X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=ocaml%2Fsimple.ml;h=4e93965e029a606419b3984a2af9e36d4792b5f8;hb=4d85faf22614fae57d4b0c45a5699258a9274272;hp=28603258c04539410f98afb02d2ac301f97c793c;hpb=62d2aea15e05a7366e0bbdc71574ad50cda28ff5;p=fireball-separation.git

diff --git a/ocaml/simple.ml b/ocaml/simple.ml
index 2860325..4e93965 100644
--- a/ocaml/simple.ml
+++ b/ocaml/simple.ml
@@ -9,38 +9,16 @@ open Pure
 type var = int;;
 type t =
  | V of var
- | A of t * t
- | L of t
- | B (* bottom *)
- | C of int
+ | A of bool * t * t
+ | L of (bool * t)
 ;;
 
-let delta = L(A(V 0, V 0));;
-
-let eta_eq' =
- let rec aux l1 l2 t1 t2 = match t1, t2 with
-  | L t1, L t2 -> aux l1 l2 t1 t2
-  | L t1, t2 -> aux l1 (l2+1) t1 t2
-  | t1, L t2 -> aux (l1+1) l2 t1 t2
-  | V a, V b -> a + l1 = b + l2
-  | C a, C b -> a = b
-  | A(t1,t2), A(u1,u2) -> aux l1 l2 t1 u1 && aux l1 l2 t2 u2
-  | _, _ -> false
- in aux ;;
-let eta_eq = eta_eq' 0 0;;
-
-(* is arg1 eta-subterm of arg2 ? *)
-let eta_subterm u =
- let rec aux lev t = eta_eq' lev 0 u t || match t with
- | L t -> aux (lev+1) t
- | A(t1, t2) -> aux lev t1 || aux lev t2
- | _ -> false
- in aux 0
+let rec measure_of_t = function
+ | V _ -> 0
+ | A(b,t1,t2) -> (if b then 1 else 0) + measure_of_t t1 + measure_of_t t2
+ | L(b,t) -> if b then measure_of_t t else 0
 ;;
 
-(* does NOT lift the argument *)
-let mk_lams = fold_nat (fun x _ -> L x) ;;
-
 let string_of_t =
   let string_of_bvar =
    let bound_vars = ["x"; "y"; "z"; "w"; "q"] in
@@ -49,38 +27,42 @@ let string_of_t =
   let rec string_of_term_w_pars level = function
     | V v -> if v >= level then "`" ^ string_of_int (v-level) else
        string_of_bvar (level - v-1)
-    | C n -> "c" ^ string_of_int n
     | A _
     | L _ as t -> "(" ^ string_of_term_no_pars level t ^ ")"
-    | B -> "BOT"
   and string_of_term_no_pars_app level = function
-    | A(t1,t2) -> string_of_term_no_pars_app level t1 ^ " " ^ string_of_term_w_pars level t2
+    | A(b,t1,t2) -> string_of_term_no_pars_app level t1 ^ (if b then "," else " ") ^ 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(true,V 0, V 0));;
+
+(* does NOT lift the argument *)
+let mk_lams = fold_nat (fun x _ -> L(false,x)) ;;
+
 type problem = {
    orig_freshno: int
  ; freshno : int
  ; div : t
  ; conv : t
  ; sigma : (var * t) list (* substitutions *)
- ; stepped : var list
  ; phase : [`One | `Two] (* :'( *)
 }
 
 let string_of_problem p =
  let lines = [
-  "[stepped] " ^ String.concat " " (List.map string_of_int p.stepped);
+  "[measure] " ^ string_of_int (measure_of_t p.div);
   "[DV] " ^ string_of_t p.div;
   "[CV] " ^ string_of_t p.conv;
  ] in
  String.concat "\n" lines
 ;;
 
+exception B;;
 exception Done of (var * t) list (* substitution *);;
 exception Fail of int * string;;
 
@@ -96,71 +78,87 @@ let freshvar ({freshno} as p) =
 
 let rec is_inert =
  function
- | A(t,_) -> is_inert t
+ | A(_,t,_) -> is_inert t
  | V _ -> true
- | C _
- | L _ | B -> false
+ | L _ -> false
 ;;
 
 let is_var = function V _ -> true | _ -> false;;
 let is_lambda = function L _ -> true | _ -> false;;
 
-let rec no_leading_lambdas = function
- | L t -> 1 + no_leading_lambdas t
- | _ -> 0
-;;
-
 let rec get_inert = function
  | V n -> (n,0)
- | A(t, _) -> let hd,args = get_inert t in hd,args+1
+ | A(_,t,_) -> let hd,args = get_inert t in hd,args+1
  | _ -> assert false
 ;;
 
