did some work on conversion

lib/Convert.ml

@@ -0,0 +1,38 @@
+module V = Value
+module E = Eval
+
+exception Unequal (* todo, better exception *)
+
+let rec conv_tp (len : int) (v1 : V.value) (v2 : V.value) =
+  match v1, v2 with
+  | Type,                Type                    -> ()
+  | T0,                  T0                      -> ()
+  | T1,                  T1                      -> ()
+  | TNat,                TNat                    -> ()
+  | TBool,               TBool                   -> ()
+  | Pi (a1, C (env1, b1)), Pi (a2, C (env2, b2)) (* fallthrough *)
+  | Sg (a1, C (env1, b1)), Sg (a2, C (env2, b2)) -> 
+      conv_tp len a1 a2;
+      let fresh = V.Stuck (V.Var (V.Lvl len), a1) in
+      conv_tp (len+1) (E.eval (fresh :: env1) b1) (E.eval (fresh :: env2) b2)
+  | Stuck (s1, Type), Stuck (s2, Type)           -> conv_stuck len s1 s2
+  | _ -> raise Unequal
+
+and conv_tr (len : int) (ty : V.value) (v1 : V.value) (v2 : V.value) =
+  match ty with
+  | Type -> conv_tp len v1 v2
+  | T1                 -> () (* unit η-law, this still requires evaluation :/ *)
+  | Pi (a, C (env, b)) ->
+      let fresh = V.Stuck (V.Var (V.Lvl len), a) in
+      conv_tr (len+1) (E.eval (fresh :: env) b) (E.app v1 a) (E.app v2 a)
+  | Sg (a, C (env, b)) ->
+      let f1 = E.fst v1 in
+      conv_tr len a                      f1         (E.fst v2);
+      conv_tr len (E.eval (f1 :: env) b) (E.snd v1) (E.snd v2)
+  | _ ->
+      begin match v1, v2 with
+      | _ -> failwith "todo"
+      end
+
+and conv_stuck (len : int) (s1 : V.stuck) (s2 : V.stuck) =
+  failwith "todo"

lib/Eval.ml

@@ -49,10 +49,23 @@ and indN (env : V.env) (b : T.term) (tz : V.value) (ts : T.term) (n : V.value) =
   | _               -> failwith "eval IndN impossible error"
 
 and app (f : V.value) (x : V.value) =
-  failwith "todo"
+  match f with
+  | Lam (C (env, tr)) -> eval (x :: env) tr
+  | Stuck (s, t)      -> begin
+    match t with
+    | Pi (_, C (env, tr)) -> V.Stuck (V.App (s, x, t), eval (x :: env) tr)
+    | _                   -> failwith "eval app stuck f not of pi type"
+    end
+  | _                 -> failwith "eval app impossible error"
 
 and fst (p : V.value) =
-  failwith "todo"
+  match p with
+  | Pair  (a, _) -> a
+  | Stuck (s, Sg (a, _)) -> V.Stuck (V.Fst s, a)
+  | _            -> failwith "eval fst impossible error"
 
 and snd (p : V.value) =
-  failwith "todo"
+  match p with
+  | Pair  (_, b) -> b
+  | Stuck (s, Sg (_, C (env, b))) -> V.Stuck (V.Snd s, (eval (fst p :: env) b))
+  | _            -> failwith "eval fst impossible error"