diff --git a/code/compiler/04/ast.cpp b/code/compiler/04/ast.cpp
index bdee157..b9f920f 100644
--- a/code/compiler/04/ast.cpp
+++ b/code/compiler/04/ast.cpp
@@ -1,4 +1,5 @@
 #include "ast.hpp"
+#include <ostream>
 
 std::string op_name(binop op) {
     switch(op) {
@@ -10,18 +11,44 @@ std::string op_name(binop op) {
     throw 0;
 }
 
+void print_indent(int n, std::ostream& to) {
+    while(n--) to << "  ";
+}
+
+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_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_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_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(mgr, env);
     type_ptr rtype = right->typecheck(mgr, env);
@@ -36,6 +63,13 @@ type_ptr ast_binop::typecheck(type_mgr& mgr, const type_env& env) const {
     return return_type;
 }
 
+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(mgr, env);
     type_ptr rtype = right->typecheck(mgr, env);
@@ -46,6 +80,17 @@ type_ptr ast_app::typecheck(type_mgr& mgr, const type_env& env) const {
     return return_type;
 }
 
+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_ptr case_type = of->typecheck(mgr, env);
     type_ptr branch_type = mgr.new_type();
@@ -60,10 +105,21 @@ type_ptr ast_case::typecheck(type_mgr& mgr, const type_env& env) const {
     return branch_type;
 }
 
+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 0;
diff --git a/code/compiler/04/ast.hpp b/code/compiler/04/ast.hpp
index c658be7..fcfed19 100644
--- a/code/compiler/04/ast.hpp
+++ b/code/compiler/04/ast.hpp
@@ -7,6 +7,7 @@
 struct ast {
     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;
 };
 
@@ -15,6 +16,7 @@ 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;
 };
 
@@ -62,6 +64,7 @@ struct ast_int : public ast {
     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;
 };
 
@@ -71,6 +74,7 @@ struct ast_lid : public ast {
     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;
 };
 
@@ -80,6 +84,7 @@ struct ast_uid : public ast {
     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;
 };
 
@@ -91,6 +96,7 @@ struct ast_binop : public ast {
     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;
 };
 
@@ -101,6 +107,7 @@ struct ast_app : public ast {
     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;
 };
 
@@ -111,6 +118,7 @@ struct ast_case : public ast {
     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;
 };
 
@@ -120,6 +128,7 @@ struct pattern_var : public pattern {
     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;
 };
 
@@ -130,6 +139,7 @@ struct pattern_constr : public pattern {
     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;
 };
 
diff --git a/code/compiler/04/definition.cpp b/code/compiler/04/definition.cpp
index 69b3196..f0889b6 100644
--- a/code/compiler/04/definition.cpp
+++ b/code/compiler/04/definition.cpp
@@ -34,8 +34,8 @@ void definition_data::typecheck_first(type_mgr& mgr, type_env& env) {
     for(auto& constructor : constructors) {
         type_ptr full_type = return_type;
 
-        for(auto& type_name : constructor->types) {
-            type_ptr type = type_ptr(new type_base(type_name));
+        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));
         }
 
diff --git a/code/compiler/04/main.cpp b/code/compiler/04/main.cpp
index 43c1b4f..337bc7c 100644
--- a/code/compiler/04/main.cpp
+++ b/code/compiler/04/main.cpp
@@ -1,6 +1,7 @@
 #include "ast.hpp"
 #include "parser.hpp"
 #include "type.hpp"
+#include <iostream>
 
 void yy::parser::error(const std::string& msg) {
     std::cout << "An error occured: " << msg << std::endl;
@@ -29,11 +30,27 @@ void typecheck_program(const std::vector<definition_ptr>& prog) {
     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;
+    }
 }
 
 int main() {
     yy::parser parser;
     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);
+    }
     typecheck_program(program);
     std::cout << program.size() << std::endl;
 }
diff --git a/code/compiler/04/parser.y b/code/compiler/04/parser.y
index fdb72c9..3874aca 100644
--- a/code/compiler/04/parser.y
+++ b/code/compiler/04/parser.y
@@ -107,7 +107,7 @@ case
     ;
 
 branches
-    : branches branch { $$ = std::move($1); $1.push_back(std::move($2)); }
+    : branches branch { $$ = std::move($1); $$.push_back(std::move($2)); }
     | branch { $$ = std::vector<branch_ptr>(); $$.push_back(std::move($1));}
     ;
 
diff --git a/code/compiler/04/type.cpp b/code/compiler/04/type.cpp
index f370a91..8a8e22d 100644
--- a/code/compiler/04/type.cpp
+++ b/code/compiler/04/type.cpp
@@ -2,6 +2,26 @@
 #include <sstream>
 #include <algorithm>
 
