open Utils;;
+type equality =
+ Cic.term * (* proof *)
+ (Cic.term * (* type *)
+ Cic.term * (* left side *)
+ Cic.term * (* right side *)
+ Utils.comparison) * (* ordering *)
+ Cic.metasenv * (* environment for metas *)
+ Cic.term list (* arguments *)
+;;
+
+
+type proof =
+ | BasicProof of Cic.term
+ | ProofBlock of
+ Cic.substitution * UriManager.uri * Cic.term * (Utils.pos * equality) *
+ equality
+ | NoProof
+;;
+
+
+let string_of_equality ?env =
+ match env with
+ | None -> (
+ function
+ | _, (ty, left, right, o), _, _ ->
+ Printf.sprintf "{%s}: %s =(%s) %s" (CicPp.ppterm ty)
+ (CicPp.ppterm left) (string_of_comparison o) (CicPp.ppterm right)
+ )
+ | Some (_, context, _) -> (
+ let names = names_of_context context in
+ function
+ | _, (ty, left, right, o), _, _ ->
+ Printf.sprintf "{%s}: %s =(%s) %s" (CicPp.pp ty names)
+ (CicPp.pp left names) (string_of_comparison o)
+ (CicPp.pp right names)
+ )
+;;
+
+
+let prooftable = Hashtbl.create 2001;;
+
+let store_proof equality proof =
+ if not (Hashtbl.mem prooftable equality) then
+ Hashtbl.add prooftable equality proof
+;;
+
+
+let delete_proof equality =
+(* Printf.printf "| Removing proof of %s" (string_of_equality equality); *)
+(* print_newline (); *)
+ Hashtbl.remove prooftable equality
+;;
+
+
+let rec build_term_proof equality =
+(* Printf.printf "build_term_proof %s" (string_of_equality equality); *)
+(* print_newline (); *)
+ let proof = try Hashtbl.find prooftable equality with Not_found -> NoProof in
+ match proof with
+ | NoProof ->
+ Printf.fprintf stderr "WARNING: no proof for %s\n"
+ (string_of_equality equality);
+ Cic.Implicit None
+ | BasicProof term -> term
+ | ProofBlock (subst, eq_URI, t', (pos, eq), eq') ->
+(* Printf.printf " ProofBlock: eq = %s, eq' = %s" *)
+(* (string_of_equality eq) (string_of_equality eq'); *)
+(* print_newline (); *)
+ let proof' = build_term_proof eq in
+ let eqproof = build_term_proof eq' in
+ let _, (ty, what, other, _), menv', args' = eq in
+ let what, other = if pos = Utils.Left then what, other else other, what in
+ CicMetaSubst.apply_subst subst
+ (Cic.Appl [Cic.Const (eq_URI, []); ty;
+ what; t'; eqproof; other; proof'])
+;;
+
+
+let rec metas_of_term = function
+ | Cic.Meta (i, c) -> [i]
+ | Cic.Var (_, ens)
+ | Cic.Const (_, ens)
+ | Cic.MutInd (_, _, ens)
+ | Cic.MutConstruct (_, _, _, ens) ->
+ List.flatten (List.map (fun (u, t) -> metas_of_term t) ens)
+ | Cic.Cast (s, t)
+ | Cic.Prod (_, s, t)
+ | Cic.Lambda (_, s, t)
+ | Cic.LetIn (_, s, t) -> (metas_of_term s) @ (metas_of_term t)
+ | Cic.Appl l -> List.flatten (List.map metas_of_term l)
+ | Cic.MutCase (uri, i, s, t, l) ->
+ (metas_of_term s) @ (metas_of_term t) @
+ (List.flatten (List.map metas_of_term l))
+ | Cic.Fix (i, il) ->
+ List.flatten
+ (List.map (fun (s, i, t1, t2) ->
+ (metas_of_term t1) @ (metas_of_term t2)) il)
+ | Cic.CoFix (i, il) ->
+ List.flatten
+ (List.map (fun (s, t1, t2) ->
+ (metas_of_term t1) @ (metas_of_term t2)) il)
+ | _ -> []
+;;
+
+
exception NotMetaConvertible;;
let meta_convertibility_aux table t1 t2 =
let module C = Cic in
- let rec aux table t1 t2 =
+ let print_table t =
+ String.concat ", "
+ (List.map
+ (fun (k, v) -> Printf.sprintf "(%d, %d)" k v) t)
+ in
+ let rec aux ((table_l, table_r) as table) t1 t2 =
+(* Printf.printf "aux %s, %s\ntable_l: %s, table_r: %s\n" *)
+(* (CicPp.ppterm t1) (CicPp.ppterm t2) *)
+(* (print_table table_l) (print_table table_r); *)
match t1, t2 with
- | t1, t2 when t1 = t2 -> table
| C.Meta (m1, tl1), C.Meta (m2, tl2) ->
- let m1_binding, m2_binding, table =
- let m1b, table =
- try List.assoc m1 table, table
- with Not_found -> m2, (m1, m2)::table
- in
- let m2b, table =
- try List.assoc m2 table, table
- with Not_found -> m1, (m2, m1)::table
- in
- m1b, m2b, table
+ let m1_binding, table_l =
+ try List.assoc m1 table_l, table_l
+ with Not_found -> m2, (m1, m2)::table_l
+ and m2_binding, table_r =
+ try List.assoc m2 table_r, table_r
+ with Not_found -> m1, (m2, m1)::table_r
in
- if m1_binding <> m2 || m2_binding <> m1 then
+(* let m1_binding, m2_binding, table = *)
+(* let m1b, table = *)
+(* try List.assoc m1 table, table *)
+(* with Not_found -> m2, (m1, m2)::table *)
+(* in *)
+(* let m2b, table = *)
+(* try List.assoc m2 table, table *)
+(* with Not_found -> m1, (m2, m1)::table *)
+(* in *)
+(* m1b, m2b, table *)
+(* in *)
+(* Printf.printf "table_l: %s\ntable_r: %s\n\n" *)
+(* (print_table table_l) (print_table table_r); *)
+ if (m1_binding <> m2) || (m2_binding <> m1) then
raise NotMetaConvertible
else (
try
| None, Some _ | Some _, None -> raise NotMetaConvertible
| None, None -> res
| Some t1, Some t2 -> (aux res t1 t2))
