* http://cs.unibo.it/helm/.
*)
-exception UnificationFailed;;
-exception Free;;
-exception OccurCheck;;
-exception RelToHiddenHypothesis;;
-exception OpenTerm;;
+open Printf
-(**** DELIFT ****)
+exception UnificationFailure of string;;
+exception Uncertain of string;;
+exception AssertFailure of string;;
-(* the delift function takes in input an ordered list of integers [n1,...,nk]
- and a term t, and relocates rel(nk) to k. Typically, the list of integers
- is a parameter of a metavariable occurrence. *)
+let debug_print = prerr_endline
-exception NotInTheList;;
+let type_of_aux' metasenv subst context term =
+ try
+ CicTypeChecker.type_of_aux' ~subst metasenv context term
+ with
+ CicTypeChecker.TypeCheckerFailure msg ->
+ let msg =
+ (sprintf
+ "Kernel Type checking error:
+%s\n%s\ncontext=\n%s\nmetasenv=\n%s\nsubstitution=\n%s\nException:\n%s.\nToo bad."
+ (CicMetaSubst.ppterm subst term)
+ (CicMetaSubst.ppterm [] term)
+ (CicMetaSubst.ppcontext subst context)
+ (CicMetaSubst.ppmetasenv metasenv subst)
+ (CicMetaSubst.ppsubst subst) msg) in
+ raise (AssertFailure msg);;
+(*
+ try
+ CicMetaSubst.type_of_aux' metasenv subst context term
+ with
+ | CicMetaSubst.MetaSubstFailure msg ->
+ raise (AssertFailure
+ ((sprintf
+ "Type checking error: %s in context\n%s\nand metasenv\n%s.\nException: %s.\nBroken invariant: unification must be invoked only on well typed terms"
+ (CicMetaSubst.ppterm subst term)
+ (CicMetaSubst.ppcontext subst context)
+ (CicMetaSubst.ppmetasenv metasenv subst) msg))) *)
-let position n =
- let rec aux k =
- function
- [] -> raise NotInTheList
- | (Some (Cic.Rel m))::_ when m=n -> k
- | _::tl -> aux (k+1) tl in
- aux 1
+let rec deref subst =
+ function
+ Cic.Meta(n,l) as t ->
+ (try
+ deref subst
+ (CicSubstitution.lift_meta
+ l (snd (CicUtil.lookup_subst n subst)))
+ with
+ CicUtil.Subst_not_found _ -> t)
+ | t -> t
;;
-
-let restrict to_be_restricted =
- let rec erase i n =
- function
- [] -> []
- | _::tl when List.mem (n,i) to_be_restricted ->
- None::(erase (i+1) n tl)
- | he::tl -> he::(erase (i+1) n tl) in
- let rec aux =
- function
- [] -> []
- | (n,context,t)::tl -> (n,erase 1 n context,t)::(aux tl) in
- aux
-;;
-
-let delift context metasenv l t =
+let rec beta_expand test_equality_only metasenv subst context t arg =
let module S = CicSubstitution in
- let to_be_restricted = ref [] in
- let rec deliftaux k =
- let module C = Cic in
- function
- C.Rel m ->
- if m <=k then
- C.Rel m (*CSC: che succede se c'e' un Def? Dovrebbe averlo gia' *)
- (*CSC: deliftato la regola per il LetIn *)
- else
- (match List.nth context (m-k-1) with
- Some (_,C.Def (t,_)) -> deliftaux k (S.lift m t)
- | Some (_,C.Decl t) ->
- (* It may augment to_be_restricted *)
- ignore (deliftaux k (S.lift m t)) ;
- C.Rel ((position (m-k) l) + k)
- | None -> raise RelToHiddenHypothesis)
- | C.Var (uri,exp_named_subst) ->
- let exp_named_subst' =
- List.map (function (uri,t) -> uri,deliftaux k t) exp_named_subst
- in
- C.Var (uri,exp_named_subst')
- | C.Meta (i, l1) as t ->
- let rec deliftl j =
- function
- [] -> []
- | None::tl -> None::(deliftl (j+1) tl)
- | (Some t)::tl ->
- let l1' = (deliftl (j+1) tl) in
- try
- Some (deliftaux k t)::l1'
- with
- RelToHiddenHypothesis
- | NotInTheList ->
- to_be_restricted := (i,j)::!to_be_restricted ; None::l1'
- in
- let l' = deliftl 1 l1 in
- C.Meta(i,l')
- | C.Sort _ as t -> t
- | C.Implicit as t -> t
- | C.Cast (te,ty) -> C.Cast (deliftaux k te, deliftaux k ty)
- | C.Prod (n,s,t) -> C.Prod (n, deliftaux k s, deliftaux (k+1) t)
- | C.Lambda (n,s,t) -> C.Lambda (n, deliftaux k s, deliftaux (k+1) t)
- | C.LetIn (n,s,t) -> C.LetIn (n, deliftaux k s, deliftaux (k+1) t)
- | C.Appl l -> C.Appl (List.map (deliftaux k) l)
- | C.Const (uri,exp_named_subst) ->
- let exp_named_subst' =
- List.map (function (uri,t) -> uri,deliftaux k t) exp_named_subst
- in
- C.Const (uri,exp_named_subst')
- | C.MutInd (uri,typeno,exp_named_subst) ->
- let exp_named_subst' =
- List.map (function (uri,t) -> uri,deliftaux k t) exp_named_subst
- in
