exception TheTypeOfTheCurrentGoalIsAMetaICannotChooseTheRightElimiantionPrinciple
exception NotAnInductiveTypeToEliminate
exception WrongUriToVariable of string
+exception NotAnEliminator
(* lambda_abstract newmeta ty *)
(* returns a triple [bo],[context],[ty'] where *)
| C.Prod (n,s,t) ->
let n' = mk_fresh_name metasenv context n ~typ:s in
let (context',ty,bo) =
- collect_context ((Some (n',(C.Decl s)))::context) (howmany - 1) do_whd t
+ let ctx = (Some (n',(C.Decl s)))::context in
+ collect_context ctx (howmany - 1) do_whd t
in
(context',ty,C.Lambda(n',s,bo))
| C.LetIn (n,s,t) ->
mk_tactic (exact_tac ~term)
(* not really "primitive" tactics .... *)
-let elim_tac ?using ~term =
+
+module TC = CicTypeChecker
+module U = UriManager
+module R = CicReduction
+module C = Cic
+module PET = ProofEngineTypes
+module PEH = ProofEngineHelpers
+module PER = ProofEngineReduction
+module MS = CicMetaSubst
+module S = CicSubstitution
+module T = Tacticals
+module RT = ReductionTactics
+
+let elim_tac ?using ?(pattern = PET.conclusion_pattern None) term =
let elim_tac (proof, goal) =
- let module T = CicTypeChecker in
- let module U = UriManager in
- let module R = CicReduction in
- let module C = Cic in
- let (curi,metasenv,proofbo,proofty, attrs) = proof in
- let metano,context,ty = CicUtil.lookup_meta goal metasenv in
- let termty,_ = T.type_of_aux' metasenv context term CicUniv.empty_ugraph in
+ let ugraph = CicUniv.empty_ugraph in
+ let curi, metasenv, proofbo, proofty, attrs = proof in
+ let conjecture = CicUtil.lookup_meta goal metasenv in
+ let metano, context, ty = conjecture in
+(* let (term, metasenv, _ugraph), cpatt = match pattern with
+ | Some f, [], Some cpatt -> f context metasenv ugraph, cpatt
+ | _ -> assert false
+ in
+*)
+ let termty,_ugraph = TC.type_of_aux' metasenv context term ugraph in
let termty = CicReduction.whd context termty in
- let (termty,metasenv',arguments,fresh_meta) =
+ let (termty,metasenv',arguments,_fresh_meta) =
TermUtil.saturate_term
(ProofEngineHelpers.new_meta_of_proof proof) metasenv context termty 0 in
let term = if arguments = [] then term else Cic.Appl (term::arguments) in
let eliminator_uri =
let buri = U.buri_of_uri uri in
let name =
- let o,_ = CicEnvironment.get_obj CicUniv.empty_ugraph uri in
+ let o,_ugraph = CicEnvironment.get_obj ugraph uri in
match o with
C.InductiveDefinition (tys,_,_,_) ->
let (name,_,_,_) = List.nth tys typeno in
name
| _ -> assert false
in
- let ty_ty,_ = T.type_of_aux' metasenv' context ty CicUniv.empty_ugraph in
+ let ty_ty,_ugraph = TC.type_of_aux' metasenv' context ty ugraph in
let ext =
match ty_ty with
C.Sort C.Prop -> "_ind"
| None -> C.Const (eliminator_uri,exp_named_subst)
| Some t -> t
in
- let ety,_ =
- T.type_of_aux' metasenv' context eliminator_ref CicUniv.empty_ugraph in
- let rec find_args_no =
- function
- C.Prod (_,_,t) -> 1 + find_args_no t
- | C.Cast (s,_) -> find_args_no s
- | C.LetIn (_,_,t) -> 0 + find_args_no t
- | _ -> 0
- in
- let args_no = find_args_no ety in
- let term_to_refine =
