From: acondolu <andrea.condoluci@unibo.it>
Date: Thu, 14 Jun 2018 21:16:14 +0000 (+0200)
Subject: Improved flag for A, removed flag from L
X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=commitdiff_plain;h=dc6b7a6afe8b1fcf4f5998089ed2ef28f255da0a;p=fireball-separation.git

Improved flag for A, removed flag from L
---

diff --git a/ocaml/simple.ml b/ocaml/simple.ml
index b640a0f..45e605b 100644
--- a/ocaml/simple.ml
+++ b/ocaml/simple.ml
@@ -6,11 +6,19 @@ let print_hline = Console.print_hline;;
 
 open Pure
 
+type var_flag = [
+ `Inherit | `Some of bool ref
+ (* bool:
+     true if original application and may determine a distinction
+  *)
+  | `Duplicate
+] ;;
+
 type var = int;;
 type t =
  | V of var
- | A of (bool ref) * t * t
- | L of (bool * t)
+ | A of var_flag * t * t
+ | L of t
 ;;
 
 let measure_of_t =
@@ -19,8 +27,10 @@ let measure_of_t =
  | A(b,t1,t2) ->
    let acc, m1 = aux acc t1 in
    let acc, m2 = aux acc t2 in
-   if not (List.memq b acc) && !b then b::acc, 1 + m1 + m2 else acc, m1 + m2
- | L(b,t) -> if b then aux acc t else acc, 0
+   (match b with
+   | `Some b when !b && not (List.memq b acc) -> b::acc, 1 + m1 + m2
+   | _ -> acc, m1 + m2)
+ | L t -> aux acc t
  in snd ++ (aux [])
 ;;
 
@@ -46,6 +56,12 @@ let sep_of_app =
          List.length !apps
     in " " ^ string_of_int i ^ ":"
 ;;
+let string_of_var_flag = function
+ | `Some b -> sep_of_app b
+ | `Inherit -> " ?"
+ | `Duplicate -> " !"
+ ;;
+
 
 let string_of_t =
   let string_of_bvar =
@@ -58,19 +74,19 @@ let string_of_t =
     | A _
     | L _ as t -> "(" ^ string_of_term_no_pars level t ^ ")"
   and string_of_term_no_pars_app level = function
-    | A(b,t1,t2) -> string_of_term_no_pars_app level t1 ^ sep_of_app b ^ string_of_term_w_pars level t2
+    | A(b,t1,t2) -> string_of_term_no_pars_app level t1 ^ string_of_var_flag b ^ string_of_term_w_pars level t2
     | _ as t -> string_of_term_w_pars level t
   and string_of_term_no_pars level = function
-    | L(_,t) -> "λ" ^ string_of_bvar level ^ ". " ^ string_of_term_no_pars (level+1) t
+    | L t -> "λ" ^ string_of_bvar level ^ ". " ^ string_of_term_no_pars (level+1) t
     | _ as t -> string_of_term_no_pars_app level t
   in string_of_term_no_pars 0
 ;;
 
 
-let delta = L(true,A(ref true,V 0, V 0));;
+let delta = L(A(`Some (ref true),V 0, V 0));;
 
 (* does NOT lift the argument *)
-let mk_lams = fold_nat (fun x _ -> L(false,x)) ;;
+let mk_lams = fold_nat (fun x _ -> L x) ;;
 
 type problem = {
    orig_freshno: int
@@ -123,48 +139,62 @@ let rec get_inert = function
 (* precomputes the number of leading lambdas in a term,
    after replacing _v_ w/ a term starting with n lambdas *)
 let rec no_leading_lambdas v n = function
- | L(_,t) -> 1 + no_leading_lambdas (v+1) n t
+ | L t -> 1 + no_leading_lambdas (v+1) n t
  | A _ as t -> let v', m = get_inert t in if v = v' then max 0 (n - m) else 0
  | V v' -> if v = v' then n else 0
 ;;
 
