-let debug_print = fun _ -> ()
-
-let rec injection_tac ~term ~liftno ~continuation =
- 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 term = CicSubstitution.lift liftno term 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") ; *) 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
- [],[] -> continuation
- | 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"))
- | _ -> continuation ~liftno (*raise (ProofEngineTypes.Fail (lazy "Injection: not a projectable equality"))*)
- )
- | _ -> continuation ~liftno (*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)
-
-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 C = Cic in
- let module S = CicSubstitution in
- 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
- 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 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 ~liftno:0 ~term:(C.Rel 1)
- ~continuation:(fun ~liftno:x -> continuation ~liftno:(liftno + 1 + x)))
- ~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,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 "Injection: not an equality over elements of an inductive type"))
- )
- | _ -> raise (ProofEngineTypes.Fail (lazy "Injection: not an equality"))
- in
- ProofEngineTypes.mk_tactic (injection1_tac ~term ~i)