- let rec make_tl base_case =
- function
- 0 -> [base_case]
- | n -> (C.Implicit None)::(make_tl base_case (n - 1))
- in
- C.Appl (eliminator_ref :: make_tl term (args_no - 1))
+ let ety,_ugraph =
+ TC.type_of_aux' metasenv' context eliminator_ref ugraph in
+(* FG: ADDED PART ***********************************************************)
+(* FG: we can not assume eliminator is the default eliminator ***************)
+(*
+ let add_lambdas n t =
+ let rec aux n t =
+ if n <= 0 then t
+ else C.Lambda (C.Anonymous, C.Implicit None, aux (pred n) t)
+ in
+ aux n (S.lift n t)
+ in
+*)
+ let rec args_init n f =
+ if n <= 0 then [] else f n :: args_init (pred n) f
+ in
+ let splits, args_no = PEH.split_with_whd (context, ety) in
+ let pred_pos = match List.hd splits with
+ | _, C.Rel i when i > 1 && i <= args_no -> i
+ | _, C.Appl (C.Rel i :: _) when i > 1 && i <= args_no -> i
+ | _ -> raise NotAnEliminator
+ in
+(*
+ let _, lambdas = PEH.split_with_whd (List.nth splits pred_pos) in
+ let termty_ty =
+ let termty_ty,_ugraph = TC.type_of_aux' metasenv' context termty ugraph in
+ CicReduction.whd context termty_ty
+ in
+*)
+(*
+ let metasenv', term, pred, upto = match cpatt, termty_ty with
+ | C.Implicit (Some `Hole), _
+ | _, C.Sort C.Prop when lambdas = 0 -> metasenv', term, C.Implicit None, 0
+ | _ ->
+(* FG: we find the predicate for the eliminator as in the rewrite tactic ****)
+ let fresh_name =
+ FreshNamesGenerator.mk_fresh_name
+ ~subst:[] metasenv' context C.Anonymous ~typ:termty
+ in
+ let lazy_term c m u =
+ let distance = List.length c - List.length context in
+ S.lift distance term, m, u
+ in
+ let pattern = Some lazy_term, [], Some cpatt in
+ let subst, metasenv', _ugraph, _conjecture, selected_terms =
+ ProofEngineHelpers.select
+ ~metasenv:metasenv' ~ugraph ~conjecture ~pattern
+ in
+ let metasenv' = MS.apply_subst_metasenv subst metasenv' in
+ let map (_context_of_t, t) l = t :: l in
+ let what = List.fold_right map selected_terms [] in
+ let ty = MS.apply_subst subst ty in
+ let term = MS.apply_subst subst term in
+ let termty = MS.apply_subst subst termty in
+ let abstr_ty = PER.replace_with_rel_1_from ~equality:(==) ~what 1 ty in
+ let abstr_ty = MS.apply_subst subst abstr_ty in
+ let pred_body = C.Lambda (fresh_name, termty, abstr_ty) in
+ metasenv', term, add_lambdas (pred lambdas) pred_body, lambdas
+ in
+(* FG: END OF ADDED PART ****************************************************)
+*)
+ let pred, upto = C.Implicit None, 0 in
+
+ let term_to_refine =
+ let f n =
+ if n = pred_pos then pred else
+ if n = 1 then term else C.Implicit None
+ in
+ C.Appl (eliminator_ref :: args_init args_no f)
in
- let refined_term,_,metasenv'',_ =
+ let refined_term,_refined_termty,metasenv'',_ugraph =
CicRefine.type_of_aux' metasenv' context term_to_refine
- CicUniv.empty_ugraph
+ ugraph
in
let new_goals =
ProofEngineHelpers.compare_metasenvs
in
let proof' = curi,metasenv'',proofbo,proofty, attrs in
let proof'', new_goals' =
- apply_tactic (apply_tac ~term:refined_term) (proof',goal)