- table tl1 tl2
+ (table_l, table_r) tl1 tl2
with Invalid_argument _ ->
raise NotMetaConvertible
)
table il1 il2
with Invalid_argument _ -> raise NotMetaConvertible
)
+ | t1, t2 when t1 = t2 -> table
| _, _ -> raise NotMetaConvertible
and aux_ens table ens1 ens2 =
let meta_convertibility_eq eq1 eq2 =
- let _, (ty, left, right), _, _ = eq1
- and _, (ty', left', right'), _, _ = eq2 in
+ let _, (ty, left, right, _), _, _ = eq1
+ and _, (ty', left', right', _), _, _ = eq2 in
if ty <> ty' then
false
+ else if (left = left') && (right = right') then
+ true
+ else if (left = right') && (right = left') then
+ true
else
- let print_table t w =
- Printf.printf "table %s is:\n" w;
- List.iter
- (fun (k, v) -> Printf.printf "?%d: ?%d\n" k v)
- t;
- print_newline ();
- in
try
- let table = meta_convertibility_aux [] left left' in
+ let table = meta_convertibility_aux ([], []) left left' in
let _ = meta_convertibility_aux table right right' in
-(* Printf.printf "meta_convertibility_eq, ok:\n%s\n%s\n" *)
-(* (string_of_equality eq1) (string_of_equality eq2); *)
-(* print_newline (); *)
true
with NotMetaConvertible ->
try
- let table = meta_convertibility_aux [] left right' in
+ let table = meta_convertibility_aux ([], []) left right' in
let _ = meta_convertibility_aux table right left' in
-(* Printf.printf "meta_convertibility_eq, ok:\n%s\n%s\n" *)
-(* (string_of_equality eq1) (string_of_equality eq2); *)
-(* print_newline (); *)
true
with NotMetaConvertible ->
false
let meta_convertibility t1 t2 =
- try
- let _ = meta_convertibility_aux [] t1 t2 in
+ let f t =
+ String.concat ", "
+ (List.map
+ (fun (k, v) -> Printf.sprintf "(%d, %d)" k v) t)
+ in
+ if t1 = t2 then
true
- with NotMetaConvertible ->
- false
+ else
+ try
+ let l, r = meta_convertibility_aux ([], []) t1 t2 in
+ (* Printf.printf "meta_convertibility:\n%s\n%s\n\n" (f l) (f r); *)
+ true
+ with NotMetaConvertible ->
+ false
+;;
+
+
+let replace_metas (* context *) term =
+ let module C = Cic in
+ let rec aux = function
+ | C.Meta (i, c) ->
+(* let irl = *)
+(* CicMkImplicit.identity_relocation_list_for_metavariable context *)
+(* in *)
+(* if c = irl then *)
+(* C.Implicit (Some (`MetaIndex i)) *)
+(* else ( *)
+(* Printf.printf "WARNING: c non e` un identity_relocation_list!\n%s\n" *)
+(* (String.concat "\n" *)
+(* (List.map *)
+(* (function None -> "" | Some t -> CicPp.ppterm t) c)); *)
+(* C.Meta (i, c) *)
+(* ) *)
+ C.Implicit (Some (`MetaInfo (i, c)))
+ | C.Var (u, ens) -> C.Var (u, aux_ens ens)
+ | C.Const (u, ens) -> C.Const (u, aux_ens ens)
+ | C.Cast (s, t) -> C.Cast (aux s, aux t)
+ | C.Prod (name, s, t) -> C.Prod (name, aux s, aux t)
+ | C.Lambda (name, s, t) -> C.Lambda (name, aux s, aux t)
+ | C.LetIn (name, s, t) -> C.LetIn (name, aux s, aux t)
+ | C.Appl l -> C.Appl (List.map aux l)
+ | C.MutInd (uri, i, ens) -> C.MutInd (uri, i, aux_ens ens)
+ | C.MutConstruct (uri, i, j, ens) -> C.MutConstruct (uri, i, j, aux_ens ens)
+ | C.MutCase (uri, i, s, t, l) ->
+ C.MutCase (uri, i, aux s, aux t, List.map aux l)
+ | C.Fix (i, il) ->
+ let il' =
+ List.map (fun (s, i, t1, t2) -> (s, i, aux t1, aux t2)) il in
+ C.Fix (i, il')
+ | C.CoFix (i, il) ->
+ let il' =
+ List.map (fun (s, t1, t2) -> (s, aux t1, aux t2)) il in
+ C.CoFix (i, il')
+ | t -> t
+ and aux_ens ens =
+ List.map (fun (u, t) -> (u, aux t)) ens
+ in
+ aux term
+;;
+
+
+let restore_metas (* context *) term =
+ let module C = Cic in
+ let rec aux = function
+ | C.Implicit (Some (`MetaInfo (i, c))) ->
+(* let c = *)
+(* CicMkImplicit.identity_relocation_list_for_metavariable context *)
+(* in *)
+(* C.Meta (i, c) *)
+(* let local_context:(C.term option) list = *)
+(* Marshal.from_string mc 0 *)
+(* in *)
+(* C.Meta (i, local_context) *)
+ C.Meta (i, c)
+ | C.Var (u, ens) -> C.Var (u, aux_ens ens)
+ | C.Const (u, ens) -> C.Const (u, aux_ens ens)
+ | C.Cast (s, t) -> C.Cast (aux s, aux t)
+ | C.Prod (name, s, t) -> C.Prod (name, aux s, aux t)
+ | C.Lambda (name, s, t) -> C.Lambda (name, aux s, aux t)
+ | C.LetIn (name, s, t) -> C.LetIn (name, aux s, aux t)
+ | C.Appl l -> C.Appl (List.map aux l)
+ | C.MutInd (uri, i, ens) -> C.MutInd (uri, i, aux_ens ens)
+ | C.MutConstruct (uri, i, j, ens) -> C.MutConstruct (uri, i, j, aux_ens ens)
+ | C.MutCase (uri, i, s, t, l) ->
+ C.MutCase (uri, i, aux s, aux t, List.map aux l)
+ | C.Fix (i, il) ->
+ let il' =
+ List.map (fun (s, i, t1, t2) -> (s, i, aux t1, aux t2)) il in
+ C.Fix (i, il')
+ | C.CoFix (i, il) ->
+ let il' =
+ List.map (fun (s, t1, t2) -> (s, aux t1, aux t2)) il in
+ C.CoFix (i, il')
+ | t -> t
+ and aux_ens ens =
+ List.map (fun (u, t) -> (u, aux t)) ens
+ in
+ aux term
