(* 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
(* TODO cacciare anche altre eccezioni? *)
with CicUnification.UnificationFailure _ as e ->
raise (Fail (Printexc.to_string e))
+ in
+ mk_tactic (apply_tac ~term)
-let intros_tac
- ?(mk_fresh_name_callback = FreshNamesGenerator.mk_fresh_name) ()
- (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 metasenv context newmeta ty mk_fresh_name_callback
- in
- let (newproof, _) =
- subst_meta_in_proof proof metano bo' [newmeta,context',ty']
- in
- (newproof, [newmeta])
-
-let cut_tac
- ?(mk_fresh_name_callback = FreshNamesGenerator.mk_fresh_name)
- 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 newmeta1ty = CicSubstitution.lift 1 ty in
- let bo' =
- C.Appl
- [C.Lambda (fresh_name,term,C.Meta (newmeta1,irl1)) ;
- C.Meta (newmeta2,irl2)]
- in
- let (newproof, _) =
- subst_meta_in_proof proof metano bo'
- [newmeta2,context,term; newmeta1,context_for_newmeta1,newmeta1ty];
- in
- (newproof, [newmeta1 ; newmeta2])
-
-let letin_tac
- ?(mk_fresh_name_callback = FreshNamesGenerator.mk_fresh_name)
- 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 _ = CicTypeChecker.type_of_aux' metasenv context term in
+let intros_tac ?(mk_fresh_name_callback = FreshNamesGenerator.mk_fresh_name) ()=
+ let intros_tac
+ ?(mk_fresh_name_callback = FreshNamesGenerator.mk_fresh_name) ()
+ (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 metasenv context newmeta ty mk_fresh_name_callback
+ in
+ 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) term=
+ let cut_tac
+ ?(mk_fresh_name_callback = FreshNamesGenerator.mk_fresh_name)
+ 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 "Hletin") ~typ:term in
- let context_for_newmeta =
- (Some (fresh_name,C.Def (term,None)))::context in
- let irl =
+ 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_newmeta
+ context_for_newmeta1
+ in
+ let irl2 =
+ CicMkImplicit.identity_relocation_list_for_metavariable context
in
- let newmetaty = CicSubstitution.lift 1 ty in
- let bo' = C.LetIn (fresh_name,term,C.Meta (newmeta,irl)) 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)]
+ 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 (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
- 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) term=
+ let letin_tac
+ ?(mk_fresh_name_callback = FreshNamesGenerator.mk_fresh_name)
+ 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 _ = CicTypeChecker.type_of_aux' metasenv context term 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
+ 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.")
+ in
+ mk_tactic (exact_tac ~term)
(* not really "primitive" tactics .... *)
-
-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,_,_) = proof in
- let metano,context,ty = CicUtil.lookup_meta 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" (* TASSI *)
- | _ -> 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,_,_) = proof in
+ let metano,context,ty = CicUtil.lookup_meta 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_ref = C.Const (eliminator_uri,exp_named_subst) in
- let ety = T.type_of_aux' metasenv context eliminator_ref in
- let newmeta = new_meta_of_proof ~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,_) =
- CicUtil.lookup_meta (lastmeta - 1) newmetas
- in
- let irl =
- CicMkImplicit.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 =
+ 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" (* TASSI *)
+ | _ -> 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 in
+ let newmeta = new_meta_of_proof ~proof in
+ let (econclusion,newmetas,arguments,lastmeta) =
+ new_metasenv_for_apply newmeta proof context ety
in
- let ueconclusion = CicMetaSubst.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
+ (* 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,_) =
+ CicUtil.lookup_meta (lastmeta - 1) newmetas
in
- let ty' = CicMetaSubst.apply_subst subst1 ty in
- let eta_expanded_ty =
-(*CSC: newmetasenv' era metasenv ??????????? *)
- List.fold_left (eta_expand newmetasenv' context) ty' fargs
+ let irl =
+ CicMkImplicit.identity_relocation_list_for_metavariable
+ canonical_context
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
+ Cic.Meta (lastmeta - 1, irl)
+ in
+ let newmetasenv = newmetas @ metasenv in
+ let subst1,newmetasenv' =
+ CicUnification.fo_unif newmetasenv context term meta_of_corpse
+ in
+ let ueconclusion = CicMetaSubst.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
+ in
+ let ty' = CicMetaSubst.apply_subst subst1 ty in
+ let eta_expanded_ty =
+ (*CSC: newmetasenv' era metasenv ??????????? *)
+ List.fold_left (eta_expand newmetasenv' context) ty' fargs
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
+ 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
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' = CicMetaSubst.apply_subst subst1 t in
- CicMetaSubst.apply_subst_reducing
- (Some (emeta,List.length fargs)) subst2 t'
+ 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
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' = CicMetaSubst.apply_subst subst1 t in
- CicMetaSubst.apply_subst_reducing
- (Some (emeta,List.length fargs))
- ((metano,bo')::subst2) t'
- in
- subst_meta_and_metasenv_in_proof
- proof metano apply_subst' newmetasenv'''
+ (* 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' = CicMetaSubst.apply_subst subst1 t in
+ CicMetaSubst.apply_subst_reducing
+ (Some (emeta,List.length fargs)) subst2 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
- (newproof,
- List.map (function (i,_,_) -> i) new_uninstantiatedmetas)
+ 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' = CicMetaSubst.apply_subst subst1 t in
+ CicMetaSubst.apply_subst_reducing
+ (Some (emeta,List.length fargs))
+ ((metano,bo')::subst2) t'
+ in
+ subst_meta_and_metasenv_in_proof
+ proof metano apply_subst' newmetasenv'''
+ in
+ (newproof,
+ List.map (function (i,_,_) -> i) new_uninstantiatedmetas)
+ in
+ mk_tactic (elim_tac ~term)
;;
(* The simplification is performed only on the conclusion *)
(*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 (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 *)
- 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' =
+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 *)
+ 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
- (n,_,_) when n = metano -> (metano,context',ty')
- | _ as t -> t
- ) metasenv
+ 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
- (curi,metasenv',pbo,pty), [metano]
- end
- else
- raise (ProofEngineTypes.Fail "Not convertible")
+ 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")
+ in
+ mk_tactic (change_tac ~what ~with_what)
projects / helm.git / blobdiff