( \text{PushInt} \; n : i \quad s \quad d \quad h \quad m \)
+    {{< /gmachine_inner >}}
+    {{< gmachine_inner "After" >}}
+    \( i \quad a : s \quad d \quad h[a : \text{NInt} \; n] \quad m \)
+    {{< /gmachine_inner >}}
+    {{< gmachine_inner "Description" >}}
+    Push an integer \(n\) onto the stack.
+    {{< /gmachine_inner >}}
+{{< /gmachine >}}
+
+Let's go through this. We start with an instruction queue
+with `PushInt n` on top. We allocate a new `NInt` with the
+number `n` on the heap at address \\(a\\). We then push
+the address of the `NInt` node on top of the stack. Next,
+__PushGlobal__:
+
+{{< gmachine "PushGlobal" >}}
+    {{< gmachine_inner "Before">}}
+    \( \text{PushGlobal} \; f : i \quad s \quad d \quad h \quad m[f : a] \)
+    {{< /gmachine_inner >}}
+    {{< gmachine_inner "After" >}}
+    \( i \quad a : s \quad d \quad h \quad m[f : a] \)
+    {{< /gmachine_inner >}}
+    {{< gmachine_inner "Description" >}}
+    Push a global function \(f\) onto the stack.
+    {{< /gmachine_inner >}}
+{{< /gmachine >}}
+
+We don't allocate anything new on the heap for this one - 
+we already have a node for the global function. Next up,
+__Push__:
+
+{{< gmachine "Push" >}}
+    {{< gmachine_inner "Before">}}
+    \( \text{Push} \; n : i \quad a_0, a_1, ..., a_n : s \quad d \quad h \quad m \)
+    {{< /gmachine_inner >}}
+    {{< gmachine_inner "After" >}}
+    \( i \quad a_n, a_0, a_1, ..., a_n : s \quad d \quad h \quad m \)
+    {{< /gmachine_inner >}}
+    {{< gmachine_inner "Description" >}}
+    Push a value at offset \(n\) from the top of the stack onto the stack.
+    {{< /gmachine_inner >}}
+{{< /gmachine >}}
+
+We define this instruction to work if and only if there exists an address
+on the stack at offset \\(n\\). We take the value at that offset, and
+push it onto the stack again. This can be helpful for something like
+`f x x`, where we use the same tree twice. Speaking of that - let's
+define an instruction to combine two nodes into an application:
+
+{{< gmachine "MkApp" >}}
+    {{< gmachine_inner "Before">}}
+    \( \text{MkApp} : i \quad a_0, a_1 : s \quad d \quad h \quad m \)
+    {{< /gmachine_inner >}}
+    {{< gmachine_inner "After" >}}
+    \( i \quad a : s \quad d \quad h[ a : \text{NApp} \; a_0 \; a_1] \quad m \)
+    {{< /gmachine_inner >}}
+    {{< gmachine_inner "Description" >}}
+    Apply a function at the top of the stack to a value after it.
+    {{< /gmachine_inner >}}
+{{< /gmachine >}}
+
+We pop two things off the stack: first, the thing we're applying, then
+the thing we apply it to. We then create a new node on the heap
+that is an `NApp` node, with its two children being the nodes we popped off.
+Finally, we push it onto the stack.
+
+Let's try use these instructions to get a feel for it. In
+order to conserve space, let's use \\(\\text{G}\\) for PushGlobal,
+\\(\\text{I}\\) for PushInt, and \\(\\text{A}\\) for PushApp.
+Let's say we want to construct a graph for `double 326`. We'll
+use the instructions \\(\\text{I} \; 326\\), \\(\\text{G} \; \\text{double}\\),
+and \\(\\text{A}\\). Let's watch these instructions play out:
+$$
+\\begin{align}
+[\\text{I} \; 326, \\text{G} \; \text{double}, \\text{A}] & \\quad s \\quad & d \\quad & h \\quad & m[\\text{double} : a\_d] \\\\\\
+[\\text{G} \; \text{double}, \\text{A}] & \\quad a\_1 : s \\quad & d \\quad & h[a\_1 : \\text{NInt} \; 326] \\quad & m[\\text{double} : a\_d] \\\\\\
+[\\text{A}] & \\quad a\_d, a\_1 : s \\quad & d \\quad & h[a\_1 : \\text{NInt} \; 326] \\quad & m[\\text{double} : a\_d] \\\\\\
+[] & \\quad a\_2 : s \\quad & d \\quad & h[\\substack{\\begin{aligned}a\_1 & : \\text{NInt} \; 326 \\\\ a\_2 & : \\text{NApp} \; a\_d \; a\_1 \\end{aligned}}] \\quad & m[\\text{double} : a\_d] \\\\\\
+\\end{align}
+$$
+How did we come up with these instructions? We'll answer this question with
+more generality later, but let's take a look at this particular expression
+right now. We know it's an application, so we'll be using MkApp eventually.
