(* $Id$ *)
-let debug_print = fun _ -> ()
+module C = Cic
+module U = UriManager
+module P = PrimitiveTactics
+module T = Tacticals
+module CR = CicReduction
+module PST = ProofEngineStructuralRules
+module PET = ProofEngineTypes
+module CTC = CicTypeChecker
+module CU = CicUniv
+module S = CicSubstitution
+module RT = ReductionTactics
+module PEH = ProofEngineHelpers
+module ET = EqualityTactics
-let rec injection_tac ~term =
- let injection_tac ~term status =
- let (proof, goal) = status in
- let module C = Cic in
- let module U = UriManager in
- let module P = PrimitiveTactics in
- let module T = Tacticals in
- let _,metasenv,_,_ = proof in
- let _,context,_ = CicUtil.lookup_meta goal metasenv in
- let termty,_ = (* TASSI: FIXME *)
- CicTypeChecker.type_of_aux' metasenv context term CicUniv.empty_ugraph in
- ProofEngineTypes.apply_tactic
- (match termty with
- (C.Appl [(C.MutInd (equri, 0, [])) ; tty ; t1 ; t2])
- when LibraryObjects.is_eq_URI equri -> (
- match tty with
- (C.MutInd (turi,typeno,exp_named_subst))
- | (C.Appl (C.MutInd (turi,typeno,exp_named_subst)::_)) -> (
- match t1,t2 with
- ((C.MutConstruct (uri1,typeno1,consno1,exp_named_subst1)),
- (C.MutConstruct (uri2,typeno2,consno2,exp_named_subst2)))
- when (uri1 = uri2) && (typeno1 = typeno2) &&
- (consno1 = consno2) && (exp_named_subst1 = exp_named_subst2) ->
- (* raise (ProofEngineTypes.Fail "Injection: nothing to do") ; *) T.id_tac
- | ((C.Appl ((C.MutConstruct (uri1,typeno1,consno1,exp_named_subst1))::applist1)),
- (C.Appl ((C.MutConstruct (uri2,typeno2,consno2,exp_named_subst2))::applist2)))
- when (uri1 = uri2) && (typeno1 = typeno2) && (consno1 = consno2) && (exp_named_subst1 = exp_named_subst2) ->
- let rec traverse_list i l1 l2 =
- match l1,l2 with
- [],[] -> T.id_tac
- | hd1::tl1,hd2::tl2 ->
- T.then_
- ~start:(injection1_tac ~i ~term)
- ~continuation:(traverse_list (i+1) tl1 tl2)
- | _ -> raise (ProofEngineTypes.Fail (lazy "Discriminate: i 2 termini hanno in testa lo stesso costruttore, ma applicato a un numero diverso di termini. possibile???"))
- in traverse_list 1 applist1 applist2
- | ((C.MutConstruct (uri1,typeno1,consno1,exp_named_subst1)),
- (C.MutConstruct (uri2,typeno2,consno2,exp_named_subst2)))
- | ((C.MutConstruct (uri1,typeno1,consno1,exp_named_subst1)),
- (C.Appl ((C.MutConstruct (uri2,typeno2,consno2,exp_named_subst2))::_)))
- | ((C.Appl ((C.MutConstruct (uri1,typeno1,consno1,exp_named_subst1))::_)),
- (C.MutConstruct (uri2,typeno2,consno2,exp_named_subst2)))
- | ((C.Appl ((C.MutConstruct (uri1,typeno1,consno1,exp_named_subst1))::_)),
- (C.Appl ((C.MutConstruct (uri2,typeno2,consno2,exp_named_subst2))::_)))
- when (consno1 <> consno2) || (exp_named_subst1 <> exp_named_subst2) ->
- (* raise (ProofEngineTypes.Fail "Injection: not a projectable equality but a discriminable one") ; *) T.id_tac
- | _ -> (* raise (ProofEngineTypes.Fail "Injection: not a projectable equality") ; *) T.id_tac
- )
- | _ -> raise (ProofEngineTypes.Fail (lazy "Injection: not a projectable equality"))
- )
- | _ -> raise (ProofEngineTypes.Fail (lazy "Injection: not an equation"))
- ) status
- in
- ProofEngineTypes.mk_tactic (injection_tac ~term)
+let debug = false
+let debug_print =
+ if debug then (fun x -> prerr_endline (Lazy.force x)) else (fun _ -> ())
-and injection1_tac ~term ~i =
- let injection1_tac ~term ~i status =
- let (proof, goal) = status in
- (* precondizione: t1 e t2 hanno in testa lo stesso costruttore ma differiscono (o potrebbero differire?) nell'i-esimo parametro del costruttore *)
- let module C = Cic in
- let module S = CicSubstitution in
- let module U = UriManager in
- let module P = PrimitiveTactics in
- let module T = Tacticals in
- let _,metasenv,_,_ = proof in
- let _,context,_ = CicUtil.lookup_meta goal metasenv in
- let termty,_ = (* TASSI: FIXME *)
- CicTypeChecker.type_of_aux' metasenv context term CicUniv.empty_ugraph in
- match termty with (* an equality *)
- (C.Appl [(C.MutInd (equri, 0, [])) ; tty ; t1 ; t2])
- when LibraryObjects.is_eq_URI equri -> (
- match tty with (* some inductive type *)
- (C.MutInd (turi,typeno,exp_named_subst))
- | (C.Appl (C.MutInd (turi,typeno,exp_named_subst)::_)) ->
- let t1',t2',consno = (* sono i due sottotermini che differiscono *)
- match t1,t2 with
- ((C.Appl ((C.MutConstruct (uri1,typeno1,consno1,exp_named_subst1))::applist1)),
- (C.Appl ((C.MutConstruct (uri2,typeno2,consno2,exp_named_subst2))::applist2)))
- when (uri1 = uri2) && (typeno1 = typeno2) && (consno1 = consno2) && (exp_named_subst1 = exp_named_subst2) -> (* controllo ridondante *)
