(* $Id$ *)
-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!) *)
match ty with
C.Cast (te,_) -> collect_context context howmany do_whd te
| C.Prod (n,s,t) ->
- let n' = mk_fresh_name metasenv context n ~typ:s in
+ let n' = mk_fresh_name metasenv context n ~typ:s in
let (context',ty,bo) =
- let ctx = (Some (n',(C.Decl s)))::context in
+ let entry = match n' with
+ | C.Name _ -> Some (n',(C.Decl s))
+ | C.Anonymous -> None
+ in
+ let ctx = entry :: context in
collect_context ctx (howmany - 1) do_whd t
in
(context',ty,C.Lambda(n',s,bo))
- | C.LetIn (n,s,t) ->
+ | C.LetIn (n,s,sty,t) ->
let (context',ty,bo) =
- collect_context ((Some (n,(C.Def (s,None))))::context) (howmany - 1) do_whd t
+ collect_context ((Some (n,(C.Def (s,sty))))::context) (howmany - 1) do_whd t
in
- (context',ty,C.LetIn(n,s,bo))
+ (context',ty,C.LetIn(n,s,sty,bo))
| _ as t ->
if howmany <= 0 then
let irl =
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
| C.Cast (te,ty) -> C.Cast (aux n te, aux n ty)
| C.Prod (nn,s,t) -> C.Prod (nn, aux n s, aux (n+1) t)
| C.Lambda (nn,s,t) -> C.Lambda (nn, aux n s, aux (n+1) t)
- | C.LetIn (nn,s,t) -> C.LetIn (nn, aux n s, aux (n+1) t)
+ | C.LetIn (nn,s,ty,t) -> C.LetIn (nn, aux n s, aux n ty, aux (n+1) t)
| C.Appl l -> C.Appl (List.map (aux n) l)
| C.Const (uri,exp_named_subst) ->
let exp_named_subst' = aux_exp_named_subst n exp_named_subst in
List.map (function uri,t -> uri,aux n t)
in
let argty,_ =
- T.type_of_aux' metasenv context arg CicUniv.empty_ugraph (* TASSI: FIXME *)
+ T.type_of_aux' metasenv context arg CicUniv.oblivion_ugraph (* TASSI: FIXME *)
in
let fresh_name =
FreshNamesGenerator.mk_fresh_name ~subst:[]
match entry with
Some (n,Cic.Decl s) ->
Some (n,Cic.Decl (subst_in canonical_context' s))
- | Some (n,Cic.Def (s,None)) ->
- Some (n,Cic.Def ((subst_in canonical_context' s),None))
| None -> None
- | Some (n,Cic.Def (bo,Some ty)) ->
+ | Some (n,Cic.Def (bo,ty)) ->
Some
(n,
Cic.Def
(subst_in canonical_context' bo,
- Some (subst_in canonical_context' ty)))
+ subst_in canonical_context' ty))
in
entry'::canonical_context'
) canonical_context []
=
let module C = Cic in
let params =
- let o,_ = CicEnvironment.get_obj CicUniv.empty_ugraph uri in
+ let o,_ = CicEnvironment.get_obj CicUniv.oblivion_ugraph uri in
CicUtil.params_of_obj o
in
let exp_named_subst_diff,new_fresh_meta,newmetasenvfragment,exp_named_subst'=
[],[] -> []
| uri::tl,[] ->
let ty =
- let o,_ = CicEnvironment.get_obj CicUniv.empty_ugraph uri in
+ let o,_ = CicEnvironment.get_obj CicUniv.oblivion_ugraph uri in
match o with
C.Variable (_,_,ty,_,_) ->
CicSubstitution.subst_vars !exp_named_subst_diff ty
new_fresh_meta,newmetasenvfragment,exp_named_subst',exp_named_subst_diff
;;
-let new_metasenv_and_unify_and_t newmeta' metasenv' context term' ty termty goal_arity =
+let new_metasenv_and_unify_and_t newmeta' metasenv' subst context term' ty termty goal_arity =
let (consthead,newmetasenv,arguments,_) =
TermUtil.saturate_term newmeta' metasenv' context termty
goal_arity in
let subst,newmetasenv',_ =
- CicUnification.fo_unif newmetasenv context consthead ty CicUniv.empty_ugraph
+ CicUnification.fo_unif_subst
+ subst context newmetasenv consthead ty CicUniv.oblivion_ugraph
in
let t =
if List.length arguments = 0 then term' else Cic.Appl (term'::arguments)