+ apply_tactic (apply_tac ~term:refined_term) (proof',goal)
in
(* The apply_tactic can have closed some of the new_goals *)
let patched_new_goals =
(function i -> List.exists (function (j,_,_) -> j=i) metasenv'''
) new_goals @ new_goals'
in
- proof'', patched_new_goals
+ let res = proof'', patched_new_goals in
+ if upto = 0 then res else
+ let pattern = PET.conclusion_pattern None in
+ let continuation =
+ RT.simpl_tac ~pattern
+ (* RT.head_beta_reduce_tac ~delta:false ~upto ~pattern *)
+ in
+ let dummy_status = proof,goal in
+ PET.apply_tactic
+ (T.then_ ~start:(PET.mk_tactic (fun _ -> res)) ~continuation)
+ dummy_status
in
mk_tactic elim_tac
;;
let cases_intros_tac ?(mk_fresh_name_callback = FreshNamesGenerator.mk_fresh_name ~subst:[]) term =
let cases_tac ~term (proof, goal) =
- let module T = CicTypeChecker in
+ let module TC = CicTypeChecker in
let module U = UriManager in
let module R = CicReduction in
let module C = Cic in
- let (curi,metasenv,proofbo,proofty, attrs) = proof in
- let metano,context,ty = CicUtil.lookup_meta goal metasenv in
- let termty,_ = T.type_of_aux' metasenv context term CicUniv.empty_ugraph in
- let termty = CicReduction.whd context termty in
- let (termty,metasenv',arguments,fresh_meta) =
- TermUtil.saturate_term
- (ProofEngineHelpers.new_meta_of_proof proof) metasenv context termty 0 in
- let term = if arguments = [] then term else Cic.Appl (term::arguments) in
- let uri,exp_named_subst,typeno,args =
- match termty with
- C.MutInd (uri,typeno,exp_named_subst) -> (uri,exp_named_subst,typeno,[])
- | C.Appl ((C.MutInd (uri,typeno,exp_named_subst))::args) ->
- (uri,exp_named_subst,typeno,args)
- | _ -> raise NotAnInductiveTypeToEliminate
- in
- let paramsno,itty,patterns =
- match CicEnvironment.get_obj CicUniv.empty_ugraph uri with
- C.InductiveDefinition (tys,_,paramsno,_),_ ->
- let _,_,itty,cl = List.nth tys typeno in
- let rec aux n context t =
- match n,CicReduction.whd context t with
- 0,C.Prod (name,source,target) ->
- let fresh_name =
- mk_fresh_name_callback metasenv' context name
- (*CSC: WRONG TYPE HERE: I can get a "bad" name*)
- ~typ:source
- in
- C.Lambda (fresh_name,C.Implicit None,
- aux 0 (Some (fresh_name,C.Decl source)::context) target)
- | n,C.Prod (name,source,target) ->
- let fresh_name =
- mk_fresh_name_callback metasenv' context name
- (*CSC: WRONG TYPE HERE: I can get a "bad" name*)
- ~typ:source
- in
- aux (n-1) (Some (fresh_name,C.Decl source)::context) target
- | 0,_ -> C.Implicit None
- | _,_ -> assert false
- in
- paramsno,itty,
- List.map (function (_,cty) -> aux paramsno context cty) cl
- | _ -> assert false
- in
- let outtype =
- let target =
- C.Lambda (C.Name "fixme",C.Implicit None,
- ProofEngineReduction.replace_lifting
- ~equality:(ProofEngineReduction.alpha_equivalence)
- ~what:[CicSubstitution.lift (paramsno+1) term]
- ~with_what:[C.Rel (paramsno+1)]
- ~where:(CicSubstitution.lift (paramsno+1) ty))
+ let (curi,metasenv,proofbo,proofty, attrs) = proof in
+ let metano,context,ty = CicUtil.lookup_meta goal metasenv in