-let rec subst level delift sub =
+(* 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
+ | 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' defaults to false *)
+let rec subst b' level delift 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 t -> let t = subst (level + 1) delift sub t in if t = B then B else L t
- | A (t1,t2) ->
-  let t1 = subst level delift sub t1 in
-  let t2 = subst level delift sub t2 in
-  mk_app t1 t2
- | C _ as t -> t
- | B -> B
-and mk_app t1 t2 = if t2 = B || (t1 = delta && t2 = delta) then B
+ | 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 b' (subst b' level delift sub t1) (subst b' level delift sub t2)
+ | A(b,t1,t2) ->
+    mk_app b (subst b' level delift sub t1) (subst b' level delift sub t2)
+and mk_app b' t1 t2 = if t1 = delta && t2 = delta then raise B
  else match t1 with
- | C _ as t -> t
- | B -> B
- | L t1 -> subst 0 true (0, t2) t1
- | _ -> A (t1, t2)
+ | L(b,t1) -> subst (b' && not b) 0 true (0, t2) t1
+ | _ -> A (b', t1, t2)
 and lift n =
  let rec aux lev =
   function
   | V m -> V (if m >= lev then m + n else m)
-  | L t -> L (aux (lev+1) t)
-  | A (t1, t2) -> A (aux lev t1, aux lev t2)
-  | C _ as t -> t
-  | B -> B
+  | L(b,t) -> L(b,aux (lev+1) t)
+  | A (b,t1, t2) -> A (b,aux lev t1, aux lev t2)
  in aux 0
 ;;
-let subst = subst 0 false;;
-
-let subst_in_problem (sub: var * t) (p: problem) =
-print_endline ("-- SUBST " ^ string_of_t (V (fst sub)) ^ " |-> " ^ string_of_t (snd sub));
- {p with
-  div=subst sub p.div;
-  conv=subst sub p.conv;
-  stepped=(fst sub)::p.stepped;
-  sigma=sub::p.sigma}
+let subst = subst false 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(true,lift 1 t2,V 0))
+  | t1, L(_,t2) -> aux (A(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
+ in aux ;;
+
+(* 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
+ | A(_, t1, t2) -> aux lev t1 || aux lev t2
+ | _ -> false
+ in aux 0
+;;
+
+let subst_in_problem ((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
+ {p with div; conv; sigma}
 ;;
 
 let get_subterm_with_head_and_args hd_var n_args =
  let rec aux lev = function
- | C _
- | V _ | B -> None
- | L t -> aux (lev+1) t
- | A(t1,t2) as t ->
+ | V _ -> None
+ | 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'
+    (* the `+1` above is because of t2 *)
     then Some (lift ~-lev t)
     else match aux lev t2 with
     | None -> aux lev t1
@@ -169,11 +167,9 @@ let get_subterm_with_head_and_args hd_var n_args =
 ;;
 
 let rec purify = function
- | L t -> Pure.L (purify t)
- | A (t1,t2) -> Pure.A (purify t1, purify t2)
+ | L(_,t) -> Pure.L (purify t)
+ | A(_,t1,t2) -> Pure.A (purify t1, purify t2)
  | V n -> Pure.V n
- | C _ -> Pure.V max_int (* FIXME *)
- | B -> Pure.B
 ;;
 
 let check p sigma =
@@ -181,7 +177,7 @@ let check p sigma =
  let div = purify p.div in
  let conv = purify p.conv in
  let sigma = List.map (fun (v,t) -> v, purify t) sigma in
- let freshno = List.fold_right (fun (x,_) -> max x) sigma 0 in
+ let freshno = List.fold_right (max ++ fst) sigma 0 in
  let env = Pure.env_of_sigma freshno sigma in
  assert (Pure.diverged (Pure.mwhd (env,div,[])));
  print_endline " D diverged.";
@@ -192,19 +188,19 @@ let check p sigma =
 
 let sanity p =
  print_endline (string_of_problem p); (* non cancellare *)
- if p.conv = B then problem_fail p "p.conv diverged";
- if p.div = B then raise (Done p.sigma);
  if p.phase = `Two && p.div = delta then raise (Done p.sigma);
  if not (is_inert p.div) then problem_fail p "p.div converged";
  p
 ;;
 