let module T = CicTypeChecker in
let module R = CicReduction in
let module C = Cic in
- let (_,metasenv,_,_, _) = proof in
+ let (_,metasenv,_subst,_,_, _) = proof in
let metano,context,ty = CicUtil.lookup_meta goal metasenv in
let newmeta = max (CicMkImplicit.new_meta metasenv subst) maxmeta in
let exp_named_subst_diff,newmeta',newmetasenvfragment,term' =
in
let metasenv' = metasenv@newmetasenvfragment in
let termty,_ =
- CicTypeChecker.type_of_aux' metasenv' context term' CicUniv.empty_ugraph
+ CicTypeChecker.type_of_aux' metasenv' context term' CicUniv.oblivion_ugraph
in
let termty =
CicSubstitution.subst_vars exp_named_subst_diff termty in
let subst,newmetasenv',t =
let rec add_one_argument n =
try
- new_metasenv_and_unify_and_t newmeta' metasenv' context term' ty
+ new_metasenv_and_unify_and_t newmeta' metasenv' subst context term' ty
termty n
with CicUnification.UnificationFailure _ when n > 0 ->
add_one_argument (n - 1)
let subst_in =
(* if we just apply the subtitution, the type is irrelevant:
we may use Implicit, since it will be dropped *)
- CicMetaSubst.apply_subst ((metano,(context,bo',Cic.Implicit None))::subst)
+ ((metano,(context,bo',Cic.Implicit None))::subst)
in
let (newproof, newmetasenv''') =
ProofEngineHelpers.subst_meta_and_metasenv_in_proof proof metano subst_in
newmetasenv''
in
- let subst = ((metano,(context,bo',Cic.Implicit None))::subst) in
+ let subst = ((metano,(context,bo',ty))::subst) in
subst,
(newproof, List.map (function (i,_,_) -> i) new_uninstantiatedmetas),
max maxmeta (CicMkImplicit.new_meta newmetasenv''' subst)
(* 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 applyP_tac ~term =
+ let applyP_tac status =
+ let res = PET.apply_tactic (apply_tac ~term) status in res
+ in
+ PET.mk_tactic applyP_tac
let intros_tac ?howmany ?(mk_fresh_name_callback = FreshNamesGenerator.mk_fresh_name ~subst:[]) ()=
- let intros_tac
- ?(mk_fresh_name_callback = (FreshNamesGenerator.mk_fresh_name ~subst:[])) ()
- (proof, goal)
+ let intros_tac (proof, goal)
=
let module C = Cic in
let module R = CicReduction in
- let (_,metasenv,_,_, _) = proof in
+ let (_,metasenv,_subst,_,_, _) = proof in
let metano,context,ty = CicUtil.lookup_meta goal metasenv in
let newmeta = ProofEngineHelpers.new_meta_of_proof ~proof in
let (context',ty',bo') =
in
(newproof, [newmeta])
in
- mk_tactic (intros_tac ~mk_fresh_name_callback ())
+ PET.mk_tactic intros_tac
let cut_tac ?(mk_fresh_name_callback = FreshNamesGenerator.mk_fresh_name ~subst:[]) term =
let cut_tac
term (proof, goal)
=
let module C = Cic in
- let curi,metasenv,pbo,pty, attrs = proof in
+ let curi,metasenv,_subst,pbo,pty, attrs = proof in
let metano,context,ty = CicUtil.lookup_meta goal metasenv in
let newmeta1 = ProofEngineHelpers.new_meta_of_proof ~proof in
let newmeta2 = newmeta1 + 1 in
CicMkImplicit.identity_relocation_list_for_metavariable context
in
let newmeta1ty = CicSubstitution.lift 1 ty in
- let bo' =
- C.Appl
- [C.Lambda (fresh_name,term,C.Meta (newmeta1,irl1)) ;
- C.Meta (newmeta2,irl2)]
- in
+ let bo' =
+ Cic.LetIn (fresh_name, C.Meta (newmeta2,irl2), term, C.Meta (newmeta1,irl1))
+ in
let (newproof, _) =
ProofEngineHelpers.subst_meta_in_proof proof metano bo'
[newmeta2,context,term; newmeta1,context_for_newmeta1,newmeta1ty];