+We also know that MkApp expects two values on top of the stack from
+which to make an application. The node on top has to be the function, and the next
+node is the value to be passed into that function. Since a stack is first-in-last-out,
+for the function (`double`, in our case) to be on top, we need
+to push it last. Thus, we push `double` first, then 326. Finally,
+we call MkApp now that the stack is in the right state.
+
+Having defined instructions to __build__ graphs, it's now time
+to move on to instructions to __reduce__ graphs - after all,
+we're performing graph reduction. A crucial instruction for the
+G-machine is __Unwind__. What Unwind does depends on what
+nodes are on the stack. Its name comes from how it behaves
+when the top of the stack is an `NApp` node that is at
+the top of a potentially long chain of applications: given
+an application node, it pushes its left hand side onto the stack.
+It then __continues to run Unwind__. This is effectively a while loop:
+applications nodes continue to be expanded this way until the left
+hand side of an application is finally something
+that __isn't__ an application. Let's write this rule as follows:
+
+{{< gmachine "Unwind-App" >}}
+    {{< gmachine_inner "Before">}}
+    \( \text{Unwind} : i \quad a : s \quad d \quad h[a : \text{NApp} \; a_0 \; a_1] \quad m \)
+    {{< /gmachine_inner >}}
+    {{< gmachine_inner "After" >}}
+    \( \text{Unwind} : i \quad a_0, a : s \quad d \quad h[ a : \text{NApp} \; a_0 \; a_1] \quad m \)
+    {{< /gmachine_inner >}}
+    {{< gmachine_inner "Description" >}}
+    Unwind an application by pushing its left node.
+    {{< /gmachine_inner >}}
+{{< /gmachine >}}
+
+Let's talk about what happens when Unwind hits a node that isn't an application. Of all nodes
+we have described, `NGlobal` seems to be the most likely to be on top of the stack after
+an application chain has finished unwinding. In this case we want to run the instructions
+for building the referenced global function. Naturally, these instructions
+may reference the arguments of the application. We can find the first argument
+by looking at offset 1 on the stack, which will be an `NApp` node, and then going
+to its right child. The same can be done for the second and third arguments, if
+they exist. But this doesn't feel right - we don't want to constantly be looking
+at the right child of a node on the stack. Instead, we replace each application
+node on the stack with its right child. Once that's done, we run the actual
+code for the global function:
+
+{{< gmachine "Unwind-Global" >}}
+    {{< gmachine_inner "Before">}}
+    \( \text{Unwind} : i \quad a, a_0, a_1, ..., a_n : s \quad d \quad h[\substack{a : \text{NGlobal} \; n \; c \\ a_k : \text{NApp} \; a_{k-1} \; a_k'}] \quad m \)
+    {{< /gmachine_inner >}}
+    {{< gmachine_inner "After" >}}
+    \( c \quad a_0', a_1', ..., a_n', a_n : s \quad d \quad h[\substack{a : \text{NGlobal} \; n \; c \\ a_k : \text{NApp} \; a_{k-1} \; a_k'}] \quad m \)
+    {{< /gmachine_inner >}}
+    {{< gmachine_inner "Description" >}}
+    Call a global function.
+    {{< /gmachine_inner >}}
+{{< /gmachine >}}
+
+In this rule, we used a general rule for \\(a\_k\\), in which \\(k\\) is any number
+between 0 and \\(n\\). We also expect the `NGlobal` node to contain two parameters,
+\\(n\\) and \\(c\\). \\(n\\) is the arity of the function (the number of arguments
+it expects), and \\(c\\) are the instructions to construct the function's tree.
+
+The attentive reader will have noticed a catch: we kept \\(a\_n\\) on the stack!
+This once again goes back to replacing a node in-place. \\(a\_n\\) is the address of the "root" of the
+whole expression we're simplifying. Thus, to replace the value at this address, we need to keep
+the address until we have something to replace it with.
