* http://cs.unibo.it/helm/.
*)
-let proof =
- ref (None : (UriManager.uri * Cic.metasenv * Cic.term * Cic.term) option)
-;;
-let goal = ref (None : int option);;
-
-(*CSC: commento vecchio *)
-(* refine_meta_with_brand_new_metasenv meta term subst_in newmetasenv *)
-(* This (heavy) function must be called when a tactic can instantiate old *)
-(* metavariables (i.e. existential variables). It substitues the metasenv *)
-(* of the proof with the result of removing [meta] from the domain of *)
-(* [newmetasenv]. Then it replaces Cic.Meta [meta] with [term] everywhere *)
-(* in the current proof. Finally it applies [apply_subst_replacing] to *)
-(* current proof. *)
-(*CSC: A questo punto perche' passare un bo' gia' istantiato, se tanto poi *)
-(*CSC: ci ripasso sopra apply_subst!!! *)
-(*CSC: Attenzione! Ora questa funzione applica anche [subst_in] a *)
-(*CSC: [newmetasenv]. *)
-let subst_meta_and_metasenv_in_current_proof meta subst_in newmetasenv =
- let (uri,bo,ty) =
- match !proof with
- None -> assert false
- | Some (uri,_,bo,ty) -> uri,bo,ty
- in
- let bo' = subst_in bo in
- let metasenv' =
- List.fold_right
- (fun metasenv_entry i ->
- match metasenv_entry with
- (m,canonical_context,ty) when m <> meta ->
- let canonical_context' =
- List.map
- (function
- None -> None
- | Some (i,Cic.Decl t) -> Some (i,Cic.Decl (subst_in t))
- | Some (i,Cic.Def t) -> Some (i,Cic.Def (subst_in t))
- ) canonical_context
- in
- (m,canonical_context',subst_in ty)::i
- | _ -> i
- ) newmetasenv []
- in
- proof := Some (uri,metasenv',bo',ty) ;
- metasenv'
-;;
+open ProofEngineHelpers
+open ProofEngineTypes
+
+ (* proof assistant status *)
-let subst_meta_in_current_proof meta term newmetasenv =
- let (uri,metasenv,bo,ty) =
- match !proof with
+let proof = ref (None : proof option)
+let goal = ref (None : goal option)
+
+let get_proof () = !proof;;
+let set_proof p = proof := p;;
+
+let get_current_status_as_xml () =
+ match get_proof () with
None -> assert false
- | Some (uri,metasenv,bo,ty) -> uri,metasenv,bo,ty
- in
- let subst_in = CicUnification.apply_subst [meta,term] in
- let metasenv' =
- newmetasenv @ (List.filter (function (m,_,_) -> m <> meta) metasenv)
- in
- let metasenv'' =
- List.map
- (function i,canonical_context,ty ->
- let canonical_context' =
- List.map
- (function
- Some (n,Cic.Decl s) -> Some (n,Cic.Decl (subst_in s))
- | Some (n,Cic.Def s) -> Some (n,Cic.Def (subst_in s))
- | None -> None
- ) canonical_context
+ | Some (uri, metasenv, bo, ty) ->
+ let uri = match uri with Some uri -> uri | None -> assert false in
+ let currentproof =
+ (*CSC: Wrong: [] is just plainly wrong *)
+ Cic.CurrentProof (UriManager.name_of_uri uri,metasenv,bo,ty,[],[])
+ in
+ let (acurrentproof,_,_,ids_to_inner_sorts,_,_,_) =
+ Cic2acic.acic_object_of_cic_object ~eta_fix:false currentproof
+ in
+ let xml, bodyxml =
+ match
+ Cic2Xml.print_object uri ~ids_to_inner_sorts
+ ~ask_dtd_to_the_getter:true acurrentproof
+ with
+ xml,Some bodyxml -> xml,bodyxml
+ | _,None -> assert false
in
- i,canonical_context',(subst_in ty)
- ) metasenv'
- in
- let bo' = subst_in bo in
- proof := Some (uri,metasenv'',bo',ty) ;
- metasenv''
+ (xml, bodyxml)
;;
-(* Returns the first meta whose number is above the *)
-(* number of the higher meta. *)
-let new_meta () =
- let metasenv =
- match !proof with
- None -> assert false
- | Some (_,metasenv,_,_) -> metasenv
- in
- let rec aux =
- function
- None,[] -> 1
- | Some n,[] -> n
