diff --git a/code/compiler/13/ast.cpp b/code/compiler/13/ast.cpp
index d66ee4e..693cafd 100644
--- a/code/compiler/13/ast.cpp
+++ b/code/compiler/13/ast.cpp
@@ -287,6 +287,7 @@ struct case_strategy_bool {
             repr_type repr,
             std::vector<instruction_ptr>& into) {
         branch->expr->compile(env_ptr(new env_offset(1, env)), into);
+        into.push_back(instruction_ptr(new instruction_slide(1)));
     }
 
     size_t case_count(const type* type) {
diff --git a/code/compiler/13/binop.cpp b/code/compiler/13/binop.cpp
index 3a5f0ca..f311007 100644
--- a/code/compiler/13/binop.cpp
+++ b/code/compiler/13/binop.cpp
@@ -6,6 +6,9 @@ std::string op_name(binop op) {
         case MINUS: return "-";
         case TIMES: return "*";
         case DIVIDE: return "/";
+        case MODULO: return "%";
+        case EQUALS: return "==";
+        case LESS_EQUALS: return "<=";
     }
     return "??";
 }
@@ -16,6 +19,9 @@ std::string op_action(binop op) {
         case MINUS: return "minus";
         case TIMES: return "times";
         case DIVIDE: return "divide";
+        case MODULO: return "modulo";
+        case EQUALS: return "equals";
+        case LESS_EQUALS: return "less_equals";
     }
     return "??";
 }
diff --git a/code/compiler/13/binop.hpp b/code/compiler/13/binop.hpp
index 8d07858..90b4c89 100644
--- a/code/compiler/13/binop.hpp
+++ b/code/compiler/13/binop.hpp
@@ -5,7 +5,10 @@ enum binop {
     PLUS,
     MINUS,
     TIMES,
-    DIVIDE
+    DIVIDE,
+    MODULO,
+    EQUALS,
+    LESS_EQUALS,
 };
 
 std::string op_name(binop op);
diff --git a/code/compiler/13/instruction.cpp b/code/compiler/13/instruction.cpp
index 80ae40c..afe80aa 100644
--- a/code/compiler/13/instruction.cpp
+++ b/code/compiler/13/instruction.cpp
@@ -153,7 +153,7 @@ void instruction_if::gen_llvm(llvm_context& ctx, llvm::Function* f) const {
     ctx.builder.CreateBr(resume_block);
 
     ctx.builder.SetInsertPoint(zero_block);
-    for(auto& instruction : on_true) {
+    for(auto& instruction : on_false) {
         instruction->gen_llvm(ctx, f);
     }
     ctx.builder.CreateBr(resume_block);
@@ -184,6 +184,9 @@ void instruction_binop::gen_llvm(llvm_context& ctx, Function* f) const {
         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;
+        case MODULO: result = ctx.builder.CreateSRem(left_int, right_int); break;
+        case EQUALS: result = ctx.builder.CreateICmpEQ(left_int, right_int); break;
+        case LESS_EQUALS: result = ctx.builder.CreateICmpSLE(left_int, right_int); break;
     }
     ctx.create_push(f, ctx.create_num(f, result));
 }
diff --git a/code/compiler/13/main.cpp b/code/compiler/13/main.cpp
index aa3bcef..7ad06c0 100644
--- a/code/compiler/13/main.cpp
+++ b/code/compiler/13/main.cpp
@@ -34,10 +34,16 @@ void prelude_types(definition_group& defs, type_env_ptr env) {
     type_ptr binop_type = type_ptr(new type_arr(
                 int_type_app,
                 type_ptr(new type_arr(int_type_app, int_type_app))));
+    type_ptr cmp_type = type_ptr(new type_arr(
+                int_type_app,
+                type_ptr(new type_arr(int_type_app, bool_type_app))));
     env->bind("+", binop_type, visibility::global);
     env->bind("-", binop_type, visibility::global);
     env->bind("*", binop_type, visibility::global);
     env->bind("/", binop_type, visibility::global);
+    env->bind("%", binop_type, visibility::global);
+    env->bind("==", cmp_type, visibility::global);
+    env->bind("<=", cmp_type, visibility::global);
 
