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 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 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 = 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 ->
+ if howmany <= 0 then
+ let irl =
+ CicMkImplicit.identity_relocation_list_for_metavariable context
+ in
+ context, t, (C.Meta (newmeta,irl))
+ else
+ raise (Fail (lazy "intro(s): not enough products or let-ins"))
in
- collect_context context ty
+ collect_context context howmany ty
let eta_expand metasenv context t arg =
let module T = CicTypeChecker in
| C.Var (uri,exp_named_subst) ->
let exp_named_subst' = aux_exp_named_subst n exp_named_subst in
C.Var (uri,exp_named_subst')
- | C.Meta _
+ | C.Meta (i,l) ->
+ let l' =
+ List.map (function None -> None | Some t -> Some (aux n t)) l
+ in
+ C.Meta (i, l')
| C.Sort _
- | C.Implicit as t -> t
+ | C.Implicit _ as t -> t
| C.Cast (te,ty) -> C.Cast (aux n te, aux n ty)
| C.Prod (nn,s,t) -> C.Prod (nn, aux n s, aux (n+1) t)
| C.Lambda (nn,s,t) -> C.Lambda (nn, aux n s, aux (n+1) t)
and aux_exp_named_subst n =
List.map (function uri,t -> uri,aux n t)
in
- let argty =
- T.type_of_aux' metasenv context arg
+ let argty,_ =
+ T.type_of_aux' metasenv context arg CicUniv.empty_ugraph (* TASSI: FIXME *)
in
let fresh_name =
- ProofEngineHelpers.mk_fresh_name context (Cic.Name "Heta") ~typ:argty
+ FreshNamesGenerator.mk_fresh_name ~subst:[]
+ metasenv context (Cic.Name "Heta") ~typ:argty
in
(C.Appl [C.Lambda (fresh_name,argty,aux 0 t) ; arg])
| Some (n,Cic.Def (s,None)) ->
Some (n,Cic.Def ((subst_in canonical_context' s),None))
| None -> None
- | Some (_,Cic.Def (_,Some _)) -> assert false
+ | Some (n,Cic.Def (bo,Some ty)) ->
+ Some
+ (n,
+ Cic.Def
+ (subst_in canonical_context' bo,
+ Some (subst_in canonical_context' ty)))
in
entry'::canonical_context'
) canonical_context []
old_uninst,((i,canonical_context',ty')::new_uninst)
) metasenv ([],[])
-(* Auxiliary function for apply: given a type (a backbone), it returns its *)
-(* head, a META environment in which there is new a META for each hypothesis,*)
-(* a list of arguments for the new applications and the indexes of the first *)
-(* and last new METAs introduced. The nth argument in the list of arguments *)
-(* is just the nth new META. *)
-let new_metasenv_for_apply newmeta proof context ty =
- let module C = Cic in
- let module S = CicSubstitution in
- let rec aux newmeta =
- function
- C.Cast (he,_) -> aux newmeta he
- | C.Prod (name,s,t) ->
- let irl = 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
- res,(newmeta,context,s)::newmetasenv,newargument::arguments,lastmeta
- | t -> 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,newmetasenv,arguments,lastmeta
-
(* Useful only inside apply_tac *)
let
generalize_exp_named_subst_with_fresh_metas context newmeta uri exp_named_subst
=
let module C = Cic in
let params =
- match CicEnvironment.get_obj uri with
- C.Constant (_,_,_,params)
- | C.CurrentProof (_,_,_,_,params)
- | C.Variable (_,_,_,params)
- | C.InductiveDefinition (_,params,_) -> params
+ let o,_ = CicEnvironment.get_obj CicUniv.empty_ugraph uri in
+ CicUtil.params_of_obj o
in
let exp_named_subst_diff,new_fresh_meta,newmetasenvfragment,exp_named_subst'=
let next_fresh_meta = ref newmeta in
[],[] -> []
| uri::tl,[] ->
let ty =
- match CicEnvironment.get_obj uri with
- C.Variable (_,_,ty,_) ->
- CicSubstitution.subst_vars !exp_named_subst_diff ty
- | _ -> raise (WrongUriToVariable (UriManager.string_of_uri uri))
+ let o,_ = CicEnvironment.get_obj CicUniv.empty_ugraph uri in