- | None,(n,_,_)::tl -> aux (Some n,tl)
- | Some m,(n,_,_)::tl -> if n > m then aux (Some n,tl) else aux (Some m,tl)
- in
- 1 + aux (None,metasenv)
+let apply_tactic ~tactic =
+ let module PET = ProofEngineTypes in
+ match get_proof (),!goal with
+ | None,_
+ | _,None -> assert false
+ | Some proof', Some goal' ->
+ let (newproof, newgoals) = PET.apply_tactic tactic (proof', goal') in
+ set_proof (Some newproof);
+ goal :=
+ (match newgoals, newproof with
+ goal::_, _ -> Some goal
+ | [], (_,(goal,_,_)::_,_,_) ->
+ (* the tactic left no open goal ; let's choose the first open goal *)
+ (*CSC: here we could implement and use a proof-tree like notion... *)
+ Some goal
+ | _, _ -> None)
;;
(* metas_in_term term *)
let module C = Cic in
let rec aux =
function
- C.Rel _
- | C.Var _ -> []
+ C.Rel _ -> []
| C.Meta (n,_) -> [n]
| C.Sort _
- | C.Implicit -> []
+ | C.Implicit _ -> []
| C.Cast (te,ty) -> (aux te) @ (aux ty)
| C.Prod (_,s,t) -> (aux s) @ (aux t)
| C.Lambda (_,s,t) -> (aux s) @ (aux t)
| C.LetIn (_,s,t) -> (aux s) @ (aux t)
| C.Appl l -> List.fold_left (fun i t -> i @ (aux t)) [] l
- | C.Const _
- | C.Abst _
- | C.MutInd _
- | C.MutConstruct _ -> []
- | C.MutCase (sp,cookingsno,i,outt,t,pl) ->
+ | C.Var (_,exp_named_subst)
+ | C.Const (_,exp_named_subst)
+ | C.MutInd (_,_,exp_named_subst)
+ | C.MutConstruct (_,_,_,exp_named_subst) ->
+ List.fold_left (fun i (_,t) -> i @ (aux t)) [] exp_named_subst
+ | C.MutCase (_,_,outt,t,pl) ->
(aux outt) @ (aux t) @
(List.fold_left (fun i t -> i @ (aux t)) [] pl)
- | C.Fix (i,fl) ->
+ | C.Fix (_,fl) ->
List.fold_left (fun i (_,_,ty,bo) -> i @ (aux bo) @ (aux ty)) [] fl
- | C.CoFix (i,fl) ->
+ | C.CoFix (_,fl) ->
List.fold_left (fun i (_,ty,bo) -> i @ (aux bo) @ (aux ty)) [] fl
in
let metas = aux term in
he::(elim_duplicates (List.filter (function el -> he <> el) tl))
in
elim_duplicates metas
-;;
-
-(* identity_relocation_list_for_metavariable i canonical_context *)
-(* returns the identity relocation list, which is the list [1 ; ... ; n] *)
-(* where n = List.length [canonical_context] *)
-(*CSC: ma mi basta la lunghezza del contesto canonico!!!*)
-let identity_relocation_list_for_metavariable canonical_context =
- let canonical_context_length = List.length canonical_context in
- let rec aux =
- function
- (_,[]) -> []
- | (n,None::tl) -> None::(aux ((n+1),tl))
- | (n,_::tl) -> (Some (Cic.Rel n))::(aux ((n+1),tl))
- in
- aux (1,canonical_context)
-;;
(* perforate context term ty *)
(* replaces the term [term] in the proof with a new metavariable whose type *)
(* are efficiency reasons. *)
let perforate context term ty =
let module C = Cic in
- let newmeta = new_meta () in
- match !proof with
- None -> assert false
- | Some (uri,metasenv,bo,gty) ->
+ match get_proof () with
+ None -> assert false
+ | Some (uri,metasenv,bo,gty as proof') ->
+ let newmeta = new_meta_of_proof proof' in
(* We push the new meta at the end of the list for pretty-printing *)
(* purposes: in this way metas are ordered. *)
let metasenv' = metasenv@[newmeta,context,ty] in
- let irl = identity_relocation_list_for_metavariable context in
+ let irl =
+ CicMkImplicit.identity_relocation_list_for_metavariable context
+ in
(*CSC: Bug: se ci sono due term uguali nella prova dovrei bucarne uno solo!!!*)
let bo' =
- ProofEngineReduction.replace (==) term (C.Meta (newmeta,irl)) bo
+ ProofEngineReduction.replace (==) [term] [C.Meta (newmeta,irl)] bo
in