- (List.nth applist1 (i-1)),(List.nth applist2 (i-1)),consno2
- | _ -> assert false
- in
- let tty',_ =
- CicTypeChecker.type_of_aux' metasenv context t1'
- CicUniv.empty_ugraph in
- let pattern =
- match fst(CicEnvironment.get_obj
- CicUniv.empty_ugraph turi ) with
- C.InductiveDefinition (ind_type_list,_,nr_ind_params_dx,_) ->
- let _,_,_,constructor_list = (List.nth ind_type_list typeno) in
- let i_constr_id,_ = List.nth constructor_list (consno - 1) in
- List.map
- (function (id,cty) ->
- let reduced_cty = CicReduction.whd context cty in
- let rec aux t k =
- match t with
- C.Prod (_,_,target) when (k <= nr_ind_params_dx) ->
- aux target (k+1)
- | C.Prod (binder,source,target) when (k > nr_ind_params_dx) ->
- let binder' =
- match binder with
- C.Name b -> C.Name b
- | C.Anonymous -> C.Name "y"
- in
- C.Lambda (binder',source,(aux target (k+1)))
- | _ ->
- let nr_param_constr = k - 1 - nr_ind_params_dx in
- if (id = i_constr_id)
- then C.Rel (nr_param_constr - i + 1)
- else S.lift (nr_param_constr + 1) t1' (* + 1 per liftare anche il lambda agguinto esternamente al case *)
- in aux reduced_cty 1
- )
- constructor_list
- | _ -> raise (ProofEngineTypes.Fail (lazy "Discriminate: object is not an Inductive Definition: it's imposible"))
- in
- ProofEngineTypes.apply_tactic
- (T.thens
- ~start:(P.cut_tac (C.Appl [(C.MutInd (equri,0,[])) ; tty' ; t1' ; t2']))
- ~continuations:[
- T.then_
- ~start:(injection_tac ~term:(C.Rel 1))
- ~continuation:T.id_tac (* !!! qui devo anche fare clear di term tranne al primo passaggio *)
- ;
- T.then_
- ~start:(ProofEngineTypes.mk_tactic
- (fun status ->
- let (proof, goal) = status in
- let _,metasenv,_,_ = proof in
- let _,context,gty = CicUtil.lookup_meta goal metasenv in
- let new_t1' =
- match gty with
- (C.Appl (C.MutInd (_,_,_)::arglist)) ->
- List.nth arglist 1
- | _ -> raise (ProofEngineTypes.Fail (lazy "Injection: goal after cut is not correct"))
- in
- ProofEngineTypes.apply_tactic
- (ReductionTactics.change_tac
- ~pattern:(ProofEngineTypes.conclusion_pattern
- (Some new_t1'))
- (fun _ m u ->
- C.Appl [ C.Lambda (C.Name "x", tty,
- C.MutCase (turi, typeno,
- (C.Lambda ((C.Name "x"),
- (S.lift 1 tty),
- (S.lift 2 tty'))),
- (C.Rel 1), pattern
- )
- );
- t1], m, u))
- status
- ))
- ~continuation:
- (T.then_
- ~start:
- (EqualityTactics.rewrite_simpl_tac
- ~direction:`LeftToRight
- ~pattern:(ProofEngineTypes.conclusion_pattern None)
- term)
- ~continuation:EqualityTactics.reflexivity_tac
- )
- ])
- status
- | _ -> raise (ProofEngineTypes.Fail (lazy "Discriminate: not a discriminable equality"))
- )
- | _ -> raise (ProofEngineTypes.Fail (lazy "Discriminate: not an equality"))
- in
- ProofEngineTypes.mk_tactic (injection1_tac ~term ~i)
-;;
+(* funzione generale di rilocazione dei riferimenti locali *)
-exception TwoDifferentSubtermsFound of int
+let relocate_term map t =
+ let rec map_xnss k xnss =
+ let imap (uri, t) = uri, map_term k t in
+ List.map imap xnss
+ and map_mss k mss =
+ let imap = function
+ | None -> None
+ | Some t -> Some (map_term k t)
+ in
+ List.map imap mss
+ and map_fs len k fs =
+ let imap (name, i, ty, bo) = name, i, map_term k ty, map_term (k + len) bo in
+ List.map imap fs
+ and map_cfs len k cfs =
+ let imap (name, ty, bo) = name, map_term k ty, map_term (k + len) bo in
+ List.map imap cfs
+ and map_term k = function
+ | C.Rel m -> if m < k then C.Rel m else C.Rel (map (m - k))
+ | C.Sort _ as t -> t
+ | C.Implicit _ as t -> t
+ | C.Var (uri, xnss) -> C.Var (uri, map_xnss k xnss)
+ | C.Const (uri, xnss) -> C.Const (uri, map_xnss k xnss)
+ | C.MutInd (uri, tyno, xnss) -> C.MutInd (uri, tyno, map_xnss k xnss)
+ | C.MutConstruct (uri, tyno, consno, xnss) ->
+ C.MutConstruct (uri, tyno, consno, map_xnss k xnss)
+ | C.Meta (i, mss) -> C.Meta(i, map_mss k mss)
+ | C.Cast (te, ty) -> C.Cast (map_term k te, map_term k ty)
+ | C.Appl ts -> C.Appl (List.map (map_term k) ts)
+ | C.MutCase (sp, i, outty, t, pl) ->
+ C.MutCase (sp, i, map_term k outty, map_term k t, List.map (map_term k) pl)
+ | C.Prod (n, s, t) -> C.Prod (n, map_term k s, map_term (succ k) t)
+ | C.Lambda (n, s, t) -> C.Lambda (n, map_term k s, map_term (succ k) t)
+ | C.LetIn (n, s, t) -> C.LetIn (n, map_term k s, map_term (succ k) t)
+ | C.Fix (i, fs) -> C.Fix (i, map_fs (List.length fs) k fs)
+ | C.CoFix (i, cfs) -> C.CoFix (i, map_cfs (List.length cfs) k cfs)
+ in
+ map_term 0 t
+
+let id n = n
+
+let after continuation aftermap beforemap =
+ continuation ~map:(fun n -> aftermap (beforemap n))
