diff --git a/packages/boringlang/src/types/trait_checker.ts b/packages/boringlang/src/types/trait_checker.ts
index 581b996..7692d04 100644
--- a/packages/boringlang/src/types/trait_checker.ts
+++ b/packages/boringlang/src/types/trait_checker.ts
@@ -1,29 +1,10 @@
 import { Impl, Module, TraitTypeDeclaration, TypeUsage } from "../parse/ast";
+import { compareTypes } from "./type_system";
 
 interface Context {
   environment: Record<string, TraitTypeDeclaration>;
 }
 
-const compareTypes = (typeA: TypeUsage, typeB: TypeUsage) => {
-  if (typeA.typeUsage !== typeB.typeUsage) {
-    throw Error(`Mismatched types: ${typeA.typeUsage} ${typeB.typeUsage}`);
-  }
-  if (typeA.typeUsage == "NamedTypeUsage" && typeB.typeUsage == "NamedTypeUsage") {
-    if (typeA.name.name !== typeB.name.name) {
-      throw Error(`Mismatched types: ${typeA.name.name} ${typeB.name.name}`);
-    }
-  }
-  if (typeA.typeUsage == "FunctionTypeUsage" && typeB.typeUsage == "FunctionTypeUsage") {
-    if (typeA.arguments.length !== typeB.arguments.length) {
-      throw Error(`Mismatched arg lengths: ${typeA.arguments.length} ${typeB.arguments.length}`);
-    }
-    for (let i = 0; i < typeA.arguments.length; i++) {
-      compareTypes(typeA.arguments[i], typeB.arguments[i]);
-    }
-    compareTypes(typeA.returnType, typeB.returnType);
-  }
-};
-
 export default class TraitChecker {
   withModule = (module: Module) => {
     let ctx: Context = { environment: {} };
diff --git a/packages/boringlang/src/types/type_checker.ts b/packages/boringlang/src/types/type_checker.ts
new file mode 100644
index 0000000..e69de29
diff --git a/packages/boringlang/src/types/type_system.ts b/packages/boringlang/src/types/type_system.ts
new file mode 100644
index 0000000..a405b5a
--- /dev/null
+++ b/packages/boringlang/src/types/type_system.ts
@@ -0,0 +1,165 @@
+import { TypeUsage } from "../parse/ast";
+
+export const compareTypes = (typeA: TypeUsage, typeB: TypeUsage) => {
+  if (typeA.typeUsage !== typeB.typeUsage) {
+    throw Error(`Mismatched types: ${typeA.typeUsage} ${typeB.typeUsage}`);
+  }
+  if (typeA.typeUsage == "NamedTypeUsage" && typeB.typeUsage == "NamedTypeUsage") {
+    if (typeA.name.name !== typeB.name.name) {
+      throw Error(`Mismatched types: ${typeA.name.name} ${typeB.name.name}`);
+    }
+  }
+  if (typeA.typeUsage == "FunctionTypeUsage" && typeB.typeUsage == "FunctionTypeUsage") {
+    if (typeA.arguments.length !== typeB.arguments.length) {
+      throw Error(`Mismatched arg lengths: ${typeA.arguments.length} ${typeB.arguments.length}`);
+    }
+    for (let i = 0; i < typeA.arguments.length; i++) {
+      compareTypes(typeA.arguments[i], typeB.arguments[i]);
+    }
+    compareTypes(typeA.returnType, typeB.returnType);
+  }
+};
+
+interface Equals {
+  operation: "equals";
+}
+
+interface Argument {
+  operation: "argument";
+  argNum: number;
+}
+
+interface ReturnValue {
+  operation: "return";
+}
+
+interface Comparison {
+  left: TypeUsage;
+  operation: Equals | Argument | ReturnValue;
+  right: TypeUsage;
+}
+
+class TypeSystem {
+  comparisons: Comparison[];
+  result: Record<string, TypeUsage>;
+
+  constructor() {
+    this.comparisons = [];
+    this.result = {};
+  }
+
+  compare = (comparison: Comparison) => {
+    this.comparisons.push(comparison);
+  };
+
+  solve = () => {
+    let foundUpdate = false;
+    let containsUnknown = false;
+    while (true) {
+      for (const comparison of this.comparisons) {
+        // if already found, just update
+        if (comparison.left.typeUsage === "UnknownTypeUsage" && this.result[comparison.left.name]) {
+          foundUpdate = true;
+          comparison.left = this.result[comparison.left.name];
+        }
+        if (
+          comparison.right.typeUsage === "UnknownTypeUsage" &&
