X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=ocaml%2Fsimple.ml;h=185c54ef2f025afeea14d38d6bfa74d2423722de;hb=47a9f6a73ecea5a2e60932ce324e21f4a90315c2;hp=28603258c04539410f98afb02d2ac301f97c793c;hpb=62d2aea15e05a7366e0bbdc71574ad50cda28ff5;p=fireball-separation.git

diff --git a/ocaml/simple.ml b/ocaml/simple.ml
index 2860325..185c54e 100644
--- a/ocaml/simple.ml
+++ b/ocaml/simple.ml
@@ -1,5 +1,4 @@
 let (++) f g x = f (g x);;
-let id x = x;;
 let rec fold_nat f x n = if n = 0 then x else f (fold_nat f x (n-1)) n ;;
 
 let print_hline = Console.print_hline;;
@@ -10,20 +9,28 @@ type var = int;;
 type t =
  | V of var
  | A of t * t
- | L of t
- | B (* bottom *)
- | C of int
+ | 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
+ | A(t,_) -> is_stuck t
+ | _ -> false
+;;
 
 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
+ 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
-  | 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 ;;
@@ -31,15 +38,15 @@ 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
+ let rec aux lev t = if t = C then false else (eta_eq' lev 0 u t || match t with
+ | L(t,g) -> List.exists (aux (lev+1)) (t::g)
  | A(t1, t2) -> aux lev t1 || aux lev t2
- | _ -> false
- in aux 0
+ | _ -> 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 =
@@ -49,15 +56,15 @@ 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
+    | 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
 ;;
@@ -65,138 +72,175 @@ 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 s -> (if s <> "" then print_endline ("\n<< BACKTRACK: "^s)); try_all label f xs)
+ | [] -> raise (Backtrack label)
+;;
+let try_both label f x g y =
+ try_all label (function `L x -> f x | `R y -> g y) [`L x ; `R y]
+;;
 
 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
+ | C
+ | 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 is_constant =
+ function
+    C -> true
+  | V _ -> false
+  | A(t,_)
+  | L(t,_) -> is_constant t
 ;;
 
 let rec get_inert = function
- | V n -> (n,0)
+ | V _ | C as t -> (t,0)
  | A(t, _) -> let hd,args = get_inert t in hd,args+1
  | _ -> 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
+ | 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
+ | 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 _ as t -> t
- | B -> B
-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
- | C _ as t -> t
- | 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 _ as t -> t
-  | B -> B
+  | C -> C
  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;;
+let subst = subst' 0 false;;
+
+let rec mk_apps t = function
+ | u::us -> mk_apps (A(t,u)) us
+ | [] -> t
 ;;
 
-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
+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, 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 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 hd_var' = hd_var + lev && n_args <= 1 + n_args'
-    then Some (lift ~-lev t)
-    else match aux lev t2 with
-    | None -> aux lev t1
-    | Some _ as res -> res
- in aux 0
+   if not inert_done && hd_var' = V (hd_var + lev)
+    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
- | C _ -> Pure.V max_int (* FIXME *)
- | B -> Pure.B
+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)
+ in aux
 ;;
 
 let check p sigma =
- print_endline "Checking...";
+ print_endline "\nChecking...";
  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.";
- 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";
- p
+ print_endline (string_of_problem p) (* non cancellare *); p
 ;;
 
 (* drops the arguments of t after the n-th *)
@@ -212,64 +256,56 @@ 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
- 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)
- | _, _ -> assert false
- in aux p.div t n_args
+(* return the index of the first argument with a difference
+   (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 =
  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 t2)
-      else id) (max (aux hd t1) (aux hd t2))
- | L t -> aux (hd+1) t
- | V _ -> 0
- | _ -> assert false
+ | A(t1,t2) -> max (max (aux hd t1) (aux hd t2))
+    (if get_inert t1 = (V hd, j)
+      then no_leading_lambdas hd (j+1) t2
+      else 0)
+ | L(t,_) -> aux (hd+1) t
+ | V _
+ | C -> 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, t =
-  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
-      (* 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 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
- sanity p
+let print_cmd s1 s2 = print_endline ("\n>> " ^ s1 ^ " " ^ s2);;
+
+(* 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 p i 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 var, _ = get_inert p.div in
-print_cmd "STEP" ("on " ^ string_of_t (V var) ^ " (of:" ^ string_of_int n ^ ")");
+ let hd, _ = get_inert p.div in
+ match hd with
+ | 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 *)
   fold_nat (fun (p, t) _ ->
     let p, v = freshvar p in
@@ -279,111 +315,125 @@ print_cmd "STEP" ("on " ^ string_of_t (V var) ^ " (of:" ^ string_of_int n ^ ")")
   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 divs, p = subst_in_problem subst p in
+ divs, 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 arity =
+ (* 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
+ (* 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 | _ -> raise (Backtrack "Cannot finish on constant tm") in
+ let j = match
+  smallest_such_that (fun i t -> i >= arity && not (is_constant t)) (args_of_inert p.div)
+  with Some j -> j | None -> raise (Backtrack "") in
+ print_endline "\n>> FINISHING";
+ 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
+ ignore (subst_in_problem (div_hd, mk_lams delta (m-1)) 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 - 1 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 auto p =
+ let rec aux p =
+ if eta_subterm p.div p.conv
+ then raise (Backtrack "div is subterm of conv");
+ match p.div with
+ | L _ as t -> (* case p.div is an abstraction *)
+    print_endline "\nSOTTO UN LAMBDA";
+    let t, g = mk_app t C in
+    aux ({p with div=mk_apps C (t::g)})
+ | V _ | C -> raise (Backtrack "V | C")
+ | A _ -> (
+   if is_constant p.div (* case p.div is rigid inert *)
+   then (print_endline "\nSOTTO UN C"; try_all "auto.C"
+    (fun div -> aux (sanity {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
+   let arity = List.fold_right (max ++ (snd ++ get_inert)) tms 0 in
+   try_both "???" (finish p) arity
+    (fun _ ->
+      let jss = List.concat (List.map (find_eta_difference p) tms) in
+      let jss = List.sort_uniq compare jss in
+      let f = try_all "no differences"
+       (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
+         ) in
+       try_both "step, then diverge arguments"
+        f jss
+        (try_all "tried p.div arguments" (fun div -> aux {p with div})) (args_of_inert p.div)
+      ) ()
+ ) in try
+  aux p
+ with Done sigma -> sigma
 ;;
 
-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 lev = function
+ | `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 -> 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 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^")")
 ;;
 
-let run x y = solve (problem_of x y);;
-
-(* 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]
-;; *)
-
-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 <<<"
+Problems.main (solve ++ problem_of);