+
+let after2 continuation aftermap beforemap ~map =
+ continuation ~map:(fun n -> map (aftermap (beforemap n)))
(* term ha tipo t1=t2; funziona solo se t1 e t2 hanno in testa costruttori
diversi *)
-let discriminate'_tac ~term =
- let module C = Cic in
- let module U = UriManager in
- let module P = PrimitiveTactics in
- let module T = Tacticals in
- let fail msg = raise (ProofEngineTypes.Fail (lazy ("Discriminate: " ^ msg))) in
+let discriminate_tac ~term =
+ let true_URI =
+ match LibraryObjects.true_URI () with
+ Some uri -> uri
+ | None -> raise (PET.Fail (lazy "You need to register the default \"true\" definition first. Please use the \"default\" command")) in
+ let false_URI =
+ match LibraryObjects.false_URI () with
+ Some uri -> uri
+ | None -> raise (PET.Fail (lazy "You need to register the default \"false\" definition first. Please use the \"default\" command")) in
+ let fail msg = raise (PET.Fail (lazy ("Discriminate: " ^ msg))) in
let find_discriminating_consno t1 t2 =
let rec aux t1 t2 =
match t1, t2 with
in
aux t1 t2
in
- let mk_pattern turi typeno consno context left_args =
+ let mk_branches_and_outtype turi typeno consno context args =
(* a list of "True" except for the element in position consno which
* is "False" *)
match fst (CicEnvironment.get_obj CicUniv.empty_ugraph turi) with
- | C.InductiveDefinition (ind_type_list,_,nr_ind_params,_) ->
- let _,_,_,constructor_list = List.nth ind_type_list typeno in
+ | C.InductiveDefinition (ind_type_list,_,paramsno,_) ->
+ let _,_,rty,constructor_list = List.nth ind_type_list typeno in
let false_constr_id,_ = List.nth constructor_list (consno - 1) in
- List.map
- (fun (id,cty) ->
- (* dubbio: e' corretto ridurre in questo context ??? *)
- let red_ty = CicReduction.whd context cty in
- let rec aux t k =
- match t with
- | C.Prod (_,_,target) when (k <= nr_ind_params) ->
- CicSubstitution.subst (List.nth left_args (k-1))
- (aux target (k+1))
- | C.Prod (binder,source,target) when (k > nr_ind_params) ->
- C.Lambda (binder, source, (aux target (k+1)))
- | _ ->
- if (id = false_constr_id)
- then (C.MutInd(LibraryObjects.false_URI (),0,[]))
- else (C.MutInd(LibraryObjects.true_URI (),0,[]))
- in
- (CicSubstitution.lift 1 (aux red_ty 1)))
- constructor_list
- | _ -> (* object is not an inductive definition *)
- assert false
+ let branches =
+ List.map
+ (fun (id,cty) ->
+ (* dubbio: e' corretto ridurre in questo context ??? *)
+ let red_ty = CR.whd context cty in
+ let rec aux t k =
+ match t with
+ | C.Prod (_,_,target) when (k <= paramsno) ->
+ S.subst (List.nth args (k-1))
+ (aux target (k+1))
+ | C.Prod (binder,source,target) when (k > paramsno) ->
+ C.Lambda (binder, source, (aux target (k+1)))
+ | _ ->
+ if (id = false_constr_id)
+ then (C.MutInd(false_URI,0,[]))
+ else (C.MutInd(true_URI,0,[]))
+ in
+ (S.lift 1 (aux red_ty 1)))
+ constructor_list in
+ let outtype =
+ let seed = ref 0 in
+ let rec mk_lambdas rev_left_args =
+ function
+ 0, args, C.Prod (_,so,ta) ->
+ C.Lambda
+ (C.Name (incr seed; "x" ^ string_of_int !seed),
+ so,
+ mk_lambdas rev_left_args (0,args,ta))
+ | 0, args, C.Sort _ ->
+ let rec mk_rels =
+ function
+ 0 -> []
+ | n -> C.Rel n :: mk_rels (n - 1) in
+ let argsno = List.length args in
+ C.Lambda
+ (C.Name "x",
+ (if argsno + List.length rev_left_args > 0 then
+ C.Appl
+ (C.MutInd (turi, typeno, []) ::
+ (List.map
+ (S.lift (argsno + 1))
+ (List.rev rev_left_args)) @
+ mk_rels argsno)
+ else
+ C.MutInd (turi,typeno,[])),
+ C.Sort C.Prop)
+ | 0, _, _ -> assert false (* seriously screwed up *)
+ | n, he::tl, C.Prod (_,_,ta) ->
+ mk_lambdas (he::rev_left_args)(n-1,tl,S.subst he ta)
+ | n,_,_ ->
+ assert false (* we should probably reduce in some context *)
+ in
+ mk_lambdas [] (paramsno, args, rty)
+ in
+ branches, outtype
+ | _ -> assert false
in
let discriminate'_tac ~term status =
let (proof, goal) = status in
- let _,metasenv,_,_ = proof in
+ let _,metasenv,_subst,_,_, _ = proof in
let _,context,_ = CicUtil.lookup_meta goal metasenv in
let termty,_ =
- CicTypeChecker.type_of_aux' metasenv context term CicUniv.empty_ugraph
+ CTC.type_of_aux' metasenv context term CicUniv.empty_ugraph
in
match termty with
- | (C.Appl [(C.MutInd (equri, 0, [])) ; tty ; t1 ; t2])
- when LibraryObjects.is_eq_URI equri ->
- let turi,typeno,exp_named_subst,left_args =
+ | C.Appl [(C.MutInd (equri, 0, [])) ; tty ; t1 ; t2]
+ when LibraryObjects.is_eq_URI equri ->
+ let turi,typeno,exp_named_subst,args =
match tty with
| (C.MutInd (turi,typeno,exp_named_subst)) ->