+          this.result[comparison.right.name]
+        ) {
+          foundUpdate = true;
+          comparison.right = this.result[comparison.right.name];
+        }
+        // equals
+        if (comparison.operation.operation === "equals") {
+          // solve left
+          if (
+            comparison.left.typeUsage === "UnknownTypeUsage" &&
+            comparison.right.typeUsage !== "UnknownTypeUsage"
+          ) {
+            foundUpdate = true;
+            this.result[comparison.left.name] = comparison.right;
+            comparison.left = comparison.right;
+          }
+          // solve right
+          if (
+            comparison.left.typeUsage !== "UnknownTypeUsage" &&
+            comparison.right.typeUsage === "UnknownTypeUsage"
+          ) {
+            foundUpdate = true;
+            this.result[comparison.right.name] = comparison.left;
+            comparison.right = comparison.left;
+          }
+          if (
+            comparison.left.typeUsage !== "UnknownTypeUsage" &&
+            comparison.right.typeUsage !== "UnknownTypeUsage"
+          ) {
+            compareTypes(comparison.left, comparison.right);
+          }
+        }
+        // argument
+        if (comparison.operation.operation === "argument") {
+          if (comparison.left.typeUsage !== "FunctionTypeUsage") {
+            throw Error("Argument for something that isn't a function");
+          }
+          // solve left
+          const argument = comparison.left.arguments[comparison.operation.argNum];
+          if (
+            argument.typeUsage === "UnknownTypeUsage" &&
+            comparison.right.typeUsage !== "UnknownTypeUsage"
+          ) {
+            foundUpdate = true;
+            this.result[argument.name] = comparison.right;
+            comparison.left.arguments[comparison.operation.argNum] = comparison.right;
+          }
+          // solve right
+          if (
+            argument.typeUsage !== "UnknownTypeUsage" &&
+            comparison.right.typeUsage === "UnknownTypeUsage"
+          ) {
+            foundUpdate = true;
+            this.result[comparison.right.name] =
+              comparison.left.arguments[comparison.operation.argNum];
+            comparison.right = comparison.left.arguments[comparison.operation.argNum];
+          }
+        }
+        // return type
+        if (comparison.operation.operation === "return") {
+          if (comparison.left.typeUsage !== "FunctionTypeUsage") {
+            throw Error("return type for something that isn't a function");
+          }
+          // solve left
+          if (
+            comparison.left.returnType.typeUsage === "UnknownTypeUsage" &&
+            comparison.right.typeUsage !== "UnknownTypeUsage"
+          ) {
+            foundUpdate = true;
+            this.result[comparison.left.returnType.name] = comparison.right;
+            comparison.left.returnType = comparison.right;
+          }
+          // solve right
+          if (
+            comparison.left.returnType.typeUsage !== "UnknownTypeUsage" &&
+            comparison.right.typeUsage === "UnknownTypeUsage"
+          ) {
+            foundUpdate = true;
+            this.result[comparison.right.name] = comparison.left.returnType;
+            comparison.right = comparison.left.returnType;
+          }
+        }
+        if (
+          comparison.left.typeUsage === "UnknownTypeUsage" ||
+          comparison.right.typeUsage === "UnknownTypeUsage"
+        ) {
+          containsUnknown = true;
+        }
+      }
+      if (!foundUpdate && containsUnknown) {
+        throw Error("Type system failed to resolve all unknowns");
+      }
+      if (!foundUpdate) {
+        break;
+      }
+    }
+    return this.result;
+  };
+}