(* $Id$ *)
-open ProofEngineTypes
-
exception TheTypeOfTheCurrentGoalIsAMetaICannotChooseTheRightElimiantionPrinciple
exception NotAnInductiveTypeToEliminate
exception WrongUriToVariable of string
exception NotAnEliminator
+module PET = ProofEngineTypes
+
(* lambda_abstract newmeta ty *)
(* returns a triple [bo],[context],[ty'] where *)
(* [ty] = Pi/LetIn [context].[ty'] ([context] is a vector!) *)
let t = CicReduction.whd ~delta:true context t in
collect_context context howmany false t
else
- raise (Fail (lazy "intro(s): not enough products or let-ins"))
+ raise (PET.Fail (lazy "intro(s): not enough products or let-ins"))
in
collect_context context howmany true ty
(* TODO cacciare anche altre eccezioni? *)
with
| CicUnification.UnificationFailure msg
- | CicTypeChecker.TypeCheckerFailure msg -> raise (Fail msg)
+ | CicTypeChecker.TypeCheckerFailure msg -> raise (PET.Fail msg)
(* ALB *)
let apply_tac_verbose ~term status =
with
| CicUnification.UnificationFailure msg
| CicTypeChecker.TypeCheckerFailure msg ->
- raise (Fail msg)
+ raise (PET.Fail msg)
in
- mk_tactic (apply_tac ~term)
+ PET.mk_tactic (apply_tac ~term)
let intros_tac ?howmany ?(mk_fresh_name_callback = FreshNamesGenerator.mk_fresh_name ~subst:[]) ()=
let intros_tac
in
(newproof, [newmeta])
in
- mk_tactic (intros_tac ~mk_fresh_name_callback ())
+ PET.mk_tactic (intros_tac ~mk_fresh_name_callback ())
let cut_tac ?(mk_fresh_name_callback = FreshNamesGenerator.mk_fresh_name ~subst:[]) term =
let cut_tac
in
(newproof, [newmeta1 ; newmeta2])
in
- mk_tactic (cut_tac ~mk_fresh_name_callback term)
+ PET.mk_tactic (cut_tac ~mk_fresh_name_callback term)
let letin_tac ?(mk_fresh_name_callback=FreshNamesGenerator.mk_fresh_name ~subst:[]) term =
let letin_tac
in
(newproof, [newmeta])
in
- mk_tactic (letin_tac ~mk_fresh_name_callback term)
+ PET.mk_tactic (letin_tac ~mk_fresh_name_callback term)
(** functional part of the "exact" tactic *)
let exact_tac ~term =
(newproof, [])
end
else
- raise (Fail (lazy "The type of the provided term is not the one expected."))
+ raise (PET.Fail (lazy "The type of the provided term is not the one expected."))
in
- mk_tactic (exact_tac ~term)
+ PET.mk_tactic (exact_tac ~term)
(* not really "primitive" tactics .... *)
module TC = CicTypeChecker
-module U = UriManager
+module UM = UriManager
module R = CicReduction
module C = Cic
-module PET = ProofEngineTypes
module PEH = ProofEngineHelpers
module PER = ProofEngineReduction
module MS = CicMetaSubst
module T = Tacticals
module RT = ReductionTactics
+let beta_after_elim_tac upto predicate =
+ let beta_after_elim_tac status =
+ let proof, goal = status in
+ let _, metasenv, _, _, _ = proof in
+ let _, _, ty = CicUtil.lookup_meta goal metasenv in
+ let mk_pattern ~equality ~upto ~predicate ty =
+ (* code adapted from ProceduralConversion.generalize *)
+ let meta = C.Implicit None in
+ let hole = C.Implicit (Some `Hole) in
+ let anon = C.Anonymous in
+ let is_meta =
+ let map b = function
+ | C.Implicit None when b -> b
+ | _ -> false
+ in
+ List.fold_left map true
+ in
+ let rec gen_fix len k (name, i, ty, bo) =
+ name, i, gen_term k ty, gen_term (k + len) bo
+ and gen_cofix len k (name, ty, bo) =
+ name, gen_term k ty, gen_term (k + len) bo
+ and gen_term k = function
+ | C.Sort _