+ let termty,_ = TC.type_of_aux' metasenv context term CicUniv.empty_ugraph in
+ let termty = CicReduction.whd context termty in
+ let (termty,metasenv',arguments,fresh_meta) =
+ TermUtil.saturate_term
+ (ProofEngineHelpers.new_meta_of_proof proof) metasenv context termty 0 in
+ let term = if arguments = [] then term else Cic.Appl (term::arguments) in
+ let uri,exp_named_subst,typeno,args =
+ match termty with
+ | C.MutInd (uri,typeno,exp_named_subst) -> (uri,exp_named_subst,typeno,[])
+ | C.Appl ((C.MutInd (uri,typeno,exp_named_subst))::args) ->
+ (uri,exp_named_subst,typeno,args)
+ | _ -> raise NotAnInductiveTypeToEliminate
+ in
+ let paramsno,itty,patterns,right_args =
+ match CicEnvironment.get_obj CicUniv.empty_ugraph uri with
+ | C.InductiveDefinition (tys,_,paramsno,_),_ ->
+ let _,left_parameters,right_args =
+ List.fold_right
+ (fun x (n,acc1,acc2) ->
+ if n > 0 then (n-1,acc1,x::acc2) else (n,x::acc1,acc2))
+ args (List.length args - paramsno, [],[])
in
- let rec add_lambdas =
- function
- 0 -> target
- | n -> C.Lambda (C.Name "fixme",C.Implicit None,add_lambdas (n-1))
- in
- add_lambdas (count_prods context itty - paramsno)
- in
- let term_to_refine =
- C.MutCase (uri,typeno,outtype,term,patterns)
+ let _,_,itty,cl = List.nth tys typeno in
+ let rec aux left_parameters context t =
+ match left_parameters,CicReduction.whd context t with
+ | [],C.Prod (name,source,target) ->
+ let fresh_name =
+ mk_fresh_name_callback metasenv' context name ~typ:source
+ in
+ C.Lambda (fresh_name,C.Implicit None,
+ aux [] (Some (fresh_name,C.Decl source)::context) target)
+ | hd::tl,C.Prod (name,source,target) ->
+ (* left parameters instantiation *)
+ aux tl context (CicSubstitution.subst hd target)
+ | [],_ -> C.Implicit None
+ | _ -> assert false
in
- let refined_term,_,metasenv'',_ =
- CicRefine.type_of_aux' metasenv' context term_to_refine
- CicUniv.empty_ugraph
+ paramsno,itty,
+ List.map (function (_,cty) -> aux left_parameters context cty) cl,
+ right_args
+ | _ -> assert false
+ in
+ let outtype =
+ let n_right_args = List.length right_args in
+ let n_lambdas = n_right_args + 1 in
+ let lifted_ty = CicSubstitution.lift n_lambdas ty in
+ let captured_ty =
+ let what =
+ List.map (CicSubstitution.lift n_lambdas) (right_args)
+ in
+ let with_what meta =
+ let rec mkargs = function
+ | 0 -> assert false
+ | 1 -> []
+ | n ->
+ (if meta then Cic.Implicit None else Cic.Rel n)::(mkargs (n-1))
in
- let new_goals =
- ProofEngineHelpers.compare_metasenvs
- ~oldmetasenv:metasenv ~newmetasenv:metasenv''
- in
- let proof' = curi,metasenv'',proofbo,proofty, attrs in
- let proof'', new_goals' =
- apply_tactic (apply_tac ~term:refined_term) (proof',goal)
- in
- (* The apply_tactic can have closed some of the new_goals *)
- let patched_new_goals =
- let (_,metasenv''',_,_,_) = proof'' in
- List.filter
- (function i -> List.exists (function (j,_,_) -> j=i) metasenv'''
- ) new_goals @ new_goals'
- in
- proof'', patched_new_goals
- in
+ mkargs n_lambdas
+ in
+ let replaced = ref false in
+ let replace = ProofEngineReduction.replace_lifting