turi,typeno,exp_named_subst,[]
- | (C.Appl (C.MutInd (turi,typeno,exp_named_subst)::left_args)) ->
- turi,typeno,exp_named_subst,left_args
+ | (C.Appl (C.MutInd (turi,typeno,exp_named_subst)::args)) ->
+ turi,typeno,exp_named_subst,args
| _ -> fail "not a discriminable equality"
in
let consno =
| Some consno -> consno
| None -> fail "discriminating terms are structurally equal"
in
- let pattern = mk_pattern turi typeno consno context left_args in
- let (proof',goals') =
- ProofEngineTypes.apply_tactic
- (EliminationTactics.elim_type_tac
- (C.MutInd (LibraryObjects.false_URI (), 0, [])))
- status
+ let branches,outtype =
+ mk_branches_and_outtype turi typeno consno context args
in
- (match goals' with
- | [goal'] ->
- let _,metasenv',_,_ = proof' in
- let _,context',gty' = CicUtil.lookup_meta goal' metasenv' in
- ProofEngineTypes.apply_tactic
- (T.then_
- ~start:
- (ReductionTactics.change_tac
- ~pattern:(ProofEngineTypes.conclusion_pattern (Some gty'))
- (fun _ m u ->
- C.Appl [
- C.Lambda ( C.Name "x", tty,
- C.MutCase (turi, typeno,
- (C.Lambda ((C.Name "x"),
- (CicSubstitution.lift 1 tty),
- (C.Sort C.Prop))),
- (C.Rel 1), pattern));
- t2 ], m, u))
- ~continuation:
- (T.then_
- ~start:
- (EqualityTactics.rewrite_simpl_tac
- ~direction:`RightToLeft
- ~pattern:(ProofEngineTypes.conclusion_pattern None)
- term)
- ~continuation:
- (IntroductionTactics.constructor_tac ~n:1)))
- (proof',goal')
- | [] -> fail "ElimType False left no goals"
- | _ -> fail "ElimType False left more than one goal")
+ PET.apply_tactic
+ (T.then_
+ ~start:(EliminationTactics.elim_type_tac (C.MutInd (false_URI, 0, [])))
+ ~continuation:
+ (T.then_
+ ~start:
+ (RT.change_tac
+ ~pattern:(PET.conclusion_pattern None)
+ (fun _ m u ->
+ C.Appl [
+ C.Lambda ( C.Name "x", tty,
+ C.MutCase (turi, typeno, outtype, (C.Rel 1), branches));
+ t2 ],
+ m, u))
+ ~continuation:
+ (T.then_
+ ~start:
+ (ET.rewrite_simpl_tac
+ ~direction:`RightToLeft
+ ~pattern:(PET.conclusion_pattern None)
+ term [])
+ ~continuation:
+ (IntroductionTactics.constructor_tac ~n:1)))) status
| _ -> fail "not an equality"
in
- ProofEngineTypes.mk_tactic (discriminate'_tac ~term)
+ PET.mk_tactic (discriminate'_tac ~term)
-let discriminate_tac ~term =
- let discriminate_tac ~term status =
- ProofEngineTypes.apply_tactic
- (Tacticals.then_
- ~start:(* (injection_tac ~term) *) Tacticals.id_tac
- ~continuation:(discriminate'_tac ~term)) (* NOOO!!! non term ma una (qualunque) delle nuove hyp introdotte da inject *)
- status
- in
- ProofEngineTypes.mk_tactic (discriminate_tac ~term)
-
-let decide_equality_tac =
-(* il goal e' un termine della forma t1=t2\/~t1=t2; la tattica decide se l'uguaglianza
-e' vera o no e lo risolve *)
- Tacticals.id_tac
+let exn_nonproj =
+ PET.Fail (lazy "Injection: not a projectable equality")
+let exn_noneq =
+ PET.Fail (lazy "Injection: not an equality")
+let exn_nothingtodo =
+ PET.Fail (lazy "Nothing to do")
+let exn_discrnonind =
+ PET.Fail (lazy "Discriminate: object is not an Inductive Definition: it's imposible")
+let exn_injwronggoal =
+ PET.Fail (lazy "Injection: goal after cut is not correct")
+let exn_noneqind =
+ PET.Fail (lazy "Injection: not an equality over elements of an inductive type")
-let compare_tac ~term = Tacticals.id_tac
- (*
-(* term is in the form t1=t2; the tactic leaves two goals: in the first you have to *)
-(* demonstrate the goal with the additional hyp that t1=t2, in the second the hyp is ~t1=t2 *)
- let module C = Cic in
- let module U = UriManager in
- let module P = PrimitiveTactics in
- let module T = Tacticals in
- let _,metasenv,_,_ = proof in
- let _,context,gty = CicUtil.lookup_meta goal metasenv in
- let termty = (CicTypeChecker.type_of_aux' metasenv context term) in
- match termty with
- (C.Appl [(C.MutInd (uri, 0, [])); _; t1; t2]) when (uri = (U.uri_of_string "cic:/Coq/Init/Logic/eq.ind")) ->
-
- let term' = (* (t1=t2)\/~(t1=t2) *)
- C.Appl [
- (C.MutInd ((U.uri_of_string "cic:/Coq/Init/Logic/or.ind"), 0, [])) ;
- term ;
- C.Appl [
- (C.MutInd ((U.uri_of_string "cic:/Coq/Init/Logic/eq.ind"), 1, [])) ;
- t1 ;
- C.Appl [C.Const ((U.uri_of_string "cic:/Coq/Init/Logic/not.con"), []) ; t2]
- ]
- ]
- in
- T.thens
- ~start:(P.cut_tac ~term:term')
- ~continuations:[
- T.then_ ~start:(P.intros_tac) ~continuation:(P.elim_intros_simpl_tac ~term:(C.Rel 1)) ;
- decide_equality_tac]
- status
- | (C.Appl [(C.MutInd (uri, 0, [])); _; t1; t2]) when (uri = (U.uri_of_string "cic:/Coq/Init/Logic_Type/eqT.ind")) ->
- let term' = (* (t1=t2) \/ ~(t1=t2) *)
- C.Appl [