+ match o with
+ C.Variable (_,_,ty,_,_) ->
+ CicSubstitution.subst_vars !exp_named_subst_diff ty
+ | _ -> raise (WrongUriToVariable (UriManager.string_of_uri uri))
in
- let irl = identity_relocation_list_for_metavariable context in
- let subst_item = uri,C.Meta (!next_fresh_meta,irl) in
- newmetasenvfragment :=
- (!next_fresh_meta,context,ty)::!newmetasenvfragment ;
- exp_named_subst_diff := !exp_named_subst_diff @ [subst_item] ;
- incr next_fresh_meta ;
- subst_item::(aux (tl,[]))
+(* CSC: patch to generate ?1 : ?2 : Type in place of ?1 : Type to simulate ?1 :< Type
+ (match ty with
+ C.Sort (C.Type _) as s -> (* TASSI: ?? *)
+ let fresh_meta = !next_fresh_meta in
+ let fresh_meta' = fresh_meta + 1 in
+ next_fresh_meta := !next_fresh_meta + 2 ;
+ let subst_item = uri,C.Meta (fresh_meta',[]) in
+ newmetasenvfragment :=
+ (fresh_meta,[],C.Sort (C.Type (CicUniv.fresh()))) ::
+ (* TASSI: ?? *)
+ (fresh_meta',[],C.Meta (fresh_meta,[])) :: !newmetasenvfragment ;
+ exp_named_subst_diff := !exp_named_subst_diff @ [subst_item] ;
+ subst_item::(aux (tl,[]))
+ | _ ->
+*)
+ let irl =
+ CicMkImplicit.identity_relocation_list_for_metavariable context
+ in
+ let subst_item = uri,C.Meta (!next_fresh_meta,irl) in
+ newmetasenvfragment :=
+ (!next_fresh_meta,context,ty)::!newmetasenvfragment ;
+ exp_named_subst_diff := !exp_named_subst_diff @ [subst_item] ;
+ incr next_fresh_meta ;
+ subst_item::(aux (tl,[]))(*)*)
| uri::tl1,((uri',_) as s)::tl2 ->
assert (UriManager.eq uri uri') ;
s::(aux (tl1,tl2))
!exp_named_subst_diff,!next_fresh_meta,
List.rev !newmetasenvfragment, exp_named_subst'
in
-prerr_endline ("@@@ " ^ CicPp.ppterm (Cic.Var (uri,exp_named_subst)) ^ " |--> " ^ CicPp.ppterm (Cic.Var (uri,exp_named_subst'))) ;
new_fresh_meta,newmetasenvfragment,exp_named_subst',exp_named_subst_diff
;;
-let apply_tac ~term ~status:(proof, goal) =
+let new_metasenv_and_unify_and_t newmeta' metasenv' context term' ty termty goal_arity =
+ let (consthead,newmetasenv,arguments,_) =
+ saturate_term newmeta' metasenv' context termty goal_arity in
+ let subst,newmetasenv',_ =
+ CicUnification.fo_unif newmetasenv context consthead ty CicUniv.empty_ugraph
+ in
+ let t =
+ if List.length arguments = 0 then term' else Cic.Appl (term'::arguments)
+ in
+ subst,newmetasenv',t
+
+let rec count_prods context ty =
+ match CicReduction.whd context ty with
+ Cic.Prod (n,s,t) -> 1 + count_prods (Some (n,Cic.Decl s)::context) t
+ | _ -> 0
+
+let apply_tac_verbose_with_subst ~term (proof, goal) =
(* Assumption: The term "term" must be closed in the current context *)
let module T = CicTypeChecker in
let module R = CicReduction in
let module C = Cic in
let (_,metasenv,_,_) = proof in
- let metano,context,ty = List.find (function (m,_,_) -> m=goal) metasenv in
- let newmeta = new_meta ~proof in
+ let metano,context,ty = CicUtil.lookup_meta goal metasenv in
+ let newmeta = new_meta_of_proof ~proof in
let exp_named_subst_diff,newmeta',newmetasenvfragment,term' =
match term with
C.Var (uri,exp_named_subst) ->
| _ -> [],newmeta,[],term
in
let metasenv' = metasenv@newmetasenvfragment in
-prerr_endline ("^^^^^TERM': " ^ CicPp.ppterm term') ;
- let termty =
- CicSubstitution.subst_vars exp_named_subst_diff
- (CicTypeChecker.type_of_aux' metasenv' context term)
+ let termty,_ =
+ CicTypeChecker.type_of_aux' metasenv' context term' CicUniv.empty_ugraph
in
-prerr_endline ("^^^^^TERMTY: " ^ CicPp.ppterm termty) ;
- (* newmeta is the lowest index of the new metas introduced *)