+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 = "";
diff --git a/code/compiler/04/type.hpp b/code/compiler/04/type.hpp
index e63040e..2774c29 100644
--- a/code/compiler/04/type.hpp
+++ b/code/compiler/04/type.hpp
@@ -2,8 +2,12 @@
 #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>;
@@ -13,6 +17,8 @@ struct type_var : public type {
 
     type_var(std::string n)
         : name(std::move(n)) {}
+
+    void print(const type_mgr& mgr, std::ostream& to) const;
 };
 
 struct type_base : public type {
@@ -20,6 +26,8 @@ struct type_base : public type {
 
     type_base(std::string n) 
         : name(std::move(n)) {}
+
+    void print(const type_mgr& mgr, std::ostream& to) const;
 };
 
 struct type_arr : public type {
@@ -28,6 +36,8 @@ struct type_arr : public type {
 
     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 {
diff --git a/content/blog/04_compiler_improvements.md b/content/blog/04_compiler_improvements.md
index 5c71a06..fe795d1 100644
--- a/content/blog/04_compiler_improvements.md
+++ b/content/blog/04_compiler_improvements.md
@@ -29,6 +29,103 @@ to only compile source files that have changed,
 and we want to have a standard definition of how to
 build our program.
 
+### Printing Syntax Trees
+Let's start by printing the trees we get from our parser.
+This is long overdue - we had no way to verify the structure
+of what our parser returned to us since Part 2. We'll print
+the trees top-down, with the children of a node
+indent one block further than the node itself. For this,
+we'll make a new virtual function with the signature:
+```
+virtual void print(int indent, std::ostream& to) const;
+```
+We'll include a similar printing function into our
+pattern struct, too:
+```
+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" 27 30 >}}
+{{< codelines "C++" "compiler/04/ast.cpp" 36 39 >}}
+
+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 >}}
+
+The same idea for `ast_app`:
+{{< codelines "C++" "compiler/04/ast.cpp" 66 71 >}}
+
+Finally, just like `ast_case::typecheck` called 
+`pattern::match`, `ast_case::print` calls `pattern::print`:
+{{< codelines "C++" "compiler/04/ast.cpp" 83 92 >}}
+
+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" 116 121 >}}
+
+Let's print the bodies of each function we receive from the parser:
+{{< codelines "C++" "compiler/04/main.cpp" 35 50 >}}
+
+### Printing Types
+Types are another thing that we want to be able to inspect, so let's
+add a similar print method to them:
+```
+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 >}}
+
+Let's also print out the types we infer. We'll make it a separate loop
+in the `typecheck_program` function, because it's mostly just
+for debugging purposes.
+
+### Fixing Bugs
+We actually discover not one, but two bugs in our implementation thanks
+to this output. Observe the output for `works3.txt`:
+```
+length l:
+  CASE:
+    Nil
+      INT: 0
+*: Int -> (Int -> (Int))
++: Int -> (Int -> (Int))
+-: Int -> (Int -> (Int))
+/: Int -> (Int -> (Int))
+Cons: List -> (Int -> (List))
+Nil: List
+length: List -> (Int)
+2
+```
+
+First, we're missing the `Cons` branch. The culprit is `parser.y`, specifically
+this line:
+```C++
+    : branches branch { $$ = std::move($1); $1.push_back(std::move($2)); }
+```
+Notice that we move our list of branches out of `$1`. However, when we
+`push_back`, we use `$1` again. That's wrong! We need to `push_back`
+to `$$` instead:
+{{< codelines "C++" "compiler/04/parser.y" 110 110 >}}
+
+Next, observe that `Cons` has type `List -> Int -> List`. That's not right,
+since `Int` comes first in our definition. The culprit is this fragment of code:
+```C++
+        for(auto& type_name : constructor->types) {
+            type_ptr type = type_ptr(new type_base(type_name));
+            full_type = type_ptr(new type_arr(type, full_type));
+        }
+```
+Remember how we build the function type backwards in Part 3? We have to do the same here.
+We replace the fragment with the proper reverse iteration:
+{{< codelines "C++" "compiler/04/definition.cpp" 37 40 >}}
+
+
 ### Setting up CMake
 This would be extremely easy if not for Flex and Bison. We start with the usual:
 {{< codelines "CMake" "compiler/04/CMakeLists.txt" 1 2 >}}