- C.MutInd (uri,typeno,exp_named_subst')
- | C.MutConstruct (uri,typeno,consno,exp_named_subst) ->
- let exp_named_subst' =
- List.map (function (uri,t) -> uri,deliftaux k t) exp_named_subst
- in
- C.MutConstruct (uri,typeno,consno,exp_named_subst')
- | C.MutCase (sp,i,outty,t,pl) ->
- C.MutCase (sp, i, deliftaux k outty, deliftaux k t,
- List.map (deliftaux k) pl)
- | C.Fix (i, fl) ->
- let len = List.length fl in
- let liftedfl =
- List.map
- (fun (name, i, ty, bo) ->
- (name, i, deliftaux k ty, deliftaux (k+len) bo))
- fl
- in
- C.Fix (i, liftedfl)
- | C.CoFix (i, fl) ->
- let len = List.length fl in
- let liftedfl =
- List.map
- (fun (name, ty, bo) -> (name, deliftaux k ty, deliftaux (k+len) bo))
- fl
- in
- C.CoFix (i, liftedfl)
- in
- let res = deliftaux 0 t in
- res, restrict !to_be_restricted metasenv
-;;
+ let module C = Cic in
+ let rec aux metasenv subst n context t' =
+ try
+ let subst,metasenv =
+ fo_unif_subst test_equality_only subst context metasenv
+ (CicSubstitution.lift n arg) t'
+ in
+ subst,metasenv,C.Rel (1 + n)
+ with
+ Uncertain _
+ | UnificationFailure _ ->
+ match t' with
+ | C.Rel m -> subst,metasenv, if m <= n then C.Rel m else C.Rel (m+1)
+ | C.Var (uri,exp_named_subst) ->
+ let subst,metasenv,exp_named_subst' =
+ aux_exp_named_subst metasenv subst n context exp_named_subst
+ in
+ subst,metasenv,C.Var (uri,exp_named_subst')
+ | C.Meta (i,l) ->
+ (* andrea: in general, beta_expand can create badly typed
+ terms. This happens quite seldom in practice, UNLESS we
+ iterate on the local context. For this reason, we renounce
+ to iterate and just lift *)
+ let l =
+ List.map
+ (function
+ Some t -> Some (CicSubstitution.lift 1 t)
+ | None -> None) l in
+ subst, metasenv, C.Meta (i,l)
+ (*
+ let (subst, metasenv, context, local_context) =
+ List.fold_right
+ (fun t (subst, metasenv, context, local_context) ->
+ match t with
+ | None -> (subst, metasenv, context, None :: local_context)
+ | Some t ->
+ let (subst, metasenv, t) =
+ aux metasenv subst n context t
+ in
+ (subst, metasenv, context, Some t :: local_context))
+ l (subst, metasenv, context, [])
+ in
+ prerr_endline ("nuova meta :" ^ (CicPp.ppterm (C.Meta (i, local_context))));
+ (subst, metasenv, C.Meta (i, local_context)) *)
+ | C.Sort _
+ | C.Implicit _ as t -> subst,metasenv,t
+ | C.Cast (te,ty) ->
+ let subst,metasenv,te' = aux metasenv subst n context te in
+ let subst,metasenv,ty' = aux metasenv subst n context ty in
+ subst,metasenv,C.Cast (te', ty')
+ | C.Prod (nn,s,t) ->
+ let subst,metasenv,s' = aux metasenv subst n context s in
+ let subst,metasenv,t' =
+ aux metasenv subst (n+1) ((Some (nn, C.Decl s))::context) t
+ in
+ subst,metasenv,C.Prod (nn, s', t')
+ | C.Lambda (nn,s,t) ->
+ let subst,metasenv,s' = aux metasenv subst n context s in
+ let subst,metasenv,t' =
+ aux metasenv subst (n+1) ((Some (nn, C.Decl s))::context) t
+ in
+ subst,metasenv,C.Lambda (nn, s', t')
+ | C.LetIn (nn,s,t) ->
+ let subst,metasenv,s' = aux metasenv subst n context s in
+ let subst,metasenv,t' =
+ aux metasenv subst (n+1) ((Some (nn, C.Def (s,None)))::context) t
+ in
+ subst,metasenv,C.LetIn (nn, s', t')
+ | C.Appl l ->
+ let subst,metasenv,revl' =
+ List.fold_left
+ (fun (subst,metasenv,appl) t ->
+ let subst,metasenv,t' = aux metasenv subst n context t in
+ subst,metasenv,t'::appl
+ ) (subst,metasenv,[]) l
+ in
+ subst,metasenv,C.Appl (List.rev revl')
+ | C.Const (uri,exp_named_subst) ->
+ let subst,metasenv,exp_named_subst' =
+ aux_exp_named_subst metasenv subst n context exp_named_subst
+ in
+ subst,metasenv,C.Const (uri,exp_named_subst')
+ | C.MutInd (uri,i,exp_named_subst) ->
+ let subst,metasenv,exp_named_subst' =
+ aux_exp_named_subst metasenv subst n context exp_named_subst
+ in
+ subst,metasenv,C.MutInd (uri,i,exp_named_subst')
+ | C.MutConstruct (uri,i,j,exp_named_subst) ->
+ let subst,metasenv,exp_named_subst' =
+ aux_exp_named_subst metasenv subst n context exp_named_subst
+ in
+ subst,metasenv,C.MutConstruct (uri,i,j,exp_named_subst')
+ | C.MutCase (sp,i,outt,t,pl) ->
