;;
(** finds the _pointers_ to subterms that are alpha-equivalent to wanted in t *)
-let find_subterms ~wanted ~context t =
- let rec find context w t =
- if ProofEngineReduction.alpha_equivalence w t then
- [context,t]
- else
+let find_subterms ~subst ~metasenv ~ugraph ~wanted ~context t =
+ let rec find subst metasenv ugraph context w t =
+ try
+ let subst,metasenv,ugraph =
+ CicUnification.fo_unif_subst subst context metasenv w t ugraph
+ in
+ subst,metasenv,ugraph,[context,t]
+ with
+ CicUnification.UnificationFailure _
+ | CicUnification.Uncertain _ ->
match t with
| Cic.Sort _
- | Cic.Rel _ -> []
+ | Cic.Rel _ -> subst,metasenv,ugraph,[]
| Cic.Meta (_, ctx) ->
List.fold_left (
- fun acc e ->
+ fun (subst,metasenv,ugraph,acc) e ->
match e with
- | None -> acc
- | Some t -> find context w t @ acc
- ) [] ctx
+ | None -> subst,metasenv,ugraph,acc
+ | Some t ->
+ let subst,metasenv,ugraph,res =
+ find subst metasenv ugraph context w t
+ in
+ subst,metasenv,ugraph, res @ acc
+ ) (subst,metasenv,ugraph,[]) ctx
| Cic.Lambda (name, t1, t2)
| Cic.Prod (name, t1, t2) ->
- find context w t1 @
- find (Some (name, Cic.Decl t1)::context)
+ let subst,metasenv,ugraph,rest1 =
+ find subst metasenv ugraph context w t1 in
+ let subst,metasenv,ugraph,rest2 =
+ find subst metasenv ugraph (Some (name, Cic.Decl t1)::context)
(CicSubstitution.lift 1 w) t2
+ in
+ subst,metasenv,ugraph,rest1 @ rest2
| Cic.LetIn (name, t1, t2) ->
- find context w t1 @
- find (Some (name, Cic.Def (t1,None))::context)
+ let subst,metasenv,ugraph,rest1 =
+ find subst metasenv ugraph context w t1 in
+ let subst,metasenv,ugraph,rest2 =
+ find subst metasenv ugraph (Some (name, Cic.Def (t1,None))::context)
(CicSubstitution.lift 1 w) t2
+ in
+ subst,metasenv,ugraph,rest1 @ rest2
| Cic.Appl l ->
- List.fold_left (fun acc t -> find context w t @ acc) [] l
- | Cic.Cast (t, ty) -> find context w t @ find context w ty
+ List.fold_left
+ (fun (subst,metasenv,ugraph,acc) t ->
+ let subst,metasenv,ugraph,res =
+ find subst metasenv ugraph context w t
+ in
+ subst,metasenv,ugraph,res @ acc)
+ (subst,metasenv,ugraph,[]) l
+ | Cic.Cast (t, ty) ->
+ let subst,metasenv,ugraph,rest =
+ find subst metasenv ugraph context w t in
+ let subst,metasenv,ugraph,resty =
+ find subst metasenv ugraph context w ty
+ in
+ subst,metasenv,ugraph,rest @ resty
| Cic.Implicit _ -> assert false
| Cic.Const (_, esubst)
| Cic.Var (_, esubst)
| Cic.MutInd (_, _, esubst)
| Cic.MutConstruct (_, _, _, esubst) ->
- List.fold_left (fun acc (_, t) -> find context w t @ acc) [] esubst
+ List.fold_left
+ (fun (subst,metasenv,ugraph,acc) (_, t) ->
+ let subst,metasenv,ugraph,res =
+ find subst metasenv ugraph context w t
+ in
+ subst,metasenv,ugraph,res @ acc)
+ (subst,metasenv,ugraph,[]) esubst
| Cic.MutCase (_, _, outty, indterm, patterns) ->
- find context w outty @ find context w indterm @
- List.fold_left (fun acc p -> find context w p @ acc) [] patterns
+ let subst,metasenv,ugraph,resoutty =
+ find subst metasenv ugraph context w outty in
+ let subst,metasenv,ugraph,resindterm =
+ find subst metasenv ugraph context w indterm in
+ let subst,metasenv,ugraph,respatterns =
+ List.fold_left
+ (fun (subst,metasenv,ugraph,acc) p ->
+ let subst,metaseng,ugraph,res =
+ find subst metasenv ugraph context w p
+ in
+ subst,metasenv,ugraph,res @ acc
+ ) (subst,metasenv,ugraph,[]) patterns
+ in
+ subst,metasenv,ugraph,resoutty @ resindterm @ respatterns
| Cic.Fix (_, funl) ->
let tys =
List.map (fun (n,_,ty,_) -> Some (Cic.Name n,(Cic.Decl ty))) funl