- let (consthead,newmetas,arguments,_) =
- new_metasenv_for_apply newmeta' proof context termty
+ let termty =
+ CicSubstitution.subst_vars exp_named_subst_diff termty in
+ let goal_arity = count_prods context ty in
+ let subst,newmetasenv',t =
+ let rec add_one_argument n =
+ try
+ new_metasenv_and_unify_and_t newmeta' metasenv' context term' ty
+ termty n
+ with CicUnification.UnificationFailure _ when n > 0 ->
+ add_one_argument (n - 1)
in
- let newmetasenv = metasenv'@newmetas in
- let subst,newmetasenv' =
- CicUnification.fo_unif newmetasenv context consthead ty
- in
- let in_subst_domain i = List.exists (function (j,_) -> i=j) subst in
- let apply_subst = CicUnification.apply_subst subst in
- let old_uninstantiatedmetas,new_uninstantiatedmetas =
- (* subst_in doesn't need the context. Hence the underscore. *)
- let subst_in _ = CicUnification.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
-prerr_endline ("XXXX " ^ CicPp.ppterm (if List.length newmetas = 0 then term' else Cic.Appl (term'::arguments)) ^ " |>>> " ^ CicPp.ppterm bo') ;
- let newmetasenv'' = new_uninstantiatedmetas@old_uninstantiatedmetas in
- let (newproof, newmetasenv''') =
- let subst_in = CicUnification.apply_subst ((metano,bo')::subst) in
- subst_meta_and_metasenv_in_proof
- proof metano subst_in newmetasenv''
- in
- (newproof, List.map (function (i,_,_) -> i) new_uninstantiatedmetas)
+ add_one_argument goal_arity
+ 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
+ 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
+ (((metano,(context,bo',Cic.Implicit None))::subst)(* subst_in *), (* ALB *)
+ (newproof,
+ List.map (function (i,_,_) -> i) new_uninstantiatedmetas))
+
+
+(* ALB *)
+let apply_tac_verbose_with_subst ~term status =
+ try
+(* apply_tac_verbose ~term status *)
+ apply_tac_verbose_with_subst ~term status
+ (* TODO cacciare anche altre eccezioni? *)
+ with
+ | CicUnification.UnificationFailure msg
+ | CicTypeChecker.TypeCheckerFailure msg ->
+ raise (Fail msg)
+
+(* ALB *)
+let apply_tac_verbose ~term status =
+ let subst, status = apply_tac_verbose_with_subst ~term status in
+ (CicMetaSubst.apply_subst subst), status
+
+let apply_tac ~term status = snd (apply_tac_verbose ~term status)
(* TODO per implementare i tatticali e' necessario che tutte le tattiche
sollevino _solamente_ Fail *)
-let apply_tac ~term ~status =
+let apply_tac ~term =
+ let apply_tac ~term status =
try
- apply_tac ~term ~status
+ apply_tac ~term status
(* TODO cacciare anche altre eccezioni? *)
- with CicUnification.UnificationFailed as e ->
- raise (Fail (Printexc.to_string e))
+ with
+ | CicUnification.UnificationFailure msg
+ | CicTypeChecker.TypeCheckerFailure msg ->
+ raise (Fail msg)
+ in
+ mk_tactic (apply_tac ~term)
-let intros_tac
- ?(mk_fresh_name_callback = ProofEngineHelpers.mk_fresh_name) ()
- ~status:(proof, goal)
-=
- let module C = Cic in
- let module R = CicReduction in
- let (_,metasenv,_,_) = proof in
- let metano,context,ty = List.find (function (m,_,_) -> m=goal) metasenv in
- let newmeta = new_meta ~proof in
- let (context',ty',bo') =
- lambda_abstract context newmeta ty mk_fresh_name_callback
- in
- let (newproof, _) =
- subst_meta_in_proof proof metano bo' [newmeta,context',ty']
+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 module C = Cic in
+ let module R = CicReduction in
+ let (_,metasenv,_,_) = proof in
+ let metano,context,ty = CicUtil.lookup_meta goal metasenv in
+ let newmeta = new_meta_of_proof ~proof in
+ let (context',ty',bo') =
+ lambda_abstract ?howmany metasenv context newmeta ty mk_fresh_name_callback