+ let subst,metasenv,outt' = aux metasenv subst n context outt in
+ let subst,metasenv,t' = aux metasenv subst n context t in
+ let subst,metasenv,revpl' =
+ List.fold_left
+ (fun (subst,metasenv,pl) t ->
+ let subst,metasenv,t' = aux metasenv subst n context t in
+ subst,metasenv,t'::pl
+ ) (subst,metasenv,[]) pl
+ in
+ subst,metasenv,C.MutCase (sp,i,outt', t', List.rev revpl')
+ | C.Fix (i,fl) ->
+(*CSC: not implemented
+ let tylen = List.length fl in
+ let substitutedfl =
+ List.map
+ (fun (name,i,ty,bo) -> (name, i, aux n ty, aux (n+tylen) bo))
+ fl
+ in
+ C.Fix (i, substitutedfl)
+*) (* subst,metasenv,CicMetaSubst.lift subst 1 t' *)
+ subst,metasenv,CicSubstitution.lift 1 t'
+ | C.CoFix (i,fl) ->
+(*CSC: not implemented
+ let tylen = List.length fl in
+ let substitutedfl =
+ List.map
+ (fun (name,ty,bo) -> (name, aux n ty, aux (n+tylen) bo))
+ fl
+ in
+ C.CoFix (i, substitutedfl)
+*) (* subst,metasenv,CicMetasubst.lift subst 1 t' *)
+ subst,metasenv,CicSubstitution.lift 1 t'
-(**** END OF DELIFT ****)
+ and aux_exp_named_subst metasenv subst n context ens =
+ List.fold_right
+ (fun (uri,t) (subst,metasenv,l) ->
+ let subst,metasenv,t' = aux metasenv subst n context t in
+ subst,metasenv,(uri,t')::l) ens (subst,metasenv,[])
+ in
+ let argty = type_of_aux' metasenv subst context arg in
+ let fresh_name =
+ FreshNamesGenerator.mk_fresh_name
+ metasenv context (Cic.Name "Heta") ~typ:argty
+ in
+ let subst,metasenv,t' = aux metasenv subst 0 context t in
+ (* prova *)
+ (* old
+ subst, metasenv, C.Appl [C.Lambda (fresh_name,argty,t') ; arg]
+ *)
+ subst, metasenv, C.Lambda (fresh_name,argty,t')
-type substitution = (int * Cic.term) list
+and beta_expand_many test_equality_only metasenv subst context t args =
+ let subst,metasenv,hd =
+ List.fold_right
+ (fun arg (subst,metasenv,t) ->
+ let subst,metasenv,t =
+ beta_expand test_equality_only metasenv subst context t arg in
+ subst,metasenv,t
+ ) args (subst,metasenv,t) in
+ subst,metasenv,hd
(* NUOVA UNIFICAZIONE *)
(* A substitution is a (int * Cic.term) list that associates a
fo_unif_new takes a metasenv, a context, two terms t1 and t2 and gives back
a new substitution which is _NOT_ unwinded. It must be unwinded before
applying it. *)
-
-let rec fo_unif_subst subst context metasenv t1 t2 =
+
+and fo_unif_subst test_equality_only subst context metasenv t1 t2 =
let module C = Cic in
let module R = CicReduction in
let module S = CicSubstitution in
+ let t1 = deref subst t1 in
+ let t2 = deref subst t2 in
match (t1, t2) with
(C.Meta (n,ln), C.Meta (m,lm)) when n=m ->
- let ok =
- List.fold_left2
- (fun b t1 t2 ->
- b &&
- match t1,t2 with
- None,_
- | _,None -> true
- | Some t1', Some t2' ->
- (* First possibility: restriction *)
- (* Second possibility: unification *)
- (* Third possibility: convertibility *)
- R.are_convertible context t1' t2'
- ) true ln lm
- in
- if ok then subst,metasenv else raise UnificationFailed
- | (C.Meta (n,l), C.Meta (m,_)) when n>m ->
- fo_unif_subst subst context metasenv t2 t1
+ let _,subst,metasenv =
+ (try
+ List.fold_left2
+ (fun (j,subst,metasenv) t1 t2 ->
+ match t1,t2 with
+ None,_
+ | _,None -> j+1,subst,metasenv
+ | Some t1', Some t2' ->
+ (* First possibility: restriction *)
+ (* Second possibility: unification *)
+ (* Third possibility: convertibility *)
+ if R.are_convertible ~subst ~metasenv context t1' t2' then
+ j+1,subst,metasenv
+ else
+ (try
+ let subst,metasenv =
+ fo_unif_subst
+ test_equality_only
+ subst context metasenv t1' t2'
+ in
+ j+1,subst,metasenv
+ with
+ Uncertain _
+ | UnificationFailure _ ->
+prerr_endline ("restringo Meta n." ^ (string_of_int n) ^ "on variable n." ^ (string_of_int j));
+ let metasenv, subst =
+ CicMetaSubst.restrict
+ subst [(n,j)] metasenv in
+ j+1,subst,metasenv)
+ ) (1,subst,metasenv) ln lm
+ with
+ Exit ->
+ raise
+ (UnificationFailure "1")
+(*
+ (sprintf
+ "Error trying to unify %s with %s: the algorithm tried to check whether the two substitutions are convertible; if they are not, it tried to unify the two substitutions. No restriction was attempted."