+ | C.Implicit _
+ | C.Const (_, _)
+ | C.Var (_, _)
+ | C.MutInd (_, _, _)
+ | C.MutConstruct (_, _, _, _)
+ | C.Meta (_, _)
+ | C.Rel _ -> meta
+ | C.Appl (hd :: tl) when equality hd (S.lift k predicate) ->
+ assert (List.length tl = upto);
+ hole
+ | C.Appl ts ->
+ let ts = List.map (gen_term k) ts in
+ if is_meta ts then meta else C.Appl ts
+ | C.Cast (te, ty) ->
+ let te, ty = gen_term k te, gen_term k ty in
+ if is_meta [te; ty] then meta else C.Cast (te, ty)
+ | C.MutCase (sp, i, outty, t, pl) ->
+ let outty, t, pl = gen_term k outty, gen_term k t, List.map (gen_term k) pl in
+ if is_meta (outty :: t :: pl) then meta else hole (* C.MutCase (sp, i, outty, t, pl) *)
+ | C.Prod (_, s, t) ->
+ let s, t = gen_term k s, gen_term (succ k) t in
+ if is_meta [s; t] then meta else C.Prod (anon, s, t)
+ | C.Lambda (_, s, t) ->
+ let s, t = gen_term k s, gen_term (succ k) t in
+ if is_meta [s; t] then meta else C.Lambda (anon, s, t)
+ | C.LetIn (_, s, t) ->
+ let s, t = gen_term k s, gen_term (succ k) t in
+ if is_meta [s; t] then meta else C.LetIn (anon, s, t)
+ | C.Fix (i, fl) -> C.Fix (i, List.map (gen_fix (List.length fl) k) fl)
+ | C.CoFix (i, fl) -> C.CoFix (i, List.map (gen_cofix (List.length fl) k) fl)
+ in
+ None, [], Some (gen_term 0 ty)
+ in
+ let equality = CicUtil.alpha_equivalence in
+ let pattern = mk_pattern ~equality ~upto ~predicate ty in
+ let tactic = RT.head_beta_reduce_tac ~delta:false ~upto ~pattern in
+ PET.apply_tactic tactic status
+ in
+ PET.mk_tactic beta_after_elim_tac
+
let elim_tac ?using ?(pattern = PET.conclusion_pattern None) term =
let elim_tac (proof, goal) =
+ let cpatt = match pattern with
+ | None, [], Some cpatt -> cpatt
+ | _ -> raise (PET.Fail (lazy "not implemented"))
+ 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 metano, context, ty = conjecture 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 uri,exp_named_subst,typeno,args =
+ 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) ->
| _ -> raise NotAnInductiveTypeToEliminate
in
let eliminator_uri =
- let buri = U.buri_of_uri uri in
+ let buri = UM.buri_of_uri uri in
let name =
let o,_ugraph = CicEnvironment.get_obj ugraph uri in
match o with
| C.Meta (_,_) -> raise TheTypeOfTheCurrentGoalIsAMetaICannotChooseTheRightElimiantionPrinciple
| _ -> assert false
in
- U.uri_of_string (buri ^ "/" ^ name ^ ext ^ ".con")
+ UM.uri_of_string (buri ^ "/" ^ name ^ ext ^ ".con")
in
let eliminator_ref = match using with
- | None -> C.Const (eliminator_uri,exp_named_subst)
+ | None -> C.Const (eliminator_uri, exp_named_subst)
| Some t -> t
in
- let ety,_ugraph =
+ 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
| _, 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
+ let upto, metasenv', pred, term = match pattern with
+ | None, [], Some (C.Implicit (Some `Hole)) ->
+ 0, metasenv', C.Implicit None, term
+ | _ ->
+ let instantiated_eliminator =
+ let f n = if n = 1 then term else C.Implicit None in
+ C.Appl (eliminator_ref :: args_init args_no f)
in
- let lazy_term c m u =
- let distance = List.length c - List.length context in
- S.lift distance term, m, u
+ let _actual_term, iety, _metasenv'', _ugraph =
+ CicRefine.type_of_aux' metasenv' context instantiated_eliminator ugraph
in
- let pattern = Some lazy_term, [], Some cpatt in
