diff --git a/src/front/check.ts b/src/front/check.ts
index 0246e6d..5c1c151 100644
--- a/src/front/check.ts
+++ b/src/front/check.ts
@@ -94,7 +94,7 @@ class CheckerCx {
     }
 
     assertCompatible(left: Ty, right: Ty, loc: Loc): void {
-        if (!left.compatibleWith(right)) {
+        if (!left.resolvableWith(right)) {
             this.error(
                 loc,
                 `type '${left.pretty()}' not compatible with type '${right.pretty()}'`,
@@ -122,7 +122,7 @@ class StmtChecker {
                     const ty = node.kind.expr
                         ? this.cx.expr(node.kind.expr)
                         : Ty.Void;
-                    if (!ty.compatibleWith(retTy)) {
+                    if (!ty.resolvableWith(retTy)) {
                         this.cx.error(
                             node.loc,
                             `type '${ty.pretty()}' not compatible with return type '${retTy.pretty()}'`,
@@ -292,13 +292,13 @@ class ExprChecker {
         const argTy = this.cx.expr(node.kind.arg);
         if (
             (exprTy.is("Array") || exprTy.is("Slice")) &&
-            argTy.compatibleWith(Ty.I32)
+            argTy.resolvableWith(Ty.I32)
         ) {
             return exprTy.kind.ty;
         }
         if (
             (exprTy.is("Array") || exprTy.is("Slice")) &&
-            argTy.compatibleWith(Ty.create("Range", {}))
+            argTy.resolvableWith(Ty.create("Range", {}))
         ) {
             return Ty.create("Slice", { ty: exprTy.kind.ty });
         }
@@ -345,7 +345,7 @@ class ExprChecker {
             );
         }
         for (const i of args.keys()) {
-            if (!args[i].compatibleWith(params[i])) {
+            if (!args[i].resolvableWith(params[i])) {
                 this.reportArgTypeNotCompatible(
                     node,
                     args,
@@ -404,10 +404,10 @@ class ExprChecker {
 
     private checkUnaryExpr(node: ast.NodeWithKind<"UnaryExpr">): Ty {
         const exprTy = this.cx.expr(node.kind.expr);
-        if (node.kind.op === "Neg" && exprTy.compatibleWith(Ty.I32)) {
+        if (node.kind.op === "Neg" && exprTy.resolvableWith(Ty.I32)) {
             return Ty.I32;
         }
-        if (node.kind.op === "Not" && exprTy.compatibleWith(Ty.Bool)) {
+        if (node.kind.op === "Not" && exprTy.resolvableWith(Ty.Bool)) {
             return Ty.Bool;
         }
         if (node.kind.op === "Ref") {
@@ -455,7 +455,7 @@ class ExprChecker {
     private checkRangeExpr(node: ast.NodeWithKind<"RangeExpr">): Ty {
         for (const operandExpr of [node.kind.begin, node.kind.end]) {
             const operandTy = operandExpr && this.cx.expr(operandExpr);
-            if (operandTy && !operandTy.compatibleWith(Ty.I32)) {
+            if (operandTy && !operandTy.resolvableWith(Ty.I32)) {
                 this.cx.error(
                     operandExpr.loc,
                     `range operand must be '${Ty.I32.pretty()}', not '${operandTy.pretty()}'`,
@@ -567,7 +567,7 @@ class TyChecker {
         if (node.is("ArrayTy")) {
             const ty = this.cx.ty(node.kind.ty);
             const lengthTy = this.cx.expr(node.kind.length);
-            if (!lengthTy.compatibleWith(Ty.I32)) {
+            if (!lengthTy.resolvableWith(Ty.I32)) {
                 this.cx.error(
                     node.kind.length.loc,
                     `for array length, expected 'int', got '${lengthTy.pretty()}'`,
@@ -606,7 +606,7 @@ const binaryOpTests: BinaryOpTest[] = [
             "Rem",
         ];
         if (
-            ops.includes(op) && left.is("Int") && left.compatibleWith(right)
+            ops.includes(op) && left.is("Int") && left.resolvableWith(right)
         ) {
             return left;
         }
@@ -615,7 +615,7 @@ const binaryOpTests: BinaryOpTest[] = [
     (op, left, right) => {
         const ops: ast.BinaryOp[] = ["Eq", "Ne", "Lt", "Gt", "Lte", "Gte"];
         if (
-            ops.includes(op) && left.is("Int") && left.compatibleWith(right)
+            ops.includes(op) && left.is("Int") && left.resolvableWith(right)
         ) {
             return Ty.Bool;
         }
diff --git a/src/front/check2.ts b/src/front/check2.ts
index 77c384a..2cbe3d7 100644
--- a/src/front/check2.ts
+++ b/src/front/check2.ts
@@ -1,32 +1,195 @@
 import { Syms } from "./resolve.ts";
 import * as ast from "../ast.ts";
 import { Ty } from "../ty.ts";
+import { FileReporter, Loc } from "../diagnostics.ts";
 