+;;
+
+
+let rec restore_subst (* context *) subst =
+ List.map
+ (fun (i, (c, t, ty)) ->
+ i, (c, restore_metas (* context *) t, ty))
+ subst
+;;
+
+
+let rec check_irl start = function
+ | [] -> true
+ | None::tl -> check_irl (start+1) tl
+ | (Some (Cic.Rel x))::tl ->
+ if x = start then check_irl (start+1) tl else false
+ | _ -> false
+;;
+
+let rec is_simple_term = function
+ | Cic.Appl ((Cic.Meta _)::_) -> false
+ | Cic.Appl l -> List.for_all is_simple_term l
+ | Cic.Meta (i, l) -> check_irl 1 l
+ | Cic.Rel _ -> true
+ | _ -> false
+;;
+
+
+let lookup_subst meta subst =
+ match meta with
+ | Cic.Meta (i, _) -> (
+ try let _, (_, t, _) = List.find (fun (m, _) -> m = i) subst in t
+ with Not_found -> meta
+ )
+ | _ -> assert false
+;;
+
+
+let unification_simple metasenv context t1 t2 ugraph =
+ let module C = Cic in
+ let module M = CicMetaSubst in
+ let module U = CicUnification in
+ let lookup = lookup_subst in
+ let rec occurs_check subst what where =
+ (* Printf.printf "occurs_check %s %s" *)
+ (* (CicPp.ppterm what) (CicPp.ppterm where); *)
+ (* print_newline (); *)
+ match where with
+ | t when what = t -> true
+ | C.Appl l -> List.exists (occurs_check subst what) l
+ | C.Meta _ ->
+ let t = lookup where subst in
+ if t <> where then occurs_check subst what t else false
+ | _ -> false
+ in
+ let rec unif subst menv s t =
+(* Printf.printf "unif %s %s\n%s\n" (CicPp.ppterm s) (CicPp.ppterm t) *)
+(* (print_subst subst); *)
+(* print_newline (); *)
+ let s = match s with C.Meta _ -> lookup s subst | _ -> s
+ and t = match t with C.Meta _ -> lookup t subst | _ -> t
+ in
+ (* Printf.printf "after apply_subst: %s %s\n%s" *)
+ (* (CicPp.ppterm s) (CicPp.ppterm t) (print_subst subst); *)
+ (* print_newline (); *)
+ match s, t with
+ | s, t when s = t -> subst, menv
+ | C.Meta (i, _), C.Meta (j, _) when i > j ->
+ unif subst menv t s
+ | C.Meta _, t when occurs_check subst s t ->
+ raise (U.UnificationFailure "Inference.unification.unif")
+(* | C.Meta (i, l), C.Meta (j, l') -> *)
+(* let _, _, ty = CicUtil.lookup_meta i menv in *)
+(* let _, _, ty' = CicUtil.lookup_meta j menv in *)
+(* let binding1 = lookup s subst in *)
+(* let binding2 = lookup t subst in *)
+(* let subst, menv = *)
+(* if binding1 != s then *)
+(* if binding2 != t then *)
+(* unif subst menv binding1 binding2 *)
+(* else *)
+(* if binding1 = t then *)
+(* subst, menv *)
+(* else *)
+(* ((j, (context, binding1, ty'))::subst, *)
+(* List.filter (fun (m, _, _) -> j <> m) menv) *)
+(* else *)
+(* if binding2 != t then *)
+(* if s = binding2 then *)
+(* subst, menv *)
+(* else *)
+(* ((i, (context, binding2, ty))::subst, *)
+(* List.filter (fun (m, _, _) -> i <> m) menv) *)
+(* else *)
+(* ((i, (context, t, ty))::subst, *)
+(* List.filter (fun (m, _, _) -> i <> m) menv) *)
+(* in *)
+(* subst, menv *)
+
+ | C.Meta (i, l), t ->
+ let _, _, ty = CicUtil.lookup_meta i menv in
+ let subst =
+ if not (List.mem_assoc i subst) then (i, (context, t, ty))::subst
+ else subst
+ in
+ let menv = List.filter (fun (m, _, _) -> i <> m) menv in
+ subst, menv
+ | _, C.Meta _ -> unif subst menv t s
+ | C.Appl (hds::_), C.Appl (hdt::_) when hds <> hdt ->
+ raise (U.UnificationFailure "Inference.unification.unif")
+ | C.Appl (hds::tls), C.Appl (hdt::tlt) -> (
+ try
+ List.fold_left2
+ (fun (subst', menv) s t -> unif subst' menv s t)
+ (subst, menv) tls tlt
+ with e ->
+ raise (U.UnificationFailure "Inference.unification.unif")
+ )
+ | _, _ -> raise (U.UnificationFailure "Inference.unification.unif")
+ in
+ let subst, menv = unif [] metasenv t1 t2 in
+ (* Printf.printf "DONE!: subst = \n%s\n" (print_subst subst); *)
+ (* print_newline (); *)
+(* let rec fix_term = function *)
+(* | (C.Meta (i, l) as t) -> *)
+(* lookup t subst *)
+(* | C.Appl l -> C.Appl (List.map fix_term l) *)
+(* | t -> t *)
+(* in *)
+(* let rec fix_subst = function *)
+(* | [] -> [] *)
+(* | (i, (c, t, ty))::tl -> (i, (c, fix_term t, fix_term ty))::(fix_subst tl) *)
+(* in *)
+(* List.rev (fix_subst subst), menv, ugraph *)
+ List.rev subst, menv, ugraph
+;;
+
+
+let unification metasenv context t1 t2 ugraph =
+(* Printf.printf "| unification %s %s\n" (CicPp.ppterm t1) (CicPp.ppterm t2); *)
+ let subst, menv, ug =
+ if not (is_simple_term t1) || not (is_simple_term t2) then
+ CicUnification.fo_unif metasenv context t1 t2 ugraph
+ else
+ unification_simple metasenv context t1 t2 ugraph
+ in
+ let rec fix_term = function
+ | (Cic.Meta (i, l) as t) ->
+ let t' = lookup_subst t subst in
+ if t <> t' then fix_term t' else t
+ | Cic.Appl l -> Cic.Appl (List.map fix_term l)
+ | t -> t
+ in
+ let rec fix_subst = function
+ | [] -> []
