feat(wpcarro/scratch): Implement "Algorithm W"

I've been wanting to grok Haskell-style type inference for awhile, so instead of
just watching conference talks and reading papers about it, I've decided to
attempt to implement it to more readily test my understanding of it.

Change-Id: I69261202a3d74d55c6e38763d7ddfec73c392465
Reviewed-on: https://cl.tvl.fyi/c/depot/+/6988
Tested-by: BuildkiteCI
Reviewed-by: wpcarro <wpcarro@gmail.com>
Autosubmit: wpcarro <wpcarro@gmail.com>

users/wpcarro/scratch/compiler/tests.ml

@@ -0,0 +1,43 @@
+open Expr_parser
+open Type_parser
+open Inference
+
+type test = { input : string; expect : string; }
+(* type sub_test = { s1 : string; s2 : string; s3 : string } *)
+
+let ( let* ) = Option.bind
+
+let tests = [
+    { input = "((fn x x) 10)"; expect = "Integer"; };
+    { input = "(let f (fn x x) f)"; expect = "a -> a"; };
+]
+
+(* let sub_tests = [ *)
+(*     { *)
+(*       s1 = "{b |-> b -> Int}"; *)
+(*       s2 = "{a: Bool, b: Int, c: Bool}"; *)
+(*       s3 = "{a: Bool, b: Int -> Int, c: Bool}"; *)
+(*     } *)
+(* ] *)
+
+exception FailedAssertion
+exception TestError
+
+let main =
+  tests
+  |> List.iter (fun { input; expect } ->
+         Printf.sprintf ":t %s == %s\n" input expect |> print_string;
+         match (parse_language input, parse_input expect) with
+         | Some ast, Some expected ->
+            (match do_infer ast with
+             | Some actual ->
+                if actual != expected then
+                  begin
+                    print_type actual;
+                    raise FailedAssertion
+                  end
+                else
+                  print_string "Test passed.\n"
+             | _ -> raise TestError)
+         | _ -> raise TestError);
+  print_string "All tests pass!"