-export function checkFn(fn: ast.FnStmt, syms: Syms) {
+export function checkFn(
+    fn: ast.FnStmt,
+    syms: Syms,
+    reporter: FileReporter,
+): CheckedFn {
+    return new TypeChecker(fn, syms, reporter).check();
 }
 
-export class FnTys {
+export class CheckedFn {
     constructor(
+        private fnTy: Ty,
         private nodeTys: Map<ast.Node, Ty>,
     ) {}
 
-    get(node: ast.Node): Ty {
-        const ty = this.nodeTys.get(node);
+    ty(): Ty {
+        return this.fnTy;
+    }
+
+    exprTy(expr: ast.Node): Ty {
+        const ty = this.nodeTys.get(expr);
         if (ty === undefined) {
-            throw new Error(`no type for '${node.kind.tag}'`);
+            throw new Error(`no type for '${expr.kind.tag}'`);
         }
         return ty;
     }
 }
 
-class FnChecker {
+class TypeChecker {
     private nodeTys = new Map<ast.Node, Ty>();
 
     constructor(
         private fn: ast.FnStmt,
         private syms: Syms,
+        private reporter: FileReporter,
     ) {}
 
-    check() {
+    check(): CheckedFn {
+        const params = this.fn.kind.params
+            .map((node) => {
+                const param = node.as("Param");
+                if (!param.kind.ty) {
+                    this.reporter
+                        .error(param.loc, `parameter must have a type`);
+                    this.reporter.abort();
+                }
+                return this.ty(param.kind.ty);
+            });
+
+        const retTy = this.fn.kind.retTy
+            ? this.ty(this.fn.kind.retTy)
+            : Ty.Void;
+
+        this.fn.kind.body.visit({
+            visit: (node) => {
+                if (!node.is("ReturnStmt")) {
+                    return;
+                }
+                const ty = node.kind.expr
+                    ? this.expr(node.kind.expr, retTy)
+                    : Ty.Void;
+                if (!ty.resolvableWith(retTy)) {
+                    this.reporter.error(
+                        node.loc,
+                        `type '${ty.pretty()}' not compatible with return type '${retTy.pretty()}'`,
+                    );
+                    this.reporter.info(
+                        this.fn.kind.retTy?.loc ?? this.fn.loc,
+                        `return type '${retTy}' defined here`,
+                    );
+                    this.reporter.abort();
+                }
+            },
+        });
+
+        const ty = Ty.create("FnStmt", {
+            stmt: this.fn,
+            ty: Ty.create("Fn", { params, retTy }),
+        });
+
+        return new CheckedFn(ty, this.nodeTys);
+    }
+
+    private expr(expr: ast.Node, expected: Ty): Ty {
+        return this.cachedCheck(expr, () => this.checkExpr(expr, expected));
+    }
+
+    private checkExpr(expr: ast.Node, expected: Ty): Ty {
+        const k = expr.kind;
+        switch (k.tag) {
+            case "Error":
+            case "File":
+            case "Block":
+            case "ExprStmt":
+            case "AssignStmt":
+            case "FnStmt":
+            case "ReturnStmt":
+            case "LetStmt":
+            case "IfStmt":
+            case "WhileStmt":
+            case "BreakStmt":
+            case "Param":
+            case "IdentTy":
+            case "PtrTy":
+            case "PtrMutTy":
+            case "ArrayTy":
+            case "SliceTy":
+                throw new Error(`node '${k.tag}' not an expression`);
+            case "IdentExpr": {
+                throw new Error("not implemented");
+            }
+            case "IntExpr": {
+                return this.resolve(Ty.AnyInt, expected, expr.loc).ty;
+            }
+            case "StrExpr": {
+                return this.resolve(
+                    Ty.Ptr(Ty.Slice(Ty.U8)),
+                    expected,
+                    expr.loc,
+                ).ty;
+            }
+            case "ArrayExpr": {
+                if (k.values.length === 0) {
+                    if (expected.is("Any")) {
+                        return Ty.Array(Ty.Any, 0);
+                    } else {
+                        return this.resolve(
+                            Ty.Array(Ty.Any, 0),
+                            expected,
+                            expr.loc,
+                        ).ty;
+                    }
+                }
+
+                throw new Error("not implemented");
+            }
+            case "IndexExpr": {