in
List.fold_left (
- fun acc (_, _, ty, bo) ->
- find context w ty @ find (tys @ context) w bo @ acc
- ) [] funl
+ fun (subst,metasenv,ugraph,acc) (_, _, ty, bo) ->
+ let subst,metasenv,ugraph,resty =
+ find subst metasenv ugraph context w ty in
+ let subst,metasenv,ugraph,resbo =
+ find subst metasenv ugraph (tys @ context) w bo
+ in
+ subst,metasenv,ugraph, resty @ resbo @ acc
+ ) (subst,metasenv,ugraph,[]) funl
| Cic.CoFix (_, funl) ->
let tys =
List.map (fun (n,ty,_) -> Some (Cic.Name n,(Cic.Decl ty))) funl
in
List.fold_left (
- fun acc (_, ty, bo) ->
- find context w ty @ find (tys @ context) w bo @ acc
- ) [] funl
+ fun (subst,metasenv,ugraph,acc) (_, ty, bo) ->
+ let subst,metasenv,ugraph,resty =
+ find subst metasenv ugraph context w ty in
+ let subst,metasenv,ugraph,resbo =
+ find subst metasenv ugraph (tys @ context) w bo
+ in
+ subst,metasenv,ugraph, resty @ resbo @ acc
+ ) (subst,metasenv,ugraph,[]) funl
in
- find context wanted t
+ find subst metasenv ugraph context wanted t
-let select_in_term ~context ~term ~pattern:(wanted,where) =
+let select_in_term ~metasenv ~context ~ugraph ~term ~pattern:(wanted,where) =
let add_ctx context name entry =
(Some (name, entry)) :: context
in
let context_len = List.length context in
let roots = aux context where term in
match wanted with
- None -> roots
+ None -> [],metasenv,ugraph,roots
| Some wanted ->
let rec find_in_roots =
function
- [] -> []
+ [] -> [],metasenv,ugraph,[]
| (context',where)::tl ->
- let tl' = find_in_roots tl in
+ let subst,metasenv,ugraph,tl' = find_in_roots tl in
let context'_len = List.length context' in
- let found =
+ let subst,metasenv,ugraph,found =
let wanted =
CicSubstitution.lift (context'_len - context_len) wanted
in
- find_subterms ~wanted ~context where
+ find_subterms ~subst ~metasenv ~ugraph ~wanted ~context where
in
- found @ tl'
+ subst,metasenv,ugraph,found @ tl'
in
find_in_roots roots
+(** create a pattern from a term and a list of subterms.
+* the pattern is granted to have a ? for every subterm that has no selected
+* subterms
+* @param equality equality function used while walking the term. Defaults to
+* physical equality (==) *)
+let pattern_of ?(equality=(==)) ~term terms =
+ let (===) x y = equality x y in
+ let not_found = false, Cic.Implicit None in
+ let rec aux t =
+ match t with
+ | t when List.exists (fun t' -> t === t') terms ->
+ true,Cic.Implicit (Some `Hole)
+ | Cic.Var (uri, subst) ->
+ let b,subst = aux_subst subst in
+ if b then
+ true,Cic.Var (uri, subst)
+ else
+ not_found
+ | Cic.Meta (i, ctxt) ->
+ let b,ctxt =
+ List.fold_right
+ (fun e (b,ctxt) ->
+ match e with
+ None -> b,None::ctxt
+ | Some t -> let bt,t = aux t in b||bt ,Some t::ctxt
+ ) ctxt (false,[])
+ in
+ if b then
+ true,Cic.Meta (i, ctxt)
+ else
+ not_found
+ | Cic.Cast (te, ty) ->
+ let b1,te = aux te in
+ let b2,ty = aux ty in
+ if b1||b2 then true,Cic.Cast (te, ty)
+ else
+ not_found
+ | Cic.Prod (name, s, t) ->
+ let b1,s = aux s in
+ let b2,t = aux t in
+ if b1||b2 then
+ true, Cic.Prod (name, s, t)
+ else
+ not_found
+ | Cic.Lambda (name, s, t) ->
+ let b1,s = aux s in
+ let b2,t = aux t in
+ if b1||b2 then
+ true, Cic.Lambda (name, s, t)
+ else
+ not_found
+ | Cic.LetIn (name, s, t) ->
+ let b1,s = aux s in
+ let b2,t = aux t in
+ if b1||b2 then
+ true, Cic.LetIn (name, s, t)
+ else
+ not_found
+ | Cic.Appl terms ->
+ let b,terms =
+ List.fold_right
+ (fun t (b,terms) ->
+ let bt,t = aux t in
+ b||bt,t::terms
+ ) terms (false,[])