+ | (i, (c, t, ty))::tl -> (i, (c, fix_term t, fix_term ty))::(fix_subst tl)
+ in
+(* Printf.printf "| subst: %s\n" (print_subst ~prefix:" ; " subst); *)
+(* print_endline "|"; *)
+ (* fix_subst *) subst, menv, ug
;;
+(* let unification = CicUnification.fo_unif;; *)
+
+exception MatchingFailure;;
+
+
+let matching_simple metasenv context t1 t2 ugraph =
+ let module C = Cic in
+ let module M = CicMetaSubst in
+ let module U = CicUnification in
+ let lookup meta subst =
+ match meta with
+ | C.Meta (i, _) -> (
+ try let _, (_, t, _) = List.find (fun (m, _) -> m = i) subst in t
+ with Not_found -> meta
+ )
+ | _ -> assert false
+ in
+ let rec do_match subst menv s t =
+(* Printf.printf "do_match %s %s\n%s\n" (CicPp.ppterm s) (CicPp.ppterm t) *)
+(* (print_subst subst); *)
+(* print_newline (); *)
+(* let s = match s with C.Meta _ -> lookup s subst | _ -> s *)
+(* let t = match t with C.Meta _ -> lookup t subst | _ -> t in *)
+ (* Printf.printf "after apply_subst: %s %s\n%s" *)
+ (* (CicPp.ppterm s) (CicPp.ppterm t) (print_subst subst); *)
+ (* print_newline (); *)
+ match s, t with
+ | s, t when s = t -> subst, menv
+(* | C.Meta (i, _), C.Meta (j, _) when i > j -> *)
+(* do_match subst menv t s *)
+(* | C.Meta _, t when occurs_check subst s t -> *)
+(* raise MatchingFailure *)
+(* | s, C.Meta _ when occurs_check subst t s -> *)
+(* raise MatchingFailure *)
+ | s, C.Meta (i, l) ->
+ let filter_menv i menv =
+ List.filter (fun (m, _, _) -> i <> m) menv
+ in
+ let subst, menv =
+ let value = lookup t subst in
+ match value with
+(* | C.Meta (i', l') when Hashtbl.mem table i' -> *)
+(* (i', (context, s, ty))::subst, menv (\* filter_menv i' menv *\) *)
+ | value when value = t ->
+ let _, _, ty = CicUtil.lookup_meta i menv in
+ (i, (context, s, ty))::subst, filter_menv i menv
+ | value when value <> s ->
+ raise MatchingFailure
+ | value -> do_match subst menv s value
+ in
+ subst, menv
+(* else if value <> s then *)
+(* raise MatchingFailure *)
+(* else subst *)
+(* if not (List.mem_assoc i subst) then (i, (context, t, ty))::subst *)
+(* else subst *)
+(* in *)
+(* let menv = List.filter (fun (m, _, _) -> i <> m) menv in *)
+(* subst, menv *)
+(* | _, C.Meta _ -> do_match subst menv t s *)
+(* | C.Appl (hds::_), C.Appl (hdt::_) when hds <> hdt -> *)
+(* raise MatchingFailure *)
+ | C.Appl ls, C.Appl lt -> (
+ try
+ List.fold_left2
+ (fun (subst, menv) s t -> do_match subst menv s t)
+ (subst, menv) ls lt
+ with e ->
+(* print_endline (Printexc.to_string e); *)
+(* Printf.printf "NO MATCH: %s %s\n" (CicPp.ppterm s) (CicPp.ppterm t); *)
+(* print_newline (); *)
+ raise MatchingFailure
+ )
+ | _, _ ->
+(* Printf.printf "NO MATCH: %s %s\n" (CicPp.ppterm s) (CicPp.ppterm t); *)
+(* print_newline (); *)
+ raise MatchingFailure
+ in
+ let subst, menv = do_match [] metasenv t1 t2 in
+ (* Printf.printf "DONE!: subst = \n%s\n" (print_subst subst); *)
+ (* print_newline (); *)
+ subst, menv, ugraph
+;;
+
+
+let matching metasenv context t1 t2 ugraph =
+(* if (is_simple_term t1) && (is_simple_term t2) then *)
+(* let subst, menv, ug = *)
+(* matching_simple metasenv context t1 t2 ugraph in *)
+(* (\* Printf.printf "matching %s %s:\n%s\n" *\) *)
+(* (\* (CicPp.ppterm t1) (CicPp.ppterm t2) (print_subst subst); *\) *)
+(* (\* print_newline (); *\) *)
+(* subst, menv, ug *)
+(* else *)
+ try
+ let subst, metasenv, ugraph =
+ (* CicUnification.fo_unif metasenv context t1 t2 ugraph *)
+ unification metasenv context t1 t2 ugraph
+ in
+ let t' = CicMetaSubst.apply_subst subst t1 in
+ if not (meta_convertibility t1 t') then
+ raise MatchingFailure
+ else
+ let metas = metas_of_term t1 in
+ let fix_subst = function
+ | (i, (c, Cic.Meta (j, lc), ty)) when List.mem i metas ->
+ (j, (c, Cic.Meta (i, lc), ty))
+ | s -> s
+ in
+ let subst = List.map fix_subst subst in
+
+(* Printf.printf "matching %s %s:\n%s\n" *)
+(* (CicPp.ppterm t1) (CicPp.ppterm t2) (print_subst subst); *)
+(* print_newline (); *)
+
+ subst, metasenv, ugraph
+ with e ->
+(* Printf.printf "failed to match %s %s\n" *)
+(* (CicPp.ppterm t1) (CicPp.ppterm t2); *)
+ raise MatchingFailure
+;;
+
+(* let matching = *)
+(* let profile = CicUtil.profile "Inference.matching" in *)
+(* (fun metasenv context t1 t2 ugraph -> *)
+(* profile (matching metasenv context t1 t2) ugraph) *)
+(* ;; *)
+
let beta_expand ?(metas_ok=true) ?(match_only=false)
what type_of_what where context metasenv ugraph =
let module S = CicSubstitution in
let module C = Cic in
+
+ let print_info = false in
+
(* let _ = *)
(* let names = names_of_context context in *)
(* Printf.printf "beta_expand:\nwhat: %s, %s\nwhere: %s, %s\n" *)