+
+There's one more thing that can be found at the leftmost end of a tree of applications: `NInd`.
+We simply replace `NInd` with the node it points to, and resume Unwind:
+
+{{< gmachine "Unwind-Ind" >}}
+    {{< gmachine_inner "Before">}}
+    \( \text{Unwind} : i \quad a : s \quad d \quad h[a : \text{NInd} \; a' ] \quad m \)
+    {{< /gmachine_inner >}}
+    {{< gmachine_inner "After" >}}
+    \( \text{Unwind} : i \quad a' : s \quad d \quad h[a : \text{NInd} \; a' ] \quad m \)
+    {{< /gmachine_inner >}}
+    {{< gmachine_inner "Description" >}}
+    Replace indirection node with its target.
+    {{< /gmachine_inner >}}
+{{< /gmachine >}}
+
+We've talked about replacing a node, and we've talked about indirection, but we
+haven't yet an instruction to perform these actions. Let's do so now:
+
+{{< gmachine "Update" >}}
+    {{< gmachine_inner "Before">}}
+    \( \text{Update} \; n : i \quad a,a_0,a_1,...a_n : s \quad d \quad h \quad m \)
+    {{< /gmachine_inner >}}
+    {{< gmachine_inner "After" >}}
+    \( i \quad a_0,a_1,...,a_n : s \quad d \quad h[a_n : \text{NInd} \; a ] \quad m \)
+    {{< /gmachine_inner >}}
+    {{< gmachine_inner "Description" >}}
+    Transform node at offset into an indirection.
+    {{< /gmachine_inner >}}
+{{< /gmachine >}}
+
+This instruction pops an address from the top of the stack, and replaces
+a node at the given offset with an indirection to the popped node. After
+we evaluate a function call, we will use `update` to make sure it's
+not evaluated again.
+
+Now, let's talk about data structures. We have mentioned an `NData` node,
+but we've given no explanation of how it will work. Obviously, we need
+to distinguish values of a type created by different constructors:
+If we have a value of type `List`, it could have been created either
+using `Nil` or `Cons`. Depending on which constructor was used to
+create a value of a type, we might treat it differently. Furthermore,
+it's not always possible to know what constructor was used to
+create what value at compile time. So, we need a way to know,
+at runtime, how the value was constructed. We do this using
+a __tag__. A tag is an integer value that will be contained in
+the `NData` node. We assign a tag number to each constructor,
+and when we create a node with that constructor, we set
+the node's tag accordingly. This way, we can easily
+tell if a `List` value is a `Nil` or a `Cons`, or
+if a `Tree` value is a `Node` or a `Leaf`.
+
+To operate on `NData` nodes, we will need two primitive operations: __Pack__ and __Split__.
+Pack will create an `NData` node with a tag from some number of nodes
+on the stack. These nodes will be placed into a dynamically
+allocated array:
+
+{{< gmachine "Pack" >}}
+    {{< gmachine_inner "Before">}}
+    \( \text{Pack} \; t \; n : i \quad a_1,a_2,...a_n : s \quad d \quad h \quad m \)
+    {{< /gmachine_inner >}}
+    {{< gmachine_inner "After" >}}
+    \( i \quad a : s \quad d \quad h[a : \text{NData} \; t \; [a_1, a_2, ..., a_n] ] \quad m \)
+    {{< /gmachine_inner >}}
+    {{< gmachine_inner "Description" >}}
+    Pack \(n\) nodes from the stack into a node with tag \(t\).
+    {{< /gmachine_inner >}}
+{{< /gmachine >}}
+
+Split will do the opposite, by popping
+of an `NData` node and moving the contents of its
+array onto the stack:
+
+{{< gmachine "Split" >}}
+    {{< gmachine_inner "Before">}}
+    \( \text{Split} : i \quad a : s \quad d \quad h[a : \text{NData} \; t \; [a_1, a_2, ..., a_n] ] \quad m \)
+    {{< /gmachine_inner >}}
+    {{< gmachine_inner "After" >}}
+    \( i \quad a_1, a_2, ...,a_n : s \quad d \quad h[a : \text{NData} \; t \; [a_1, a_2, ..., a_n] ] \quad m \)
+    {{< /gmachine_inner >}}
+    {{< gmachine_inner "Description" >}}
+    Unpack a data node on top of the stack.