- (C.MutInd ((U.uri_of_string "cic:/Coq/Init/Logic/or.ind"), 0, [])) ;
- term ;
- C.Appl [
- (C.MutInd ((U.uri_of_string "cic:/Coq/Init/Logic_Type/eqT.ind"), 1, [])) ;
- t1 ;
- C.Appl [C.Const ((U.uri_of_string "cic:/Coq/Init/Logic/not.con"), []) ; t2]
- ]
- ]
- in
- T.thens
- ~start:(P.cut_tac ~term:term')
- ~continuations:[
- T.then_ ~start:(P.intros_tac) ~continuation:(P.elim_intros_simpl_tac ~term:(C.Rel 1)) ;
- decide_equality_tac]
- status
- | _ -> raise (ProofEngineTypes.Fail "Compare: Not an equality")
-*)
-;;
+let pp ctx t =
+ let names = List.map (function Some (n,_) -> Some n | None -> None) ctx in
+ CicPp.pp t names
+let clear_term first_time context term =
+ let g () = if first_time then raise exn_nothingtodo else T.id_tac in
+ match term with
+ | C.Rel n ->
+ begin match List.nth context (pred n) with
+ | Some (C.Name id, _) -> PST.clear ~hyps:[id]
+ | _ -> assert false
+ end
+ | _ -> g ()
+let simpl_in_term context = function
+ | Cic.Rel i ->
+ let name = match List.nth context (pred i) with
+ | Some (Cic.Name s, Cic.Def _) -> s
+ | Some (Cic.Name s, Cic.Decl _) -> s
+ | _ -> assert false
+ in
+ RT.simpl_tac ~pattern:(None,[name,Cic.Implicit (Some `Hole)],None)
+ | _ -> raise exn_nonproj
-(* DISCRIMINTATE SENZA INJECTION
-
-exception TwoDifferentSubtermsFound of (Cic.term * Cic.term * int)
-
-let discriminate_tac ~term status =
- let module C = Cic in
- let module U = UriManager in
- let module P = PrimitiveTactics in
- let module T = Tacticals in
+(* ~term vive nel contesto della tattica una volta ~mappato
+ * ~continuation riceve la mappa assoluta
+ *)
+let rec injection_tac ~map ~term ~i ~continuation =
+ let give_name seed = function
+ | C.Name _ as name -> name
+ | C.Anonymous -> C.Name (incr seed; "y" ^ string_of_int !seed)
+ in
+ let rec mk_rels = function | 0 -> [] | n -> C.Rel n :: (mk_rels (n - 1)) in
+ let injection_tac status =
let (proof, goal) = status in
- let _,metasenv,_,_ = proof in
- let _,context,_ = CicUtil.lookup_meta goal metasenv in
- let termty = (CicTypeChecker.type_of_aux' metasenv context term) in
- match termty with
- (C.Appl [(C.MutInd (equri, 0, [])) ; tty ; t1 ; t2])
- when (U.eq equri (U.uri_of_string "cic:/Coq/Init/Logic/eq.ind"))
- or (U.eq equri (U.uri_of_string "cic:/Coq/Init/Logic_Type/eqT.ind")) -> (
- match tty with
- (C.MutInd (turi,typeno,exp_named_subst))
- | (C.Appl (C.MutInd (turi,typeno,exp_named_subst)::_)) ->
+ (* precondizione: t1 e t2 hanno in testa lo stesso costruttore ma
+ * differiscono (o potrebbero differire?) nell'i-esimo parametro
+ * del costruttore *)
+ let _,metasenv,_subst,_,_, _ = proof in
+ let _,context,_ = CicUtil.lookup_meta goal metasenv in
+ let term = relocate_term map term in
+ let termty,_ =
+ CTC.type_of_aux' metasenv context term CicUniv.empty_ugraph
+ in
+ debug_print (lazy ("\ninjection su : " ^ pp context termty));
+ match termty with (* an equality *)
+ | C.Appl [(C.MutInd (equri, 0, [])) ; tty ; t1 ; t2]
+ when LibraryObjects.is_eq_URI equri ->
+ let turi,typeno,ens,params =
+ match tty with (* some inductive type *)
+ | C.MutInd (turi,typeno,ens) -> turi,typeno,ens,[]
+ | C.Appl (C.MutInd (turi,typeno,ens)::params) -> turi,typeno,ens,params
+ | _ -> raise exn_noneqind
+ in
+ let t1',t2',consno = (* sono i due sottotermini che differiscono *)
+ match t1,t2 with
+ | C.Appl ((C.MutConstruct (uri1,typeno1,consno1,ens1))::applist1),
+ C.Appl ((C.MutConstruct (uri2,typeno2,consno2,ens2))::applist2)
+ when (uri1 = uri2) && (typeno1 = typeno2) &&
+ (consno1 = consno2) && (ens1 = ens2) ->
+ (* controllo ridondante *)
+ List.nth applist1 (pred i),List.nth applist2 (pred i),consno2
+ | _ -> assert false
+ in
+ let tty',_ = CTC.type_of_aux' metasenv context t1' CU.empty_ugraph in
+ let patterns,outtype =
+ match fst (CicEnvironment.get_obj CicUniv.empty_ugraph turi) with
+ | C.InductiveDefinition (ind_type_list,_,paramsno,_)->
+ let left_params, right_params = HExtlib.split_nth paramsno params in
+ let _,_,_,constructor_list = List.nth ind_type_list typeno in
+ let i_constr_id,_ = List.nth constructor_list (consno - 1) in
+ let patterns =
+ let seed = ref 0 in
+ List.map
+ (function (id,cty) ->
+ let reduced_cty = CR.whd context cty in
+ let rec aux k = function
+ | C.Prod (_,_,tgt) when k <= paramsno ->
+ let left = List.nth left_params (k-1) in
+ aux (k+1) (S.subst left tgt)
+ | C.Prod (binder,source,target) when k > paramsno ->
+ let binder' = give_name seed binder in
+ C.Lambda (binder',source,(aux (k+1) target))
+ | _ ->
+ let nr_param_constr = k - paramsno - 1 in