+ (CicMetaSubst.ppterm subst t1) (CicMetaSubst.ppterm subst t2))) *)
+ | Invalid_argument _ ->
+ raise
+ (UnificationFailure "2"))
+(*
+ (sprintf
+ "Error trying to unify %s with %s: the lengths of the two local contexts do not match." (CicMetaSubst.ppterm subst t1) (CicMetaSubst.ppterm subst t2))))*)
+ in subst,metasenv
+ | (C.Meta (n,_), C.Meta (m,_)) when n>m ->
+ fo_unif_subst test_equality_only subst context metasenv t2 t1
| (C.Meta (n,l), t)
| (t, C.Meta (n,l)) ->
- let subst',metasenv' =
- try
- let oldt = (List.assoc n subst) in
- let lifted_oldt = S.lift_meta l oldt in
- fo_unif_subst subst context metasenv lifted_oldt t
- with Not_found ->
- let t',metasenv' = delift context metasenv l t in
- (n, t')::subst, metasenv'
+ let swap =
+ match t1,t2 with
+ C.Meta (n,_), C.Meta (m,_) when n < m -> false
+ | _, C.Meta _ -> false
+ | _,_ -> true
+ in
+ let lower = fun x y -> if swap then y else x in
+ let upper = fun x y -> if swap then x else y in
+ let fo_unif_subst_ordered
+ test_equality_only subst context metasenv m1 m2 =
+ fo_unif_subst test_equality_only subst context metasenv
+ (lower m1 m2) (upper m1 m2)
in
- let (_,_,meta_type) =
- List.find (function (m,_,_) -> m=n) metasenv' in
- let tyt = CicTypeChecker.type_of_aux' metasenv' context t in
- fo_unif_subst subst' context metasenv' (S.lift_meta l meta_type) tyt
+ begin
+ let subst,metasenv =
+ let (_,_,meta_type) = CicUtil.lookup_meta n metasenv in
+ (try
+ let tyt = type_of_aux' metasenv subst context t in
+ fo_unif_subst
+ test_equality_only
+ subst context metasenv tyt (S.lift_meta l meta_type)
+ with
+ UnificationFailure msg
+ | Uncertain msg ->
+ prerr_endline msg;raise (UnificationFailure msg)
+ | AssertFailure _ ->
+ prerr_endline "siamo allo huge hack";
+ (* TODO huge hack!!!!
+ * we keep on unifying/refining in the hope that
+ * the problem will be eventually solved.
+ * In the meantime we're breaking a big invariant:
+ * the terms that we are unifying are no longer well
+ * typed in the current context (in the worst case
+ * we could even diverge) *)
+ (subst, metasenv)) in
+ let t',metasenv,subst =
+ try
+ CicMetaSubst.delift n subst context metasenv l t
+ with
+ (CicMetaSubst.MetaSubstFailure msg)->
+ raise (UnificationFailure msg)
+ | (CicMetaSubst.Uncertain msg) -> raise (Uncertain msg)
+ in
+ let t'' =
+ match t' with
+ C.Sort (C.Type u) when not test_equality_only ->
+ let u' = CicUniv.fresh () in
+ let s = C.Sort (C.Type u') in
+ ignore (CicUniv.add_ge (upper u u') (lower u u')) ;
+ s
+ | _ -> t'
+ in
+ (* Unifying the types may have already instantiated n. Let's check *)
+ try
+ let (_, oldt) = CicUtil.lookup_subst n subst in
+ let lifted_oldt = S.lift_meta l oldt in
+ fo_unif_subst_ordered
+ test_equality_only subst context metasenv t lifted_oldt
+ with
+ CicUtil.Subst_not_found _ ->
+ let (_, context, _) = CicUtil.lookup_meta n metasenv in
+ let subst = (n, (context, t'')) :: subst in
+ let metasenv =
+ List.filter (fun (m,_,_) -> not (n = m)) metasenv in
+ subst, metasenv
+ end
| (C.Var (uri1,exp_named_subst1),C.Var (uri2,exp_named_subst2))
| (C.Const (uri1,exp_named_subst1),C.Const (uri2,exp_named_subst2)) ->
if UriManager.eq uri1 uri2 then
- fo_unif_subst_exp_named_subst subst context metasenv
+ fo_unif_subst_exp_named_subst test_equality_only subst context metasenv
exp_named_subst1 exp_named_subst2
else
- raise UnificationFailed
+ raise (UnificationFailure "3")
+ (* (sprintf
+ "Can't unify %s with %s due to different constants"
+ (CicMetaSubst.ppterm subst t1) (CicMetaSubst.ppterm subst t2))) *)
| C.MutInd (uri1,i1,exp_named_subst1),C.MutInd (uri2,i2,exp_named_subst2) ->
if UriManager.eq uri1 uri2 && i1 = i2 then
- fo_unif_subst_exp_named_subst subst context metasenv
+ fo_unif_subst_exp_named_subst test_equality_only subst context metasenv
exp_named_subst1 exp_named_subst2
else
- raise UnificationFailed
+ raise (UnificationFailure "4")
+ (* (sprintf
+ "Can't unify %s with %s due to different inductive principles"
+ (CicMetaSubst.ppterm subst t1) (CicMetaSubst.ppterm subst t2))) *)
| C.MutConstruct (uri1,i1,j1,exp_named_subst1),
C.MutConstruct (uri2,i2,j2,exp_named_subst2) ->
if UriManager.eq uri1 uri2 && i1 = i2 && j1 = j2 then
- fo_unif_subst_exp_named_subst subst context metasenv
+ fo_unif_subst_exp_named_subst test_equality_only subst context metasenv