+                throw new Error("not implemented");
+            }
+            case "CallExpr": {
+                throw new Error("not implemented");
+            }
+            case "UnaryExpr": {
+                throw new Error("not implemented");
+            }
+            case "BinaryExpr": {
+                throw new Error("not implemented");
+            }
+            case "RangeExpr": {
+                throw new Error("not implemented");
+            }
+            default:
+                k satisfies never;
+                throw new Error();
+        }
+    }
+
+    private ty(ty: ast.Node): Ty {
+        return this.cachedCheck(ty, () => this.checkTy(ty));
+    }
+
+    private checkTy(ty: ast.Node): Ty {
+        throw new Error("not implemented");
+    }
+
+    private cachedCheck(node: ast.Node, func: () => Ty) {
+        const existing = this.nodeTys.get(node);
+        if (existing !== undefined) {
+            return existing;
+        }
+        const ty = func();
+        this.nodeTys.set(node, ty);
+        return ty;
+    }
+
+    private resolve(ty: Ty, expected: Ty, loc: Loc): TyRes {
+        if (!ty.resolvableWith(expected)) {
+            this.reporter.error(
+                loc,
+                `expected type '${expected.pretty()}', got '${ty.pretty()}'`,
+            );
+            this.reporter.abort();
+        }
+        throw new Error("not implemented");
     }
 }
+
+type TyRes = {
+    ty: Ty;
+    rewriteSubtree: boolean;
+};
diff --git a/src/middle.ts b/src/middle.ts
index 410a472..7339bf0 100644
--- a/src/middle.ts
+++ b/src/middle.ts
@@ -346,16 +346,16 @@ class FnLowerer {
         const operandTy = this.tys.expr(expr.kind.expr);
         if (
             expr.kind.op === "Neg" &&
-            operandTy.compatibleWith(Ty.I32) &&
-            resultTy.compatibleWith(Ty.I32)
+            operandTy.resolvableWith(Ty.I32) &&
+            resultTy.resolvableWith(Ty.I32)
         ) {
             const operand = this.lowerExpr(expr.kind.expr);
             return this.pushInst(Ty.I32, "Negate", { source: operand });
         }
         if (
             expr.kind.op === "Not" &&
-            operandTy.compatibleWith(Ty.Bool) &&
-            resultTy.compatibleWith(Ty.Bool)
+            operandTy.resolvableWith(Ty.Bool) &&
+            resultTy.resolvableWith(Ty.Bool)
         ) {
             const operand = this.lowerExpr(expr.kind.expr);
             return this.pushInst(Ty.Bool, "Not", { source: operand });
@@ -428,8 +428,8 @@ const binaryOpTests: BinaryOpTest[] = [
         if (
             ops.includes(op) &&
             left.is("Int") &&
-            left.compatibleWith(right) &&
-            result.compatibleWith(left)
+            left.resolvableWith(right) &&
+            result.resolvableWith(left)
         ) {
             return op as BinaryOp;
         }
@@ -440,7 +440,7 @@ const binaryOpTests: BinaryOpTest[] = [
         if (
             ops.includes(op) &&
             left.is("Int") &&
-            left.compatibleWith(right) &&
+            left.resolvableWith(right) &&
             result.is("Bool")
         ) {
             return op as BinaryOp;
diff --git a/src/ty.ts b/src/ty.ts
index bec9a77..f406c28 100644
--- a/src/ty.ts
+++ b/src/ty.ts
@@ -24,7 +24,6 @@ export class Ty {
 
     static Error = Ty.create("Error", {});
     static Void = Ty.create("Void", {});
-    static IntLiteral = Ty.create("IntLiteral", {});
     static I8 = Ty.create("Int", { intTy: "i8" });
     static I16 = Ty.create("Int", { intTy: "i16" });
     static I32 = Ty.create("Int", { intTy: "i32" });
@@ -37,6 +36,24 @@ export class Ty {
     static USize = Ty.create("Int", { intTy: "usize" });
     static Bool = Ty.create("Bool", {});
 
+    static Ptr(ty: Ty): Ty {
+        return this.create("Ptr", { ty });
+    }
+    static PtrMut(ty: Ty): Ty {
+        return this.create("PtrMut", { ty });
+    }
+    static Slice(ty: Ty): Ty {
+        return this.create("Slice", { ty });
+    }
+    static Array(ty: Ty, length: number): Ty {
+        return this.create("Array", { ty, length });
+    }
+
+    /** Only used in type checker. */
+    static Any = Ty.create("Any", {});
+    /** Only used in type checker. */
+    static AnyInt = Ty.create("AnyInt", {});
+
     private internHash(): string {
         return JSON.stringify(this.kind);
     }
@@ -52,7 +69,28 @@ export class Ty {
         return this.kind.tag === tag;
     }
 