| C.Meta _ when (not metas_ok) ->
res, lifted_term
| _ ->
+(* let term' = *)
+(* if match_only then replace_metas context term *)
+(* else term *)
+(* in *)
try
let subst', metasenv', ugraph' =
(* Printf.printf "provo a unificare %s e %s\n" *)
(* (CicPp.ppterm (S.lift lift_amount what)) (CicPp.ppterm term); *)
- CicUnification.fo_unif metasenv context
- (S.lift lift_amount what) term ugraph
+ if match_only then
+ matching metasenv context term (S.lift lift_amount what) ugraph
+ else
+ CicUnification.fo_unif metasenv context
+ (S.lift lift_amount what) term ugraph
in
(* Printf.printf "Ok, trovato: %s\n\nwhat: %s" (CicPp.ppterm term) *)
(* (CicPp.ppterm (S.lift lift_amount what)); *)
(* Printf.printf "substitution:\n%s\n\n" (print_subst subst'); *)
(* Printf.printf "metasenv': %s\n" (print_metasenv metasenv'); *)
(* Printf.printf "metasenv: %s\n\n" (print_metasenv metasenv); *)
- if match_only then
- let t' = CicMetaSubst.apply_subst subst' term in
- if not (meta_convertibility term t') then (
- let names = names_of_context context in
-(* Printf.printf "\nbeta_expand: term e t' sono diversi!:\n%s\n%s\n\n" *)
-(* (CicPp.pp term names) (CicPp.pp t' names); *)
- res, lifted_term
- )
- else
- ((C.Rel (1 + lift_amount), subst', metasenv', ugraph')::res,
- lifted_term)
- else
+(* if match_only then *)
+(* let t' = CicMetaSubst.apply_subst subst' term in *)
+(* if not (meta_convertibility term t') then ( *)
+(* res, lifted_term *)
+(* ) else ( *)
+(* let metas = metas_of_term term in *)
+(* let fix_subst = function *)
+(* | (i, (c, C.Meta (j, lc), ty)) when List.mem i metas -> *)
+(* (j, (c, C.Meta (i, lc), ty)) *)
+(* | s -> s *)
+(* in *)
+(* let subst' = List.map fix_subst subst' in *)
+(* ((C.Rel (1 + lift_amount), subst', metasenv', ugraph')::res, *)
+(* lifted_term) *)
+(* ) *)
+(* else *)
((C.Rel (1 + lift_amount), subst', metasenv', ugraph')::res,
lifted_term)
with e ->
-(* print_endline ("beta_expand ERROR!: " ^ (Printexc.to_string e)); *)
+ if print_info then (
+ print_endline ("beta_expand ERROR!: " ^ (Printexc.to_string e));
+ );
res, lifted_term
in
(* Printf.printf "exit aux\n"; *)
) exp_named_subst ([], [])
in
- let expansions, _ = aux 0 where context metasenv [] ugraph in
- List.map
- (fun (term, subst, metasenv, ugraph) ->
- let term' = C.Lambda (C.Anonymous, type_of_what, term) in
-(* Printf.printf "term is: %s\nsubst is:\n%s\n\n" *)
-(* (CicPp.ppterm term') (print_subst subst); *)
- (term', subst, metasenv, ugraph))
- expansions
-;;
-
-
-type equality =
- Cic.term * (* proof *)
- (Cic.term * (* type *)
- Cic.term * (* left side *)
- Cic.term) * (* right side *)
- Cic.metasenv * (* environment for metas *)
- Cic.term list (* arguments *)
+ let expansions, _ =
+(* let where = *)
+(* if match_only then replace_metas (\* context *\) where *)
+(* else where *)
+(* in *)
+ if print_info then (
+ Printf.printf "searching %s inside %s\n"
+ (CicPp.ppterm what) (CicPp.ppterm where);
+ );
+ aux 0 where context metasenv [] ugraph
+ in
+ let mapfun =
+(* if match_only then *)
+(* (fun (term, subst, metasenv, ugraph) -> *)
+(* let term' = *)
+(* C.Lambda (C.Anonymous, type_of_what, restore_metas term) *)
+(* and subst = restore_subst subst in *)
+(* (term', subst, metasenv, ugraph)) *)
+(* else *)
+ (fun (term, subst, metasenv, ugraph) ->
+ let term' = C.Lambda (C.Anonymous, type_of_what, term) in
+ (term', subst, metasenv, ugraph))
+ in
+ List.map mapfun expansions
;;
match head with
| C.Appl [C.MutInd (uri, _, _); ty; t1; t2] when uri = eq_uri ->
Printf.printf "OK: %s\n" (CicPp.ppterm term);
- Some (p, (ty, t1, t2), newmetas, args), (newmeta+1)
+ let o = !Utils.compare_terms t1 t2 in
+ let e = (p, (ty, t1, t2, o), newmetas, args) in
+ store_proof e (BasicProof p);
+ Some e, (newmeta+1)
| _ -> None, newmeta
)
| C.Appl [C.MutInd (uri, _, _); ty; t1; t2] when uri = eq_uri ->
- Some (C.Rel index,
- (ty, S.lift index t1, S.lift index t2), [], []), (newmeta+1)
+ let t1 = S.lift index t1
+ and t2 = S.lift index t2 in
+ let o = !Utils.compare_terms t1 t2 in
+ let e = (C.Rel index, (ty, t1, t2, o), [], []) in
+ store_proof e (BasicProof (C.Rel index));
+ Some e, (newmeta+1)
| _ -> None, newmeta
in (
match do_find context term with
;;
-let fix_metas newmeta ((proof, (ty, left, right), menv, args) as equality) =
+let fix_metas newmeta ((proof, (ty, left, right, o), menv, args) as equality) =
let table = Hashtbl.create (List.length args) in
let newargs, _ =
List.fold_right
(i, context, term)::menv)
menv []
in
+ let ty = repl ty
+ and left = repl left
+ and right = repl right in
+ let metas = (metas_of_term left) @ (metas_of_term right) in
+ let menv' = List.filter (fun (i, _, _) -> List.mem i metas) menv'
