open ProofEngineHelpers
open ProofEngineTypes
+exception TheTypeOfTheCurrentGoalIsAMetaICannotChooseTheRightElimiantionPrinciple
exception NotAnInductiveTypeToEliminate
-exception NotTheRightEliminatorShape
-exception NoHypothesesFound
exception WrongUriToVariable of string
(* lambda_abstract newmeta ty *)
(* and [bo] = Lambda/LetIn [context].(Meta [newmeta]) *)
(* So, lambda_abstract is the core of the implementation of *)
(* the Intros tactic. *)
-let lambda_abstract metasenv context newmeta ty mk_fresh_name =
+(* howmany = -1 means Intros, howmany > 0 means Intros n *)
+let lambda_abstract ?(howmany=(-1)) metasenv context newmeta ty mk_fresh_name =
let module C = Cic in
- let rec collect_context context =
- function
- C.Cast (te,_) -> collect_context context te
- | C.Prod (n,s,t) ->
- let n' = mk_fresh_name metasenv context n ~typ:s in
- let (context',ty,bo) =
- collect_context ((Some (n',(C.Decl s)))::context) t
+ let rec collect_context context howmany ty =
+ match howmany with
+ | 0 ->
+ let irl =
+ CicMkImplicit.identity_relocation_list_for_metavariable context
in
- (context',ty,C.Lambda(n',s,bo))
- | C.LetIn (n,s,t) ->
- let (context',ty,bo) =
- collect_context ((Some (n,(C.Def (s,None))))::context) t
- in
- (context',ty,C.LetIn(n,s,bo))
- | _ as t ->
- let irl =
- CicMkImplicit.identity_relocation_list_for_metavariable context
- in
- context, t, (C.Meta (newmeta,irl))
+ context, ty, (C.Meta (newmeta,irl))
+ | _ ->
+ match ty with
+ C.Cast (te,_) -> collect_context context howmany te
+ | C.Prod (n,s,t) ->
+ let n' = mk_fresh_name metasenv context n ~typ:s in
+ let (context',ty,bo) =
+ collect_context ((Some (n',(C.Decl s)))::context) (howmany - 1) t
+ in
+ (context',ty,C.Lambda(n',s,bo))
+ | C.LetIn (n,s,t) ->
+ let (context',ty,bo) =
+ collect_context ((Some (n,(C.Def (s,None))))::context) (howmany - 1) t
+ in
+ (context',ty,C.LetIn(n,s,bo))
+ | _ as t ->
+ let irl =
+ CicMkImplicit.identity_relocation_list_for_metavariable context
+ in
+ context, t, (C.Meta (newmeta,irl))
in
- collect_context context ty
+ collect_context context howmany ty
let eta_expand metasenv context t arg =
let module T = CicTypeChecker in
let new_metasenv_for_apply newmeta proof context ty =
let module C = Cic in
let module S = CicSubstitution in
- let rec aux newmeta =
- function
+ 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 ==>
let (res,newmetasenv,arguments,lastmeta) =
aux (newmeta + 1) (S.subst newargument t)
in
- res,(newmeta,context,s)::newmetasenv,newargument::arguments,lastmeta
- | t -> t,[],[],newmeta
+ 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. *)
new_fresh_meta,newmetasenvfragment,exp_named_subst',exp_named_subst_diff
;;
+let new_metasenv_and_unify_and_t newmeta' metasenv' proof context term' ty termty =
+ let (consthead,newmetas,arguments,_) =
+ new_metasenv_for_apply newmeta' proof context termty
+ in
+ let newmetasenv = metasenv'@newmetas in
+ let subst,newmetasenv',_ =
+ CicUnification.fo_unif newmetasenv context consthead ty CicUniv.empty_ugraph
+ in
+ let t =
+ if List.length newmetas = 0 then term' else Cic.Appl (term'::arguments)
+ in
+ subst,newmetasenv',t
+
let apply_tac_verbose ~term (proof, goal) =