+    {{< /gmachine_inner >}}
+{{< /gmachine >}}
+
+These two instructions are a good start, but we're missing something
+fairly big: case analysis. After we've constructed a data type,
+to perform operations on it, we want to figure out what
+constructor and values which were used to create it. In order
+to implement patterns and case expressions, we'll need another
+instruction that's capable of making a decision based on
+the tag of an `NData` node. We'll call this instruction __Jump__,
+and define it to contain a mapping from tags to instructions
+to be executed for a value of that tag. For instance,
+if the constructor `Nil` has tag 0, and `Cons` has tag 1,
+the mapping for the case expression of a length function
+could be written as \\([0 \\rightarrow [\\text{PushInt} \; 0], 1 \\rightarrow [\\text{PushGlobal} \; \\text{length}, ...] ]\\).
+Let's define the rule for it:
+
+{{< gmachine "Jump" >}}
+    {{< gmachine_inner "Before">}}
+    \( \text{Jump} [..., t \rightarrow i_t, ...] : i \quad a : s \quad d \quad h[a : \text{NData} \; t \; as ] \quad m \)
+    {{< /gmachine_inner >}}
+    {{< gmachine_inner "After" >}}
+    \( i_t, i \quad a : s \quad d \quad h[a : \text{NData} \; t \; as ] \quad m \)
+    {{< /gmachine_inner >}}
+    {{< gmachine_inner "Description" >}}
+    Execute instructions corresponding to a tag.
+    {{< /gmachine_inner >}}
+{{< /gmachine >}}
+
+Alright, we've made it through the interesting instructions,
+but there's still a few that are needed, but less shiny and cool.
+For instance: imagine we've made a function call. As per the
+rules for Unwind, we've placed the right hand sides of all applications
+on the stack, and ran the instructions provided by the function,
+creating a final graph. We then continue to reduce this final
+graph. But we've left the function parameters on the stack!
+This is untidy. We define a __Slide__ instruction,
+which keeps the address at the top of the stack, but gets
+rid of the next \\(n\\) addresses:
+
+{{< gmachine "Slide" >}}
+    {{< gmachine_inner "Before">}}
+    \( \text{Slide} \; n : i \quad a_0, a_1, ..., a_n : s \quad d \quad h \quad m \)
+    {{< /gmachine_inner >}}
+    {{< gmachine_inner "After" >}}
+    \( i \quad a_0 : s \quad d \quad h \quad m \)
+    {{< /gmachine_inner >}}
+    {{< gmachine_inner "Description" >}}
+    Remove \(n\) addresses after the top from the stack.
+    {{< /gmachine_inner >}}
+{{< /gmachine >}}
+
+Just a few more. Next up, we observe that we have not
+defined any way for our G-machine to perform arithmetic,
+or indeed, any primitive operations. Since we've
+not defined any built-in type for booleans,
+let's avoid talking about operations like `<`, `==`,
+and so on (in fact, we've omitted them from the grammar so far).
+So instead, let's talk about the [closed](https://en.wikipedia.org/wiki/Closure_(mathematics)) operations,
+namely `+`, `-`, `*`, and `/`. We'll define a special instruction for
+them, called __BinOp__:
+
+{{< gmachine "BinOp" >}}
+    {{< gmachine_inner "Before">}}
+    \( \text{BinOp} \; \text{op} : i \quad a_0, a_1 : s \quad d \quad h[\substack{a_0 : \text{NInt} \; n \\ a_1 : \text{NInt} \; m}] \quad m \)
+    {{< /gmachine_inner >}}
+    {{< gmachine_inner "After" >}}
+    \( i \quad a : s \quad d \quad h[\substack{a_0 : \text{NInt} \; n \\ a_1 : \text{NInt} \; m \\ a : \text{NInt} \; (\text{op} \; n \; m)}] \quad m \)
+    {{< /gmachine_inner >}}
+    {{< gmachine_inner "Description" >}}
+    Apply a binary operator on integers.
+    {{< /gmachine_inner >}}
+{{< /gmachine >}}
+
+Nothing should be particularly surprising here:
+the instruction pops two integers off the stack, applies the given
+binary operation to them, and places the result on the stack.
+
+We're not yet done with primitive operations, though.
+We have a lazy graph reduction machine, which means
+something like the expression `3*(2+6)` might not
+be a binary operator applied to two `NInt` nodes.