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
term (proof, goal)
=
let module C = Cic in
- let curi,metasenv,pbo,pty, attrs = proof in
+ let curi,metasenv,_subst,pbo,pty, attrs = proof in
(* occur check *)
let occur i t =
let m = CicUtil.metas_of_term t in
raise
(ProofEngineTypes.Fail (lazy
"You can't letin a term containing the current goal"));
- let _,_ =
- CicTypeChecker.type_of_aux' metasenv context term CicUniv.empty_ugraph in
+ let tty,_ =
+ CicTypeChecker.type_of_aux' metasenv context term CicUniv.oblivion_ugraph in
let newmeta = ProofEngineHelpers.new_meta_of_proof ~proof in
let fresh_name =
mk_fresh_name_callback metasenv context (Cic.Name "Hletin") ~typ:term in
let context_for_newmeta =
- (Some (fresh_name,C.Def (term,None)))::context in
+ (Some (fresh_name,C.Def (term,tty)))::context in
let irl =
CicMkImplicit.identity_relocation_list_for_metavariable
context_for_newmeta
in
let newmetaty = CicSubstitution.lift 1 ty in
- let bo' = C.LetIn (fresh_name,term,C.Meta (newmeta,irl)) in
+ let bo' = C.LetIn (fresh_name,term,tty,C.Meta (newmeta,irl)) in
let (newproof, _) =
ProofEngineHelpers.subst_meta_in_proof
proof metano bo'[newmeta,context_for_newmeta,newmetaty]
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 =
- let exact_tac ~term (proof, goal) =
- (* Assumption: the term bo must be closed in the current context *)
- let (_,metasenv,_,_, _) = proof in
- let metano,context,ty = CicUtil.lookup_meta goal metasenv in
- let module T = CicTypeChecker in
- let module R = CicReduction in
- let ty_term,u = T.type_of_aux' metasenv context term CicUniv.empty_ugraph in
- let b,_ = R.are_convertible context ty_term ty u in (* TASSI: FIXME *)
- if b then
- begin
- let (newproof, metasenv') =
- ProofEngineHelpers.subst_meta_in_proof proof metano term [] in
- (newproof, [])
- end
- else
- raise (Fail (lazy "The type of the provided term is not the one expected."))
- in
- mk_tactic (exact_tac ~term)
+(* FG: exact_tac := apply_tac as in NTactics *)
+let exact_tac ~term = apply_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 rec args_init n f =
+ if n <= 0 then [] else f n :: args_init (pred n) f
+
+let mk_predicate_for_elim
+ ~context ~metasenv ~ugraph ~goal ~arg ~using ~cpattern ~args_no =
+ let instantiated_eliminator =
+ let f n = if n = 1 then arg else C.Implicit None in
+ C.Appl (using :: args_init args_no f)
+ in
+ let _actual_arg, iety, _metasenv', _ugraph =
+ CicRefine.type_of_aux' metasenv context instantiated_eliminator ugraph
+ in
+ let _actual_meta, actual_args = match iety with
+ | C.Meta (i, _) -> i, []
+ | C.Appl (C.Meta (i, _) :: args) -> i, args
+ | _ -> assert false
+ in
+(* let _, upto = PEH.split_with_whd (List.nth splits pred_pos) in *)
+ let rec mk_pred metasenv context' pred arg' cpattern' = function
+ | [] -> metasenv, pred, arg'
+ | arg :: tail ->
+(* FG: we find the predicate for the eliminator as in the rewrite tactic ****)
+ let argty, _ugraph = TC.type_of_aux' metasenv context arg ugraph in
+ let argty = CicReduction.whd context argty in
+ let fresh_name =
+ FreshNamesGenerator.mk_fresh_name
+ ~subst:[] metasenv context' C.Anonymous ~typ:argty in
+ let hyp = Some (fresh_name, C.Decl argty) in
+ let lazy_term c m u =
+ let distance = List.length c - List.length context in