+ in
+ if b then
+ true,Cic.Appl terms
+ else
+ not_found
+ | Cic.Const (uri, subst) ->
+ let b,subst = aux_subst subst in
+ if b then
+ true, Cic.Const (uri, subst)
+ else
+ not_found
+ | Cic.MutInd (uri, tyno, subst) ->
+ let b,subst = aux_subst subst in
+ if b then
+ true, Cic.MutInd (uri, tyno, subst)
+ else
+ not_found
+ | Cic.MutConstruct (uri, tyno, consno, subst) ->
+ let b,subst = aux_subst subst in
+ if b then
+ true, Cic.MutConstruct (uri, tyno, consno, subst)
+ else
+ not_found
+ | Cic.MutCase (uri, tyno, outty, t, pat) ->
+ let b1,outty = aux outty in
+ let b2,t = aux t in
+ let b3,pat =
+ List.fold_right
+ (fun t (b,pat) ->
+ let bt,t = aux t in
+ bt||b,t::pat
+ ) pat (false,[])
+ in
+ if b1 || b2 || b3 then
+ true, Cic.MutCase (uri, tyno, outty, t, pat)
+ else
+ not_found
+ | Cic.Fix (funno, funs) ->
+ let b,funs =
+ List.fold_right
+ (fun (name, i, ty, bo) (b,funs) ->
+ let b1,ty = aux ty in
+ let b2,bo = aux bo in
+ b||b1||b2, (name, i, ty, bo)::funs) funs (false,[])
+ in
+ if b then
+ true, Cic.Fix (funno, funs)
+ else
+ not_found
+ | Cic.CoFix (funno, funs) ->
+ let b,funs =
+ List.fold_right
+ (fun (name, ty, bo) (b,funs) ->
+ let b1,ty = aux ty in
+ let b2,bo = aux bo in
+ b||b1||b2, (name, ty, bo)::funs) funs (false,[])
+ in
+ if b then
+ true, Cic.CoFix (funno, funs)
+ else
+ not_found
+ | Cic.Rel _
+ | Cic.Sort _
+ | Cic.Implicit _ -> not_found
+ and aux_subst subst =
+ List.fold_right
+ (fun (uri, t) (b,subst) ->
+ let b1,t = aux t in
+ b||b1,(uri, t)::subst) subst (false,[])
+ in
+ snd (aux term)
+
exception Fail of string
-(** select metasenv conjecture pattern
-* select all subterms of [conjecture] matching [pattern].
-* It returns the set of matched terms (that can be compared using physical
-* equality to the subterms of [conjecture]) together with their contexts.
-* The representation of the set mimics the ProofEngineTypes.pattern type:
-* a list of hypothesis (names of) together with the list of its matched
-* subterms (and their contexts) + the list of matched subterms of the
-* with their context conclusion. Note: in the result the list of hypothesis
-* has an entry for each entry in the context and in the same order.
-* Of course the list of terms (with their context) associated to the
-* hypothesis name may be empty. *)
-let select ~metasenv ~conjecture:(_,context,ty) ~pattern:(what,hyp_patterns,goal_pattern) =
- let find_pattern_for name =
- try Some (snd (List.find (fun (n, pat) -> Cic.Name n = name) hyp_patterns))
- with Not_found -> None in
- let ty_terms = select_in_term ~context ~term:ty ~pattern:(what,goal_pattern) in
- let context_len = List.length context in
- let context_terms =
- fst
- (List.fold_right
- (fun entry (res,context) ->
- match entry with
- None -> (None::res),(None::context)
- | Some (name,Cic.Decl term) ->
- (match find_pattern_for name with
- | None -> ((Some (`Decl []))::res),(entry::context)
- | Some pat ->
- try
- let what =
- match what with
- None -> None
- | Some what ->
- let what,subst',metasenv' =
- CicMetaSubst.delift_rels [] metasenv
- (context_len - List.length context) what
- in
- assert (subst' = []);
- assert (metasenv' = metasenv);
- Some what in
- let terms = select_in_term ~context ~term ~pattern:(what,pat) in
- ((Some (`Decl terms))::res),(entry::context)
- with
- CicMetaSubst.DeliftingARelWouldCaptureAFreeVariable ->
- raise
- (Fail
- ("The term the user wants to convert is not closed " ^
- "in the context of the position of the substitution.")))