- let subst, metasenv', _ugraph, _conjecture, selected_terms =
- ProofEngineHelpers.select
- ~metasenv:metasenv' ~ugraph ~conjecture ~pattern
+ let _actual_meta, actual_args = match iety with
+ | C.Meta (i, _) -> i, []
+ | C.Appl (C.Meta (i, _) :: args) -> i, args
+ | _ -> assert false
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
+ (* let _, upto = PEH.split_with_whd (List.nth splits pred_pos) in *)
+ let upto = List.length actual_args in
+ let rec mk_pred metasenv context' pred term' = function
+ | [] -> metasenv, pred, term'
+ | term :: tail ->
+(* FG: we find the predicate for the eliminator as in the rewrite tactic ****)
+ let termty, _ugraph = TC.type_of_aux' metasenv context' term ugraph in
+ let termty = CicReduction.whd context' termty in
+ let fresh_name =
+ FreshNamesGenerator.mk_fresh_name
+ ~subst:[] metasenv context' C.Anonymous ~typ:termty
+ in
+ let hyp = Some (fresh_name, C.Decl 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 ~ugraph ~conjecture:(metano, context, pred) ~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 term' = MS.apply_subst subst term' in
+ let termty = MS.apply_subst subst termty in
+ let pred = PER.replace_with_rel_1_from ~equality:(==) ~what 1 pred in
+ let pred = MS.apply_subst subst pred in
+ let pred = C.Lambda (fresh_name, termty, pred) in
+ mk_pred metasenv (hyp :: context') pred term' tail
+ in
+ let metasenv', pred, term = mk_pred metasenv' context ty term actual_args in
+ HLog.debug ("PRED: " ^ CicPp.ppterm ~metasenv:metasenv' pred ^ " ARGS: " ^ String.concat " " (List.map (CicPp.ppterm ~metasenv:metasenv') actual_args));
+ upto, metasenv', pred, term
+ 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)
+ let term_to_refine =
+ let f n =
+ if n = pred_pos then pred else
+ if n = 1 then term else C.Implicit None
in
- let refined_term,_refined_termty,metasenv'',_ugraph =
- CicRefine.type_of_aux' metasenv' context term_to_refine
- 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
- 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
+ C.Appl (eliminator_ref :: args_init args_no f)
+ in
+ let refined_term,_refined_termty,metasenv'',_ugraph =
+ CicRefine.type_of_aux' metasenv' context term_to_refine 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' =
+ PET.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
+ let res = proof'', patched_new_goals in
+ if upto = 0 then res else
+ let continuation = beta_after_elim_tac upto pred in
+ let dummy_status = proof,goal in
+ PET.apply_tactic
+ (T.then_ ~start:(PET.mk_tactic (fun _ -> res)) ~continuation)
+ dummy_status
+ in
+ PET.mk_tactic elim_tac
;;
let cases_intros_tac ?(mk_fresh_name_callback = FreshNamesGenerator.mk_fresh_name ~subst:[]) term =
in
let proof' = curi,metasenv'',proofbo,proofty, attrs in
let proof'', new_goals' =
- apply_tactic (apply_tac ~term:refined_term) (proof',goal)
+ PET.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 =
in
proof'', patched_new_goals
in
- mk_tactic (cases_tac ~term)
+ PET.mk_tactic (cases_tac ~term)
;;
let newproof, _ = ProofEngineHelpers.subst_meta_in_proof proof metano bo'[newmeta,context_for_newmeta,newmetaty] in
newproof, [newmeta]
in
- mk_tactic letout_tac
+ PET.mk_tactic letout_tac
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