exp_named_subst1 exp_named_subst2
else
- raise UnificationFailed
- | (C.Rel _, _)
- | (_, C.Rel _)
- | (C.Sort _ ,_)
- | (_, C.Sort _)
- | (C.Implicit, _)
- | (_, C.Implicit) ->
- if R.are_convertible context t1 t2 then
- subst, metasenv
- else
- raise UnificationFailed
- | (C.Cast (te,ty), t2) -> fo_unif_subst subst context metasenv te t2
- | (t1, C.Cast (te,ty)) -> fo_unif_subst subst context metasenv t1 te
+ raise (UnificationFailure "5")
+ (* (sprintf
+ "Can't unify %s with %s due to different inductive constructors"
+ (CicMetaSubst.ppterm subst t1) (CicMetaSubst.ppterm subst t2))) *)
+ | (C.Implicit _, _) | (_, C.Implicit _) -> assert false
+ | (C.Cast (te,ty), t2) -> fo_unif_subst test_equality_only
+ subst context metasenv te t2
+ | (t1, C.Cast (te,ty)) -> fo_unif_subst test_equality_only
+ subst context metasenv t1 te
| (C.Prod (n1,s1,t1), C.Prod (_,s2,t2)) ->
- let subst',metasenv' = fo_unif_subst subst context metasenv s1 s2 in
- fo_unif_subst subst' ((Some (n1,(C.Decl s1)))::context) metasenv' t1 t2
+ (* TASSI: this is the only case in which we want == *)
+ let subst',metasenv' = fo_unif_subst true
+ subst context metasenv s1 s2 in
+ fo_unif_subst test_equality_only
+ subst' ((Some (n1,(C.Decl s1)))::context) metasenv' t1 t2
| (C.Lambda (n1,s1,t1), C.Lambda (_,s2,t2)) ->
- let subst',metasenv' = fo_unif_subst subst context metasenv s1 s2 in
- fo_unif_subst subst' ((Some (n1,(C.Decl s1)))::context) metasenv' t1 t2
+ (* TASSI: ask someone a reason for not putting true here *)
+ let subst',metasenv' = fo_unif_subst test_equality_only
+ subst context metasenv s1 s2 in
+ fo_unif_subst test_equality_only
+ subst' ((Some (n1,(C.Decl s1)))::context) metasenv' t1 t2
| (C.LetIn (_,s1,t1), t2)
| (t2, C.LetIn (_,s1,t1)) ->
- fo_unif_subst subst context metasenv t2 (S.subst s1 t1)
+ fo_unif_subst
+ test_equality_only subst context metasenv t2 (S.subst s1 t1)
| (C.Appl l1, C.Appl l2) ->
- let lr1 = List.rev l1 in
- let lr2 = List.rev l2 in
- let rec fo_unif_l subst metasenv =
- function
- [],_
- | _,[] -> assert false
- | ([h1],[h2]) ->
- fo_unif_subst subst context metasenv h1 h2
- | ([h],l)
- | (l,[h]) ->
- fo_unif_subst subst context metasenv h (C.Appl (List.rev l))
- | ((h1::l1),(h2::l2)) ->
- let subst', metasenv' =
- fo_unif_subst subst context metasenv h1 h2
- in
- fo_unif_l subst' metasenv' (l1,l2)
- in
- fo_unif_l subst metasenv (lr1, lr2)
- | (C.Const _, _)
- | (_, C.Const _)
- | (C.MutInd _, _)
- | (_, C.MutInd _)
- | (C.MutConstruct _, _)
- | (_, C.MutConstruct _) ->
- if R.are_convertible context t1 t2 then
- subst, metasenv
- else
- raise UnificationFailed
- | (C.MutCase (_,_,outt1,t1,pl1), C.MutCase (_,_,outt2,t2,pl2))->
+ (* andrea: this case should be probably rewritten in the
+ spirit of deref *)
+ let rec beta_reduce =
+ function
+ (Cic.Appl (Cic.Lambda (_,_,t)::he'::tl')) ->
+ let he'' = CicSubstitution.subst he' t in
+ if tl' = [] then
+ he''
+ else
+ beta_reduce (Cic.Appl(he''::tl'))
+ | t -> t in
+ (match l1,l2 with
+ C.Meta (i,_)::args1, C.Meta (j,_)::args2 when i = j ->
+ (try
+ List.fold_left2
+ (fun (subst,metasenv) ->
+ fo_unif_subst test_equality_only subst context metasenv)
+ (subst,metasenv) l1 l2
+ with (Invalid_argument msg) -> raise (UnificationFailure msg))
+ | C.Meta (i,l)::args, _ ->
+ (try
+ let (_,t) = CicUtil.lookup_subst i subst in
+ let lifted = S.lift_meta l t in
+ let reduced = beta_reduce (Cic.Appl (lifted::args)) in
+ fo_unif_subst
+ test_equality_only
+ subst context metasenv reduced t2
+ with CicUtil.Subst_not_found _ ->
+ let subst,metasenv,beta_expanded =
+ beta_expand_many
+ test_equality_only metasenv subst context t2 args in
+ fo_unif_subst test_equality_only subst context metasenv
+ (C.Meta (i,l)) beta_expanded)
+ | _, C.Meta (i,l)::args ->
+ (try
+ let (_,t) = CicUtil.lookup_subst i subst in
+ let lifted = S.lift_meta l t in
+ let reduced = beta_reduce (Cic.Appl (lifted::args)) in
+ fo_unif_subst
+ test_equality_only
+ subst context metasenv t1 reduced
+ with CicUtil.Subst_not_found _ ->
+ let subst,metasenv,beta_expanded =
+ beta_expand_many
+ test_equality_only metasenv subst context t1 args in
+ fo_unif_subst test_equality_only subst context metasenv
+ (C.Meta (i,l)) beta_expanded)
+ | _,_ ->
+ let lr1 = List.rev l1 in
+ let lr2 = List.rev l2 in