(* It may be possible that some metavariables occurred only in *)
(* the term we are perforating and they now occurs no more. We *)
let metasenv'' =
List.filter (function (n,_,_) -> List.mem n newmetas) metasenv'
in
- proof := Some (uri,metasenv'',bo',gty) ;
+ set_proof (Some (uri,metasenv'',bo',gty)) ;
goal := Some newmeta
-;;
+
(************************************************************)
(* Some easy tactics. *)
(************************************************************)
-exception Fail of string;;
-
-(*CSC: generatore di nomi? Chiedere il nome? *)
-let fresh_name =
- let next_fresh_index = ref 0
-in
- function () ->
- incr next_fresh_index ;
- "fresh_name" ^ string_of_int !next_fresh_index
+(* Reduces [term] using [reduction_function] in the current scratch goal [ty] *)
+let reduction_tactic_in_scratch reduction_function terms ty =
+ let metasenv =
+ match get_proof () with
+ None -> []
+ | Some (_,metasenv,_,_) -> metasenv
+ in
+ let metano,context,_ =
+ match !goal with
+ None -> assert false
+ | Some metano -> List.find (function (m,_,_) -> m=metano) metasenv
+ in
+ let terms' = List.map (reduction_function context) terms in
+ ProofEngineReduction.replace
+ ~equality:(==) ~what:terms ~with_what:terms' ~where:ty
;;
-(* lambda_abstract newmeta ty *)
-(* returns a triple [bo],[context],[ty'] where *)
-(* [ty] = Pi/LetIn [context].[ty'] ([context] is a vector!) *)
-(* 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 =
- 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' =
- match n with
- C.Name _ -> n
-(*CSC: generatore di nomi? Chiedere il nome? *)
- | C.Anonimous -> C.Name (fresh_name ())
- in
- let (context',ty,bo) =
- collect_context ((Some (n',(C.Decl s)))::context) 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)))::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))
- in
- collect_context context ty
-;;
+let whd_in_scratch = reduction_tactic_in_scratch CicReduction.whd
+let reduce_in_scratch = reduction_tactic_in_scratch ProofEngineReduction.reduce
+let simpl_in_scratch = reduction_tactic_in_scratch ProofEngineReduction.simpl
-let intros () =
- let module C = Cic in
- let module R = CicReduction in
- let metasenv =
- match !proof with
- None -> assert false
- | Some (_,metasenv,_,_) -> metasenv
- in
- let metano,context,ty =
- match !goal with
- None -> assert false
- | Some metano -> List.find (function (m,_,_) -> m=metano) metasenv
- in
- let newmeta = new_meta () in
- let (context',ty',bo') = lambda_abstract context newmeta ty in
- let _ = subst_meta_in_current_proof metano bo' [newmeta,context',ty'] in
- goal := Some newmeta
-;;
+(************************************************************)
+(* Tactics defined elsewhere *)
+(************************************************************)
-(* The term bo must be closed in the current context *)
-let exact bo =
- let module T = CicTypeChecker in
- let module R = CicReduction in
- let metasenv =
- match !proof with
- None -> assert false
- | Some (_,metasenv,_,_) -> metasenv
- in
- let metano,context,ty =
- match !goal with
- None -> assert false
- | Some metano -> List.find (function (m,_,_) -> m=metano) metasenv
- in
- if R.are_convertible context (T.type_of_aux' metasenv context bo) ty then
- begin
- let metasenv' = subst_meta_in_current_proof metano bo [] in
- goal :=
- match metasenv' with
- [] -> None
- | (n,_,_)::_ -> Some n
- end
- else
- raise (Fail "The type of the provided term is not the one expected.")