in
- (newproof, [newmeta])
-
-let cut_tac
- ?(mk_fresh_name_callback = ProofEngineHelpers.mk_fresh_name)
- term ~status:(proof, goal)
-=
- let module C = Cic in
- let curi,metasenv,pbo,pty = proof in
- let metano,context,ty = List.find (function (m,_,_) -> m=goal) metasenv in
- let newmeta1 = new_meta ~proof in
- let newmeta2 = newmeta1 + 1 in
- let fresh_name =
- mk_fresh_name_callback context (Cic.Name "Hcut") ~typ:term in
- let context_for_newmeta1 =
- (Some (fresh_name,C.Decl term))::context in
- let irl1 =
- identity_relocation_list_for_metavariable context_for_newmeta1 in
- let irl2 = identity_relocation_list_for_metavariable context in
- let newmeta1ty = CicSubstitution.lift 1 ty in
- let bo' =
- C.Appl
- [C.Lambda (fresh_name,term,C.Meta (newmeta1,irl1)) ;
- C.Meta (newmeta2,irl2)]
+ let (newproof, _) =
+ subst_meta_in_proof proof metano bo' [newmeta,context',ty']
+ in
+ (newproof, [newmeta])
+ 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 (proof, goal)
+ =
+ let module C = Cic in
+ let curi,metasenv,pbo,pty = proof in
+ let metano,context,ty = CicUtil.lookup_meta goal metasenv in
+ let newmeta1 = new_meta_of_proof ~proof in
+ let newmeta2 = newmeta1 + 1 in
+ let fresh_name =
+ mk_fresh_name_callback metasenv context (Cic.Name "Hcut") ~typ:term in
+ let context_for_newmeta1 =
+ (Some (fresh_name,C.Decl term))::context in
+ let irl1 =
+ CicMkImplicit.identity_relocation_list_for_metavariable
+ context_for_newmeta1
+ in
+ let irl2 =
+ CicMkImplicit.identity_relocation_list_for_metavariable context
in
- let (newproof, _) =
- subst_meta_in_proof proof metano bo'
- [newmeta2,context,term; newmeta1,context_for_newmeta1,newmeta1ty];
+ let newmeta1ty = CicSubstitution.lift 1 ty in
+ let bo' =
+ C.Appl
+ [C.Lambda (fresh_name,term,C.Meta (newmeta1,irl1)) ;
+ C.Meta (newmeta2,irl2)]
in
- (newproof, [newmeta1 ; newmeta2])
-
-let letin_tac
- ?(mk_fresh_name_callback = ProofEngineHelpers.mk_fresh_name)
- term ~status:(proof, goal)
-=
- let module C = Cic in
- let curi,metasenv,pbo,pty = proof in
- let metano,context,ty = List.find (function (m,_,_) -> m=goal) metasenv in
- let _ = CicTypeChecker.type_of_aux' metasenv context term in
- let newmeta = new_meta ~proof in
- let fresh_name =
- mk_fresh_name_callback context (Cic.Name "Hletin") ~typ:term in
- let context_for_newmeta =
- (Some (fresh_name,C.Def (term,None)))::context in
- let irl =
- identity_relocation_list_for_metavariable context_for_newmeta in
- let newmetaty = CicSubstitution.lift 1 ty in
- let bo' = C.LetIn (fresh_name,term,C.Meta (newmeta,irl)) in
let (newproof, _) =
- subst_meta_in_proof
- proof metano bo'[newmeta,context_for_newmeta,newmetaty]
+ subst_meta_in_proof proof metano bo'
+ [newmeta2,context,term; newmeta1,context_for_newmeta1,newmeta1ty];
in
- (newproof, [newmeta])
+ (newproof, [newmeta1 ; newmeta2])
+ in
+ mk_tactic (cut_tac ~mk_fresh_name_callback term)
- (** functional part of the "exact" tactic *)
-let exact_tac ~term ~status:(proof, goal) =
- (* Assumption: the term bo must be closed in the current context *)
- let (_,metasenv,_,_) = proof in
- let metano,context,ty = List.find (function (m,_,_) -> m=goal) metasenv in
- let module T = CicTypeChecker in
- let module R = CicReduction in
- if R.are_convertible context (T.type_of_aux' metasenv context term) ty then
- begin
- let (newproof, metasenv') =
- subst_meta_in_proof proof metano term [] in
- (newproof, [])
- end
- else
- raise (Fail "The type of the provided term is not the one expected.")
