X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=ocaml%2Fsimple.ml;h=7c372cbe7191c71c0fe8749b543cda39d1794501;hb=ee4df074206dd7decd12984fbfc6a4751b53eb0e;hp=bac3ddf98a532784a587fa90cd9cbd67ca1f1e0a;hpb=2b941d27823cb7d06bbf83353c21779c866f3161;p=fireball-separation.git

diff --git a/ocaml/simple.ml b/ocaml/simple.ml
index bac3ddf..7c372cb 100644
--- a/ocaml/simple.ml
+++ b/ocaml/simple.ml
@@ -10,12 +10,11 @@ type var = int;;
 type t =
  | V of var
  | A of t * t
- | L of t
- | B (* bottom *)
+ | L of (t * t list (*garbage*))
  | C (* constant *)
 ;;
 
-let delta = L(A(V 0, V 0));;
+let delta = L(A(V 0, V 0),[]);;
 
 let rec is_stuck = function
  | C -> true
@@ -24,11 +23,14 @@ let rec is_stuck = function
 ;;
 
 let eta_eq' =
- let rec aux l1 l2 t1 t2 = match t1, t2 with
-  | _, _ when is_stuck t1 || is_stuck t2 -> true
-  | 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
+ let rec aux l1 l2 t1 t2 =
+  let stuck1, stuck2 = is_stuck t1, is_stuck t2 in
+  match t1, t2 with
+  | _, _ when not stuck1 && stuck2 -> false
+  | _, _ when stuck1 -> true
+  | L t1, L t2 -> aux l1 l2 (fst t1) (fst t2)
+  | L t1, t2 -> aux l1 (l2+1) (fst t1) t2
+  | t1, L t2 -> aux (l1+1) l2 t1 (fst 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
@@ -38,14 +40,14 @@ let eta_eq = eta_eq' 0 0;;
 (* is arg1 eta-subterm of arg2 ? *)
 let eta_subterm u =
  let rec aux lev t = if t = C then false else (eta_eq' lev 0 u t || match t with
- | L t -> aux (lev+1) t
+ | L(t,g) -> List.exists (aux (lev+1)) (t::g)
  | 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 mk_lams = fold_nat (fun x _ -> L(x,[])) ;;
 
 let string_of_t =
   let string_of_bvar =
@@ -58,12 +60,12 @@ let string_of_t =
     | C -> "C"
     | 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
     | _ 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,g) -> "λ" ^ string_of_bvar level ^ ". " ^ string_of_term_no_pars (level+1) t
+       ^ (if g = [] then "" else String.concat ", " ("" :: List.map (string_of_term_w_pars (level+1)) g))
     | _ as t -> string_of_term_no_pars_app level t
   in string_of_term_no_pars 0
 ;;
@@ -71,41 +73,56 @@ let string_of_t =
 type problem = {
    orig_freshno: int
  ; freshno : int
+ ; label : string
  ; 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);
   "[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;;
+exception Unseparable of string;;
+exception Backtrack of string;;
+
+let rec try_all label f = function
+ | x::xs -> (try f x with Backtrack _ -> try_all label f xs)
+ | [] -> raise (Backtrack label)
+;;
 
 let problem_fail p reason =
  print_endline "!!!!!!!!!!!!!!! FAIL !!!!!!!!!!!!!!!";
  print_endline (string_of_problem p);
- raise (Fail (-1, reason))
+ failwith reason
 ;;
 
 let freshvar ({freshno} as p) =
  {p with freshno=freshno+1}, freshno+1
 ;;
 
+(* CSC: rename? is an applied C an inert?
+   is_inert and get_inert work inconsistently *)
 let rec is_inert =
  function
  | A(t,_) -> is_inert t
  | V _ -> true
  | C
- | L _ | B -> false
+ | L _ -> false
+;;
+
+let rec is_constant =
+ function
+    C -> true
+  | V _ -> false
+  | A(t,_)
+  | L(t,_) -> is_constant t
 ;;
 
 let rec get_inert = function
@@ -114,67 +131,94 @@ let rec get_inert = function
  | _ -> assert false
 ;;
 