 (* drops the arguments of t after the n-th *)
+(* FIXME! E' usato in modo improprio contando sul fatto
+   errato che ritorna un inerte lungo esattamente n *)
 let inert_cut_at n t =
  let rec aux t =
   match t with
   | V _ as t -> 0, t
-  | A(t1,_) as t ->
+  | A(_,t1,_) as t ->
     let k', t' = aux t1 in
      if k' = n then n, t'
       else k'+1, t
@@ -212,29 +208,37 @@ let inert_cut_at n t =
  in snd (aux t)
 ;;
 
-let find_eta_difference p t n_args =
- let t = inert_cut_at n_args t in
+(* return the index of the first argument with a difference
+   (the first argument is 0)
+   precondition: p.div and t have n+1 arguments
+   *)
+let find_eta_difference p t argsno =
+ let t = inert_cut_at argsno t in
  let rec aux t u k = match t, u with
- | V _, V _ -> assert false (* div subterm of conv *)
- | A(t1,t2), A(u1,u2) ->
-    if not (eta_eq t2 u2) then ((*print_endline((string_of_t t2) ^ " <> " ^ (string_of_t u2));*) k)
-    else aux t1 u1 (k-1)
+ | V _, V _ -> None
+ | A(_,t1,t2), A(_,u1,u2) ->
+    (match aux t1 u1 (k-1) with
+    | None ->
+      if not (eta_eq t2 u2) then Some (k-1)
+      else None
+    | Some j -> Some j)
  | _, _ -> assert false
- in aux p.div t n_args
+ in match aux p.div t argsno with
+ | None -> problem_fail p "no eta difference found (div subterm of conv?)"
+ | Some j -> j
 ;;
 
 let compute_max_lambdas_at hd_var j =
  let rec aux hd = function
- | A(t1,t2) ->
+ | A(_,t1,t2) ->
     (if get_inert t1 = (hd, j)
       then max ( (*FIXME*)
        if is_inert t2 && let hd', j' = get_inert t2 in hd' = hd
         then let hd', j' = get_inert t2 in j - j'
-        else no_leading_lambdas t2)
+        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
- | _ -> assert false
  in aux hd_var
 ;;
 
@@ -246,23 +250,27 @@ let eat p =
 print_cmd "EAT" "";
  let var, k = get_inert p.div in
  let phase = p.phase in
- let p, t =
+ let p =
   match phase with
   | `One ->
       let n = 1 + max
-       (compute_max_lambdas_at var k p.div)
-       (compute_max_lambdas_at var k p.conv) in
+       (compute_max_lambdas_at var (k-1) p.div)
+       (compute_max_lambdas_at var (k-1) p.conv) in
       (* apply fresh vars *)
       let p, t = fold_nat (fun (p, t) _ ->
         let p, v = freshvar p in
-        p, A(t, V (v + k))
+        p, A(false, t, V (v + k))
       ) (p, V 0) n in
-      let p = {p with phase=`Two} in p, A(t, delta)
-  | `Two -> p, delta in
- let subst = var, mk_lams t k in
- let p = subst_in_problem subst p in
- sanity p;
- let p = if phase = `One then {p with div = (match p.div with A(t,_) -> t | _ -> assert false)} else p in
+      let p = {p with phase=`Two} in
+      let t = A(false, t, delta) in
+      let t = fold_nat (fun t m -> A(false, t, V (k-m))) t (k-1) in
+      let subst = var, mk_lams t k in
+      let p = subst_in_problem subst p in
+      let _, args = get_inert p.div in
+      {p with div = inert_cut_at (args-k) p.div}
+  | `Two ->
+      let subst = var, mk_lams delta k in
+      subst_in_problem subst p in
  sanity p
 ;;
 
@@ -273,32 +281,52 @@ 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(t, V (v + k + 1))
+    p, A(false, t, V (v + k + 1))
   ) (p, V 0) n in
- let t = (* apply unused bound variables V_{k-1}..V_1 *)
-  fold_nat (fun t m -> A(t, V (k-m+1))) t k in
+ let t = (* apply bound variables V_k..V_0 *)
+  fold_nat (fun t m -> A(false, 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
  sanity p
 ;;
-;;
 