+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)
+ =
+ let module C = Cic in
+ let curi,metasenv,pbo,pty = proof in
+ let metano,context,ty = CicUtil.lookup_meta goal metasenv in
+ let _,_ = (* TASSI: FIXME *)
+ CicTypeChecker.type_of_aux' metasenv context term CicUniv.empty_ugraph in
+ let newmeta = new_meta_of_proof ~proof in
+ let fresh_name =
+ mk_fresh_name_callback metasenv context (Cic.Name "Hletin") ~typ:term in
+ let context_for_newmeta =
+ (Some (fresh_name,C.Def (term,None)))::context in
+ let irl =
+ CicMkImplicit.identity_relocation_list_for_metavariable
+ context_for_newmeta
+ in
+ let newmetaty = CicSubstitution.lift 1 ty in
+ let bo' = C.LetIn (fresh_name,term,C.Meta (newmeta,irl)) in
+ let (newproof, _) =
+ subst_meta_in_proof
+ proof metano bo'[newmeta,context_for_newmeta,newmetaty]
+ in
+ (newproof, [newmeta])
+ in
+ mk_tactic (letin_tac ~mk_fresh_name_callback term)
+ (** functional part of the "exact" tactic *)
+let exact_tac ~term =
+ let exact_tac ~term (proof, goal) =
+ (* Assumption: the term bo must be closed in the current context *)
+ let (_,metasenv,_,_) = proof in
+ let metano,context,ty = CicUtil.lookup_meta goal metasenv in
+ let module T = CicTypeChecker in
+ let module R = CicReduction in
+ let ty_term,u = T.type_of_aux' metasenv context term CicUniv.empty_ugraph in
+ let b,_ = R.are_convertible context ty_term ty u in (* TASSI: FIXME *)
+ if b then
+ begin
+ let (newproof, metasenv') =
+ subst_meta_in_proof proof metano term [] in
+ (newproof, [])
+ end
+ else
+ raise (Fail (lazy "The type of the provided term is not the one expected."))
+ in
+ mk_tactic (exact_tac ~term)
(* not really "primitive" tactics .... *)
-
-let elim_tac ~term ~status:(proof, goal) =
- let module T = CicTypeChecker in
- let module U = UriManager in
- let module R = CicReduction in
- let module C = Cic in
- let (curi,metasenv,_,_) = proof in
- let metano,context,ty = List.find (function (m,_,_) -> m=goal) metasenv in
- let termty = T.type_of_aux' metasenv context term in
- let uri,exp_named_subst,typeno,args =
- match termty with
- C.MutInd (uri,typeno,exp_named_subst) -> (uri,exp_named_subst,typeno,[])
- | C.Appl ((C.MutInd (uri,typeno,exp_named_subst))::args) ->
- (uri,exp_named_subst,typeno,args)
- | _ -> raise NotAnInductiveTypeToEliminate
- in
- let eliminator_uri =
- let buri = U.buri_of_uri uri in
- let name =
- match CicEnvironment.get_obj uri with
- C.InductiveDefinition (tys,_,_) ->
- let (name,_,_,_) = List.nth tys typeno in
- name
- | _ -> assert false
- in
- let ext =
- match T.type_of_aux' metasenv context ty with
- C.Sort C.Prop -> "_ind"
- | C.Sort C.Set -> "_rec"
- | C.Sort C.CProp -> "_rec"
- | C.Sort C.Type -> "_rect"
- | _ -> assert false
- in
- U.uri_of_string (buri ^ "/" ^ name ^ ext ^ ".con")
+let elim_tac ~term =
+ let elim_tac ~term (proof, goal) =
+ let module T = CicTypeChecker in
+ let module U = UriManager in
+ let module R = CicReduction in
+ let module C = Cic in
+ let (curi,metasenv,proofbo,proofty) = proof in
+ let metano,context,ty = CicUtil.lookup_meta goal metasenv in
+ let termty,_ = T.type_of_aux' metasenv context term CicUniv.empty_ugraph in
+ let (termty,metasenv',arguments,fresh_meta) =
+ ProofEngineHelpers.saturate_term
+ (ProofEngineHelpers.new_meta_of_proof proof) metasenv context termty 0 in