-(* b' is true iff we are substituting the argument of a step
-   and the application of the redex was true. Therefore we need to
-   set the new app to true.  *)
-let rec subst b' level delift sub =
+let rec erase = function
+ | L t -> L (erase t)
+ | A(_,t1,t2) -> A(`Some(ref false), erase t1, erase t2)
+ | V _ as t -> t
+;;
+
+let rec subst top level delift ((flag, var, tm) as sub) =
  function
- | V v -> if v = level + fst sub then lift level (snd sub) else V (if delift && v > level then v-1 else v)
- | L(b,t) -> L(b, subst b' (level + 1) delift sub t)
- | A(_,t1,(V v as t2)) when b' && v = level + fst sub ->
-    mk_app (ref true) (subst b' level delift sub t1) (subst b' level delift sub t2)
+ | V v -> if v = level + var then lift level tm else V (if delift && v > level then v-1 else v)
+ | L t -> L (subst top (level + 1) delift sub t)
  | A(b,t1,t2) ->
-    mk_app b (subst b' level delift sub t1) (subst b' level delift sub t2)
-(* b is
-   - a fresh ref true if we want to create a real application from scratch
-   - a shared ref true if we substituting in the head of a real application *)
-and mk_app b' t1 t2 = if t1 = delta && t2 = delta then raise B
+    let special = b = `Duplicate && top && t2 = V (level + var) in
+    let t1' = subst (if special then false else top) level delift sub t1 in
+    let t2' = subst false level delift sub t2 in
+    match b with
+    | `Duplicate when special ->
+        assert (match t1' with L _ -> false | _ -> true) ;
+        (match flag with
+          | `Some b when !b -> b := false
+          | `Some b ->
+            print_string "WARNING! Stepping on a useless argument!";
+            ignore(read_line())
+          | `Inherit | `Duplicate -> assert false);
+        A(flag, t1', erase t2')
+    | `Inherit | `Duplicate ->
+       let b' = if t2 = V (level + var)
+        then (assert (flag <> `Inherit); flag)
+        else b in
+       assert (match t1' with L _ -> false | _ -> true) ;
+       A(b', t1', t2')
+    | `Some b' -> mk_app top b' t1' t2'
+and mk_app top flag t1 t2 = if t1 = delta && t2 = delta then raise B
  else match t1 with
- | L(b,t1) ->
-    let last_lam = match t1 with L _ -> false | _ -> true in
-    if not b && last_lam then b' := false ;
-    subst (!b' && not b && not last_lam) 0 true (0, t2) t1
- | _ -> A (b', t1, t2)
+ | L t1 -> subst top 0 true (`Some flag, 0, t2) t1
+ | _ -> A (`Some flag, t1, t2)
 and lift n =
  let rec aux lev =
   function
   | V m -> V (if m >= lev then m + n else m)
-  | L(b,t) -> L(b,aux (lev+1) t)
+  | L t -> L(aux (lev+1) t)
   | A (b,t1, t2) -> A (b,aux lev t1, aux lev t2)
  in aux 0
 ;;
-let subst = subst false 0 false;;
-let mk_app t1 = mk_app (ref true) t1;;
+let subst top = subst top 0 false;;
+let mk_app = mk_app true;;
 
 let eta_eq =
  let rec aux t1 t2 = match t1, t2 with
-  | L(_,t1), L(_,t2) -> aux t1 t2
-  | L(_,t1), t2 -> aux t1 (A(ref true,lift 1 t2,V 0))
-  | t1, L(_,t2) -> aux (A(ref true,lift 1 t1,V 0)) t2
+  | L t1, L t2 -> aux t1 t2
+  | L t1, t2 -> aux t1 (A(`Some (ref true),lift 1 t2,V 0))
+  | t1, L t2 -> aux (A(`Some (ref true),lift 1 t1,V 0)) t2
   | V a, V b -> a = b
   | A(_,t1,t2), A(_,u1,u2) -> aux t1 u1 && aux t2 u2
   | _, _ -> false
@@ -173,24 +203,25 @@ let eta_eq =
 (* is arg1 eta-subterm of arg2 ? *)
 let eta_subterm u =
  let rec aux lev t = eta_eq u (lift lev t) || match t with
- | L(_, t) -> aux (lev+1) t
+ | L t -> aux (lev+1) t
  | A(_, t1, t2) -> aux lev t1 || aux lev t2
  | _ -> false
  in aux 0
 ;;
 
