* http://cs.unibo.it/helm/.
*)
+exception Bad_pattern of string
+
let new_meta_of_proof ~proof:(_, metasenv, _, _) =
CicMkImplicit.new_meta metasenv []
;;
(** finds the _pointers_ to subterms that are alpha-equivalent to wanted in t *)
-let find_subterms ~eq ~wanted t =
- let rec find wanted t =
- if eq wanted t then
- [t]
+let find_subterms ~wanted ~context t =
+ let rec find context w t =
+ if ProofEngineReduction.alpha_equivalence w t then
+ [context,t]
else
match t with
| Cic.Sort _
fun acc e ->
match e with
| None -> acc
- | Some t -> find wanted t @ acc
+ | Some t -> find context w t @ acc
) [] ctx
- | Cic.Lambda (_, t1, t2)
- | Cic.Prod (_, t1, t2)
- | Cic.LetIn (_, t1, t2) ->
- find wanted t1 @ find (CicSubstitution.lift 1 wanted) t2
+ | Cic.Lambda (name, t1, t2)
+ | Cic.Prod (name, t1, t2) ->
+ find context w t1 @
+ find (Some (name, Cic.Decl t1)::context)
+ (CicSubstitution.lift 1 w) t2
+ | Cic.LetIn (name, t1, t2) ->
+ find context w t1 @
+ find (Some (name, Cic.Def (t1,None))::context)
+ (CicSubstitution.lift 1 w) t2
| Cic.Appl l ->
- List.fold_left (fun acc t -> find wanted t @ acc) [] l
- | Cic.Cast (t, ty) -> find wanted t @ find wanted ty
+ List.fold_left (fun acc t -> find context w t @ acc) [] l
+ | Cic.Cast (t, ty) -> find context w t @ find context w ty
| Cic.Implicit _ -> assert false
| Cic.Const (_, esubst)
| Cic.Var (_, esubst)
| Cic.MutInd (_, _, esubst)
| Cic.MutConstruct (_, _, _, esubst) ->
- List.fold_left (fun acc (_, t) -> find wanted t @ acc) [] esubst
+ List.fold_left (fun acc (_, t) -> find context w t @ acc) [] esubst
| Cic.MutCase (_, _, outty, indterm, patterns) ->
- find wanted outty @ find wanted indterm @
- List.fold_left (fun acc p -> find wanted p @ acc) [] patterns
+ find context w outty @ find context w indterm @
+ List.fold_left (fun acc p -> find context w p @ acc) [] patterns
| 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 wanted ty @ find wanted bo @ acc
+ fun acc (_, _, ty, bo) ->
+ find context w ty @ find (tys @ context) w bo @ acc
) [] 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 wanted ty @ find wanted bo @ acc
+ fun acc (_, ty, bo) ->
+ find context w ty @ find (tys @ context) w bo @ acc
) [] funl
in
- find wanted t
+ find context wanted t
+
+let select_in_term ~context ~term ~pattern:(wanted,where) =
+ let add_ctx context name entry =
+ (Some (name, entry)) :: context
+ in
+ let rec aux context where term =
+ match (where, term) with
+ | Cic.Implicit (Some `Hole), t -> [context,t]
+ | Cic.Implicit (Some `Type), t -> []
+ | Cic.Implicit None,_ -> []
+ | Cic.Meta (_, ctxt1), Cic.Meta (_, ctxt2) ->
+ List.concat
+ (List.map2
+ (fun t1 t2 ->
+ (match (t1, t2) with
+ Some t1, Some t2 -> aux context t1 t2
+ | _ -> []))
+ ctxt1 ctxt2)
+ | Cic.Cast (te1, ty1), Cic.Cast (te2, ty2) ->
