X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=ocaml%2Fsimple.ml;h=b76a654f06ffb9527789f731e6dbb8301d526b02;hb=refs%2Fheads%2Fmeasure_tmp;hp=154992dd3f056dad04a1334eff68b75b7be211b7;hpb=640e7671fac6bebe8debe37dba052018c3b4c76f;p=fireball-separation.git

diff --git a/ocaml/simple.ml b/ocaml/simple.ml
index 154992d..b76a654 100644
--- a/ocaml/simple.ml
+++ b/ocaml/simple.ml
@@ -6,50 +6,28 @@ let print_hline = Console.print_hline;;
 
 open Pure
 
+type var_flag = bool ;;
+
 type var = int;;
 type t =
  | V of var
- | A of t * t
+ | A of var_flag * t * t
  | L of 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
-  | 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
-;;
-
-(* does NOT lift the argument *)
-let mk_lams = fold_nat (fun x _ -> L x) ;;
-
 let string_of_t =
+  let sep_of_app b = if b then " +" else " " in
   let string_of_bvar =
    let bound_vars = ["x"; "y"; "z"; "w"; "q"] in
    let bvarsno = List.length bound_vars in
-   fun nn -> if nn < bvarsno then List.nth bound_vars nn else "x" ^ (string_of_int (nn - bvarsno + 1)) in
+   fun nn -> if nn < bvarsno then List.nth bound_vars nn else "v" ^ (string_of_int (nn - bvarsno + 1)) in
   let rec string_of_term_w_pars level = function
-    | V v -> if v >= level then "`" ^ string_of_int (v-level) else
+    | V v -> if v >= level then string_of_int (v-level) else
        string_of_bvar (level - v-1)
     | A _
     | L _ as t -> "(" ^ string_of_term_no_pars level t ^ ")"
   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 ^ sep_of_app 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
@@ -57,24 +35,32 @@ let string_of_t =
   in string_of_term_no_pars 0
 ;;
 
+(* does NOT lift the argument *)
+let mk_lams = fold_nat (fun x _ -> L x) ;;
+
+let measure_of_t =
+ let rec aux = function
+ | V _ -> 0
+ | A(b,t1,t2) ->
+   (if b then 1 else 0) + aux t1 + aux t2
+ | L t -> aux t
+ in aux
+;;
+
 type problem = {
    orig_freshno: int
  ; freshno : int
- ; div : t
- ; conv : t
+ ; tms : t list
  ; sigma : (var * t) list (* substitutions *)
- ; phase : [`One | `Two] (* :'( *)
 }
 
 let string_of_problem p =
- let lines = [
-  "[DV] " ^ string_of_t p.div;
-  "[CV] " ^ string_of_t p.conv;
- ] in
+ let measure = List.fold_left (+) 0 (List.map measure_of_t p.tms) in
+ let lines = ("[measure] " ^ string_of_int measure) ::
+   List.map (fun x -> "[TM] " ^ string_of_t x) p.tms in
  String.concat "\n" lines
 ;;
 
-exception B;;
 exception Done of (var * t) list (* substitution *);;
 exception Fail of int * string;;
 
@@ -90,7 +76,7 @@ let freshvar ({freshno} as p) =
 
 let rec is_inert =
  function
- | A(t,_) -> is_inert t
+ | A(_,t,_) -> is_inert t
  | V _ -> true
  | L _ -> false
 ;;
@@ -100,7 +86,7 @@ let is_lambda = function L _ -> true | _ -> false;;
 
 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
 ;;
 
@@ -112,61 +98,97 @@ let rec no_leading_lambdas v n = function
  | V v' -> if v = v' then n else 0
 ;;
 
