From: acondolu <andrea.condoluci@unibo.it>
Date: Thu, 31 May 2018 12:42:55 +0000 (+0200)
Subject: Moved andrea.ml to simple.ml
X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=commitdiff_plain;h=3d8ab5897c6aa3d9c1b317e1137b3fcd2668f25e;p=fireball-separation.git

Moved andrea.ml to simple.ml
---

diff --git a/ocaml/Makefile b/ocaml/Makefile
index 5859d51..d5c830b 100644
--- a/ocaml/Makefile
+++ b/ocaml/Makefile
@@ -2,7 +2,7 @@ OCAMLC = ocamlopt -g -rectypes
 LIB = unix.cmxa str.cmxa
 UTILS = util.cmx console.cmx listx.cmx pure.cmx num.cmx parser.cmx parser_andrea.cmx
 
-all: a.out test4.out andrea.out
+all: a.out test4.out simple.out
 
 run: test4.out
 	bash run
@@ -13,8 +13,8 @@ a.out: $(UTILS) lambda4.cmx problems.cmx
 test4.out: $(UTILS) lambda4.cmx test.ml
 	$(OCAMLC) -o test4.out $(LIB) $^
 
-andrea.out: $(UTILS) andrea.ml
-	$(OCAMLC) -o andrea.out $(LIB) $(UTILS) andrea.ml
+simple.out: $(UTILS) simple.ml
+	$(OCAMLC) -o simple.out $(LIB) $(UTILS) simple.ml
 