+ let rec fo_unif_l test_equality_only subst metasenv =
+ function
+ [],_
+ | _,[] -> assert false
+ | ([h1],[h2]) ->
+ fo_unif_subst test_equality_only subst context metasenv h1 h2
+ | ([h],l)
+ | (l,[h]) ->
+ fo_unif_subst test_equality_only subst context metasenv
+ h (C.Appl (List.rev l))
+ | ((h1::l1),(h2::l2)) ->
+ let subst', metasenv' =
+ fo_unif_subst test_equality_only subst context metasenv h1 h2
+ in
+ fo_unif_l test_equality_only subst' metasenv' (l1,l2)
+ in
+ fo_unif_l test_equality_only subst metasenv (lr1, lr2) )
+ | (C.MutCase (_,_,outt1,t1',pl1), C.MutCase (_,_,outt2,t2',pl2))->
let subst', metasenv' =
- fo_unif_subst subst context metasenv outt1 outt2 in
+ fo_unif_subst test_equality_only subst context metasenv outt1 outt2 in
let subst'',metasenv'' =
- fo_unif_subst subst' context metasenv' t1 t2 in
- List.fold_left2
- (function (subst,metasenv) ->
- fo_unif_subst subst context metasenv
- ) (subst'',metasenv'') pl1 pl2
- | (C.Fix _, _)
- | (_, C.Fix _)
- | (C.CoFix _, _)
- | (_, C.CoFix _) ->
- if R.are_convertible context t1 t2 then
+ fo_unif_subst test_equality_only subst' context metasenv' t1' t2' in
+ (try
+ List.fold_left2
+ (function (subst,metasenv) ->
+ fo_unif_subst test_equality_only subst context metasenv
+ ) (subst'',metasenv'') pl1 pl2
+ with
+ Invalid_argument _ ->
+ raise (UnificationFailure "6"))
+ (* (sprintf
+ "Error trying to unify %s with %s: the number of branches is not the same." (CicMetaSubst.ppterm subst t1) (CicMetaSubst.ppterm subst t2)))) *)
+ | (C.Rel _, _) | (_, C.Rel _) ->
+ if t1 = t2 then
+ subst, metasenv
+ else
+ raise (UnificationFailure "6")
+ (* (sprintf
+ "Can't unify %s with %s because they are not convertible"
+ (CicMetaSubst.ppterm subst t1) (CicMetaSubst.ppterm subst t2))) *)
+ | (C.Sort _ ,_) | (_, C.Sort _)
+ | (C.Const _, _) | (_, C.Const _)
+ | (C.MutInd _, _) | (_, C.MutInd _)
+ | (C.MutConstruct _, _) | (_, C.MutConstruct _)
+ | (C.Fix _, _) | (_, C.Fix _)
+ | (C.CoFix _, _) | (_, C.CoFix _) ->
+ if t1 = t2 || R.are_convertible ~subst ~metasenv context t1 t2 then
subst, metasenv
else
- raise UnificationFailed
+ raise (UnificationFailure "7")
+ (* (sprintf
+ "Can't unify %s with %s because they are not convertible"
+ (CicMetaSubst.ppterm subst t1) (CicMetaSubst.ppterm subst t2))) *)
| (_,_) ->
- if R.are_convertible context t1 t2 then
+ if R.are_convertible ~subst ~metasenv context t1 t2 then
subst, metasenv
else
- raise UnificationFailed
+ raise (UnificationFailure "8")
+ (* (sprintf
+ "Can't unify %s with %s because they are not convertible"
+ (CicMetaSubst.ppterm subst t1) (CicMetaSubst.ppterm subst t2))) *)
-and fo_unif_subst_exp_named_subst subst context metasenv
+and fo_unif_subst_exp_named_subst test_equality_only subst context metasenv
exp_named_subst1 exp_named_subst2
=
-try
- List.fold_left2
- (fun (subst,metasenv) (uri1,t1) (uri2,t2) ->
- assert (uri1=uri2) ;
- fo_unif_subst subst context metasenv t1 t2
- ) (subst,metasenv) exp_named_subst1 exp_named_subst2
-with
-e ->
-let uri = UriManager.uri_of_string "cic:/dummy.var" in
-prerr_endline ("@@@: " ^ CicPp.ppterm (Cic.Var (uri,exp_named_subst1)) ^
-" <==> " ^ CicPp.ppterm (Cic.Var (uri,exp_named_subst2))) ; raise e
-;;
-
-let unwind metasenv subst unwinded t =
- let unwinded = ref unwinded in
- let frozen = ref [] in
- let rec um_aux metasenv =
- let module C = Cic in
- let module S = CicSubstitution in
- function
- C.Rel _ as t -> t,metasenv
- | C.Var _ as t -> t,metasenv
- | C.Meta (i,l) ->
- (try
- S.lift_meta l (List.assoc i !unwinded), metasenv
- with Not_found ->
- if List.mem i !frozen then raise OccurCheck
- else
- let saved_frozen = !frozen in
- frozen := i::!frozen ;
- let res =
- try
- let t = List.assoc i subst in
- let t',metasenv' = um_aux metasenv t in
- let _,metasenv'' =
- let (_,canonical_context,_) =
- List.find (function (m,_,_) -> m=i) metasenv
- in
- delift canonical_context metasenv' l t'
- in
- unwinded := (i,t')::!unwinded ;
- S.lift_meta l t', metasenv'
- with
- Not_found ->
- (* not constrained variable, i.e. free in subst*)
- let l',metasenv' =
- List.fold_right
- (fun t (tl,metasenv) ->
- match t with
- None -> None::tl,metasenv
- | Some t ->
- let t',metasenv' = um_aux metasenv t in
- (Some t')::tl, metasenv'
- ) l ([],metasenv)
- in
