haskell: let-polymorphism tests — id/const/nested/twice at multiple types (+6 tests, 476/476)

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

lib/haskell/tests/infer.sx

@@ -134,4 +134,16 @@
 (hk-test "infer-prog double" (nth (nth results3 0) 2)     "Int -> Int")
 (hk-test "infer-prog twice"  (nth (nth results3 1) 2)     "(t3 -> t3) -> t3 -> t3")
 
+(hk-t "let id x = x in id 1" "Int")
+
+(hk-t "let id x = x in id True" "Bool")
+
+(hk-t "let id x = x in (id 1, id True)" "(Int, Bool)")
+
+(hk-t "let const x y = x in (const 1 True, const True 1)" "(Int, Bool)")
+
+(hk-t "let f x = x in let g y = f y in (g 1, g True)" "(Int, Bool)")
+
+(hk-t "let twice f x = f (f x) in twice (\x -> x + 1) 5" "Int")
+
 {:fails hk-test-fails :pass hk-test-pass :fail hk-test-fail}

plans/haskell-on-sx.md

@@ -95,7 +95,7 @@ Key mappings:
 - [x] Report type errors with meaningful positions
 - [x] Reject untypeable programs that phase 3 was accepting
 - [x] Type-sig checking: user writes `f :: Int -> Int`; verify
-- [ ] Let-polymorphism
+- [x] Let-polymorphism
 - [ ] Unit tests: inference for 50+ expressions
 
 ### Phase 5 — typeclasses (dictionary passing)
@@ -114,6 +114,14 @@ Key mappings:
 
 _Newest first._
 
+- **2026-05-05** — Phase 4 let-polymorphism tests. `hk-w-let` already
+  generalises let-bound types with `hk-generalise` before adding them to the
+  env, so `id :: ∀a. a→a` is instantiated independently at each use site.
+  6 new tests in `tests/infer.sx`: identity at Int and Bool separately, identity
+  tuple `(id 1, id True) → (Int, Bool)`, `const` at two types, nested let with
+  `f`/`g` sharing the polymorphic binding, and `twice` applied to an arithmetic
+  lambda. All use the 2-arg `hk-t` form. 476/476 green.
+
 - **2026-05-05** — Phase 4 type-sig checking. `hk-ast-type` converts parsed type
   AST nodes (`t-con`/`t-var`/`t-fun`/`t-app`/`t-list`/`t-tuple`) to internal
   type values. `hk-collect-tvars` gathers free type variable names. `hk-check-sig`