(* Assumption: The term "term" must be closed in the current context *)
let module T = CicTypeChecker in
| _ -> [],newmeta,[],term
in
let metasenv' = metasenv@newmetasenvfragment in
- let termty,_ = (* TASSI:FIXME *)
- CicTypeChecker.type_of_aux' metasenv' context term CicUniv.empty_ugraph in
+ let termty,_ =
+ CicTypeChecker.type_of_aux' metasenv' context term' CicUniv.empty_ugraph in
let termty =
CicSubstitution.subst_vars exp_named_subst_diff termty
in
- (* newmeta is the lowest index of the new metas introduced *)
- let (consthead,newmetas,arguments,_) =
- new_metasenv_for_apply newmeta' proof context termty
- in
- let newmetasenv = metasenv'@newmetas in
- let subst,newmetasenv',_ = (* TASSI:FIXME *)
- CicUnification.fo_unif newmetasenv context consthead ty
- CicUniv.empty_ugraph
- in
- let in_subst_domain i = List.exists (function (j,_) -> i=j) subst in
- let apply_subst = CicMetaSubst.apply_subst subst in
- let old_uninstantiatedmetas,new_uninstantiatedmetas =
- (* subst_in doesn't need the context. Hence the underscore. *)
- let subst_in _ = CicMetaSubst.apply_subst subst in
- classify_metas newmeta in_subst_domain subst_in newmetasenv'
- in
- let bo' =
- apply_subst
- (if List.length newmetas = 0 then
- term'
- else
- Cic.Appl (term'::arguments)
- )
- in
- let newmetasenv'' = new_uninstantiatedmetas@old_uninstantiatedmetas in
- let subst_in =
- (* if we just apply the subtitution, the type is irrelevant:
+ let subst,newmetasenv',t =
+ try
+ new_metasenv_and_unify_and_t newmeta' metasenv' proof context term' ty
+ termty
+ with CicUnification.UnificationFailure _ ->
+ new_metasenv_and_unify_and_t newmeta' metasenv' proof context term' ty
+ (CicReduction.whd context termty)
+ in
+ let in_subst_domain i = List.exists (function (j,_) -> i=j) subst in
+ let apply_subst = CicMetaSubst.apply_subst subst in
+ let old_uninstantiatedmetas,new_uninstantiatedmetas =
+ (* subst_in doesn't need the context. Hence the underscore. *)
+ let subst_in _ = CicMetaSubst.apply_subst subst in
+ classify_metas newmeta in_subst_domain subst_in newmetasenv'
+ in
+ let bo' = apply_subst t in
+ let newmetasenv'' = new_uninstantiatedmetas@old_uninstantiatedmetas in
+(* prerr_endline ("me: " ^ CicMetaSubst.ppmetasenv newmetasenv'' subst); *)
+ let subst_in =
+ (* if we just apply the subtitution, the type is irrelevant:
we may use Implicit, since it will be dropped *)
- CicMetaSubst.apply_subst
- ((metano,(context, bo', Cic.Implicit None))::subst)
- in
- let (newproof, newmetasenv''') =
- subst_meta_and_metasenv_in_proof
- proof metano subst_in newmetasenv''
- in
- (subst_in,(newproof, List.map (function (i,_,_) -> i) new_uninstantiatedmetas))
+ CicMetaSubst.apply_subst ((metano,(context,bo',Cic.Implicit None))::subst)
+ in
+ let (newproof, newmetasenv''') =
+ subst_meta_and_metasenv_in_proof proof metano subst_in newmetasenv''
+ in
+ (subst_in,
+ (newproof,
+ List.map (function (i,_,_) -> i) new_uninstantiatedmetas))
let apply_tac ~term status = snd (apply_tac_verbose ~term status)
in
mk_tactic (apply_tac ~term)
-let intros_tac ?(mk_fresh_name_callback = FreshNamesGenerator.mk_fresh_name ~subst:[]) ()=