+ S.lift distance arg, m, u in
+ let pattern = Some lazy_term, [], Some cpattern' in
+ let subst, metasenv, _ugraph, _conjecture, selected_terms =
+ ProofEngineHelpers.select ~metasenv ~ugraph
+ ~conjecture:(0, 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 arg' = MS.apply_subst subst arg' in
+ let argty = MS.apply_subst subst argty 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, argty, pred) in
+ let cpattern' = C.Lambda (C.Anonymous, C.Implicit None, cpattern') in
+ mk_pred metasenv (hyp :: context') pred arg' cpattern' tail
+ in
+ let metasenv, pred, arg =
+ mk_pred metasenv context goal arg cpattern (List.rev actual_args)
+ in
+ HLog.debug ("PREDICATE: " ^ CicPp.ppterm ~metasenv pred ^ " ARGS: " ^ String.concat " " (List.map (CicPp.ppterm ~metasenv) actual_args));
+ metasenv, pred, arg, actual_args
+
+let beta_after_elim_tac upto predicate =
+ let beta_after_elim_tac status =
+ let proof, goal = status in
+ let _, metasenv, _subst, _, _, _ = 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, ty, t) ->
+ let s,ty,t = gen_term k s, gen_term k ty, gen_term (succ k) t in
+ if is_meta [s; t] then meta else C.LetIn (anon, s, ty, 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
+
+(* ANCORA DA DEBUGGARE *)
+
+exception UnableToDetectTheTermThatMustBeGeneralizedYouMustGiveItExplicitly;;
+exception TheSelectedTermsMustLiveInTheGoalContext
+exception AllSelectedTermsMustBeConvertible;;
+exception GeneralizationInHypothesesNotImplementedYet;;
+
+let generalize_tac
+ ?(mk_fresh_name_callback = FreshNamesGenerator.mk_fresh_name ~subst:[])
+ pattern
+ =
+ let module PET = ProofEngineTypes in
+ let generalize_tac mk_fresh_name_callback
+ ~pattern:(term,hyps_pat,_) status
+ =
+ if hyps_pat <> [] then raise GeneralizationInHypothesesNotImplementedYet;
+ let (proof, goal) = status in
+ let module C = Cic in
+ let module T = Tacticals in
+ let uri,metasenv,_subst,pbo,pty, attrs = proof in
+ let (_,context,ty) as conjecture = CicUtil.lookup_meta goal metasenv in
+ let subst,metasenv,u,selected_hyps,terms_with_context =
+ ProofEngineHelpers.select ~metasenv ~ugraph:CicUniv.oblivion_ugraph
+ ~conjecture ~pattern in
+ let context = CicMetaSubst.apply_subst_context subst context in
+ let metasenv = CicMetaSubst.apply_subst_metasenv subst metasenv in
+ let pbo = lazy (CicMetaSubst.apply_subst subst (Lazy.force pbo)) in
+ let pty = CicMetaSubst.apply_subst subst pty in
+ let term =
+ match term with
+ None -> None
+ | Some term ->
+ Some (fun context metasenv ugraph ->
+ let term, metasenv, ugraph = term context metasenv ugraph in
+ CicMetaSubst.apply_subst subst term,
+ CicMetaSubst.apply_subst_metasenv subst metasenv,
+ ugraph)
+ in
+ let u,typ,term, metasenv' =
+ let context_of_t, (t, metasenv, u) =
+ match terms_with_context, term with
+ [], None ->
+ raise
+ UnableToDetectTheTermThatMustBeGeneralizedYouMustGiveItExplicitly
+ | [], Some t -> context, t context metasenv u
+ | (context_of_t, _)::_, Some t ->
+ context_of_t, t context_of_t metasenv u
+ | (context_of_t, t)::_, None -> context_of_t, (t, metasenv, u)
+ in
+ let t,subst,metasenv' =
+ try
+ CicMetaSubst.delift_rels [] metasenv
+ (List.length context_of_t - List.length context) t
+ with
+ CicMetaSubst.DeliftingARelWouldCaptureAFreeVariable ->