 %.cmi: %.mli
 	$(OCAMLC) -c $<
diff --git a/ocaml/andrea.ml b/ocaml/andrea.ml
deleted file mode 100644
index 8b47f88..0000000
--- a/ocaml/andrea.ml
+++ /dev/null
@@ -1,391 +0,0 @@
-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;;
-
-open Pure
-
-type var = int;;
-type t =
- | V of var
- | A of t * t
- | L of t
- | B (* bottom *)
- | C of int
-;;
-
-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 0 0
-;;
-
-(* does NOT lift t *)
-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
-   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
-  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
-    | _ 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
-    | _ as t -> string_of_term_no_pars_app level t
-  in string_of_term_no_pars 0
-;;
-
-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);
-  "[DV] " ^ string_of_t p.div;
-  "[CV] " ^ string_of_t p.conv;
- ] in
- String.concat "\n" lines
-;;
-
-exception Done of (var * t) list (* substitution *);;
-exception Fail of int * string;;
-
-let problem_fail p reason =
- print_endline "!!!!!!!!!!!!!!! FAIL !!!!!!!!!!!!!!!";
- print_endline (string_of_problem p);
- raise (Fail (-1, reason))
-;;
-
-let freshvar ({freshno} as p) =
- {p with freshno=freshno+1}, freshno+1
-;;
-
-let rec is_inert =
- function
- | A(t,_) -> is_inert t
- | V _ -> true
- | C _
- | L _ | B -> 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
- | _ -> assert false
-;;
-
-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
- | 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
- else match t1 with
- | C _ as t -> t
- | B -> B
- | L t1 -> subst 0 true (0, t2) t1
- | _ -> 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)
-  | A (t1, t2) -> A (aux lev t1, aux lev t2)
-  | C _ as t -> t
-  | B -> B
- 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 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 ->
-   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
-;;
-
-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 check p sigma =
- print_endline "Checking...";
- 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 env = Pure.env_of_sigma freshno sigma in
- assert (Pure.diverged (Pure.mwhd (env,div,[])));
- assert (not (Pure.diverged (Pure.mwhd (env,conv,[]))));
- ()
-;;
-
-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"
-;;
-
-(* drops the arguments of t after the n-th *)
-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)
-;;
-
-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
-;;
-
-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
- 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
- let p = if phase = `One then {p with div = (match p.div with A(t,_) -> t | _ -> assert false)} else p in
- sanity p; p
-;;
-
-(* 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; 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 problem_of div conv =
- print_hline ();
- let [@warning "-8"] [div; conv], var_names = parse ([div; conv]) 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; p
-;;
-
-let exec div conv cmds =
- let p = problem_of div conv in
- try
-  problem_fail (List.fold_left (|>) p cmds) "Problem not completed"
- with
- | Done _ -> ()
-;;
-
-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 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 _ -> ()
-;;
-
-let rec conv_join = function
- | [] -> "@"
- | x::xs -> conv_join xs ^ " ("^ x ^")"
-;;
-
-let auto' a b =
- let p = problem_of a (conv_join b) in
- let sigma = auto p in
- check p sigma
-;;
-
-(* Example usage of exec, interactive:
-
-exec
- "x x"
- (conv_join["x y"; "y y"; "y x"])
- [ step 0 1; eat ]
-;;
-
-interactive "x y"
- "@ (x x) (y x) (y z)" [step 0 1; step 0 2; eat]
-;;
-
-*)
-
-auto' "x x" ["x y"; "y y"; "y x"] ;;
-auto' "x y" ["x (_. x)"; "y z"; "y x"] ;;
-auto' "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)"] ;;
-
-auto' "x (y. x y y)" ["x (y. x y x)"] ;;
-
-auto' "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 *)
-auto' "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 "ALL DONE. "
diff --git a/ocaml/simple.ml b/ocaml/simple.ml
new file mode 100644
index 0000000..8b47f88
--- /dev/null
+++ b/ocaml/simple.ml
@@ -0,0 +1,391 @@
+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;;
+
+open Pure
+
+type var = int;;
+type t =
+ | V of var
+ | A of t * t
+ | L of t
+ | B (* bottom *)
+ | C of int
+;;
+
+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 0 0
+;;
+
+(* does NOT lift t *)
+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
+   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
+  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
+    | _ 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
+    | _ as t -> string_of_term_no_pars_app level t
+  in string_of_term_no_pars 0
+;;
+
+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);
+  "[DV] " ^ string_of_t p.div;
+  "[CV] " ^ string_of_t p.conv;
+ ] in
+ String.concat "\n" lines
+;;
+
+exception Done of (var * t) list (* substitution *);;
+exception Fail of int * string;;
+
+let problem_fail p reason =
+ print_endline "!!!!!!!!!!!!!!! FAIL !!!!!!!!!!!!!!!";
+ print_endline (string_of_problem p);
+ raise (Fail (-1, reason))
+;;
+
+let freshvar ({freshno} as p) =
+ {p with freshno=freshno+1}, freshno+1
+;;
+
+let rec is_inert =
+ function
+ | A(t,_) -> is_inert t
+ | V _ -> true
+ | C _
+ | L _ | B -> 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
+ | _ -> assert false
+;;
+
+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
+ | 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
+ else match t1 with
+ | C _ as t -> t
+ | B -> B
+ | L t1 -> subst 0 true (0, t2) t1
+ | _ -> 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)
+  | A (t1, t2) -> A (aux lev t1, aux lev t2)
+  | C _ as t -> t
+  | B -> B
+ 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 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 ->
+   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
+;;
+
+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 check p sigma =
+ print_endline "Checking...";
+ 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 env = Pure.env_of_sigma freshno sigma in
+ assert (Pure.diverged (Pure.mwhd (env,div,[])));
+ assert (not (Pure.diverged (Pure.mwhd (env,conv,[]))));
+ ()
+;;
+
+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"
+;;
+
+(* drops the arguments of t after the n-th *)
+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)
+;;
+
+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
+;;
+
+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
+ 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
+ let p = if phase = `One then {p with div = (match p.div with A(t,_) -> t | _ -> assert false)} else p in
+ sanity p; p
+;;
+
+(* 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; 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 problem_of div conv =
+ print_hline ();
+ let [@warning "-8"] [div; conv], var_names = parse ([div; conv]) 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; p
+;;
+
+let exec div conv cmds =
+ let p = problem_of div conv in
+ try
+  problem_fail (List.fold_left (|>) p cmds) "Problem not completed"
+ with
+ | Done _ -> ()
+;;
+
+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 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 _ -> ()
+;;
+
+let rec conv_join = function
+ | [] -> "@"
+ | x::xs -> conv_join xs ^ " ("^ x ^")"
+;;
+
+let auto' a b =
+ let p = problem_of a (conv_join b) in
+ let sigma = auto p in
+ check p sigma
+;;
+
+(* Example usage of exec, interactive:
+
+exec
+ "x x"
+ (conv_join["x y"; "y y"; "y x"])
+ [ step 0 1; eat ]
+;;
+
+interactive "x y"
+ "@ (x x) (y x) (y z)" [step 0 1; step 0 2; eat]
+;;
+
+*)
+
+auto' "x x" ["x y"; "y y"; "y x"] ;;
+auto' "x y" ["x (_. x)"; "y z"; "y x"] ;;
+auto' "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)"] ;;
+
+auto' "x (y. x y y)" ["x (y. x y x)"] ;;
+
+auto' "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 *)
+auto' "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 "ALL DONE. "