- | Some (name,Cic.Def (bo, ty)) ->
- (match find_pattern_for name with
- | None ->
- let selected_ty= match ty with None -> None | Some _ -> Some [] in
- ((Some (`Def ([],selected_ty)))::res),(entry::context)
- | Some pat ->
- try
- let what =
- match what with
- None -> None
- | Some what ->
- let what,subst',metasenv' =
- CicMetaSubst.delift_rels [] metasenv
- (context_len - List.length context) what
- in
- assert (subst' = []);
- assert (metasenv' = metasenv);
- Some what in
- let terms_bo =
- select_in_term ~context ~term:bo ~pattern:(what,pat) in
- let terms_ty =
- match ty with
- None -> None
- | Some ty ->
- Some (select_in_term ~context ~term:ty ~pattern:(what,pat))
- in
- ((Some (`Def (terms_bo,terms_ty)))::res),(entry::context)
- with
- CicMetaSubst.DeliftingARelWouldCaptureAFreeVariable ->
- raise
- (Fail
- ("The term the user wants to convert is not closed " ^
- "in the context of the position of the substitution.")))
- ) context ([],[]))
- in
- context_terms, ty_terms
+ (** select metasenv conjecture pattern
+ * select all subterms of [conjecture] matching [pattern].
+ * It returns the set of matched terms (that can be compared using physical
+ * equality to the subterms of [conjecture]) together with their contexts.
+ * The representation of the set mimics the ProofEngineTypes.pattern type:
+ * a list of hypothesis (names of) together with the list of its matched
+ * subterms (and their contexts) + the list of matched subterms of the
+ * with their context conclusion. Note: in the result the list of hypothesis
+ * has an entry for each entry in the context and in the same order.
+ * Of course the list of terms (with their context) associated to the
+ * hypothesis name may be empty. *)
+ let select ~metasenv ~ugraph ~conjecture:(_,context,ty)
+ ~pattern:(what,hyp_patterns,goal_pattern)
+ =
+ let find_pattern_for name =
+ try Some (snd (List.find (fun (n, pat) -> Cic.Name n = name) hyp_patterns))
+ with Not_found -> None in
+ let subst,metasenv,ugraph,ty_terms =
+ select_in_term ~metasenv ~context ~ugraph ~term:ty
+ ~pattern:(what,goal_pattern) in
+ let context_len = List.length context in
+ let subst,metasenv,ugraph,context_terms =
+ let subst,metasenv,ugraph,res,_ =
+ (List.fold_right
+ (fun entry (subst,metasenv,ugraph,res,context) ->
+ match entry with
+ None -> subst,metasenv,ugraph,(None::res),(None::context)
+ | Some (name,Cic.Decl term) ->
+ (match find_pattern_for name with
+ | None ->
+ subst,metasenv,ugraph,((Some (`Decl []))::res),(entry::context)
+ | Some pat ->
+ try
+ let what =
+ match what with
+ None -> None
+ | Some what ->
+ let what,subst',metasenv' =
+ CicMetaSubst.delift_rels [] metasenv
+ (context_len - List.length context) what
+ in
+ assert (subst' = []);
+ assert (metasenv' = metasenv);
+ Some what in
+ let subst,metasenv,ugraph,terms =
+ select_in_term ~metasenv ~context ~ugraph ~term
+ ~pattern:(what,pat)
+ in
+ subst,metasenv,ugraph,((Some (`Decl terms))::res),
+ (entry::context)
+ with
+ CicMetaSubst.DeliftingARelWouldCaptureAFreeVariable ->
+ raise
+ (Fail
+ ("The term the user wants to convert is not closed " ^
+ "in the context of the position of the substitution.")))