- C.Meta (i,l'), metasenv'
- in
- frozen := saved_frozen ;
- res
- )
- | C.Sort _
- | C.Implicit as t -> t,metasenv
- | C.Cast (te,ty) ->
- let te',metasenv' = um_aux metasenv te in
- let ty',metasenv'' = um_aux metasenv' ty in
- C.Cast (te',ty'),metasenv''
- | C.Prod (n,s,t) ->
- let s',metasenv' = um_aux metasenv s in
- let t',metasenv'' = um_aux metasenv' t in
- C.Prod (n, s', t'), metasenv''
- | C.Lambda (n,s,t) ->
- let s',metasenv' = um_aux metasenv s in
- let t',metasenv'' = um_aux metasenv' t in
- C.Lambda (n, s', t'), metasenv''
- | C.LetIn (n,s,t) ->
- let s',metasenv' = um_aux metasenv s in
- let t',metasenv'' = um_aux metasenv' t in
- C.LetIn (n, s', t'), metasenv''
- | C.Appl (he::tl) ->
- let tl',metasenv' =
- List.fold_right
- (fun t (tl,metasenv) ->
- let t',metasenv' = um_aux metasenv t in
- t'::tl, metasenv'
- ) tl ([],metasenv)
- in
- begin
- match um_aux metasenv' he with
- (C.Appl l, metasenv'') -> C.Appl (l@tl'),metasenv''
- | (he', metasenv'') -> C.Appl (he'::tl'),metasenv''
- end
- | C.Appl _ -> assert false
- | C.Const (uri,exp_named_subst) ->
- let exp_named_subst', metasenv' =
- List.fold_right
- (fun (uri,t) (tl,metasenv) ->
- let t',metasenv' = um_aux metasenv t in
- (uri,t')::tl, metasenv'
- ) exp_named_subst ([],metasenv)
- in
- C.Const (uri,exp_named_subst'),metasenv'
- | C.MutInd (uri,typeno,exp_named_subst) ->
- let exp_named_subst', metasenv' =
- List.fold_right
- (fun (uri,t) (tl,metasenv) ->
- let t',metasenv' = um_aux metasenv t in
- (uri,t')::tl, metasenv'
- ) exp_named_subst ([],metasenv)
- in
- C.MutInd (uri,typeno,exp_named_subst'),metasenv'
- | C.MutConstruct (uri,typeno,consno,exp_named_subst) ->
- let exp_named_subst', metasenv' =
- List.fold_right
- (fun (uri,t) (tl,metasenv) ->
- let t',metasenv' = um_aux metasenv t in
- (uri,t')::tl, metasenv'
- ) exp_named_subst ([],metasenv)
- in
- C.MutConstruct (uri,typeno,consno,exp_named_subst'),metasenv'
- | C.MutCase (sp,i,outty,t,pl) ->
- let outty',metasenv' = um_aux metasenv outty in
- let t',metasenv'' = um_aux metasenv' t in
- let pl',metasenv''' =
- List.fold_right
- (fun p (pl,metasenv) ->
- let p',metasenv' = um_aux metasenv p in
- p'::pl, metasenv'
- ) pl ([],metasenv'')
- in
- C.MutCase (sp, i, outty', t', pl'),metasenv'''
- | C.Fix (i, fl) ->
- let len = List.length fl in
- let liftedfl,metasenv' =
- List.fold_right
- (fun (name, i, ty, bo) (fl,metasenv) ->
- let ty',metasenv' = um_aux metasenv ty in
- let bo',metasenv'' = um_aux metasenv' bo in
- (name, i, ty', bo')::fl,metasenv''
- ) fl ([],metasenv)
- in
- C.Fix (i, liftedfl),metasenv'
- | C.CoFix (i, fl) ->
- let len = List.length fl in
- let liftedfl,metasenv' =
- List.fold_right
- (fun (name, ty, bo) (fl,metasenv) ->
- let ty',metasenv' = um_aux metasenv ty in
- let bo',metasenv'' = um_aux metasenv' bo in
- (name, ty', bo')::fl,metasenv''
- ) fl ([],metasenv)
- in
- C.CoFix (i, liftedfl),metasenv'
- in
- let t',metasenv' = um_aux metasenv t in
- t',metasenv',!unwinded
-;;
-
-(* apply_subst_reducing subst (Some (mtr,reductions_no)) t *)
-(* performs as (apply_subst subst t) until it finds an application of *)
-(* (META [meta_to_reduce]) that, once unwinding is performed, creates *)
-(* a new beta-redex; in this case up to [reductions_no] consecutive *)
-(* beta-reductions are performed. *)
-(* Hint: this function is usually called when [reductions_no] *)
-(* eta-expansions have been performed and the head of the new *)
-(* application has been unified with (META [meta_to_reduce]): *)
-(* during the unwinding the eta-expansions are undone. *)
-
-let apply_subst_reducing subst meta_to_reduce t =
- let unwinded = ref subst in
- let rec um_aux =
- let module C = Cic in
- let module S = CicSubstitution in
- function
- C.Rel _
- | C.Var _ as t -> t
- | C.Meta (i,l) as t ->
- (try
- S.lift_meta l (List.assoc i !unwinded)
- with Not_found ->
- C.Meta (i,l))
- | C.Sort _ as t -> t
- | C.Implicit as t -> t
- | C.Cast (te,ty) -> C.Cast (um_aux te, um_aux ty)
- | C.Prod (n,s,t) -> C.Prod (n, um_aux s, um_aux t)
- | C.Lambda (n,s,t) -> C.Lambda (n, um_aux s, um_aux t)
- | C.LetIn (n,s,t) -> C.LetIn (n, um_aux s, um_aux t)
- | C.Appl (he::tl) ->
- let tl' = List.map um_aux tl in
- let t' =
- match um_aux he with
- C.Appl l -> C.Appl (l@tl')
- | _ as he' -> C.Appl (he'::tl')
- in
- begin