+let args_of_inert =
+ let rec aux acc =
+  function
+   | V _ | C -> acc
+   | A(t, a) -> aux (a::acc) t
+   | _ -> assert false
+ in
+  aux []
+;;
+
 (* 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 = v' then max 0 (n - m) else 0
  | V v' -> if v = v' then n else 0
- | B | C -> 0
+ | C -> 0
 ;;
 
 let rec subst 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
+ | V v -> (if v = level + fst sub then lift level (snd sub) else V (if delift && v > level then v-1 else v)), []
+ | L x -> let t, g = subst_in_lam (level+1) delift sub x in L(t, g), []
  | A (t1,t2) ->
-  let t1 = subst level delift sub t1 in
-  let t2 = subst level delift sub t2 in
-  mk_app t1 t2
- | C | B as t -> t
-and mk_app t1 t2 = if t2 = B || (t1 = delta && t2 = delta) then B
+  let t1, g1 = subst level delift sub t1 in
+  let t2, g2 = subst level delift sub t2 in
+  let t3, g3 = mk_app t1 t2 in
+  t3, g1 @ g2 @ g3
+ | C -> C, []
+and subst_in_lam level delift sub (t, g) =
+  let t', g' = subst level delift sub t in
+  let g'' = List.fold_left
+   (fun xs t ->
+     let x,y = subst level delift sub t in
+     (x :: y @ xs)) g' g in t', g''
+and mk_app t1 t2 = if t1 = delta && t2 = delta then raise B
  else match t1 with
- | B -> B
- | L t1 -> subst 0 true (0, t2) t1
- | _ -> A (t1, t2)
+ | L x -> subst_in_lam 0 true (0, t2) x
+ | _ -> A (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)
+  | L(t,g) -> L (aux (lev+1) t, List.map (aux (lev+1)) g)
   | A (t1, t2) -> A (aux lev t1, aux lev t2)
-  | C  | B as t -> t
+  | C -> C
  in aux 0
 ;;
-let subst = subst 0 false;;
+let subst' = subst;;
+let subst = subst' 0 false;;
+
+let rec mk_apps t = function
+ | u::us -> mk_apps (A(t,u)) us
+ | [] -> t
+;;
 
 let subst_in_problem ((v, t) as sub) p =
 print_endline ("-- SUBST " ^ string_of_t (V v) ^ " |-> " ^ string_of_t t);
- {p with
-  div=subst sub p.div;
-  conv=subst sub p.conv;
-  stepped=v::p.stepped;
-  sigma=sub::p.sigma}
+ let sigma = sub :: p.sigma in
+ let div, g = try subst sub p.div with B -> raise (Done sigma) in
+ let divs = div :: g in
+ let conv, g = try subst sub p.conv with B -> raise (Backtrack "p.conv diverged") in
+ let conv = if g = [] then conv else mk_apps C (conv::g) in
+ divs, {p with div; conv; sigma}
 ;;
 
 let get_subterms_with_head hd_var =
- let rec aux lev inert_done = function
- | C | V _ | B -> []
- | L t -> aux (lev+1) false t
+ let rec aux lev inert_done g = function
+ | L(t,g') -> List.fold_left (aux (lev+1) false) g (t::g')
+ | C | V _ -> g
  | A(t1,t2) as t ->
    let hd_var', n_args' = get_inert t1 in
    if not inert_done && hd_var' = V (hd_var + lev)
-    then lift ~-lev t :: aux lev true t1 @ aux lev false t2
-    else aux lev true t1 @ aux lev false t2
- in aux 0 false
+    then lift ~-lev t :: aux lev false (aux lev true g t1) t2
+    else                 aux lev false (aux lev true g t1) t2
+ in aux 0 false []
 ;;
 
-let rec purify = function
- | L t -> Pure.L (purify t)
- | A (t1,t2) -> Pure.A (purify t1, purify t2)
- | V n -> Pure.V n
+let purify =
+ let rec aux = function
+ | L(t,g) ->
+    let t = aux (lift (List.length g) t) in
+    let t = List.fold_left (fun t g -> Pure.A(Pure.L t, aux g)) t g in
+    Pure.L t
+ | A (t1,t2) -> Pure.A (aux t1, aux t2)
+ | V n -> Pure.V (n)
  | C -> Pure.V (min_int/2)
- | B -> Pure.B
+ in aux
 ;;
 
 let check p sigma =
@@ -184,25 +228,26 @@ let check p sigma =
  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
- assert (Pure.diverged (Pure.mwhd (env,div,[])));
- print_endline " D diverged.";
- assert (not (Pure.diverged (Pure.mwhd (env,conv,[]))));
- print_endline " C converged.";
+ (if not (Pure.diverged (Pure.mwhd (env,div,[])))
+  then failwith "D converged in Pure");
+ print_endline "- D diverged.";
+ (if Pure.diverged (Pure.mwhd (env,conv,[]))
+  then failwith "C diverged in Pure");
+ print_endline "- C converged.";
  ()
 ;;
 
