let debug_print = fun _ -> ()
-let rec injection_tac ~term =
+let rec injection_tac ~first_time ~term ~liftno ~continuation =
let injection_tac ~term status =
let (proof, goal) = status in
let module C = Cic in
let module T = Tacticals in
let _,metasenv,_,_ = proof in
let _,context,_ = CicUtil.lookup_meta goal metasenv in
+ let term = CicSubstitution.lift liftno term in
let termty,_ = (* TASSI: FIXME *)
- CicTypeChecker.type_of_aux' metasenv context term CicUniv.empty_ugraph in
+ 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 termty with
+ (C.Appl [(C.MutInd (equri, 0, [])) ; tty ; t1 ; t2])
+ when LibraryObjects.is_eq_URI equri ->
+ begin
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
+ | (C.Appl (C.MutInd (turi,typeno,exp_named_subst)::_)) ->
+ begin
+ 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)
+ ->
+ if first_time then
+ raise
+ (ProofEngineTypes.Fail (lazy "Injection: nothing to do"))
+ else
+ continuation ~liftno
+ | 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
+ [],[] ->
+ if first_time then
+ continuation
+ else
+ (match term with
+ C.Rel n ->
+ (match List.nth context (n-1) with
+ Some (C.Name id,_) ->
+ fun ~liftno ->
+ T.then_
+ ~start:
+ (ProofEngineStructuralRules.clear
+ ~hyps:[id])
+ ~continuation:(continuation ~liftno)
+ | _ -> assert false)
+ | _ -> assert false)
+ | hd1::tl1,hd2::tl2 ->
+ if
+ fst
+ (CicReduction.are_convertible ~metasenv
+ context hd1 hd2 CicUniv.empty_ugraph)
+ then
+ traverse_list (i+1) tl1 tl2
+ else
+ 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 ~liftno
+ | ((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 (lazy "Injection: not a projectable equality but a discriminable one"))
+ | _ ->
+ if first_time then
+ raise (ProofEngineTypes.Fail (lazy "Injection: not a projectable equality"))
+ else
+ continuation ~liftno
+ end
+ | _ ->
+ if first_time then
+ raise (ProofEngineTypes.Fail (lazy "Injection: not a projectable equality"))
+ else
+ continuation ~liftno
+ end
+ | _ -> raise (ProofEngineTypes.Fail (lazy "Injection: not an equation"))
+ ) status
in
ProofEngineTypes.mk_tactic (injection_tac ~term)
-and injection1_tac ~term ~i =
+and injection1_tac ~term ~i ~liftno ~continuation =
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 U = UriManager in
let module P = PrimitiveTactics in
let module T = Tacticals in
+ let term = CicSubstitution.lift liftno term 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
+ 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 -> (
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"))
+ let patterns,outtype =
+ match
+ fst (CicEnvironment.get_obj CicUniv.empty_ugraph turi)
+ with
+ C.InductiveDefinition (ind_type_list,_,paramsno,_)->
+ let _,_,_,constructor_list =
+ List.nth ind_type_list typeno in
+ let i_constr_id,_ =
+ List.nth constructor_list (consno - 1) in
+ let seed = ref 0 in
+ let patterns =
+ 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 <= paramsno ->
+ aux target (k+1)
+ | C.Prod (binder,source,target) when k > paramsno ->
+ let binder' =
+ match binder with
+ C.Name _ -> binder
+ | C.Anonymous ->
+ C.Name
+ (incr seed; "y" ^ string_of_int !seed)
+ in
+ C.Lambda (binder',source,(aux target (k+1)))
+ | _ ->
+ let nr_param_constr = k - 1 - paramsno in
+ if id = i_constr_id
+ then C.Rel (k - i)
+ else S.lift (nr_param_constr + 1) t1' (* + 1 per liftare anche il lambda aggiunto esternamente al case *)
+ in aux reduced_cty 1
+ ) constructor_list in
+ let outtype =
+ let seed = ref 0 in
+ let rec to_lambdas te head =
+ match CicReduction.whd context te with
+ | C.Prod (binder,so,ta) ->
+ let binder' =
+ match binder with
+ C.Name _ -> binder
+ | C.Anonymous ->
+ C.Name (incr seed; "d" ^ string_of_int !seed)
+ in
+ C.Lambda (binder',so,to_lambdas ta head)
+ | _ -> head in
+ let rec skip_prods n te =
+ match n, CicReduction.whd context te with
+ 0, _ -> te
+ | n, C.Prod (_,_,ta) -> skip_prods (n - 1) ta
+ | _, _ -> assert false
+ in
+ let abstracted_tty =
+ match CicSubstitution.lift (paramsno + 1) tty with
+ C.MutInd _ as tty' -> tty'
+ | C.Appl l ->
+ let keep,abstract =
+ HExtlib.split_nth (paramsno +1) l in
+ let rec mk_rels =
+ function
+ 0 -> []
+ | n -> C.Rel n :: (mk_rels (n - 1))
+ in
+ C.Appl (keep@mk_rels (List.length abstract))
+ | _ -> assert false
+ in
+ match ind_type_list with
+ [] -> assert false
+ | (_,_,ty,_)::_ ->
+ to_lambdas (skip_prods paramsno ty)
+ (C.Lambda (C.Name "x", abstracted_tty,
+ S.lift (2+paramsno) tty'))
+ in
+ patterns,outtype
+ | _ -> 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
- )
+ ~start:
+ (P.cut_tac
+ (C.Appl [C.MutInd (equri,0,[]) ; tty' ; t1' ; t2']))
+ ~continuations:
+ [ injection_tac ~first_time:false ~liftno:0
+ ~term:(C.Rel 1)
+ (* here I need to lift all the continuations by 1;
+ since I am setting back liftno to 0, I actually
+ need to lift all the continuations by liftno + 1 *)
+ ~continuation:
+ (fun ~liftno:x ->
+ continuation ~liftno:(liftno + 1 + x)) ;
+ 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,outtype,C.Rel 1,patterns)) ;
+ 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 "Injection: not an equality over elements of an inductive type"))
)
- | _ -> raise (ProofEngineTypes.Fail (lazy "Discriminate: not an equality"))
+ | _ -> raise (ProofEngineTypes.Fail (lazy "Injection: not an equality"))
in
ProofEngineTypes.mk_tactic (injection1_tac ~term ~i)
;;
+let injection_tac =
+ injection_tac ~first_time:true ~liftno:0 ~continuation:(fun ~liftno -> Tacticals.id_tac)
+;;
+
exception TwoDifferentSubtermsFound of int
(* term ha tipo t1=t2; funziona solo se t1 e t2 hanno in testa costruttori
projects / helm.git / blobdiff