+ and newargs =
+ List.filter
+ (function Cic.Meta (i, _) -> List.mem i metas | _ -> assert false) newargs
+ in
(newmeta + (List.length newargs) + 1,
- (repl proof, (repl ty, repl left, repl right), menv', newargs))
+ (repl proof, (ty, left, right, o), menv', newargs))
;;
let equality_of_term ?(eq_uri=HelmLibraryObjects.Logic.eq_URI) proof = function
| Cic.Appl [Cic.MutInd (uri, _, _); ty; t1; t2] when uri = eq_uri ->
- (proof, (ty, t1, t2), [], [])
+ let o = !Utils.compare_terms t1 t2 in
+ let e = (proof, (ty, t1, t2, o), [], []) in
+ store_proof e (BasicProof proof);
+ e
+(* (proof, (ty, t1, t2, o), [], []) *)
| _ ->
raise TermIsNotAnEquality
;;
let module CR = CicReduction in
(* we assume that target is ground (does not contain metavariables): this
* should always be the case (I hope, at least) *)
- let proof, (eq_ty, left, right), _, _ = target in
- let eqproof, (ty, t1, t2), newmetas, args = source in
+ let proof, (eq_ty, left, right, t_order), _, _ = target in
+ let eqproof, (ty, t1, t2, s_order), newmetas, args = source in
- (* ALB: TODO check that ty and eq_ty are indeed equal... *)
- (* assert (eq_ty = ty); *)
+ let compare_terms = !Utils.compare_terms in
if eq_ty <> ty then
[]
else
let where, is_left =
- match nonrec_kbo left right with
+ match t_order (* compare_terms left right *) with
| Lt -> right, false
| Gt -> left, true
| _ -> (
)
in
let metasenv' = newmetas @ metasenv in
- let res1 =
- List.filter
- (fun (t, s, m, ug) ->
- nonrec_kbo (M.apply_subst s t1) (M.apply_subst s t2) = Gt)
- (beta_expand t1 ty where context metasenv' ugraph)
- and res2 =
- List.filter
- (fun (t, s, m, ug) ->
- nonrec_kbo (M.apply_subst s t2) (M.apply_subst s t1) = Gt)
- (beta_expand t2 ty where context metasenv' ugraph)
+ let result = s_order (* compare_terms t1 t2 *) in
+ let res1, res2 =
+ match result with
+ | Gt -> (beta_expand t1 ty where context metasenv' ugraph), []
+ | Lt -> [], (beta_expand t2 ty where context metasenv' ugraph)
+ | _ ->
+ let res1 =
+ List.filter
+ (fun (t, s, m, ug) ->
+ compare_terms (M.apply_subst s t1) (M.apply_subst s t2) = Gt)
+ (beta_expand t1 ty where context metasenv' ugraph)
+ and res2 =
+ List.filter
+ (fun (t, s, m, ug) ->
+ compare_terms (M.apply_subst s t2) (M.apply_subst s t1) = Gt)
+ (beta_expand t2 ty where context metasenv' ugraph)
+ in
+ res1, res2
in
(* let what, other = *)
(* if is_left then left, right *)
| _ -> assert false
in
let equation =
- if is_left then (eq_ty, newgoal, right)
- else (eq_ty, left, newgoal)
+ if is_left then (eq_ty, newgoal, right, compare_terms newgoal right)
+ else (eq_ty, left, newgoal, compare_terms left newgoal)
in
- (eqproof, equation, [], [])
+ (newgoalproof (* eqproof *), equation, [], [])
in
let new1 = List.map (build_new t1 t2 HL.Logic.eq_ind_URI) res1
and new2 = List.map (build_new t2 t1 HL.Logic.eq_ind_r_URI) res2 in
let module M = CicMetaSubst in
let module HL = HelmLibraryObjects in
let module CR = CicReduction in
- let eqproof, (eq_ty, left, right), newmetas, args = target in
- let eqp', (ty', t1, t2), newm', args' = source in
+ let eqproof, (eq_ty, left, right, t_order), newmetas, args = target in
+ let eqp', (ty', t1, t2, s_order), newm', args' = source in
let maxmeta = ref newmeta in
- (* TODO check if ty and ty' are equal... *)
- (* assert (eq_ty = ty'); *)
+ let compare_terms = !Utils.compare_terms in
if eq_ty <> ty' then
newmeta, []
(* in *)
let condition left right what other (t, s, m, ug) =
let subst = M.apply_subst s in
- let cmp1 = nonrec_kbo (subst what) (subst other) in
- let cmp2 = nonrec_kbo (subst left) (subst right) in
+ let cmp1 = compare_terms (subst what) (subst other) in
+ let cmp2 = compare_terms (subst left) (subst right) in
(* cmp1 = Gt && cmp2 = Gt *)
cmp1 <> Lt && cmp1 <> Le && cmp2 <> Lt && cmp2 <> Le
(* && (ok t s other right ug) *)
in
let metasenv' = metasenv @ newmetas @ newm' in
let beta_expand = beta_expand ~metas_ok:false in
- let res1 =
- List.filter
- (condition left right t1 t2)
- (beta_expand t1 eq_ty left context metasenv' ugraph)
- and res2 =
- List.filter
- (condition left right t2 t1)
- (beta_expand t2 eq_ty left context metasenv' ugraph)
- and res3 =
- List.filter
- (condition right left t1 t2)
- (beta_expand t1 eq_ty right context metasenv' ugraph)
- and res4 =
- List.filter
- (condition right left t2 t1)
- (beta_expand t2 eq_ty right context metasenv' ugraph)
+ let cmp1 = t_order (* compare_terms left right *)
+ and cmp2 = s_order (* compare_terms t1 t2 *) in
+ let res1, res2, res3, res4 =
+ let res l r s t =
+ List.filter
+ (condition l r s t)
+ (beta_expand s eq_ty l context metasenv' ugraph)
+ in