+let intros_tac ?howmany ?(mk_fresh_name_callback = FreshNamesGenerator.mk_fresh_name ~subst:[]) ()=
let intros_tac
?(mk_fresh_name_callback = (FreshNamesGenerator.mk_fresh_name ~subst:[])) ()
(proof, goal)
let metano,context,ty = CicUtil.lookup_meta goal metasenv in
let newmeta = new_meta_of_proof ~proof in
let (context',ty',bo') =
- lambda_abstract metasenv context newmeta ty mk_fresh_name_callback
+ lambda_abstract ?howmany metasenv context newmeta ty mk_fresh_name_callback
in
let (newproof, _) =
subst_meta_in_proof proof metano bo' [newmeta,context',ty']
in
mk_tactic (intros_tac ~mk_fresh_name_callback ())
-let cut_tac?(mk_fresh_name_callback = FreshNamesGenerator.mk_fresh_name ~subst:[]) ~term=
+let cut_tac ?(mk_fresh_name_callback = FreshNamesGenerator.mk_fresh_name ~subst:[]) term =
let cut_tac
?(mk_fresh_name_callback = FreshNamesGenerator.mk_fresh_name ~subst:[])
term (proof, goal)
in
mk_tactic (cut_tac ~mk_fresh_name_callback term)
-let letin_tac ?(mk_fresh_name_callback=FreshNamesGenerator.mk_fresh_name ~subst:[]) ~term=
+let letin_tac ?(mk_fresh_name_callback=FreshNamesGenerator.mk_fresh_name ~subst:[]) term =
let letin_tac
?(mk_fresh_name_callback = FreshNamesGenerator.mk_fresh_name ~subst:[])
term (proof, goal)
| C.Sort C.Set -> "_rec"
| C.Sort C.CProp -> "_rec"
| C.Sort (C.Type _)-> "_rect"
+ | C.Meta (_,_) -> raise TheTypeOfTheCurrentGoalIsAMetaICannotChooseTheRightElimiantionPrinciple
| _ -> assert false
in
U.uri_of_string (buri ^ "/" ^ name ^ ext ^ ".con")
mk_tactic (elim_tac ~term)
;;
+let elim_intros_tac ~term =
+ Tacticals.then_ ~start:(elim_tac ~term)
+ ~continuation:(intros_tac ())
+;;
+
(* The simplification is performed only on the conclusion *)
let elim_intros_simpl_tac ~term =
Tacticals.then_ ~start:(elim_tac ~term)
(Tacticals.thens
~start:(intros_tac ())
~continuations:
- [ReductionTactics.simpl_tac ~also_in_hypotheses:false ~terms:None])
+ [ReductionTactics.simpl_tac
+ ~pattern:(ProofEngineTypes.conclusion_pattern None)])
;;
exception NotConvertible
-(*CSC: Bug (or feature?). [with_what] is parsed in the context of the goal, *)
-(*CSC: while [what] can have a richer context (because of binders) *)
-(*CSC: So it is _NOT_ possible to use those binders in the [with_what] term. *)
-(*CSC: Is that evident? Is that right? Or should it be changed? *)
-let change_tac ~what ~with_what =
- let change_tac ~what ~with_what (proof, goal) =
- let curi,metasenv,pbo,pty = proof in
- let metano,context,ty = CicUtil.lookup_meta goal metasenv in
- (* are_convertible works only on well-typed terms *)
- let _,u =
- CicTypeChecker.type_of_aux' metasenv context with_what
- CicUniv.empty_ugraph
- in (* TASSI: FIXME *)
- let b,_ =
- CicReduction.are_convertible context what with_what u
+(* Note: this code is almost identical to ReductionTactics.reduction_tac and
+* it could be unified by making the change function a callback *)
+(* CSC: with_what is parsed in the context of the goal, but it should replace
+ something that lives in a completely different context. Thus we
+ perform a delift + lift phase to move it in the right context. However,
+ in this way the tactic is less powerful than expected: with_what cannot