+ aux context te1 te2 @ aux context ty1 ty2
+ | Cic.Prod (Cic.Anonymous, s1, t1), Cic.Prod (name, s2, t2)
+ | Cic.Lambda (Cic.Anonymous, s1, t1), Cic.Lambda (name, s2, t2) ->
+ aux context s1 s2 @ aux (add_ctx context name (Cic.Decl s2)) t1 t2
+ | Cic.Prod (Cic.Name n1, s1, t1),
+ Cic.Prod ((Cic.Name n2) as name , s2, t2)
+ | Cic.Lambda (Cic.Name n1, s1, t1),
+ Cic.Lambda ((Cic.Name n2) as name, s2, t2) when n1 = n2->
+ aux context s1 s2 @ aux (add_ctx context name (Cic.Decl s2)) t1 t2
+ | Cic.Prod (name1, s1, t1), Cic.Prod (name2, s2, t2)
+ | Cic.Lambda (name1, s1, t1), Cic.Lambda (name2, s2, t2) -> []
+ | Cic.LetIn (Cic.Anonymous, s1, t1), Cic.LetIn (name, s2, t2) ->
+ aux context s1 s2 @ aux (add_ctx context name (Cic.Def (s2,None))) t1 t2
+ | Cic.LetIn (Cic.Name n1, s1, t1),
+ Cic.LetIn ((Cic.Name n2) as name, s2, t2) when n1 = n2->
+ aux context s1 s2 @ aux (add_ctx context name (Cic.Def (s2,None))) t1 t2
+ | Cic.LetIn (name1, s1, t1), Cic.LetIn (name2, s2, t2) -> []
+ | Cic.Appl terms1, Cic.Appl terms2 -> auxs context terms1 terms2
+ | Cic.Var (_, subst1), Cic.Var (_, subst2)
+ | Cic.Const (_, subst1), Cic.Const (_, subst2)
+ | Cic.MutInd (_, _, subst1), Cic.MutInd (_, _, subst2)
+ | Cic.MutConstruct (_, _, _, subst1), Cic.MutConstruct (_, _, _, subst2) ->
+ auxs context (List.map snd subst1) (List.map snd subst2)
+ | Cic.MutCase (_, _, out1, t1, pat1), Cic.MutCase (_ , _, out2, t2, pat2) ->
+ aux context out1 out2 @ aux context t1 t2 @ auxs context pat1 pat2
+ | Cic.Fix (_, funs1), Cic.Fix (_, funs2) ->
+ let tys =
+ List.map (fun (n,_,ty,_) -> Some (Cic.Name n,(Cic.Decl ty))) funs2
+ in
+ List.concat
+ (List.map2
+ (fun (_, _, ty1, bo1) (_, _, ty2, bo2) ->
+ aux context ty1 ty2 @ aux (tys @ context) bo1 bo2)
+ funs1 funs2)
+ | Cic.CoFix (_, funs1), Cic.CoFix (_, funs2) ->
+ let tys =
+ List.map (fun (n,ty,_) -> Some (Cic.Name n,(Cic.Decl ty))) funs2
+ in
+ List.concat
+ (List.map2
+ (fun (_, ty1, bo1) (_, ty2, bo2) ->
+ aux context ty1 ty2 @ aux (tys @ context) bo1 bo2)
+ funs1 funs2)
+ | x,y ->
+ raise (Bad_pattern
+ (Printf.sprintf "Pattern %s versus term %s"
+ (CicPp.ppterm x)
+ (CicPp.ppterm y)))
+ and auxs context terms1 terms2 = (* as aux for list of terms *)
+ List.concat (List.map2 (fun t1 t2 -> aux context t1 t2) terms1 terms2)
+ in
+ let context_len = List.length context in
+ let roots = aux context where term in
+ match wanted with
+ None -> roots
+ | Some wanted ->
+ let rec find_in_roots =
+ function
+ [] -> []
+ | (context',where)::tl ->
+ let tl' = find_in_roots tl in
+ let context'_len = List.length context' in
+ let found =
+ let wanted =
+ CicSubstitution.lift (context'_len - context_len) wanted
+ in
+ find_subterms ~wanted ~context where
+ in
+ 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
projects / helm.git / blobdiff