 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";
+ (* Trailing constant args can be removed because do not contribute to eta-diff *)
+ let rec remove_trailing_constant_args = function
+ | A(t1, t2) when is_constant t2 -> remove_trailing_constant_args t1
+ | _ as t -> t in
+ let p = {p with div=remove_trailing_constant_args p.div} in
  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
@@ -216,19 +261,20 @@ let inert_cut_at n 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 _ -> []
- | A(t1,t2), A(u1,u2) ->
-    print_endline (string_of_t t2 ^ " vs " ^ string_of_t u2);
-    if not (eta_eq t2 u2) then (k-1)::aux t1 u1 (k-1)
-    else aux t1 u1 (k-1)
- | _, _ -> assert false
- in aux p.div t argsno
+   (the first argument is 0) *)
+let find_eta_difference p t =
+ let divargs = args_of_inert p.div in
+ let conargs = args_of_inert t in
+ let rec range i j =
+  if j = 0 then [] else i :: range (i+1) (j-1) in
+ let rec aux k divargs conargs =
+  match divargs,conargs with
+     [],conargs -> range k (List.length conargs)
+   | _::_,[] -> [k]
+   | t1::divargs,t2::conargs ->
+      (if not (eta_eq t1 t2) then [k] else []) @ aux (k+1) divargs conargs
+ in
+  aux 0 divargs conargs
 ;;
 
 let compute_max_lambdas_at hd_var j =
@@ -240,52 +286,30 @@ 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 _ | C -> 0
- | _ -> assert false
  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
- match var with
- | C | L _ | B | A _ -> assert false
- | V var ->
- 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
+(* returns Some i if i is the smallest integer s.t. p holds for the i-th
+   element of the list in input *)
+let smallest_such_that p =
+ let rec aux i =
+  function
+     [] -> None
+   | hd::_ when (print_endline (string_of_t hd) ; p hd) -> Some i
+   | _::tl -> aux (i+1) tl
+ in
+  aux 0
 ;;
 