+ match cmp1, cmp2 with
+ | Gt, Gt ->
+ (beta_expand t1 eq_ty left context metasenv' ugraph), [], [], []
+ | Gt, Lt ->
+ [], (beta_expand t2 eq_ty left context metasenv' ugraph), [], []
+ | Lt, Gt ->
+ [], [], (beta_expand t1 eq_ty right context metasenv' ugraph), []
+ | Lt, Lt ->
+ [], [], [], (beta_expand t2 eq_ty right context metasenv' ugraph)
+ | Gt, _ ->
+ let res1 = res left right t1 t2
+ and res2 = res left right t2 t1 in
+ res1, res2, [], []
+ | Lt, _ ->
+ let res3 = res right left t1 t2
+ and res4 = res right left t2 t1 in
+ [], [], res3, res4
+ | _, Gt ->
+ let res1 = res left right t1 t2
+ and res3 = res right left t1 t2 in
+ res1, [], res3, []
+ | _, Lt ->
+ let res2 = res left right t2 t1
+ and res4 = res right left t2 t1 in
+ [], res2, [], res4
+ | _, _ ->
+ let res1 = res left right t1 t2
+ and res2 = res left right t2 t1
+ and res3 = res right left t1 t2
+ and res4 = res right left t2 t1 in
+ res1, res2, res3, res4
in
let newmetas = newmetas @ newm' in
let newargs = args @ args' in
let left, right =
if is_left then (newterm, M.apply_subst s right)
else (M.apply_subst s left, newterm) in
+ let neworder = compare_terms left right in
fix_metas !maxmeta
- (neweqproof, (eq_ty, left, right), newmetas, newargs)
+ (neweqproof, (eq_ty, left, right, neworder), newmetas, newargs)
in
maxmeta := newmeta;
newequality
and new3 = List.map (build_new t1 t2 false HL.Logic.eq_ind_URI) res3
and new4 = List.map (build_new t2 t1 false HL.Logic.eq_ind_r_URI) res4 in
let ok = function
- | _, (_, left, right), _, _ ->
+ | _, (_, left, right, _), _, _ ->
not (fst (CR.are_convertible context left right ugraph))
in
- !maxmeta, (List.filter ok (new1 @ new2 @ new3 @ new4))
+ (!maxmeta,
+ (List.filter ok (new1 @ new2 @ new3 @ new4)))
;;
let is_identity ((_, context, ugraph) as env) = function
- | ((_, (ty, left, right), _, _) as equality) ->
+ | ((_, (ty, left, right, _), _, _) as equality) ->
let res =
(left = right ||
(fst (CicReduction.are_convertible context left right ugraph)))
let module HL = HelmLibraryObjects in
let module CR = CicReduction in
- let proof, (eq_ty, left, right), metas, args = target
- and proof', (ty, t1, t2), metas', args' = source in
+ let proof, (eq_ty, left, right, t_order), metas, args = target
+ and proof', (ty, t1, t2, s_order), metas', args' = source in
+
+ let compare_terms = !Utils.compare_terms in
+
if eq_ty <> ty then
newmeta, target
else
- let get_params step =
- match step with
- | 3 -> true, t1, t2, HL.Logic.eq_ind_URI
- | 2 -> false, t1, t2, HL.Logic.eq_ind_URI
- | 1 -> true, t2, t1, HL.Logic.eq_ind_r_URI
- | 0 -> false, t2, t1, HL.Logic.eq_ind_r_URI
- | _ -> assert false
+ let first_step, get_params =
+ match s_order (* compare_terms t1 t2 *) with
+ | Gt -> 1, (function
+ | 1 -> true, t1, t2, HL.Logic.eq_ind_URI
+ | 0 -> false, t1, t2, HL.Logic.eq_ind_URI
+ | _ -> assert false)
+ | Lt -> 1, (function
+ | 1 -> true, t2, t1, HL.Logic.eq_ind_r_URI
+ | 0 -> false, t2, t1, HL.Logic.eq_ind_r_URI
+ | _ -> assert false)
+ | _ ->
+ let first_step = 3 in
+ let get_params step =
+ match step with
+ | 3 -> true, t1, t2, HL.Logic.eq_ind_URI
+ | 2 -> false, t1, t2, HL.Logic.eq_ind_URI
+ | 1 -> true, t2, t1, HL.Logic.eq_ind_r_URI
+ | 0 -> false, t2, t1, HL.Logic.eq_ind_r_URI
+ | _ -> assert false
+ in
+ first_step, get_params
in
let rec demodulate newmeta step metasenv target =
- let proof, (eq_ty, left, right), metas, args = target in
+ let proof, (eq_ty, left, right, t_order), metas, args = target in
let is_left, what, other, eq_URI = get_params step in
let env = metasenv, context, ugraph in
(* print_newline (); *)
let ok (t, s, m, ug) =
- nonrec_kbo (M.apply_subst s what) (M.apply_subst s other) = Gt
+ compare_terms (M.apply_subst s what) (M.apply_subst s other) = Gt
in
let res =
let r = (beta_expand ~metas_ok:false ~match_only:true
what ty (if is_left then left else right)
context (metasenv @ metas) ugraph)
in
-(* print_endline "res:"; *)
-(* List.iter (fun (t, s, m, ug) -> print_endline (CicPp.pp t names)) r; *)
-(* print_newline (); *)
-(* Printf.printf "metasenv:\n%s\n" (print_metasenv (metasenv @ metas)); *)
-(* print_newline (); *)
+(* let m' = metas_of_term what *)
+(* and m'' = metas_of_term (if is_left then left else right) in *)
+(* if (List.mem 527 m'') && (List.mem 6 m') then ( *)
+(* Printf.printf *)
+(* "demodulate\ntarget: %s\nwhat: %s\nother: %s\nis_left: %s\n" *)
+(* (string_of_equality ~env target) (CicPp.pp what names) *)
+(* (CicPp.pp other names) (string_of_bool is_left); *)
+(* Printf.printf "step: %d" step; *)
+(* print_newline (); *)
+(* print_endline "res:"; *)
+(* List.iter (fun (t, s, m, ug) -> print_endline (CicPp.pp t names)) r; *)