+ raise TheSelectedTermsMustLiveInTheGoalContext
+ in
+ (*CSC: I am not sure about the following two assertions;
+ maybe I need to propagate the new subst and metasenv *)
+ assert (subst = []);
+ assert (metasenv' = metasenv);
+ let typ,u = CicTypeChecker.type_of_aux' ~subst metasenv context t u in
+ u,typ,t,metasenv
+ in
+ (* We need to check:
+ 1. whether they live in the context of the goal;
+ if they do they are also well-typed since they are closed subterms
+ of a well-typed term in the well-typed context of the well-typed
+ term
+ 2. whether they are convertible
+ *)
+ ignore (
+ List.fold_left
+ (fun u (context_of_t,t) ->
+ (* 1 *)
+ let t,subst,metasenv'' =
+ try
+ CicMetaSubst.delift_rels [] metasenv'
+ (List.length context_of_t - List.length context) t
+ with
+ CicMetaSubst.DeliftingARelWouldCaptureAFreeVariable ->
+ raise TheSelectedTermsMustLiveInTheGoalContext in
+ (*CSC: I am not sure about the following two assertions;
+ maybe I need to propagate the new subst and metasenv *)
+ assert (subst = []);
+ assert (metasenv'' = metasenv');
+ (* 2 *)
+ let b,u1 = CicReduction.are_convertible ~subst context term t u in
+ if not b then
+ raise AllSelectedTermsMustBeConvertible
+ else
+ u1
+ ) u terms_with_context) ;
+ let status = (uri,metasenv',_subst,pbo,pty, attrs),goal in
+ let proof,goals =
+ PET.apply_tactic
+ (T.thens
+ ~start:
+ (cut_tac
+ (C.Prod(
+ (mk_fresh_name_callback metasenv context C.Anonymous ~typ:typ),
+ typ,
+ (ProofEngineReduction.replace_lifting_csc 1
+ ~equality:(==)
+ ~what:(List.map snd terms_with_context)
+ ~with_what:(List.map (function _ -> C.Rel 1) terms_with_context)
+ ~where:ty)
+ )))
+ ~continuations:
+ [(apply_tac ~term:(C.Appl [C.Rel 1; CicSubstitution.lift 1 term])) ;
+ T.id_tac])
+ status
+ in
+ let _,metasenv'',_subst,_,_, _ = proof in
+ (* CSC: the following is just a bad approximation since a meta
+ can be closed and then re-opened! *)
+ (proof,
+ goals @
+ (List.filter
+ (fun j -> List.exists (fun (i,_,_) -> i = j) metasenv'')
+ (ProofEngineHelpers.compare_metasenvs ~oldmetasenv:metasenv
+ ~newmetasenv:metasenv')))
+ in
+ PET.mk_tactic (generalize_tac mk_fresh_name_callback ~pattern)
+;;
+
+let generalize_pattern_tac pattern =
+ let generalize_pattern_tac (proof,goal) =
+ let _,metasenv,_,_,_,_ = proof in
+ let conjecture = CicUtil.lookup_meta goal metasenv in
+ let _,context,_ = conjecture in
+ let generalize_hyps =
+ let _,hpatterns,_ = ProofEngineHelpers.sort_pattern_hyps context pattern in
+ List.map fst hpatterns in
+ let ids_and_patterns =
+ List.map
+ (fun id ->
+ let rel,_ = ProofEngineHelpers.find_hyp id context in
+ id,(Some (fun ctx m u -> CicSubstitution.lift (List.length ctx - List.length context) rel,m,u), [], Some (ProofEngineTypes.hole))
+ ) generalize_hyps in
+ let tactics =
+ List.map
+ (function (id,pattern) ->
+ Tacticals.then_ ~start:(generalize_tac pattern)
+ ~continuation:(Tacticals.try_tactic
+ (ProofEngineStructuralRules.clear [id]))
+ ) ids_and_patterns
+ in
+ PET.apply_tactic (Tacticals.seq tactics) (proof,goal)
+ in
+ PET.mk_tactic (generalize_pattern_tac)
+;;
+
+let pattern_after_generalize_pattern_tac (tp, hpatterns, cpattern) =
+ let cpattern =
+ match cpattern with
+ None -> ProofEngineTypes.hole
+ | Some t -> t