-let rec subst level delift sub =
+let rec erase = function
+ | L t -> L (erase t)
+ | A(_,t1,t2) -> A(false, erase t1, erase t2)
+ | V _ as t -> t
+;;
+
+let explode =
+ let rec aux args = function
+ | L _ -> assert false
+ | V _ as x -> x, args
+ | A(b,t1,t2) -> aux ((b,t2)::args) t1
+ in aux []
+;;
+
+let rec implode hd args =
+ match args with
+ | [] -> hd
+ | (f,a)::args -> implode (A(f,hd,a)) args
+;;
+
+let get_head =
+ let rec aux lev = function
+ | L t -> aux (lev+1) t
+ | A(_,t,_) -> aux lev t
+ | V v -> v - lev
+ in aux 0
+;;
+
+let rec subst level delift ((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 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
-and mk_app t1 t2 = if t1 = delta && t2 = delta then raise B
- else match t1 with
+ | 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 (level + 1) delift sub t)
+ | A(b,t1,t2) ->
+    let t1' = subst level delift sub t1 in
+    let t2' = subst level delift sub t2 in
+    mk_app b t1' t2'
+and mk_app flag t1 t2 = match t1 with
  | L t1 -> subst 0 true (0, t2) t1
- | _ -> A (t1, t2)
+ | _ -> A (flag, 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)
+  | 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 0 false;;
-
-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 mk_app = mk_app true;; *)
+let rec mk_apps t = function
+ | [] -> t
+ | (f,x)::xs -> mk_apps (mk_app f t x) xs
 ;;
 
-let get_subterm_with_head_and_args hd_var n_args =
- let rec aux lev = function
- | V _ -> None
+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(false,lift 1 t2,V 0))
+  | t1, L t2 -> aux (A(false,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) 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
-    | Some _ as res -> res
+ | A(_, t1, t2) -> aux lev t1 || aux lev t2
+ | _ -> false
  in aux 0
 ;;
 
+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 sub = (v, t) in
+ let tms = List.map (subst sub) p.tms in
+ {p with tms; sigma}
+;;
+
 let rec purify = function
  | L t -> Pure.L (purify t)
- | A (t1,t2) -> Pure.A (purify t1, purify t2)
+ | A(_,t1,t2) -> Pure.A (purify t1, purify t2)
  | V n -> Pure.V n
 ;;
 
 let check p sigma =
- print_endline "Checking...";
- let div = purify p.div in
- let conv = purify p.conv in
+ assert false (* FIXME *)
+ (* print_endline "Checking...";
+ let tms = List.map purify p.tms in
  let sigma = List.map (fun (v,t) -> v, purify t) sigma in
  let freshno = List.fold_right (max ++ fst) sigma 0 in
  let env = Pure.env_of_sigma freshno sigma in
@@ -174,183 +196,95 @@ let check p sigma =
  print_endline " D diverged.";
  assert (not (Pure.diverged (Pure.mwhd (env,conv,[]))));
  print_endline " C converged.";
- ()
+ () *)
 ;;
 
 let sanity p =
  print_endline (string_of_problem p); (* non cancellare *)
- 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";
+ let rec all_different = function
+  | [] -> true
+  | x::xs -> List.for_all ((<>) x) xs && all_different xs in
+ if List.for_all is_var p.tms && all_different p.tms
+  then raise (Done p.sigma);
+ if List.exists (not ++ is_inert) p.tms
+  then problem_fail p "used a non-effective path";
  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 ->
-    let k', t' = aux t1 in
-     if k' = n then n, t'
-      else k'+1, t
-  | _ -> assert false
- in snd (aux t)
-;;
-
-(* 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 _ -> problem_fail p "no eta difference found (div subterm of conv?)"
- | A(t1,t2), A(u1,u2) ->
-    if not (eta_eq t2 u2) then (k-1)
-    else aux t1 u1 (k-1)
- | _, _ -> assert false
- in aux p.div t argsno
-;;
-
-let compute_max_lambdas_at hd_var j =
- let rec aux hd = function
- | 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 hd_var j t2)
-      else id) (max (aux hd t1) (aux hd t2))
- | L t -> aux (hd+1) t
- | V _ -> 0
- in aux hd_var
-;;
-
 let print_cmd s1 s2 = print_endline (">> " ^ s1 ^ " " ^ s2);;
 