-;;
+ (* primitive tactics *)
-(*CSC: The call to the Intros tactic is embedded inside the code of the *)
-(*CSC: Elim tactic. Do we already need tacticals? *)
-(* 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 the nth new META lambda-abstracted as much as possible. Hence, this *)
-(* functions already provides the behaviour of Intros on the new goals. *)
-let new_metasenv_for_apply_intros 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 newcontext,ty',newargument = lambda_abstract context newmeta s in
- let (res,newmetasenv,arguments,lastmeta) =
- aux (newmeta + 1) (S.subst newargument t)
- in
- res,(newmeta,newcontext,ty')::newmetasenv,newargument::arguments,lastmeta
- | t -> t,[],[],newmeta
- in
- let newmeta = new_meta () 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,newmeta,lastmeta
-;;
+let apply term = apply_tactic (PrimitiveTactics.apply_tac ~term)
+let intros ?mk_fresh_name_callback () =
+ apply_tactic (PrimitiveTactics.intros_tac ?mk_fresh_name_callback ())
+let cut ?mk_fresh_name_callback term =
+ apply_tactic (PrimitiveTactics.cut_tac ?mk_fresh_name_callback ~term)
+let letin ?mk_fresh_name_callback term =
+ apply_tactic (PrimitiveTactics.letin_tac ?mk_fresh_name_callback ~term)
+let exact term = apply_tactic (PrimitiveTactics.exact_tac ~term)
+let elim_intros_simpl term =
+ apply_tactic (PrimitiveTactics.elim_intros_simpl_tac ~term)
+let change ~goal_input:what ~input:with_what =
+ apply_tactic (PrimitiveTactics.change_tac ~what ~with_what)
-(* 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 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
- let newmeta = new_meta () 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,newmeta,lastmeta
-;;
+ (* structural tactics *)
+let clearbody hyp = apply_tactic (ProofEngineStructuralRules.clearbody ~hyp)
+let clear hyp = apply_tactic (ProofEngineStructuralRules.clear ~hyp)
-(*CSC: ma serve solamente la prima delle new_uninst e l'unione delle due!!! *)
-let classify_metas newmeta in_subst_domain subst_in metasenv =
- List.fold_right
- (fun (i,canonical_context,ty) (old_uninst,new_uninst) ->
- if in_subst_domain i then
- old_uninst,new_uninst
- else
- let ty' = subst_in canonical_context ty in
- let canonical_context' =
- List.fold_right
- (fun entry canonical_context' ->
- let entry' =
- match entry with
- Some (n,Cic.Decl s) ->
- Some (n,Cic.Decl (subst_in canonical_context' s))
- | Some (n,Cic.Def s) ->
- Some (n,Cic.Def (subst_in canonical_context' s))
- | None -> None
- in
- entry'::canonical_context'
- ) canonical_context []
- in
- if i < newmeta then
- ((i,canonical_context',ty')::old_uninst),new_uninst
- else
- old_uninst,((i,canonical_context',ty')::new_uninst)
- ) metasenv ([],[])
-;;
+ (* reduction tactics *)
-(* The term bo must be closed in the current context *)
-let apply term =
- let module T = CicTypeChecker in
- let module R = CicReduction in
- let module C = Cic in
- let metasenv =
- match !proof with
- None -> assert false
- | Some (_,metasenv,_,_) -> metasenv
- in
- let metano,context,ty =
- match !goal with
- None -> assert false
- | Some metano ->
- List.find (function (m,_,_) -> m=metano) metasenv
- in
- let termty = CicTypeChecker.type_of_aux' metasenv context term in
- (* newmeta is the lowest index of the new metas introduced *)
- let (consthead,newmetas,arguments,newmeta,_) =
- new_metasenv_for_apply context termty
- in
- let newmetasenv = newmetas@metasenv 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' =
- if List.length newmetas = 0 then
- term
- else
- let arguments' = List.map apply_subst arguments in
- Cic.Appl (term::arguments')
- in
- let newmetasenv'' = new_uninstantiatedmetas@old_uninstantiatedmetas in
- let newmetasenv''' =
- let subst_in = CicUnification.apply_subst ((metano,bo')::subst) in
- subst_meta_and_metasenv_in_current_proof metano subst_in
- newmetasenv''
- in
- match newmetasenv''' with
- [] -> goal := None
- | (i,_,_)::_ -> goal := Some i
-;;
+let whd terms =
+ apply_tactic
+ (ReductionTactics.whd_tac ~also_in_hypotheses:true ~terms:(Some terms))