- match meta_to_reduce,he with
- Some (mtr,reductions_no), C.Meta (m,_) when m = mtr ->
- let rec beta_reduce =
- function
- (n,(C.Appl (C.Lambda (_,_,t)::he'::tl'))) when n > 0 ->
- let he'' = CicSubstitution.subst he' t in
- if tl' = [] then
- he''
- else
- beta_reduce (n-1,C.Appl(he''::tl'))
- | (_,t) -> t
- in
- beta_reduce (reductions_no,t')
- | _,_ -> t'
- end
- | C.Appl _ -> assert false
- | C.Const (uri,exp_named_subst) ->
- let exp_named_subst' =
- List.map (function (uri,t) -> (uri,um_aux t)) exp_named_subst
- in
- C.Const (uri,exp_named_subst')
- | C.MutInd (uri,typeno,exp_named_subst) ->
- let exp_named_subst' =
- List.map (function (uri,t) -> (uri,um_aux t)) exp_named_subst
- in
- C.MutInd (uri,typeno,exp_named_subst')
- | C.MutConstruct (uri,typeno,consno,exp_named_subst) ->
- let exp_named_subst' =
- List.map (function (uri,t) -> (uri,um_aux t)) exp_named_subst
- in
- C.MutConstruct (uri,typeno,consno,exp_named_subst')
- | C.MutCase (sp,i,outty,t,pl) ->
- C.MutCase (sp, i, um_aux outty, um_aux t,
- List.map um_aux pl)
- | C.Fix (i, fl) ->
- let len = List.length fl in
- let liftedfl =
- List.map
- (fun (name, i, ty, bo) -> (name, i, um_aux ty, um_aux bo))
- fl
- in
- C.Fix (i, liftedfl)
- | C.CoFix (i, fl) ->
- let len = List.length fl in
- let liftedfl =
- List.map
- (fun (name, ty, bo) -> (name, um_aux ty, um_aux bo))
- fl
- in
- C.CoFix (i, liftedfl)
- in
- um_aux t
-;;
-
-(* UNWIND THE MGU INSIDE THE MGU *)
-let unwind_subst metasenv subst =
- let identity_relocation_list_for_metavariable i =
- let (_,canonical_context,_) =
- List.find (function (m,_,_) -> m=i) metasenv
- in
- let canonical_context_length = List.length canonical_context in
- let rec aux =
- function
- n when n > canonical_context_length -> []
- | n -> (Some (Cic.Rel n))::(aux (n+1))
- in
- aux 1
- in
- List.fold_left
- (fun (unwinded,metasenv) (i,_) ->
- let identity_relocation_list =
- identity_relocation_list_for_metavariable i
- in
- let (_,metasenv',subst') =
- unwind metasenv subst unwinded (Cic.Meta (i,identity_relocation_list))
- in
- subst',metasenv'
- ) ([],metasenv) subst
-;;
-
-let apply_subst subst t =
- (* metasenv will not be used nor modified. So, let's use a dummy empty one *)
- let metasenv = [] in
- let (t',_,_) = unwind metasenv [] subst t in
- t'
-;;
+ try
+ List.fold_left2
+ (fun (subst,metasenv) (uri1,t1) (uri2,t2) ->
+ assert (uri1=uri2) ;
+ fo_unif_subst test_equality_only subst context metasenv t1 t2
+ ) (subst,metasenv) exp_named_subst1 exp_named_subst2
+ with
+ Invalid_argument _ ->
+ let print_ens ens =
+ String.concat " ; "
+ (List.map
+ (fun (uri,t) ->
+ UriManager.string_of_uri uri ^ " := " ^ (CicMetaSubst.ppterm subst t)
+ ) ens)
+ in
+ raise (UnificationFailure (sprintf
+ "Error trying to unify the two explicit named substitutions (local contexts) %s and %s: their lengths is different." (print_ens exp_named_subst1) (print_ens exp_named_subst2)))
(* A substitution is a (int * Cic.term) list that associates a *)
(* metavariable i with its body. *)
(* a new substitution which is already unwinded and ready to be applied and *)
(* a new metasenv in which some hypothesis in the contexts of the *)
(* metavariables may have been restricted. *)
-let fo_unif metasenv context t1 t2 =
- let subst_to_unwind,metasenv' = fo_unif_subst [] context metasenv t1 t2 in
- unwind_subst metasenv' subst_to_unwind
+let fo_unif metasenv context t1 t2 =
+ fo_unif_subst false [] context metasenv t1 t2 ;;
+
+let fo_unif_subst subst context metasenv t1 t2 =
+ let enrich_msg msg = (* "bella roba" *)
+ sprintf "Unification error unifying %s of type %s with %s of type %s in context\n%s\nand metasenv\n%s\nand substitution\n%s\nbecause %s"
+ (CicMetaSubst.ppterm subst t1)
+ (try
+ CicPp.ppterm (type_of_aux' metasenv subst context t1)
+ with _ -> "MALFORMED")
+ (CicMetaSubst.ppterm subst t2)
+ (try
+ CicPp.ppterm (type_of_aux' metasenv subst context t2)
+ with _ -> "MALFORMED")
+ (CicMetaSubst.ppcontext subst context)
+ (CicMetaSubst.ppmetasenv metasenv subst)
+ (CicMetaSubst.ppsubst subst) msg
+ in
+ try
+ fo_unif_subst false subst context metasenv t1 t2
+ with
+ | AssertFailure msg -> raise (AssertFailure (enrich_msg msg))
+ | UnificationFailure msg -> raise (UnificationFailure (enrich_msg msg))
;;
+
projects / helm.git / blobdiff