-let subst_in_problem ((v, t) as sub) p =
+let subst_in_problem ?(top=true) ((v, t) as sub) p =
 print_endline ("-- SUBST " ^ string_of_t (V v) ^ " |-> " ^ string_of_t t);
  let sigma = sub::p.sigma in
- let div = try subst sub p.div with B -> raise (Done sigma) in
- let conv = try subst sub p.conv with B -> raise (Fail(-1,"p.conv diverged")) in
+ let sub = (`Inherit, v, t) in
+ let div = try subst top sub p.div with B -> raise (Done sigma) in
+ let conv = try subst false sub p.conv with B -> raise (Fail(-1,"p.conv diverged")) in
  {p with div; conv; sigma}
 ;;
 
 let get_subterm_with_head_and_args hd_var n_args =
  let rec aux lev = function
  | V _ -> None
- | L(_,t) -> aux (lev+1) t
+ | L t -> aux (lev+1) t
  | A(_,t1,t2) as t ->
    let hd_var', n_args' = get_inert t1 in
    if hd_var' = hd_var + lev && n_args <= 1 + n_args'
@@ -203,7 +234,7 @@ let get_subterm_with_head_and_args hd_var n_args =
 ;;
 
 let rec purify = function
- | L(_,t) -> Pure.L (purify t)
+ | L t -> Pure.L (purify t)
  | A(_,t1,t2) -> Pure.A (purify t1, purify t2)
  | V n -> Pure.V n
 ;;
@@ -273,7 +304,7 @@ let compute_max_lambdas_at hd_var j =
         then let hd', j' = get_inert t2 in j - j'
         else no_leading_lambdas hd_var j t2)
       else id) (max (aux hd t1) (aux hd t2))
- | L(_,t) -> aux (hd+1) t
+ | L t -> aux (hd+1) t
  | V _ -> 0
  in aux hd_var
 ;;
@@ -281,19 +312,19 @@ let compute_max_lambdas_at hd_var j =
 let print_cmd s1 s2 = print_endline (">> " ^ s1 ^ " " ^ s2);;
 
 (* step on the head of div, on the k-th argument, with n fresh vars *)
-let step k n p =
+let step ?(isfinish=false) k n p =
  let var, _ = get_inert p.div in
 print_cmd "STEP" ("on " ^ string_of_t (V var) ^ " (of:" ^ string_of_int n ^ ")");
  let p, t = (* apply fresh vars *)
   fold_nat (fun (p, t) _ ->
     let p, v = freshvar p in
-    p, A(ref false, t, V (v + k + 1))
+    p, A(`Some (ref false), t, V (v + k + 1))
   ) (p, V 0) n in
  let t = (* apply bound variables V_k..V_0 *)
-  fold_nat (fun t m -> A(ref false, t, V (k-m+1))) t (k+1) in
+  fold_nat (fun t m -> A((if m = k+1 then `Duplicate else `Inherit), t, V (k-m+1))) t (k+1) in
  let t = mk_lams t (k+1) in (* make leading lambdas *)
  let subst = var, t in
- let p = subst_in_problem subst p in
+ let p = subst_in_problem ~top:(not isfinish) subst p in
  sanity p
 ;;
 
@@ -301,7 +332,7 @@ let finish p =
  let compute_max_arity =
    let rec aux n = function
    | A(_,t1,t2) -> max (aux (n+1) t1) (aux 0 t2)
-   | L(_,t) -> max n (aux 0 t)
+   | L t -> max n (aux 0 t)
    | V _ -> n
  in aux 0 in
 print_cmd "FINISH" "";
@@ -311,7 +342,7 @@ print_cmd "FINISH" "";
  let n = 1 + arity + max
   (compute_max_lambdas_at div_hd j p.div)
   (compute_max_lambdas_at div_hd j p.conv) in
- let p = step j n p in
+ let p = step ~isfinish:true j n p in
  let div_hd, div_nargs = get_inert p.div in
  let rec aux m = function
   A(_,t1,t2) -> if is_var t2 then
@@ -358,8 +389,8 @@ let rec auto p =
 let problem_of (label, div, convs, ps, var_names) =
  print_hline ();
  let rec aux = function
- | `Lam(_, t) -> L (true,aux t)
- | `I ((v,_), args) -> Listx.fold_left (fun x y -> mk_app x (aux y)) (V v) args
+ | `Lam(_,t) -> L (aux t)
+ | `I ((v,_), args) -> Listx.fold_left (fun x y -> mk_app (ref true) x (aux y)) (V v) args
  | `Var(v,_) -> V v
  | `N _ | `Match _ -> assert false in
  assert (List.length ps = 0);