+let reduce terms =
+ apply_tactic
+ (ReductionTactics.reduce_tac ~also_in_hypotheses:true ~terms:(Some terms))
+let simpl terms =
+ apply_tactic
+ (ReductionTactics.simpl_tac ~also_in_hypotheses:true ~terms:(Some terms))
-let eta_expand metasenv context t arg =
- let module T = CicTypeChecker in
- let module S = CicSubstitution in
- let module C = Cic in
- let rec aux n =
- function
- t' when t' = S.lift n arg -> C.Rel (1 + n)
- | C.Rel m -> if m <= n then C.Rel m else C.Rel (m+1)
- | C.Var _
- | C.Meta _
- | C.Sort _
- | 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)
- | C.LetIn (nn,s,t) -> C.LetIn (nn, aux n s, aux (n+1) t)
- | C.Appl l -> C.Appl (List.map (aux n) l)
- | C.Const _ as t -> t
- | C.Abst _ -> assert false
- | C.MutInd _
- | C.MutConstruct _ as t -> t
- | C.MutCase (sp,cookingsno,i,outt,t,pl) ->
- C.MutCase (sp,cookingsno,i,aux n outt, aux n t,
- List.map (aux n) pl)
- | C.Fix (i,fl) ->
- let tylen = List.length fl in
- let substitutedfl =
- List.map
- (fun (name,i,ty,bo) -> (name, i, aux n ty, aux (n+tylen) bo))
- fl
- in
- C.Fix (i, substitutedfl)
- | C.CoFix (i,fl) ->
- let tylen = List.length fl in
- let substitutedfl =
- List.map
- (fun (name,ty,bo) -> (name, aux n ty, aux (n+tylen) bo))
- fl
- in
- C.CoFix (i, substitutedfl)
- in
- let argty =
- T.type_of_aux' metasenv context arg
- in
- (C.Appl [C.Lambda ((C.Name "dummy"),argty,aux 0 t) ; arg])
-;;
+let fold_whd term =
+ apply_tactic
+ (ReductionTactics.fold_tac ~reduction:CicReduction.whd
+ ~also_in_hypotheses:true ~term)
+let fold_reduce term =
+ apply_tactic
+ (ReductionTactics.fold_tac ~reduction:ProofEngineReduction.reduce
+ ~also_in_hypotheses:true ~term)
+let fold_simpl term =
+ apply_tactic
+ (ReductionTactics.fold_tac ~reduction:ProofEngineReduction.simpl
+ ~also_in_hypotheses:true ~term)
-exception NotAnInductiveTypeToEliminate;;
-exception NotTheRightEliminatorShape;;
-exception NoHypothesesFound;;
+ (* other tactics *)
-let elim_intros_simpl term =
- let module T = CicTypeChecker in
- let module U = UriManager in
- let module R = CicReduction in
- let module C = Cic in
- let curi,metasenv =
- match !proof with
- None -> assert false
- | Some (curi,metasenv,_,_) -> curi,metasenv
- in
- let metano,context,ty =
- match !goal with
- None -> assert false
- | Some metano ->
- List.find (function (m,_,_) -> m=metano) metasenv
- in
- let termty = T.type_of_aux' metasenv context term in
- let uri,cookingno,typeno,args =
- match termty with
- C.MutInd (uri,cookingno,typeno) -> (uri,cookingno,typeno,[])
- | C.Appl ((C.MutInd (uri,cookingno,typeno))::args) ->
- (uri,cookingno,typeno,args)
- | _ -> raise NotAnInductiveTypeToEliminate
- in
- let eliminator_uri =
- let buri = U.buri_of_uri uri in
- let name =
- match CicEnvironment.get_cooked_obj uri cookingno 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.Type -> "_rect"
- | _ -> assert false
- in
- U.uri_of_string (buri ^ "/" ^ name ^ ext ^ ".con")
- in
- let eliminator_cookingno =
- UriManager.relative_depth curi eliminator_uri 0
- in
- let eliminator_ref = C.Const (eliminator_uri,eliminator_cookingno) in
- let ety =
- T.type_of_aux' [] [] eliminator_ref
- in
- let (econclusion,newmetas,arguments,newmeta,lastmeta) =
-(*
- new_metasenv_for_apply context ety
-*)
- new_metasenv_for_apply_intros 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
- 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
-(*CSC: Code to be used for Apply
- C.Appl ((C.Meta (emeta,_))::fargs) -> emeta,fargs
- | C.Meta (emeta,_) -> emeta,[]
-*)
-(*CSC: Code to be used for ApplyIntros *)
- C.Appl (he::fargs) ->
- let rec find_head =
- function
- C.Meta (emeta,_) -> emeta
- | C.Lambda (_,_,t) -> find_head t
- | C.LetIn (_,_,t) -> find_head t
- | _ ->raise NotTheRightEliminatorShape
- in
- find_head he,fargs
-(* *)
- | _ -> raise NotTheRightEliminatorShape
- 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
- 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
- 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
- in
-(*CSC: codice per l'elim
