New OCaml exercise.

ocaml/EvalCBVExercise.ml

@@ -0,0 +1,71 @@
+(* -------------------------------------------------------------------------- *)
+
+(* The type of lambda-terms, in de Bruijn's representation. *)
+
+type var = int (* a de Bruijn index *)
+type term =
+  | Var of var
+  | Lam of (* bind: *) term
+  | App of term * term
+  | Let of (* bind: *) term * term
+
+(* -------------------------------------------------------------------------- *)
+
+(* An environment-based big-step interpreter. This is the same interpreter
+   that we programmed in Coq, except here, in OCaml, fuel is not needed. *)
+
+type cvalue =
+  | Clo of (* bind: *) term * cenv
+
+and cenv =
+  cvalue list
+
+let empty : cenv =
+  []
+
+exception RuntimeError
+
+let lookup (e : cenv) (x : var) : cvalue =
+  try
+    List.nth e x
+  with Failure _ ->
+    raise RuntimeError
+
+let rec eval (e : cenv) (t : term) : cvalue =
+  match t with
+  | Var x ->
+      lookup e x
+  | Lam t ->
+      Clo (t, e)
+  | App (t1, t2) ->
+      let cv1 = eval e t1 in
+      let cv2 = eval e t2 in
+      let Clo (u1, e') = cv1 in
+      eval (cv2 :: e') u1
+  | Let (t1, t2) ->
+      eval (eval e t1 :: e) t2
+
+(* -------------------------------------------------------------------------- *)
+
+(* The CPS-transformed interpreter. *)
+
+let rec evalk (e : cenv) (t : term) (k : cvalue -> 'a) : 'a =
+  assert false
+
+let eval (e : cenv) (t : term) : cvalue =
+  evalk e t (fun cv -> cv)
+
+(* -------------------------------------------------------------------------- *)
+
+(* The CPS-transformed, defunctionalized interpreter. *)
+
+type kont
+
+let rec evalkd (e : cenv) (t : term) (k : kont) : cvalue =
+  assert false
+
+and apply (k : kont) (cv : cvalue) : cvalue =
+  assert false
+
+let eval e t =
+  evalkd e t (assert false)