+ if id = i_constr_id then C.Rel (k - i)
+ else S.lift nr_param_constr t1'
+ (* + 1 per liftare anche il lambda aggiunto
+ * esternamente al case *)
+ in S.lift 1 (aux 1 reduced_cty))
+ constructor_list
+ in
+ (* this code should be taken from cases_tac *)
+ let outtype =
+ let seed = ref 0 in
+ let rec to_lambdas te head =
+ match CR.whd context te with
+ | C.Prod (binder,so,ta) ->
+ let binder' = give_name seed binder in
+ C.Lambda (binder',so,to_lambdas ta head)
+ | _ -> head
+ in
+ let rec skip_prods params te =
+ match params, CR.whd context te with
+ | [], _ -> te
+ | left::tl, C.Prod (_,_,ta) ->
+ skip_prods tl (S.subst left ta)
+ | _, _ -> assert false
+ in
+ let abstracted_tty =
+ let tty =
+ List.fold_left (fun x y -> S.subst y x) tty left_params
+ in
+ (* non lift, ma subst coi left! *)
+ match S.lift 1 tty with
+ | C.MutInd _ as tty' -> tty'
+ | C.Appl l ->
+ let keep,abstract = HExtlib.split_nth (paramsno +1) l in
+ let keep = List.map (S.lift paramsno) keep in
+ C.Appl (keep@mk_rels (List.length abstract))
+ | _ -> assert false
+ in
+ match ind_type_list with
+ | [] -> assert false
+ | (_,_,ty,_)::_ ->
+ (* this is in general wrong, do as in cases_tac *)
+ to_lambdas (skip_prods left_params ty)
+ (C.Lambda
+ (C.Name "cased", abstracted_tty,
+ (* here we should capture right parameters *)
+ (* 1 for his Lambda, one for the Lambda outside the match
+ * and then one for each to_lambda *)
+ S.lift (2+List.length right_params) tty'))
+ in
+ patterns,outtype
+ | _ -> raise exn_discrnonind
+ in
+ let cutted = C.Appl [C.MutInd (equri,0,[]) ; tty' ; t1' ; t2'] in
+ let changed =
+ C.Appl [ C.Lambda (C.Name "x", tty,
+ C.MutCase (turi,typeno,outtype,C.Rel 1,patterns)) ; t1]
+ in
+ (* check if cutted and changed are well typed and if t1' ~ changed *)
+ let go_on =
+ try
+ let _,g = CTC.type_of_aux' metasenv context cutted
+ CicUniv.empty_ugraph
+ in
+ let _,g = CTC.type_of_aux' metasenv context changed g in
+ fst (CR.are_convertible ~metasenv context t1' changed g)
+ with
+ | CTC.TypeCheckerFailure _ -> false
+ in
+ if not go_on then
+ PET.apply_tactic (continuation ~map) status
+ else
+ let tac term =
+ let tac status =
+ debug_print (lazy "riempio il cut");
+ let (proof, goal) = status in
+ let _,metasenv,_subst,_,_, _ = proof in
+ let _,context,gty = CicUtil.lookup_meta goal metasenv in
+ let gty = Unshare.unshare gty in
+ let new_t1' = match gty with
+ | (C.Appl (C.MutInd (_,_,_)::_::t::_)) -> t
+ | _ -> raise exn_injwronggoal
+ in
+ debug_print (lazy ("metto: " ^ pp context changed));
+ debug_print (lazy ("al posto di: " ^ pp context new_t1'));
+ debug_print (lazy ("nel goal: " ^ pp context gty));
+ debug_print (lazy ("nel contesto:\n" ^ CicPp.ppcontext context));
+ debug_print (lazy ("e poi rewrite con: "^pp context term));
+ let tac = T.seq ~tactics:[
+ RT.change_tac
+ ~pattern:(None, [], Some (PEH.pattern_of ~term:gty [new_t1']))
+ (fun _ m u -> changed,m,u);
+ ET.rewrite_simpl_tac
+ ~direction:`LeftToRight
+ ~pattern:(PET.conclusion_pattern None)
+ term [];
+ ET.reflexivity_tac
+ ] in
+ PET.apply_tactic tac status
+ in
+ PET.mk_tactic tac
+ in
+ debug_print (lazy ("CUT: " ^ pp context cutted));
+ PET.apply_tactic
+ (T.thens ~start: (P.cut_tac cutted)
+ ~continuations:[
+ (destruct ~first_time:false ~term:(C.Rel 1) ~map:id
+ ~continuation:(after2 continuation succ map)
+ );
+ tac term]
+ ) status
+ | _ -> raise exn_noneq
+ in
+ PET.mk_tactic injection_tac
- let (t1',t2',consno2') = (* bruuutto: uso un eccezione per terminare con successo! buuu!! :-/ *)
- try
- let rec traverse t1 t2 =
-debug_print (lazy ("XXXX t1 " ^ CicPp.ppterm t1)) ;
-debug_print (lazy ("XXXX t2 " ^ CicPp.ppterm t2)) ;
- match t1,t2 with
- ((C.MutConstruct (uri1,typeno1,consno1,exp_named_subst1)),
- (C.MutConstruct (uri2,typeno2,consno2,exp_named_subst2)))
- when (uri1 = uri2) && (typeno1 = typeno2) && (consno1 = consno2) && (exp_named_subst1 = exp_named_subst2) ->
- t1,t2,0
- | ((C.Appl ((C.MutConstruct (uri1,typeno1,consno1,exp_named_subst1))::applist1)),
- (C.Appl ((C.MutConstruct (uri2,typeno2,consno2,exp_named_subst2))::applist2)))
- when (uri1 = uri2) && (typeno1 = typeno2) && (consno1 = consno2) && (exp_named_subst1 = exp_named_subst2) ->
- let rec traverse_list l1 l2 =
- match l1,l2 with
- [],[] -> t1,t2,0
- | hd1::tl1,hd2::tl2 -> traverse hd1 hd2; traverse_list tl1 tl2
- | _ -> raise (ProofEngineTypes.Fail "Discriminate: i 2 termini hanno in testa lo stesso costruttore, ma applicato a un numero diverso di termini. possibile???")