+(* print_newline (); *)
+(* Printf.printf "metasenv:\n%s\n" (print_metasenv (metasenv @ metas)); *)
+(* print_newline (); *)
+(* ); *)
List.filter ok r
in
match res with
let newterm, newproof =
match t with
| C.Lambda (nn, ty, bo) ->
- let bo' = M.apply_subst s (S.subst other bo) in
+(* let bo' = M.apply_subst s (S.subst other bo) in *)
+ let bo' = S.subst (M.apply_subst s other) bo in
let bo'' =
C.Appl (
[C.MutInd (HL.Logic.eq_URI, 0, []);
else [S.lift 1 left; bo'])
in
let t' = C.Lambda (nn, ty, bo'') in
- M.apply_subst s (S.subst other bo),
+(* M.apply_subst s (S.subst other bo), *)
+ bo',
M.apply_subst s
(C.Appl [C.Const (eq_URI, []); ty; what; t';
proof; other; proof'])
in
let newmeta, newtarget =
let left, right =
- if is_left then (newterm, M.apply_subst s right)
- else (M.apply_subst s left, newterm) in
- let newmetasenv = metasenv @ metas in
- let newargs = args @ args' in
- fix_metas newmeta
- (newproof, (eq_ty, left, right), newmetasenv, newargs)
+(* if is_left then (newterm, M.apply_subst s right) *)
+(* else (M.apply_subst s left, newterm) in *)
+ if is_left then newterm, right
+ else left, newterm
+ in
+ let neworder = compare_terms left right in
+(* let newmetasenv = metasenv @ metas in *)
+(* let newargs = args @ args' in *)
+(* fix_metas newmeta *)
+(* (newproof, (eq_ty, left, right), newmetasenv, newargs) *)
+ let m = (metas_of_term left) @ (metas_of_term right) in
+ let newmetasenv = List.filter (fun (i, _, _) -> List.mem i m) metas
+ and newargs =
+ List.filter
+ (function C.Meta (i, _) -> List.mem i m | _ -> assert false)
+ args
+ in
+ newmeta,
+ (newproof, (eq_ty, left, right, neworder), newmetasenv, newargs)
in
- Printf.printf
- "demodulate, newtarget: %s\ntarget was: %s\n"
- (string_of_equality ~env newtarget)
- (string_of_equality ~env target);
- print_newline ();
+(* Printf.printf *)
+(* "demodulate, newtarget: %s\ntarget was: %s\n" *)
+(* (string_of_equality ~env newtarget) *)
+(* (string_of_equality ~env target); *)
+(* (\* let _, _, newm, newa = newtarget in *\) *)
+(* (\* Printf.printf "newmetasenv:\n%s\nnewargs:\n%s\n" *\) *)
+(* (\* (print_metasenv newm) *\) *)
+(* (\* (String.concat "\n" (List.map CicPp.ppterm newa)); *\) *)
+(* print_newline (); *)
if is_identity env newtarget then
newmeta, newtarget
else
- demodulate newmeta step metasenv newtarget
+ demodulate newmeta first_step metasenv newtarget
in
- demodulate newmeta 3 (metasenv @ metas') target
+ demodulate newmeta first_step (metasenv @ metas') target
;;
*)
+let subsumption env target source =
+ let _, (ty, tl, tr, _), tmetas, _ = target
+ and _, (ty', sl, sr, _), smetas, _ = source in
+ if ty <> ty' then
+ false
+ else
+ let metasenv, context, ugraph = env in
+ let metasenv = metasenv @ tmetas @ smetas in
+ let names = names_of_context context in
+ let samesubst subst subst' =
+(* Printf.printf "samesubst:\nsubst: %s\nsubst': %s\n" *)
+(* (print_subst subst) (print_subst subst'); *)
+(* print_newline (); *)
+ let tbl = Hashtbl.create (List.length subst) in
+ List.iter (fun (m, (c, t1, t2)) -> Hashtbl.add tbl m (c, t1, t2)) subst;
+ List.for_all
+ (fun (m, (c, t1, t2)) ->
+ try
+ let c', t1', t2' = Hashtbl.find tbl m in
+ if (c = c') && (t1 = t1') && (t2 = t2') then true
+ else false
+ with Not_found ->
+ true)
+ subst'
+ in
+ let subsaux left right left' right' =
+ try
+ let subst, menv, ug = matching metasenv context left left' ugraph
+ and subst', menv', ug' = matching metasenv context right right' ugraph
+ in
+(* Printf.printf "left = right: %s = %s\n" *)
+(* (CicPp.pp left names) (CicPp.pp right names); *)
+(* Printf.printf "left' = right': %s = %s\n" *)
+(* (CicPp.pp left' names) (CicPp.pp right' names); *)
+ samesubst subst subst'
+ with e ->
+(* print_endline (Printexc.to_string e); *)
+ false
+ in
+ let res =
+ if subsaux tl tr sl sr then true
+ else subsaux tl tr sr sl
+ in
+ if res then (
+ Printf.printf "subsumption!:\ntarget: %s\nsource: %s\n"
+ (string_of_equality ~env target) (string_of_equality ~env source);
+ print_newline ();
+ );
+ res
+;;
+
+
+let extract_differing_subterms t1 t2 =
+ let module C = Cic in
+ let rec aux t1 t2 =
+ match t1, t2 with
+ | C.Appl l1, C.Appl l2 when (List.length l1) <> (List.length l2) ->
+ [(t1, t2)]
+ | C.Appl (h1::tl1), C.Appl (h2::tl2) ->
+ let res = List.concat (List.map2 aux tl1 tl2) in
+ if h1 <> h2 then
+ if res = [] then [(h1, h2)] else [(t1, t2)]
+ else
+ if List.length res > 1 then [(t1, t2)] else res
+ | t1, t2 ->
+ if t1 <> t2 then [(t1, t2)] else []
+ in
+ let res = aux t1 t2 in
+ match res with
+ | hd::[] -> Some hd
+ | _ -> None
+;;
projects / helm.git / blobdiff