+ in
+ let cpattern =
+ List.fold_left
+ (fun t (_,ty) -> Cic.Prod (Cic.Anonymous, ty, t)) cpattern hpatterns
+ in
+ tp, [], Some cpattern
+;;
+
let elim_tac ?using ?(pattern = PET.conclusion_pattern None) term =
- let elim_tac (proof, goal) =
- let ugraph = CicUniv.empty_ugraph in
- let curi, metasenv, proofbo, proofty, attrs = proof in
+ let elim_tac pattern (proof, goal) =
+ let ugraph = CicUniv.oblivion_ugraph in
+ let curi, metasenv, _subst, 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 pattern = pattern_after_generalize_pattern_tac pattern in
+ let cpattern =
+ match pattern with
+ | None, [], Some cpattern -> cpattern
+ | _ -> raise (PET.Fail (lazy "not implemented")) 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
match ty_ty with
C.Sort C.Prop -> "_ind"
| C.Sort C.Set -> "_rec"
- | C.Sort C.CProp -> "_rec"
+ | C.Sort (C.CProp _) -> "_rect"
| C.Sort (C.Type _)-> "_rect"
| 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
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
+ let metasenv', pred, term, actual_args = match pattern with
+ | None, [], Some (C.Implicit (Some `Hole)) ->
+ metasenv', C.Implicit None, term, []
+ | _ ->
+ mk_predicate_for_elim
+ ~args_no ~context ~ugraph ~cpattern
+ ~metasenv:metasenv' ~arg:term ~using:eliminator_ref ~goal:ty
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'',_subst,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''',_subst,_,_, _) = 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
+ let upto = List.length actual_args 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
+ let reorder_pattern ((proof, goal) as status) =
+ let _,metasenv,_,_,_,_ = proof in
+ let conjecture = CicUtil.lookup_meta goal metasenv in
+ let _,context,_ = conjecture in
+ let pattern = ProofEngineHelpers.sort_pattern_hyps context pattern in
+ PET.apply_tactic
+ (Tacticals.then_ ~start:(generalize_pattern_tac pattern)
+ ~continuation:(PET.mk_tactic (elim_tac pattern))) status
+ in
+ PET.mk_tactic reorder_pattern
;;
-let cases_intros_tac ?(mk_fresh_name_callback = FreshNamesGenerator.mk_fresh_name ~subst:[]) term =
- let cases_tac ~term (proof, goal) =
+let cases_intros_tac ?(howmany=(-1)) ?(mk_fresh_name_callback = FreshNamesGenerator.mk_fresh_name ~subst:[]) ?(pattern = PET.conclusion_pattern None) term =
+ let cases_tac pattern (proof, goal) =
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,_ = 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 =
- 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 _,right_args =
- List.fold_right
- (fun x (n,acc) -> if n > 0 then (n-1,x::acc) else (n,acc))
- args (List.length args - paramsno, [])
- in
- let outtype =
- let n_lambdas = List.length right_args + 1 in
- let lifted_ty = CicSubstitution.lift n_lambdas ty in
- let replace = ProofEngineReduction.replace_lifting
- ~equality:(ProofEngineReduction.alpha_equivalence)
- in
- let captured_ty =
- let what =
- List.map (CicSubstitution.lift n_lambdas) (right_args@[term])
- in
- let with_what =
- let rec mkargs = function
- | 0 -> []
- | 1 -> [Cic.Rel 1]
- | n -> (Cic.Implicit None)::(mkargs (n-1))
- in
- mkargs n_lambdas
- in
- replace ~what ~with_what ~where:lifted_ty
+ let (curi,metasenv,_subst, proofbo,proofty, attrs) = proof in