-let parse strs =
-  let rec aux level = function
-  | Parser_andrea.Lam t -> L (aux (level + 1) t)
-  | Parser_andrea.App (t1, t2) ->
-   if level = 0 then mk_app (aux level t1) (aux level t2)
-    else A(aux level t1, aux level t2)
-  | Parser_andrea.Var v -> V v in
-  let (tms, free) = Parser_andrea.parse_many strs in
-  (List.map (aux 0) tms, free)
+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)
+   | V _ -> n
+ in aux 0 in
+print_cmd "FINISH" "";
+ let div_hd, div_nargs = get_inert p.div in
+ let j = div_nargs - 1 in
+ let arity = compute_max_arity p.conv in
+ 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 div_hd, div_nargs = get_inert p.div in
+ let rec aux m = function
+  A(_,t1,t2) -> if is_var t2 then
+   (let delta_var, _ = get_inert t2 in
+     if delta_var <> div_hd && get_subterm_with_head_and_args delta_var 1 p.conv = None
+      then m, delta_var
+      else aux (m-1) t1) else aux (m-1) t1
+  | _ -> assert false in
+ let m, delta_var = aux div_nargs p.div in
+ let p = subst_in_problem (delta_var, delta) p in
+ let p = subst_in_problem (div_hd, mk_lams delta (m-1)) p in
+ sanity p
 ;;
 
 let rec auto p =
  let hd_var, n_args = get_inert p.div in
  match get_subterm_with_head_and_args hd_var n_args p.conv with
  | None ->
+   (try problem_fail (finish p) "Auto.2 did not complete the problem"
+   with Done sigma -> sigma)
+   (*
    (try
     let phase = p.phase in
      let p = eat p in
@@ -306,24 +334,37 @@ let rec auto p =
       then problem_fail p "Auto.2 did not complete the problem"
       else auto p
     with Done sigma -> sigma)
+    *)
  | Some t ->
-  let j = find_eta_difference p t n_args - 1 in
+  let j = find_eta_difference p t n_args in
   let k = 1 + max
    (compute_max_lambdas_at hd_var j p.div)
     (compute_max_lambdas_at hd_var j p.conv) in
+  let m1 = measure_of_t p.div in
   let p = step j k p in
+  let m2 = measure_of_t p.div in
+  (if m2 >= m1 then
+    (print_string "WARNING! Measure did not decrease (press <Enter>)";
+    ignore(read_line())));
   auto p
 ;;
 
-let problem_of div convs =
- let rec conv_join = function
-  | [] -> "@"
-  | x::xs -> conv_join xs ^ " ("^ x ^")" in
+let problem_of (label, div, convs, ps, var_names) =
  print_hline ();
- let conv = conv_join convs in
- let [@warning "-8"] [div; conv], var_names = parse ([div; conv]) in
+ 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
+ | `Var(v,_) -> V v
+ | `N _ | `Match _ -> assert false in
+ assert (List.length ps = 0);
+ let convs = List.rev convs in
+ let conv = List.fold_left (fun x y -> mk_app x (aux (y :> Num.nf))) (V (List.length var_names)) convs in
+ let var_names = "@" :: var_names in
+ let div = match div with
+ | Some div -> aux (div :> Num.nf)
+ | None -> assert false in
  let varno = List.length var_names in
- let p = {orig_freshno=varno; freshno=1+varno; div; conv; sigma=[]; stepped=[]; phase=`One} in
+ let p = {orig_freshno=varno; freshno=1+varno; div; conv; sigma=[]; phase=`One} in
  (* initial sanity check *)
  sanity p
 ;;
@@ -334,7 +375,7 @@ let solve p =
   else check p (auto p)
 ;;
 
-let run x y = solve (problem_of x y);;
+Problems.main (solve ++ problem_of);
 
 (* Example usage of interactive: *)
 
@@ -365,25 +406,3 @@ let run x y = solve (problem_of x y);;
 (* interactive "x y"
  "@ (x x) (y x) (y z)" [step 0 1; step 0 2; eat]
 ;; *)
-
-run "x x" ["x y"; "y y"; "y x"] ;;
-run "x y" ["x (_. x)"; "y z"; "y x"] ;;
-run "a (x. x b) (x. x c)" ["a (x. b b) @"; "a @ c"; "a (x. x x) a"; "a (a a a) (a c c)"] ;;
-
-run "x (y. x y y)" ["x (y. x y x)"] ;;
-
-run "x a a a a" [
- "x b a a a";
- "x a b a a";
- "x a a b a";
- "x a a a b";
-] ;;
-
-(* Controesempio ad usare un conto dei lambda che non considere le permutazioni *)
-run "x a a a a (x (x. x x) @ @ (_._.x. x x) x) b b b" [
- "x a a a a (_. a) b b b";
- "x a a a a (_. _. _. _. x. y. x y)";
-] ;;
-
-print_hline();
-print_endline ">>> EXAMPLES IN simple.ml FINISHED <<<"