 (* step on the head of div, on the k-th argument, with n fresh vars *)
 let step k n p =
  let hd, _ = get_inert p.div in
  match hd with
- | C | L _ | B | A _  -> assert false
+ | C | L _ | A _  -> assert false
  | V var ->
 print_cmd "STEP" ("on " ^ string_of_t (V var) ^ " (on " ^ string_of_int (k+1) ^ "th)");
  let p, t = (* apply fresh vars *)
@@ -297,76 +321,124 @@ print_cmd "STEP" ("on " ^ string_of_t (V var) ^ " (on " ^ string_of_int (k+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
+ let divs, p = subst_in_problem subst p in
+ divs, sanity p
+;;
+
+let finish p =
+ (* one-step version of eat *)
+ let compute_max_arity =
+   let rec aux n = function
+   | A(t1,t2) -> max (aux (n+1) t1) (aux 0 t2)
+   | L(t,g) -> List.fold_right (max ++ (aux 0)) (t::g) 0
+   | _ -> n
+ in aux 0 in
+print_cmd "FINISH" "";
+ (* First, a step on the last argument of the divergent.
+    Because of the sanity check, it will never be a constant term. *)
+ let div_hd, div_nargs = get_inert p.div in
+ let div_hd = match div_hd with V n -> n | _ -> assert false 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
+ (* Now, find first argument of div that is a variable never applied anywhere.
+ It must exist because of some invariant, since we just did a step,
+ and because of the arity of the divergent *)
+ let div_hd, div_nargs = get_inert p.div in
+ let div_hd = match div_hd with V n -> n | _ -> assert false in
+ let rec aux m = function
+ | A(t, V delta_var) ->
+   if delta_var <> div_hd && get_subterms_with_head delta_var p.conv = []
+   then m, delta_var
+   else aux (m-1) t
+ | A(t,_) -> aux (m-1) t
+ | _ -> 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 auto p =
  let rec aux p =
- let hd, n_args = get_inert p.div in
- match hd with
- | C | L _ | B | A _  -> assert false
- | V hd_var ->
- let tms = get_subterms_with_head hd_var p.conv in
- if List.exists (fun t -> snd (get_inert t) >= n_args) tms
-  then (
-    (* let tms = List.sort (fun t1 t2 -> - compare (snd (get_inert t1)) (snd (get_inert t2))) tms in *)
-    List.iter (fun t -> try
-      let js = find_eta_difference p t n_args in
+ match p.div with
+ | L(div,g) -> (* case p.div is an abstraction *)
+    let f l t = fst (subst' 0 true (0, C) t) :: l in
+    (* the `fst' above is because we can ignore the
+    garbage generated by the subst, because substituting
+    C does not create redexes and thus no new garbage is activated *)
+    let tms = List.fold_left f [] (div::g) in
+    try_all "auto.L"
+     (fun div -> aux {p with div}) tms
+ | _ -> (
+   if is_constant p.div (* case p.div is rigid inert *)
+   then try_all "auto.C"
+    (fun div -> aux {p with div}) (args_of_inert p.div)
+   else (* case p.div is flexible inert *)
+    let hd, n_args = get_inert p.div in
+   match hd with
+   | C | L _ | A _  -> assert false
+   | V hd_var ->
+   let tms = get_subterms_with_head hd_var p.conv in
+   if List.exists (fun t -> snd (get_inert t) >= n_args) tms
+    then (
+     (* let tms = List.sort (fun t1 t2 -> - compare (snd (get_inert t1)) (snd (get_inert t2))) tms in *)
+     try_all "no similar terms" (fun t ->
+      let js = find_eta_difference p t in
       (* print_endline (String.concat ", " (List.map string_of_int js)); *)
-      if js = [] then problem_fail p "no eta difference found (div subterm of conv?)";
       let js = List.rev js in
-       List.iter
-        (fun j ->
-         try
-          let k = 1 + max
-           (compute_max_lambdas_at hd_var j p.div)
-            (compute_max_lambdas_at hd_var j p.conv) in
-          ignore (aux (step j k p))
-         with Fail(_, s) ->
-          print_endline ("Backtracking (eta_diff) because: " ^ s)) js;
-       raise (Fail(-1, "no eta difference"))
-      with Fail(_, s) ->
-       print_endline ("Backtracking (get_subterms) because: " ^ s)) tms;
-     raise (Fail(-1, "no similar terms"))
-   )
-  else
-    (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 aux p)
-  in
-  try
-   aux p
-  with Done sigma -> sigma
+      try_all "no eta difference"
+       (fun j ->
+         let k = 1 + max
+          (compute_max_lambdas_at hd_var j p.div)
+           (compute_max_lambdas_at hd_var j p.conv) in
+         let divs, p = step j k p in
+         try_all "p.div" (fun div -> aux (sanity {p with div})) divs
+         ) js) tms)
+    else
+      problem_fail (finish p) "Finish did not complete the problem"
+ ) in try
+  aux p
+ with Done sigma -> sigma
 ;;
 
 let problem_of (label, div, convs, ps, var_names) =
  print_hline ();
  let rec aux lev = function
- | `Lam(_, t) -> L (aux (lev+1) t)
- | `I (v, args) -> Listx.fold_left (fun x y -> mk_app x (aux lev y)) (aux lev (`Var v)) args
+ | `Lam(_, t, g) -> L (aux (lev+1) t, List.map (aux (lev+1)) g)
+ | `I (v, args) -> Listx.fold_left (fun x y -> fst (mk_app x (aux lev y))) (aux lev (`Var v)) args
  | `Var(v,_) -> if v >= lev && List.nth var_names (v-lev) = "C" then C else 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 0 (y :> Num.nf))) (V (List.length var_names)) convs in
- let var_names = "@" :: var_names in
+ let conv = List.fold_left (fun x y -> fst (mk_app x (aux 0 (y :> Num.nf)))) C convs in
  let div = match div with
  | Some div -> aux 0 (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
- (* initial sanity check *)
- sanity p
+ {orig_freshno=varno; freshno=1+varno; div; conv; sigma=[]; label}
 ;;
 
 let solve p =
- if is_stuck p.div then print_endline "!!! div is stuck. Problem was not run !!!"
- else 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 c = if String.length p.label > 0 then String.sub (p.label) 0 1 else "" in
+ let module M = struct exception Okay end in
+ try
+  if eta_subterm p.div p.conv
+  then raise (Unseparable "div is subterm of conv")
+  else
+   let p = sanity p (* initial sanity check *) in
+   check p (auto p);
+   raise M.Okay
+ with
+  | M.Okay -> if c = "?" then
+    failwith "The problem succeeded, but was supposed to be unseparable"
+  | e when c = "!" ->
+    failwith ("The problem was supposed to be separable, but: "^Printexc.to_string e)
+  | e ->
+    print_endline ("The problem failed, as expected ("^Printexc.to_string e^")")
 ;;
 
 Problems.main (solve ++ problem_of);