- (* 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
-*)
-(*CSC: codice per l'elim_intros_simpl. Non effettua semplificazione. *)
- let apply_subst context t =
- let t' = CicUnification.apply_subst (subst1@subst2) t in
- ProofEngineReduction.simpl context 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 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? *)
-(*CSC: codice per l'elim
- 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
-*)
-(*CSC: codice per l'elim_intros_simpl *)
- let apply_subst' t =
- CicUnification.apply_subst
- ((metano,bo')::(subst1@subst2)) t
- in
-(* *)
- subst_meta_and_metasenv_in_current_proof metano
- apply_subst' newmetasenv'''
- in
- match newmetasenv'''' with
- [] -> goal := None
- | (i,_,_)::_ -> goal := Some i
-;;
+let elim_type term = apply_tactic (EliminationTactics.elim_type_tac ~term)
+let ring () = apply_tactic Ring.ring_tac
+let fourier () = apply_tactic FourierR.fourier_tac
-let reduction_tactic reduction_function term =
- let curi,metasenv,pbo,pty =
- match !proof with
- None -> assert false
- | Some (curi,metasenv,bo,ty) -> curi,metasenv,bo,ty
- in
- let metano,context,ty =
- match !goal with
- None -> assert false
- | Some metano -> List.find (function (m,_,_) -> m=metano) metasenv
- in
- (* We don't know if [term] is a subterm of [ty] or a subterm of *)
- (* the type of one metavariable. So we replace it everywhere. *)
- (*CSC: Il vero problema e' che non sapendo dove sia il term non *)
- (*CSC: sappiamo neppure quale sia il suo contesto!!!! Insomma, *)
- (*CSC: e' meglio prima cercare il termine e scoprirne il *)
- (*CSC: contesto, poi ridurre e infine rimpiazzare. *)
- let replace context where=
-(*CSC: Per il momento se la riduzione fallisce significa solamente che *)
-(*CSC: siamo nel contesto errato. Metto il try, ma che schifo!!!! *)
-(*CSC: Anche perche' cosi' catturo anche quelle del replace che non dovrei *)
- try
- let term' = reduction_function context term in
- ProofEngineReduction.replace ~equality:(==) ~what:term ~with_what:term'
- ~where:where
- with
- _ -> where
- in
- let ty' = replace context ty in
- let context' =
- List.fold_right
- (fun entry context ->
- match entry with
- Some (name,Cic.Def t) ->
- (Some (name,Cic.Def (replace context t)))::context
- | Some (name,Cic.Decl t) ->
- (Some (name,Cic.Decl (replace context t)))::context
- | None -> None::context
- ) context []
- in
- let metasenv' =
- List.map
- (function
- (n,_,_) when n = metano -> (metano,context',ty')
- | _ as t -> t
- ) metasenv
- in
- proof := Some (curi,metasenv',pbo,pty) ;
- goal := Some metano
-;;
+(* let auto ~dbd () = apply_tactic (AutoTactic.auto_tac ~dbd) *)
+let auto ~dbd () = apply_tactic (AutoTactic.auto_tac_new ~dbd)
-(* Reduces [term] using [reduction_function] in the current scratch goal [ty] *)
-let reduction_tactic_in_scratch reduction_function term ty =
- let metasenv =
- match !proof with
- None -> []
- | Some (_,metasenv,_,_) -> metasenv
- in
- let metano,context,_ =
- match !goal with
- None -> assert false
- | Some metano -> List.find (function (m,_,_) -> m=metano) metasenv
- in
- let term' = reduction_function context term in
- ProofEngineReduction.replace
- ~equality:(==) ~what:term ~with_what:term' ~where:ty
-;;
-let whd = reduction_tactic CicReduction.whd;;
-let reduce = reduction_tactic ProofEngineReduction.reduce;;
-let simpl = reduction_tactic ProofEngineReduction.simpl;;
+let rewrite_simpl term = apply_tactic (EqualityTactics.rewrite_simpl_tac ~term)
+let rewrite_back_simpl term = apply_tactic (EqualityTactics.rewrite_back_simpl_tac ~term)
+let replace ~goal_input:what ~input:with_what =
+ apply_tactic (EqualityTactics.replace_tac ~what ~with_what)
-let whd_in_scratch = reduction_tactic_in_scratch CicReduction.whd;;
-let reduce_in_scratch =
- reduction_tactic_in_scratch ProofEngineReduction.reduce;;
-let simpl_in_scratch =
- reduction_tactic_in_scratch ProofEngineReduction.simpl;;
+let reflexivity () = apply_tactic EqualityTactics.reflexivity_tac
+let symmetry () = apply_tactic EqualityTactics.symmetry_tac