+ let term = if arguments = [] then term else Cic.Appl (term::arguments) in
+ let uri,exp_named_subst,typeno,args =
+ match termty with
+ C.MutInd (uri,typeno,exp_named_subst) -> (uri,exp_named_subst,typeno,[])
+ | C.Appl ((C.MutInd (uri,typeno,exp_named_subst))::args) ->
+ (uri,exp_named_subst,typeno,args)
+ | _ -> raise NotAnInductiveTypeToEliminate
in
- let eliminator_ref = C.Const (eliminator_uri,exp_named_subst) in
- let ety = T.type_of_aux' metasenv context eliminator_ref in
- let newmeta = new_meta ~proof in
- let (econclusion,newmetas,arguments,lastmeta) =
- new_metasenv_for_apply newmeta proof context ety
- in
- (* Here we assume that we have only one inductive hypothesis to *)
- (* eliminate and that it is the last hypothesis of the theorem. *)
- (* A better approach would be fingering the hypotheses in some *)
- (* way. *)
- let meta_of_corpse =
- let (_,canonical_context,_) =
- List.find (function (m,_,_) -> m=(lastmeta - 1)) newmetas
- in
- let irl =
- identity_relocation_list_for_metavariable canonical_context
- in
- Cic.Meta (lastmeta - 1, irl)
- in
- let newmetasenv = newmetas @ metasenv in
- let subst1,newmetasenv' =
- CicUnification.fo_unif newmetasenv context term meta_of_corpse
+ let eliminator_uri =
+ let buri = U.buri_of_uri uri in
+ let name =
+ let o,_ = CicEnvironment.get_obj CicUniv.empty_ugraph uri in
+ match o with
+ C.InductiveDefinition (tys,_,_,_) ->
+ let (name,_,_,_) = List.nth tys typeno in
+ name
+ | _ -> assert false
+ in
+ let ty_ty,_ = T.type_of_aux' metasenv' context ty CicUniv.empty_ugraph in
+ let ext =
+ match ty_ty with
+ C.Sort C.Prop -> "_ind"
+ | 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")
+ in
+ let eliminator_ref = C.Const (eliminator_uri,exp_named_subst) in
+ let ety,_ =
+ T.type_of_aux' metasenv' context eliminator_ref CicUniv.empty_ugraph in
+ let rec find_args_no =
+ function
+ C.Prod (_,_,t) -> 1 + find_args_no t
+ | C.Cast (s,_) -> find_args_no s
+ | C.LetIn (_,_,t) -> 0 + find_args_no t
+ | _ -> 0
in
- let ueconclusion = CicUnification.apply_subst subst1 econclusion in
- (* The conclusion of our elimination principle is *)
- (* (?i farg1 ... fargn) *)
- (* The conclusion of our goal is ty. So, we can *)
- (* eta-expand ty w.r.t. farg1 .... fargn to get *)
- (* a new ty equal to (P farg1 ... fargn). Now *)
- (* ?i can be instantiated with P and we are ready *)
- (* to refine the term. *)
- let emeta, fargs =
- match ueconclusion with
- C.Appl ((C.Meta (emeta,_))::fargs) -> emeta,fargs
- | C.Meta (emeta,_) -> emeta,[]
- | _ -> raise NotTheRightEliminatorShape
+ let args_no = find_args_no ety in
+ let term_to_refine =
+ let rec make_tl base_case =
+ function
+ 0 -> [base_case]
+ | n -> (C.Implicit None)::(make_tl base_case (n - 1))
+ in
+ C.Appl (eliminator_ref :: make_tl term (args_no - 1))
+ in
+ let refined_term,_,metasenv'',_ =
+ CicRefine.type_of_aux' metasenv' context term_to_refine
+ CicUniv.empty_ugraph
in
- let ty' = CicUnification.apply_subst subst1 ty in
- let eta_expanded_ty =
-(*CSC: newmetasenv' era metasenv ??????????? *)
- List.fold_left (eta_expand newmetasenv' context) ty' fargs
+ let new_goals =
+ ProofEngineHelpers.compare_metasenvs
+ ~oldmetasenv:metasenv ~newmetasenv:metasenv''
in
- let subst2,newmetasenv'' =