+ reference variables that are local to the term that is going to be
+ replaced. To fix this we should parse with_what in the context of the
+ term(s) to be replaced. *)
+let change_tac ~pattern with_what =
+ let change_tac ~pattern ~with_what (proof, goal) =
+ let curi,metasenv,pbo,pty = proof in
+ let (metano,context,ty) as conjecture = CicUtil.lookup_meta goal metasenv in
+ let context_len = List.length context in
+ let change context'_len where terms =
+ if terms = [] then where
+ else
+ let terms, terms' =
+ List.split
+ (List.map
+ (fun (context_of_t, t) ->
+ let context_of_t_len = List.length context_of_t in
+ let with_what_in_context' =
+ if context_len > context'_len then
+ begin
+ let with_what,subst,metasenv' =
+ CicMetaSubst.delift_rels [] metasenv
+ (context_len - context'_len) with_what
+ in
+ assert (subst = []);
+ assert (metasenv = metasenv');
+ with_what
+ end
+ else
+ with_what in
+ let with_what_in_context_of_t =
+ if context_of_t_len > context'_len then
+ CicSubstitution.lift (context_of_t_len - context'_len)
+ with_what_in_context'
+ else
+ with_what in
+ let _,u =
+ CicTypeChecker.type_of_aux' metasenv context_of_t with_what
+ CicUniv.empty_ugraph in
+ let b,_ =
+ CicReduction.are_convertible ~metasenv context_of_t t with_what u in
+ if b then
+ t, with_what_in_context_of_t
+ else
+ raise NotConvertible) terms)
in
- if b then
- begin
- let replace =
- ProofEngineReduction.replace
- ~equality:(==) ~what:[what] ~with_what:[with_what]
- in
- let ty' = replace ty in
- let context' =
- List.map
- (function
- Some (name,Cic.Def (t,None))->
- Some (name,Cic.Def ((replace t),None))
- | Some (name,Cic.Decl t) -> Some (name,Cic.Decl (replace t))
- | None -> None
- | Some (_,Cic.Def (_,Some _)) -> assert false
- ) context
- in
- let metasenv' =
- List.map
- (function
- (n,_,_) when n = metano -> (metano,context',ty')
- | _ as t -> t
- ) metasenv
- in
- (curi,metasenv',pbo,pty), [metano]
- end
- else
- raise (ProofEngineTypes.Fail "Not convertible")
+ ProofEngineReduction.replace ~equality:(==) ~what:terms ~with_what:terms'
+ ~where:where in
+ let (selected_context,selected_ty) =
+ ProofEngineHelpers.select ~metasenv ~conjecture ~pattern in
+ let ty' = change context_len ty selected_ty in
+ let context' =
+ List.fold_right2
+ (fun entry selected_entry context' ->
+ let context'_len = List.length context' in
+ match entry,selected_entry with
+ None,None -> None::context'
+ | Some (name,Cic.Decl ty),Some (`Decl selected_ty) ->
+ let ty' = change context'_len ty selected_ty in
+ Some (name,Cic.Decl ty')::context'
+ | Some (name,Cic.Def (bo,ty)),Some (`Def (selected_bo,selected_ty)) ->
+ let bo' = change context'_len bo selected_bo in
+ let ty' =
+ match ty,selected_ty with
+ None,None -> None
+ | Some ty,Some selected_ty ->
+ Some (change context'_len ty selected_ty)
+ | _,_ -> assert false
+ in
+ Some (name,Cic.Def (bo',ty'))::context'
+ | _,_ -> assert false
+ ) context selected_context [] in
+ let metasenv' =
+ List.map (function
+ | (n,_,_) when n = metano -> (metano,context',ty')
+ | _ as t -> t
+ ) metasenv
+ in
+ (curi,metasenv',pbo,pty), [metano]
in
- mk_tactic (change_tac ~what ~with_what)
-
+ mk_tactic (change_tac ~pattern ~with_what)