+let transitivity term = apply_tactic (EqualityTactics.transitivity_tac ~term)
-(* It is just the opposite of whd. The code should probably be merged. *)
-let fold term =
- let curi,metasenv,pbo,pty =
- match !proof with
- None -> assert false
- | Some (curi,metasenv,bo,ty) -> curi,metasenv,bo,ty
- in
- let metano,context,ty =
- match !goal with
- None -> assert false
- | Some metano -> List.find (function (m,_,_) -> m=metano) metasenv
- in
- let term' = CicReduction.whd context term in
- (* We don't know if [term] is a subterm of [ty] or a subterm of *)
- (* the type of one metavariable. So we replace it everywhere. *)
- (*CSC: ma si potrebbe ovviare al problema. Ma non credo *)
- (*CSC: che si guadagni nulla in fatto di efficienza. *)
- let replace = ProofEngineReduction.replace
- ~equality:(==) ~what:term' ~with_what:term
- in
- let ty' = replace ty in
- let context' =
- List.map
- (function
- Some (n,Cic.Decl t) -> Some (n,Cic.Decl (replace t))
- | Some (n,Cic.Def t) -> Some (n,Cic.Def (replace t))
- | None -> None
- ) context
- in
- let metasenv' =
- List.map
- (function
- (n,_,_) when n = metano -> (metano,context',ty')
- | _ as t -> t
- ) metasenv
- in
- proof := Some (curi,metasenv',pbo,pty) ;
- goal := Some metano
-;;
+let exists () = apply_tactic IntroductionTactics.exists_tac
+let split () = apply_tactic IntroductionTactics.split_tac
+let left () = apply_tactic IntroductionTactics.left_tac
+let right () = apply_tactic IntroductionTactics.right_tac
-let cut term =
- let module C = Cic in
- let curi,metasenv,pbo,pty =
- match !proof with
- None -> assert false
- | Some (curi,metasenv,bo,ty) -> curi,metasenv,bo,ty
- in
- let metano,context,ty =
- match !goal with
- None -> assert false
- | Some metano -> List.find (function (m,_,_) -> m=metano) metasenv
- in
- let newmeta1 = new_meta () in
- let newmeta2 = newmeta1 + 1 in
- let context_for_newmeta1 =
- (Some (C.Name "dummy_for_cut",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 (C.Name "dummy_for_cut",term,C.Meta (newmeta1,irl1)) ;
- C.Meta (newmeta2,irl2)]
- in
- let _ =
- subst_meta_in_current_proof metano bo'
- [newmeta2,context,term; newmeta1,context_for_newmeta1,newmeta1ty];
- in
- goal := Some newmeta1
-;;
+let assumption () = apply_tactic VariousTactics.assumption_tac
-let letin term =
- let module C = Cic in
- let curi,metasenv,pbo,pty =
- match !proof with
- None -> assert false
- | Some (curi,metasenv,bo,ty) -> curi,metasenv,bo,ty
- in
- let metano,context,ty =
- match !goal with
- None -> assert false
- | Some metano -> List.find (function (m,_,_) -> m=metano) metasenv
- in
- let _ = CicTypeChecker.type_of_aux' metasenv context term in
- let newmeta = new_meta () in
- let context_for_newmeta =
- (Some (C.Name "dummy_for_letin",C.Def term))::context in
- let irl =
- identity_relocation_list_for_metavariable context_for_newmeta in
- let newmetaty = CicSubstitution.lift 1 ty in
- let bo' = C.LetIn (C.Name "dummy_for_letin",term,C.Meta (newmeta,irl)) in
- let _ = subst_meta_in_current_proof metano bo' [newmeta,context_for_newmeta,newmetaty] in
- goal := Some newmeta
-;;
+let generalize ?mk_fresh_name_callback terms =
+ apply_tactic (VariousTactics.generalize_tac ?mk_fresh_name_callback terms)
-exception NotConvertible;;
+let absurd term = apply_tactic (NegationTactics.absurd_tac ~term)
+let contradiction () = apply_tactic NegationTactics.contradiction_tac
-(*CSC: Bug (or feature?). [input] is parsed in the context of the goal, *)
-(*CSC: while [goal_input] can have a richer context (because of binders) *)
-(*CSC: So it is _NOT_ possible to use those binders in the [input] term. *)
-(*CSC: Is that evident? Is that right? Or should it be changed? *)
-let change ~goal_input ~input =
- let curi,metasenv,pbo,pty =
- match !proof with
- None -> assert false
- | Some (curi,metasenv,bo,ty) -> curi,metasenv,bo,ty
- in
- let metano,context,ty =
- match !goal with
- None -> assert false
- | Some metano -> List.find (function (m,_,_) -> m=metano) metasenv
- in
- (* are_convertible works only on well-typed terms *)
- ignore (CicTypeChecker.type_of_aux' metasenv context input) ;