-(*CSC: passo newmetasenv', ma alcune variabili sono gia' state sostituite
-da subst1!!!! Dovrei rimuoverle o sono innocue?*)
- CicUnification.fo_unif
- newmetasenv' context ueconclusion eta_expanded_ty
+ let proof' = curi,metasenv'',proofbo,proofty in
+ let proof'', new_goals' =
+ apply_tactic (apply_tac ~term:refined_term) (proof',goal)
in
- let in_subst_domain i =
- let eq_to_i = function (j,_) -> i=j in
- List.exists eq_to_i subst1 ||
- List.exists eq_to_i subst2
+ (* The apply_tactic can have closed some of the new_goals *)
+ let patched_new_goals =
+ let (_,metasenv''',_,_) = proof'' in
+ List.filter
+ (function i -> List.exists (function (j,_,_) -> j=i) metasenv'''
+ ) new_goals @ new_goals'
in
- (* When unwinding the META that corresponds to the elimination *)
- (* predicate (which is emeta), we must also perform one-step *)
- (* beta-reduction. apply_subst doesn't need the context. Hence *)
- (* the underscore. *)
- let apply_subst _ t =
- let t' = CicUnification.apply_subst subst1 t in
- CicUnification.apply_subst_reducing
- subst2 (Some (emeta,List.length fargs)) t'
- in
- let old_uninstantiatedmetas,new_uninstantiatedmetas =
- classify_metas newmeta in_subst_domain apply_subst
- newmetasenv''
- in
- let arguments' = List.map (apply_subst context) arguments in
- let bo' = Cic.Appl (eliminator_ref::arguments') in
- let newmetasenv''' =
- new_uninstantiatedmetas@old_uninstantiatedmetas
- in
- let (newproof, newmetasenv'''') =
- (* When unwinding the META that corresponds to the *)
- (* elimination predicate (which is emeta), we must *)
- (* also perform one-step beta-reduction. *)
- (* The only difference w.r.t. apply_subst is that *)
- (* we also substitute metano with bo'. *)
- (*CSC: Nota: sostituire nuovamente subst1 e' superfluo, *)
- (*CSC: no? *)
- let apply_subst' t =
- let t' = CicUnification.apply_subst subst1 t in
- CicUnification.apply_subst_reducing
- ((metano,bo')::subst2)
- (Some (emeta,List.length fargs)) t'
- in
- subst_meta_and_metasenv_in_proof
- proof metano apply_subst' newmetasenv'''
- in
- (newproof,
- List.map (function (i,_,_) -> i) new_uninstantiatedmetas)
+ proof'', patched_new_goals
+ in
+ mk_tactic (elim_tac ~term)
+;;
+
+let elim_intros_tac ?(mk_fresh_name_callback = FreshNamesGenerator.mk_fresh_name ~subst:[])
+ ?depth ?using what =
+ Tacticals.then_ ~start:(elim_tac ~term:what)
+ ~continuation:(intros_tac ~mk_fresh_name_callback ?howmany:depth ())
;;
(* The simplification is performed only on the conclusion *)
-let elim_intros_simpl_tac ~term =
- Tacticals.then_ ~start:(elim_tac ~term)
+let elim_intros_simpl_tac ?(mk_fresh_name_callback = FreshNamesGenerator.mk_fresh_name ~subst:[])
+ ?depth ?using what =
+ Tacticals.then_ ~start:(elim_tac ~term:what)
~continuation:
(Tacticals.thens
- ~start:(intros_tac ())
+ ~start:(intros_tac ~mk_fresh_name_callback ?howmany:depth ())
~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 ~status:(proof, goal) =
- let curi,metasenv,pbo,pty = proof in
- let metano,context,ty = List.find (function (m,_,_) -> m=goal) metasenv in
- (* are_convertible works only on well-typed terms *)
- ignore (CicTypeChecker.type_of_aux' metasenv context with_what) ;
- if CicReduction.are_convertible context what with_what 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")
projects / helm.git / blobdiff