+ ~equality:(fun _ a b -> let rc = CicUtil.alpha_equivalence a b in
+ if rc then replaced := true; rc)
+ ~context:[]
+ in
+ let captured =
+ replace ~what:[CicSubstitution.lift n_lambdas term]
+ ~with_what:[Cic.Rel 1] ~where:lifted_ty
+ in
+ if not !replaced then
+ (* this means the matched term is not there,
+ * but maybe right params are: we user rels (to right args lambdas) *)
+ replace ~what ~with_what:(with_what false) ~where:captured
+ else
+ (* since the matched is there, rights should be inferrable *)
+ replace ~what ~with_what:(with_what true) ~where:captured
+ in
+ let captured_term_ty =
+ let term_ty = CicSubstitution.lift n_right_args termty in
+ let rec mkrels = function 0 -> []|n -> (Cic.Rel n)::(mkrels (n-1)) in
+ let rec fstn acc l n =
+ if n = 0 then acc else fstn (acc@[List.hd l]) (List.tl l) (n-1)
+ in
+ match term_ty with
+ | C.MutInd _ -> term_ty
+ | C.Appl ((C.MutInd (a,b,c))::args) ->
+ C.Appl ((C.MutInd (a,b,c))::
+ fstn [] args paramsno @ mkrels n_right_args)
+ | _ -> raise NotAnInductiveTypeToEliminate
+ in
+ let rec add_lambdas = function
+ | 0 -> captured_ty
+ | 1 ->
+ C.Lambda (C.Name "matched", captured_term_ty, (add_lambdas 0))
+ | n ->
+ C.Lambda (C.Name ("right_"^(string_of_int (n-1))),
+ C.Implicit None, (add_lambdas (n-1)))
+ in
+ add_lambdas n_lambdas
+ in
+ let term_to_refine = C.MutCase (uri,typeno,outtype,term,patterns) in
+ let refined_term,_,metasenv'',_ =
+ CicRefine.type_of_aux' metasenv' context term_to_refine
+ CicUniv.empty_ugraph
+ in
+ let new_goals =
+ ProofEngineHelpers.compare_metasenvs
+ ~oldmetasenv:metasenv ~newmetasenv:metasenv''
+ in
+ let proof' = curi,metasenv'',proofbo,proofty, attrs in
+ let proof'', new_goals' =
+ apply_tactic (apply_tac ~term:refined_term) (proof',goal)
+ in
+ (* The apply_tactic can have closed some of the new_goals *)
+ let patched_new_goals =
+ let (_,metasenv''',_,_,_) = proof'' in
+ List.filter
+ (function i -> List.exists (function (j,_,_) -> j=i) metasenv''')
+ new_goals @ new_goals'
+ in
+ proof'', patched_new_goals
+ in
mk_tactic (cases_tac ~term)
;;
let elim_intros_tac ?(mk_fresh_name_callback = FreshNamesGenerator.mk_fresh_name ~subst:[])
- ?depth ?using what =
- Tacticals.then_ ~start:(elim_tac ?using ~term:what)
+ ?depth ?using ?pattern what =
+ Tacticals.then_ ~start:(elim_tac ?using ?pattern what)
~continuation:(intros_tac ~mk_fresh_name_callback ?howmany:depth ())
;;
(* The simplification is performed only on the conclusion *)
let elim_intros_simpl_tac ?(mk_fresh_name_callback = FreshNamesGenerator.mk_fresh_name ~subst:[])
- ?depth ?using what =
- Tacticals.then_ ~start:(elim_tac ?using ~term:what)
+ ?depth ?using ?pattern what =
+ Tacticals.then_ ~start:(elim_tac ?using ?pattern what)
~continuation:
(Tacticals.thens
~start:(intros_tac ~mk_fresh_name_callback ?howmany:depth ())
(* FG: insetrts a "hole" in the context (derived from letin_tac) *)
-module C = Cic
-
let letout_tac =
let mk_fresh_name_callback = FreshNamesGenerator.mk_fresh_name ~subst:[] in
let term = C.Sort C.Set in