-    compatibleWith(other: Ty): boolean {
+    assertIs<
+        Tag extends TyKind["tag"],
+    >(tag: Tag): asserts this is Ty & { kind: { tag: Tag } } {
+        if (this.kind.tag !== tag) {
+            throw new Error(`ty is not '${tag}'`);
+        }
+    }
+
+    as<
+        Tag extends TyKind["tag"],
+    >(tag: Tag): Ty & { kind: { tag: Tag } } {
+        this.assertIs(tag);
+        return this;
+    }
+
+    /**
+     * Used for checking and inference in the type checker
+     * to say if two types are able to implicitly be converted
+     * into each other or to a third type. Past type inference
+     * this function is meaningless.
+     */
+    resolvableWith(other: Ty): boolean {
         // types are interned--we can just do this
         if (this === other) {
             return true;
@@ -64,10 +102,6 @@ export class Ty {
         if (this.is("Void")) {
             return other.is("Void");
         }
-        if (this.is("IntLiteral")) {
-            // return other.is("Int") || other.is("UInt");
-            return false;
-        }
         if (this.is("Int")) {
             return other.is("Int") && this.kind.intTy == other.kind.intTy;
         }
@@ -79,7 +113,7 @@ export class Ty {
             if (!other.is("Ptr")) {
                 return false;
             }
-            if (!this.kind.ty.compatibleWith(other.kind.ty)) {
+            if (!this.kind.ty.resolvableWith(other.kind.ty)) {
                 return false;
             }
             return true;
@@ -88,7 +122,7 @@ export class Ty {
             if (!other.is("Array")) {
                 return false;
             }
-            if (!this.kind.ty.compatibleWith(other.kind.ty)) {
+            if (!this.kind.ty.resolvableWith(other.kind.ty)) {
                 return false;
             }
             if (this.kind.length !== other.kind.length) {
@@ -100,7 +134,7 @@ export class Ty {
             if (!other.is("Slice")) {
                 return false;
             }
-            if (!this.kind.ty.compatibleWith(other.kind.ty)) {
+            if (!this.kind.ty.resolvableWith(other.kind.ty)) {
                 return false;
             }
             return true;
@@ -113,28 +147,26 @@ export class Ty {
                 return false;
             }
             for (const i of this.kind.params.keys()) {
-                if (!this.kind.params[i].compatibleWith(other.kind.params[i])) {
+                if (!this.kind.params[i].resolvableWith(other.kind.params[i])) {
                     return false;
                 }
             }
-            if (!this.kind.retTy.compatibleWith(other.kind.retTy)) {
+            if (!this.kind.retTy.resolvableWith(other.kind.retTy)) {
                 return false;
             }
             return true;
         }
         if (this.is("FnStmt")) {
-            if (!other.is("FnStmt")) {
-                return false;
-            }
-            if (!this.kind.ty.compatibleWith(other.kind.ty)) {
-                return false;
-            }
-            // redundant; sanity check
-            if (this.kind.stmt.id !== other.kind.stmt.id) {
-                throw new Error();
-            }
+            // Since FnStmt tys are only compatible with itself,
+            // we can count on the ty cache for this check.
+            return false;
+        }
+        if (this.is("Any")) {
             return true;
         }
+        if (this.is("AnyInt")) {
+            return other.is("Int");
+        }
         throw new Error(`'${this.kind.tag}' not handled`);
     }
 
@@ -145,6 +177,15 @@ export class Ty {
         return true;
     }
 
+    innerFn(): Ty & { kind: { tag: "Fn" } } {
+        this.assertIs("FnStmt");
+        return this.kind.ty.as("Fn");
+    }
+
+    isCheckerInternal(): boolean {
+        return this.is("Any") || this.is("AnyInt");
+    }
+
     pretty(colors?: stringify.PrettyColors): string {
         return stringify.tyPretty(this, colors);
     }
@@ -153,7 +194,6 @@ export class Ty {
 export type TyKind =
     | { tag: "Error" }
     | { tag: "Void" }
-    | { tag: "IntLiteral" }
     | { tag: "Int"; intTy: ast.IntTy }
     | { tag: "Bool" }
     | { tag: "Ptr"; ty: Ty }
@@ -162,4 +202,5 @@ export type TyKind =
     | { tag: "Slice"; ty: Ty }
     | { tag: "Range" }
     | { tag: "Fn"; params: Ty[]; retTy: Ty }
-    | { tag: "FnStmt"; ty: Ty; stmt: ast.NodeWithKind<"FnStmt"> };
+    | { tag: "FnStmt"; ty: Ty; stmt: ast.NodeWithKind<"FnStmt"> }
+    | { tag: "Any" | "AnyInt" };