+We keep around graphs until they __really__ need to
+be reduced. So now we need an instruction to trigger
+reducing a graph, to say, "we need this value now".
+We call this instruction __Eval__. This is where
+the dump finally comes in!
+
+When we execute Eval, another graph becomes our "focus", and we switch
+to a new stack. We obviously want to return from this once we've finished
+evaluating what we "focused" on, so we must store the program state somewhere -
+on the dump. Here's the rule:
+
+{{< gmachine "Eval" >}}
+    {{< gmachine_inner "Before">}}
+    \( \text{Eval} : i \quad a : s \quad d \quad h \quad m \)
+    {{< /gmachine_inner >}}
+    {{< gmachine_inner "After" >}}
+    \( [\text{Unwind}] \quad [a] \quad \langle i, s\rangle : d \quad h \quad m \)
+    {{< /gmachine_inner >}}
+    {{< gmachine_inner "Description" >}}
+    Evaluate graph to its normal form.
+    {{< /gmachine_inner >}}
+{{< /gmachine >}}
+
+We store the current set of instructions and the current stack on the dump,
+and start with only Unwind and the value we want to evaluate.
+That does the job, but we're missing one thing - a way to return to
+the state we placed onto the dump. To do this, we add __another__
+rule to Unwind:
+
+{{< gmachine "Unwind-Return" >}}
+    {{< gmachine_inner "Before">}}
+    \( \text{Unwind} : i \quad a : s \quad \langle i', s'\rangle : d \quad h[a : \text{NInt} \; n] \quad m \)
+    {{< /gmachine_inner >}}
+    {{< gmachine_inner "After" >}}
+    \( i' \quad a : s' \quad d \quad h[a : \text{NInt} \; n] \quad m \)
+    {{< /gmachine_inner >}}
+    {{< gmachine_inner "Description" >}}
+    Return from Eval instruction.
+    {{< /gmachine_inner >}}
+{{< /gmachine >}}
+
+Just a couple more special-purpose instructions, and we're done!
+
+Sometimes, it's possible for a tree node to reference itself.
+For instance, Haskell defines the
+[fixpoint combinator](https://en.wikipedia.org/wiki/Fixed-point_combinator)
+as follows:
+```Haskell
+fix f = let x = f x in x
+```
+
+In order to do this, an address that references a node must be present
+while the node is being constructed. We define an instruction,
+__Alloc__, which helps with that:
+
+{{< gmachine "Alloc" >}}
+    {{< gmachine_inner "Before">}}
+    \( \text{Alloc} \; n : i \quad s \quad d \quad h \quad m \)
+    {{< /gmachine_inner >}}
+    {{< gmachine_inner "After" >}}
+    \( i \quad s \quad d \quad h[a_k : \text{NInd} \; \text{null}] \quad m \)
+    {{< /gmachine_inner >}}
+    {{< gmachine_inner "Description" >}}
+    Allocate indirection nodes.
+    {{< /gmachine_inner >}}
+{{< /gmachine >}}
+
+We can allocate an indirection on the stack, and call Update on it when
+we've constructed a node. While we're constructing the tree, we can
+refer to the indirection when a self-reference is required.
+
+Lastly, we also define a Pop instruction, which just removes
+some number of nodes from the stack. We want this because
+calling Update at the end of a function modifies a node further up the stack,
+leaving anything on top of the stack after that node as scratch work. We get
+rid of that scratch work simply by popping it.
+
+{{< gmachine "Pop" >}}
+    {{< gmachine_inner "Before">}}
+    \( \text{Pop} \; n : i \quad a_1, a_2, ..., a_n : s \quad d \quad h \quad m \)
+    {{< /gmachine_inner >}}
+    {{< gmachine_inner "After" >}}
+    \( i \quad s \quad d \quad h \quad m \)
+    {{< /gmachine_inner >}}
+    {{< gmachine_inner "Description" >}}
+    Pop \(n\) nodes from the stack.
+    {{< /gmachine_inner >}}
+{{< /gmachine >}}
+
+That's it for the instructions. Knowing them, however, doesn't
+tell us what to do with our `ast` structs. We'll need to define
+rules to translate trees into these instructions, and I've already
+alluded to this when we went over `double 326`.
+However, this has already gotten pretty long,
+so we'll do it in the next post: [Part 6 - Compilation]({{< relref "06_compiler_compilation.md" >}}).