     env->bind("True", bool_type_app, visibility::global);
     env->bind("False", bool_type_app, visibility::global);
@@ -146,6 +152,9 @@ void gen_llvm(global_scope& scope) {
     gen_llvm_internal_op(ctx, MINUS);
     gen_llvm_internal_op(ctx, TIMES);
     gen_llvm_internal_op(ctx, DIVIDE);
+    gen_llvm_internal_op(ctx, MODULO);
+    gen_llvm_internal_op(ctx, EQUALS);
+    gen_llvm_internal_op(ctx, LESS_EQUALS);
     gen_llvm_boolean_constructor(ctx, "True", true);
     gen_llvm_boolean_constructor(ctx, "False", false);
 
diff --git a/code/compiler/13/parser.y b/code/compiler/13/parser.y
index 1bf8c48..44c4215 100644
--- a/code/compiler/13/parser.y
+++ b/code/compiler/13/parser.y
@@ -22,6 +22,9 @@ using yyscan_t = void*;
 %token TIMES
 %token MINUS
 %token DIVIDE
+%token MODULO
+%token EQUALS
+%token LESS_EQUALS
 %token <int> INT
 %token DEFN
 %token DATA
@@ -51,7 +54,7 @@ using yyscan_t = void*;
 %type <std::vector<parsed_type_ptr>> typeList
 %type <definition_group> definitions
 %type <parsed_type_ptr> type nonArrowType typeListElement
-%type <ast_ptr> aAdd aMul case let lambda app appBase
+%type <ast_ptr> aEq aAdd aMul case let lambda app appBase
 %type <definition_data_ptr> data 
 %type <definition_defn_ptr> defn
 %type <branch_ptr> branch
@@ -73,7 +76,7 @@ definitions
     ;
 
 defn
-    : DEFN LID lowercaseParams EQUAL OCURLY aAdd CCURLY
+    : DEFN LID lowercaseParams EQUAL OCURLY aEq CCURLY
         { $$ = definition_defn_ptr(
             new definition_defn(std::move($2), std::move($3), std::move($6), @$)); }
     ;
@@ -83,6 +86,12 @@ lowercaseParams
     | lowercaseParams LID { $$ = std::move($1); $$.push_back(std::move($2)); }
     ;
 
+aEq
+    : aAdd EQUALS aAdd { $$ = ast_ptr(new ast_binop(EQUALS, std::move($1), std::move($3), @$)); }
+    | aAdd LESS_EQUALS aAdd { $$ = ast_ptr(new ast_binop(LESS_EQUALS, std::move($1), std::move($3), @$)); }
+    | aAdd { $$ = std::move($1); }
+    ;
+
 aAdd
     : aAdd PLUS aMul { $$ = ast_ptr(new ast_binop(PLUS, std::move($1), std::move($3), @$)); }
     | aAdd MINUS aMul { $$ = ast_ptr(new ast_binop(MINUS, std::move($1), std::move($3), @$)); }
@@ -92,6 +101,7 @@ aAdd
 aMul
     : aMul TIMES app { $$ = ast_ptr(new ast_binop(TIMES, std::move($1), std::move($3), @$)); }
     | aMul DIVIDE app { $$ = ast_ptr(new ast_binop(DIVIDE, std::move($1), std::move($3), @$)); }
+    | aMul MODULO app { $$ = ast_ptr(new ast_binop(MODULO, std::move($1), std::move($3), @$)); }
     | app { $$ = std::move($1); }
     ;
 
@@ -104,7 +114,7 @@ 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); }
+    | OPAREN aEq CPAREN { $$ = std::move($2); }
     | case { $$ = std::move($1); }
     | let { $$ = std::move($1); }
     | lambda { $$ = std::move($1); }
diff --git a/code/compiler/13/scanner.l b/code/compiler/13/scanner.l
index 6f201c5..162643d 100644
--- a/code/compiler/13/scanner.l
+++ b/code/compiler/13/scanner.l
@@ -26,6 +26,9 @@
 \* { return yy::parser::make_TIMES(drv.location); }
 - { return yy::parser::make_MINUS(drv.location); }
 \/ { return yy::parser::make_DIVIDE(drv.location); }
+% { return yy::parser::make_MODULO(drv.location); }
+== { return yy::parser::make_EQUALS(drv.location); }
+\<= { return yy::parser::make_LESS_EQUALS(drv.location); }
 [0-9]+ { return yy::parser::make_INT(atoi(yytext), drv.location); }
 defn { return yy::parser::make_DEFN(drv.location); }
 data { return yy::parser::make_DATA(drv.location); }