- if CicReduction.are_convertible context goal_input input then
- begin
- let replace =
- ProofEngineReduction.replace
- ~equality:(==) ~what:goal_input ~with_what:input
- in
- let ty' = replace ty in
- let context' =
- List.map
- (function
- Some (name,Cic.Def t) -> Some (name,Cic.Def (replace t))
- | Some (name,Cic.Decl t) -> Some (name,Cic.Decl (replace t))
- | None -> None
- ) context
- in
- let metasenv' =
- List.map
- (function
- (n,_,_) when n = metano -> (metano,context',ty')
- | _ as t -> t
- ) metasenv
- in
- proof := Some (curi,metasenv',pbo,pty) ;
- goal := Some metano
- end
- else
- raise NotConvertible
-;;
+let decompose ~uris_choice_callback term =
+ apply_tactic (EliminationTactics.decompose_tac ~uris_choice_callback term)
-let clearbody =
- let module C = Cic in
- function
- None -> assert false
- | Some (_, C.Decl _) -> raise (Fail "No Body To Clear")
- | Some (n_to_clear_body, C.Def term) as hyp_to_clear_body ->
- let curi,metasenv,pbo,pty =
- match !proof with
- None -> assert false
- | Some (curi,metasenv,bo,ty) -> curi,metasenv,bo,ty
- in
- let metano,_,_ =
- match !goal with
- None -> assert false
- | Some metano -> List.find (function (m,_,_) -> m=metano) metasenv
- in
- let string_of_name =
- function
- C.Name n -> n
- | C.Anonimous -> "_"
- in
- let metasenv' =
- List.map
- (function
- (m,canonical_context,ty) when m = metano ->
- let canonical_context' =
- List.fold_right
- (fun entry context ->
- match entry with
- t when t == hyp_to_clear_body ->
- let cleared_entry =
- let ty =
- CicTypeChecker.type_of_aux' metasenv context term
- in
- Some (n_to_clear_body, Cic.Decl ty)
- in
- cleared_entry::context
- | None -> None::context
- | Some (n,C.Decl t)
- | Some (n,C.Def t) ->
- let _ =
- try
- CicTypeChecker.type_of_aux' metasenv context t
- with
- _ ->
- raise
- (Fail
- ("The correctness of hypothesis " ^
- string_of_name n ^
- " relies on the body of " ^
- string_of_name n_to_clear_body)
- )
- in
- entry::context
- ) canonical_context []
- in
- let _ =
- try
- CicTypeChecker.type_of_aux' metasenv canonical_context' ty
- with
- _ ->
- raise
- (Fail
- ("The correctness of the goal relies on the body of " ^
- string_of_name n_to_clear_body))
- in
- m,canonical_context',ty
- | t -> t
- ) metasenv
- in
- proof := Some (curi,metasenv',pbo,pty)
-;;
+let injection term = apply_tactic (DiscriminationTactics.injection_tac ~term)
+let discriminate term = apply_tactic (DiscriminationTactics.discriminate_tac ~term)
+let decide_equality () = apply_tactic DiscriminationTactics.decide_equality_tac
+let compare term = apply_tactic (DiscriminationTactics.compare_tac ~term)
+
+(*
+let prova_tatticali () = apply_tactic Tacticals.prova_tac
+*)
-let clear hyp_to_clear =
- let module C = Cic in
- match hyp_to_clear with
- None -> assert false
- | Some (n_to_clear, _) ->
- let curi,metasenv,pbo,pty =
- match !proof with
- None -> assert false
- | Some (curi,metasenv,bo,ty) -> curi,metasenv,bo,ty
- in
- let metano,context,ty =
- match !goal with
- None -> assert false
- | Some metano -> List.find (function (m,_,_) -> m=metano) metasenv
- in
- let string_of_name =
- function
- C.Name n -> n
- | C.Anonimous -> "_"
- in
- let metasenv' =
- List.map
- (function
- (m,canonical_context,ty) when m = metano ->
- let canonical_context' =
- List.fold_right
- (fun entry context ->
- match entry with
- t when t == hyp_to_clear -> None::context
- | None -> None::context
- | Some (n,C.Decl t)
- | Some (n,C.Def t) ->
- let _ =
- try
- CicTypeChecker.type_of_aux' metasenv context t
- with
- _ ->
- raise
- (Fail
- ("Hypothesis " ^
- string_of_name n ^
- " uses hypothesis " ^
- string_of_name n_to_clear)
- )
- in
- entry::context
- ) canonical_context []
- in
- let _ =
- try
- CicTypeChecker.type_of_aux' metasenv canonical_context' ty
- with
- _ ->
- raise
- (Fail
- ("Hypothesis " ^ string_of_name n_to_clear ^
- " occurs in the goal"))
- in
- m,canonical_context',ty
- | t -> t
- ) metasenv
- in
- proof := Some (curi,metasenv',pbo,pty)
-;;
projects / helm.git / blobdiff