-(* eat the arguments of the divergent and explode.
- It does NOT perform any check, may fail if done unsafely *)
-let eat p =
-print_cmd "EAT" "";
- let var, k = get_inert p.div in
- let phase = p.phase in
- let p =
-  match phase with
-  | `One ->
-      let n = 1 + max
-       (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, V 0) n in
-      let p = {p with phase=`Two} in
-      let t = A(t, delta) in
-      let t = fold_nat (fun t m -> A(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
+let step var j n p =
+  let atsnd f (a,b) = (a, f b) in
+  let p, alphas = (* make fresh vars *)
+   fold_nat (fun (p, vs) _ ->
+     let p, v = freshvar p in
+     p, v::vs
+   ) (p, []) n in let alphas = List.rev alphas in
+  let rec aux lev (inside:bool) = function
+  | L t -> L (aux (lev+1) inside t)
+  | _ as x ->
+    let hd, args = explode x in
+    if hd = V (var+lev) then
+      (let nargs = List.length args in
+       let k = max 0 (j + 1 - nargs) in
+       let args = List.mapi
+        (fun i (f, t) -> f, lift k (aux lev (if i=j then true else inside) t)) args in
+       let bound = fold_nat (fun x n -> (false,V(n-1)) :: x) [] k in
+       let args = args @ bound in
+       let _, head = List.nth args j in
+       let args = List.mapi
+        (fun i (f, t) -> (if i=j && not inside then false else f), if i=j && not inside then erase t else t) args in
+       let head = (if inside then erase else id) head in
+       print_endline ("HEAD: " ^ string_of_t head);
+       let alphas = List.map (fun v -> false, V(lev+k+v)) alphas in
+       let t = mk_apps head (alphas @ args) in
+       let t = mk_lams t k in
+       t
+    ) else
+    (let args = List.map (atsnd (aux lev inside)) args in
+     implode hd args) in
+  let sigma = (var, aux 0 false (V var)) :: p.sigma in
+  {p with tms=List.map (aux 0 false) p.tms; sigma}
 ;;
 
-(* step on the head of div, on the k-th argument, with n fresh vars *)
-let step 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(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 = 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 finish p = assert false ;;
 
-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
-    let phase = p.phase in
-     let p = eat p in
-     if phase = `Two
-      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 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 p = step j k p in
-  auto p
-;;
+let rec auto p = assert false ;;
 
 let problem_of (label, div, convs, ps, var_names) =
  print_hline ();
  let rec aux = function
- | `Lam(_, t) -> L (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 true 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 convs = (List.rev convs :> Num.nf list) in
+ let tms = List.map aux (convs @ (ps :> Num.nf list)) in
+ let tms = match div with
+ | Some div -> aux (div :> Num.nf) :: tms
+ | None -> tms in
  let varno = List.length var_names in
- let p = {orig_freshno=varno; freshno=1+varno; div; conv; sigma=[]; phase=`One} in
+ let p = {orig_freshno=varno; freshno=1+varno; tms; sigma=[]} in
  (* initial sanity check *)
  sanity p
 ;;
 
+let rec interactive p =
+ print_string "[varno index alphano] ";
+ let s = read_line () in
+ let spl = Str.split (Str.regexp " +") s in
+ let nth n = int_of_string (List.nth spl n) in
+ let p = step (nth 0) (nth 1) (nth 2) p in
+ interactive (sanity p)
+;;
+
 let solve p =
- if eta_subterm p.div p.conv
-  then print_endline "!!! div is subterm of conv. Problem was not run !!!"
-  else check p (auto p)
+ let rec aux = function
+ | [] -> false
+ | x::xs -> List.exists (eta_subterm x) xs || aux xs in
+ if aux p.tms
+  then print_endline "!!! Problem stopped: subterm problem !!!"
+  else check p (interactive p)
 ;;
 
 Problems.main (solve ++ problem_of);
-
-(* Example usage of interactive: *)
-
-(* let interactive div conv cmds =
- let p = problem_of div conv in
- try (
- let p = List.fold_left (|>) p cmds in
- let rec f p cmds =
-  let nth spl n = int_of_string (List.nth spl n) in
-  let read_cmd () =
-   let s = read_line () in
-   let spl = Str.split (Str.regexp " +") s in
-   s, let uno = List.hd spl in
-    try if uno = "eat" then eat
-    else if uno = "step" then step (nth spl 1) (nth spl 2)
-    else failwith "Wrong input."
-    with Failure s -> print_endline s; (fun x -> x) in
-  let str, cmd = read_cmd () in
-  let cmds = (" " ^ str ^ ";")::cmds in
-  try
-   let p = cmd p in f p cmds
-  with
-  | Done _ -> print_endline "Done! Commands history: "; List.iter print_endline (List.rev cmds)
- in f p []
- ) with Done _ -> ()
-;; *)
-
-(* interactive "x y"
- "@ (x x) (y x) (y z)" [step 0 1; step 0 2; eat]
-;; *)