- in traverse_list applist1 applist2
+(* ~term vive nel contesto della tattica una volta ~mappato
+ * ~continuation riceve la mappa assoluta
+ *)
+and subst_tac ~map ~term ~direction ~where ~continuation =
+ let fail_tactic = continuation ~map in
+ let subst_tac status =
+ let term = relocate_term map term in
+ let tactic = match where with
+ | None ->
+ let pattern = PET.conclusion_pattern None in
+ let tactic = ET.rewrite_tac ~direction ~pattern term [] in
+ T.then_ ~start:(T.try_tactic ~tactic)
+ ~continuation:fail_tactic
+ | Some name ->
+ let pattern = None, [name, PET.hole], None in
+ let start = ET.rewrite_tac ~direction ~pattern term [] in
+ let continuation =
+ destruct ~first_time:false ~term:(C.Rel 1) ~map:id
+ ~continuation:(after2 continuation succ map)
+ in
+ T.if_ ~start ~continuation ~fail:fail_tactic
+ in
+ PET.apply_tactic tactic status
+ in
+ PET.mk_tactic subst_tac
- | ((C.MutConstruct (uri1,typeno1,consno1,exp_named_subst1)),
- (C.MutConstruct (uri2,typeno2,consno2,exp_named_subst2)))
- | ((C.MutConstruct (uri1,typeno1,consno1,exp_named_subst1)),
- (C.Appl ((C.MutConstruct (uri2,typeno2,consno2,exp_named_subst2))::_)))
- | ((C.Appl ((C.MutConstruct (uri1,typeno1,consno1,exp_named_subst1))::_)),
- (C.MutConstruct (uri2,typeno2,consno2,exp_named_subst2)))
- | ((C.Appl ((C.MutConstruct (uri1,typeno1,consno1,exp_named_subst1))::_)),
- (C.Appl ((C.MutConstruct (uri2,typeno2,consno2,exp_named_subst2))::_)))
- when (consno1 <> consno2) || (exp_named_subst1 <> exp_named_subst2) ->
- raise (TwoDifferentSubtermsFound (t1,t2,consno2))
- | _ -> raise (ProofEngineTypes.Fail "Discriminate: not a discriminable equality")
- in traverse t1 t2
- with (TwoDifferentSubtermsFound (t1,t2,consno2)) -> (t1,t2,consno2)
+(* ~term vive nel contesto della tattica una volta ~mappato
+ * ~continuation riceve la mappa assoluta
+ *)
+and destruct ~first_time ~map ~term ~continuation =
+ let are_convertible hd1 hd2 metasenv context =
+ fst (CR.are_convertible ~metasenv context hd1 hd2 CicUniv.empty_ugraph)
+ in
+ let destruct status =
+ let (proof, goal) = status in
+ let _,metasenv,_subst, _,_, _ = proof in
+ let _,context,_ = CicUtil.lookup_meta goal metasenv in
+ let term = relocate_term map term in
+ debug_print (lazy ("\nqnify di: " ^ pp context term));
+ debug_print (lazy ("nel contesto:\n" ^ CicPp.ppcontext context));
+ let termty,_ =
+ CTC.type_of_aux' metasenv context term CicUniv.empty_ugraph
+ in
+ debug_print (lazy ("\nqnify su: " ^ pp context termty));
+ let tac = match termty with
+ | C.Appl [(C.MutInd (equri, 0, [])) ; tty ; t1 ; t2]
+ when LibraryObjects.is_eq_URI equri -> begin
+ match (CR.whd ~delta:true context tty) with
+ | C.MutInd _
+ | C.Appl (C.MutInd _ :: _) ->
+ begin match t1,t2 with
+ | C.MutConstruct _,
+ C.MutConstruct _
+ when t1 = t2 ->
+ T.then_ ~start:(clear_term first_time context term)
+ ~continuation:(continuation ~map)
+ | C.Appl (C.MutConstruct _ as mc1 :: applist1),
+ C.Appl (C.MutConstruct _ as mc2 :: applist2)
+ when mc1 = mc2 ->
+ let rec traverse_list first_time i l1 l2 =
+ match l1, l2 with
+ | [], [] ->
+ fun ~map:aftermap ->
+ T.then_ ~start:(clear_term first_time context term)
+ ~continuation:(after continuation aftermap map)
+ | hd1 :: tl1, hd2 :: tl2 ->
+ if are_convertible hd1 hd2 metasenv context then
+ traverse_list first_time (succ i) tl1 tl2
+ else
+ injection_tac ~i ~term ~continuation:
+ (traverse_list false (succ i) tl1 tl2)
+ | _ -> assert false
+ (* i 2 termini hanno in testa lo stesso costruttore,
+ * ma applicato a un numero diverso di termini *)
in
-debug_print (lazy ("XXXX consno2' " ^ (string_of_int consno2'))) ;
- if consno2' = 0
- then raise (ProofEngineTypes.Fail "Discriminate: Discriminating terms are structurally equal")
- else
-
- let pattern =
- (* a list of "True" except for the element in position consno2' which is "False" *)
- match fst(CicEnvironment.get_obj turi
- CicUniv.empty_ugraph) with
- C.InductiveDefinition (ind_type_list,_,nr_ind_params) ->
-debug_print (lazy ("XXXX nth " ^ (string_of_int (List.length ind_type_list)) ^ " " ^ (string_of_int typeno))) ;
- let _,_,_,constructor_list = (List.nth ind_type_list typeno) in
-debug_print (lazy ("XXXX nth " ^ (string_of_int (List.length constructor_list)) ^ " " ^ (string_of_int consno2'))) ;
- let false_constr_id,_ = List.nth constructor_list (consno2' - 1) in
-debug_print (lazy "XXXX nth funzionano ") ;