+ | Some (name,Cic.Def (bo, ty)) ->
+ (match find_pattern_for name with
+ | None ->
+ let selected_ty=match ty with None -> None | Some _ -> Some [] in
+ subst,metasenv,ugraph,((Some (`Def ([],selected_ty)))::res),
+ (entry::context)
+ | Some pat ->
+ try
+ let what =
+ match what with
+ None -> None
+ | Some what ->
+ let what,subst',metasenv' =
+ CicMetaSubst.delift_rels [] metasenv
+ (context_len - List.length context) what
+ in
+ assert (subst' = []);
+ assert (metasenv' = metasenv);
+ Some what in
+ let subst,metasenv,ugraph,terms_bo =
+ select_in_term ~metasenv ~context ~ugraph ~term:bo
+ ~pattern:(what,pat) in
+ let subst,metasenv,ugraph,terms_ty =
+ match ty with
+ None -> subst,metasenv,ugraph,None
+ | Some ty ->
+ let subst,metasenv,ugraph,res =
+ select_in_term ~metasenv ~context ~ugraph ~term:ty
+ ~pattern:(what,pat)
+ in
+ subst,metasenv,ugraph,Some res
+ in
+ subst,metasenv,ugraph,((Some (`Def (terms_bo,terms_ty)))::res),
+ (entry::context)
+ with
+ CicMetaSubst.DeliftingARelWouldCaptureAFreeVariable ->
+ raise
+ (Fail
+ ("The term the user wants to convert is not closed " ^
+ "in the context of the position of the substitution.")))
+ ) context (subst,metasenv,ugraph,[],[]))
+ in
+ subst,metasenv,ugraph,res
+ in
+ subst,metasenv,ugraph,context_terms, ty_terms
+
+(* saturate_term newmeta metasenv context ty *)
+(* Given a type [ty] (a backbone), it returns its head and a new metasenv in *)
+(* which there is new a META for each hypothesis, a list of arguments for the *)
+(* new applications and the index of the last new META introduced. The nth *)
+(* argument in the list of arguments is just the nth new META. *)
+let saturate_term newmeta metasenv context ty =
+ let module C = Cic in
+ let module S = CicSubstitution in
+ let rec aux newmeta ty =
+ let ty' = ty in
+ match ty' with
+ C.Cast (he,_) -> aux newmeta he
+(* CSC: patch to generate ?1 : ?2 : Type in place of ?1 : Type to simulate ?1 :< Type
+ (* If the expected type is a Type, then also Set is OK ==>
+ * we accept any term of type Type *)
+ (*CSC: BUG HERE: in this way it is possible for the term of
+ * type Type to be different from a Sort!!! *)
+ | C.Prod (name,(C.Sort (C.Type _) as s),t) ->
+ (* TASSI: ask CSC if BUG HERE refers to the C.Cast or C.Propd case *)
+ let irl =
+ CicMkImplicit.identity_relocation_list_for_metavariable context
+ in
+ let newargument = C.Meta (newmeta+1,irl) in
+ let (res,newmetasenv,arguments,lastmeta) =
+ aux (newmeta + 2) (S.subst newargument t)
+ in
+ res,
+ (newmeta,[],s)::(newmeta+1,context,C.Meta (newmeta,[]))::newmetasenv,
+ newargument::arguments,lastmeta
+*)
+ | C.Prod (name,s,t) ->
+ let irl =
+ CicMkImplicit.identity_relocation_list_for_metavariable context
+ in
+ let newargument = C.Meta (newmeta,irl) in
+ let (res,newmetasenv,arguments,lastmeta) =
+ aux (newmeta + 1) (S.subst newargument t)
+ in
+ let s' = CicReduction.normalize ~delta:false context s in
+ res,(newmeta,context,s')::newmetasenv,newargument::arguments,lastmeta
+ (** NORMALIZE RATIONALE
+ * we normalize the target only NOW since we may be in this case:
+ * A1 -> A2 -> T where T = (\lambda x.A3 -> P) k
+ * and we want a mesasenv with ?1:A1 and ?2:A2 and not
+ * ?1, ?2, ?3 (that is the one we whould get if we start from the
+ * beta-normalized A1 -> A2 -> A3 -> P **)
+ | t -> (CicReduction.normalize ~delta:false context t),[],[],newmeta
+ in
+ (* WARNING: here we are using the invariant that above the most *)
+ (* recente new_meta() there are no used metas. *)
+ let (res,newmetasenv,arguments,lastmeta) = aux newmeta ty in
+ res,metasenv @ newmetasenv,arguments,lastmeta
+
projects / helm.git / blobdiff