- List.map
- (function (id,cty) ->
- let red_ty = CicReduction.whd context cty in (* dubbio: e' corretto ridurre in questo context ??? *)
- let rec aux t k =
- match t with
- C.Prod (_,_,target) when (k <= nr_ind_params) ->
- aux target (k+1)
- | C.Prod (binder,source,target) when (k > nr_ind_params) ->
- C.Lambda (binder,source,(aux target (k+1)))
- | _ ->
- if (id = false_constr_id)
- then (C.MutInd (U.uri_of_string "cic:/Coq/Init/Logic/False.ind") 0 [])
- else (C.MutInd (U.uri_of_string "cic:/Coq/Init/Logic/True.ind") 0 [])
- in aux red_ty 1
- )
- constructor_list
- | _ -> raise (ProofEngineTypes.Fail "Discriminate: object is not an Inductive Definition: it's imposible")
- in
-
- let (proof',goals') =
- EliminationTactics.elim_type_tac
- ~term:(C.MutInd (U.uri_of_string "cic:/Coq/Init/Logic/False.ind") 0 [] )
- status
- in
- (match goals' with
- [goal'] ->
- let _,metasenv',_,_ = proof' in
- let _,context',gty' =
- CicUtil.lookup_meta goal' metasenv'
- in
- T.then_
- ~start:
- (P.change_tac
- ~what:gty'
- ~with_what:
- (C.Appl [
- C.Lambda (
- C.Name "x", tty,
- C.MutCase (
- turi, typeno,
- (C.Lambda ((C.Name "x"),tty,(C.Sort C.Prop))),
- (C.Rel 1), pattern
- )
- );
- t2']
- )
- )
- ~continuation:
- (
-debug_print (lazy ("XXXX rewrite<-: " ^ CicPp.ppterm (CicTypeChecker.type_of_aux' metasenv' context' (C.Appl [(C.MutInd (equri,0,[])) ; tty ; t1' ; t2']))));
-debug_print (lazy ("XXXX rewrite<-: " ^ CicPp.ppterm (C.Appl [(C.MutInd (equri,0,[])) ; tty ; t1' ; t2']))) ;
-debug_print (lazy ("XXXX equri: " ^ U.string_of_uri equri)) ;
-debug_print (lazy ("XXXX tty : " ^ CicPp.ppterm tty)) ;
-debug_print (lazy ("XXXX tt1': " ^ CicPp.ppterm (CicTypeChecker.type_of_aux' metasenv' context' t1'))) ;
-debug_print (lazy ("XXXX tt2': " ^ CicPp.ppterm (CicTypeChecker.type_of_aux' metasenv' context' t2'))) ;
-if (CicTypeChecker.type_of_aux' metasenv' context' t1') <> tty then debug_print (lazy ("XXXX tt1': " ^ CicPp.ppterm (CicTypeChecker.type_of_aux' metasenv' context' t1'))) ;
-if (CicTypeChecker.type_of_aux' metasenv' context' t2') <> tty then debug_print (lazy ("XXXX tt2': " ^ CicPp.ppterm (CicTypeChecker.type_of_aux' metasenv' context' t2'))) ;
-if (CicTypeChecker.type_of_aux' metasenv' context' t1') <> (CicTypeChecker.type_of_aux' metasenv' context' t2')
- then debug_print (lazy ("XXXX tt1': " ^ CicPp.ppterm (CicTypeChecker.type_of_aux'
- metasenv' context' t1'))) ; debug_print (lazy ("XXXX tt2': " ^ CicPp.ppterm (CicTypeChecker.type_of_aux' metasenv' context' t2'))) ;
-
- let termty' = ProofEngineReduction.replace_lifting ~equality:(==) ~what:t1 ~with_what:t1' ~where:termty in
- let termty'' = ProofEngineReduction.replace_lifting ~equality:(==) ~what:t2 ~with_what:t2' ~where:termty' in
-
-debug_print (lazy ("XXXX rewrite<- " ^ CicPp.ppterm term ^ " : " ^ CicPp.ppterm (CicTypeChecker.type_of_aux' metasenv' context' term)));
- T.then_
- ~start:(EqualityTactics.rewrite_back_simpl_tac ~term:term)
- ~continuation:(IntroductionTactics.constructor_tac ~n:1)
- )
- (proof',goal')
- | _ -> raise (ProofEngineTypes.Fail "Discriminate: ElimType False left more (or less) than one goal")
- )
- | _ -> raise (ProofEngineTypes.Fail "Discriminate: not a discriminable equality")
- )
- | _ -> raise (ProofEngineTypes.Fail "Discriminate: not an equality")
-;;
-
-*)
-
-
+ traverse_list first_time 1 applist1 applist2 ~map:id
+ | C.MutConstruct (_,_,consno1,ens1),
+ C.MutConstruct (_,_,consno2,ens2)
+ | C.MutConstruct (_,_,consno1,ens1),
+ C.Appl ((C.MutConstruct (_,_,consno2,ens2))::_)
+ | C.Appl ((C.MutConstruct (_,_,consno1,ens1))::_),
+ C.MutConstruct (_,_,consno2,ens2)
+ | C.Appl ((C.MutConstruct (_,_,consno1,ens1))::_),
+ C.Appl ((C.MutConstruct (_,_,consno2,ens2))::_)
+ when (consno1 <> consno2) || (ens1 <> ens2) ->
+ discriminate_tac ~term
+ | _ when not first_time -> continuation ~map
+ | _ (* when first_time *) ->
+ T.then_ ~start:(simpl_in_term context term)
+ ~continuation:(destruct ~first_time:false ~term ~map ~continuation)
+ end
+ | _ when not first_time -> continuation ~map
+ | _ (* when first_time *) -> raise exn_nonproj
+ end
+ | _ -> raise exn_nonproj
+ in
+ PET.apply_tactic tac status
+ in
+ PET.mk_tactic destruct
+(* destruct performs either injection or discriminate *)
+(* equivalent to Coq's "analyze equality" *)
+let destruct_tac =
+ destruct
+ ~first_time:true ~map:id ~continuation:(fun ~map -> T.id_tac)
projects / helm.git / blobdiff