+ let metano,context,ty = CicUtil.lookup_meta goal metasenv in
+ let pattern = pattern_after_generalize_pattern_tac pattern in
+ let _cpattern =
+ match pattern with
+ | None, [], Some cpattern ->
+ let rec is_hole =
+ function
+ Cic.Implicit (Some `Hole) -> true
+ | Cic.Prod (Cic.Anonymous,so,tgt) -> is_hole so && is_hole tgt
+ | _ -> false
+ in
+ if not (is_hole cpattern) then
+ raise (PET.Fail (lazy "not implemented"))
+ | _ -> raise (PET.Fail (lazy "not implemented")) in
+ let termty,_ = TC.type_of_aux' metasenv context term CicUniv.oblivion_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.oblivion_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 captured_term_ty =
- let term_ty = CicSubstitution.lift (n_lambdas-1) 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_lambdas -1))
- | _ -> raise NotAnInductiveTypeToEliminate
+ 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 rec add_lambdas = function
- | 0 -> captured_ty
- | 1 ->
- C.Lambda (C.Name "matched", captured_term_ty, (add_lambdas 0))
+ paramsno,itty,
+ List.map (function (_,cty) -> aux left_parameters context cty) cl,
+ right_args
+ | _ -> assert false
+ in
+ let outtypes =
+ 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 ->
- C.Lambda (C.Name ("right_"^(string_of_int (n-1))),
- C.Implicit None, (add_lambdas (n-1)))
+ (if meta then Cic.Implicit None else Cic.Rel n)::(mkargs (n-1))
in
- add_lambdas n_lambdas
+ mkargs n_lambdas
in
- let term_to_refine =
- C.MutCase (uri,typeno,outtype,term,patterns)
- in
- let refined_term,_,metasenv'',_ =
+ 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 false) ~where:captured;
+ 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 captured_ty = function
+ | 0 -> captured_ty
+ | 1 ->
+ C.Lambda (C.Name "matched", captured_term_ty, (add_lambdas captured_ty 0))
+ | n ->
+ C.Lambda (C.Name ("right_"^(string_of_int (n-1))),
+ C.Implicit None, (add_lambdas captured_ty (n-1)))
+ in
+ List.map (fun x -> add_lambdas x n_lambdas) captured_ty
+ in
+ let rec first = (* easier than using tacticals *)
+ function
+ | [] -> raise (PET.Fail (lazy ("unable to generate a working outtype")))
+ | outtype::rest ->
+ let term_to_refine = C.MutCase (uri,typeno,outtype,term,patterns) in
+ try
+ let refined_term,_,metasenv'',_ =
CicRefine.type_of_aux' metasenv' context term_to_refine
- CicUniv.empty_ugraph
- in
- let new_goals =
- ProofEngineHelpers.compare_metasenvs
+ CicUniv.oblivion_ugraph
+ in
+ let new_goals =
+ ProofEngineHelpers.compare_metasenvs
~oldmetasenv:metasenv ~newmetasenv:metasenv''
+ in
+ let proof' = curi,metasenv'',_subst,proofbo,proofty, attrs in
+ let proof'', new_goals' =
+ PET.apply_tactic (apply_tac ~term:refined_term) (proof',goal)
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
+ (* The apply_tactic can have closed some of the new_goals *)
+ let patched_new_goals =
+ let (_,metasenv''',_subst,_,_,_) = proof'' in
List.filter
- (function i -> List.exists (function (j,_,_) -> j=i) metasenv'''
- ) new_goals @ new_goals'
- in
- proof'', patched_new_goals
+ (function i -> List.exists (function (j,_,_) -> j=i) metasenv''')
+ new_goals @ new_goals'
+ in
+ proof'', patched_new_goals
+ with PET.Fail _ | CicRefine.RefineFailure _ | CicRefine.Uncertain _ -> first rest
+ in
+ first outtypes
in
- mk_tactic (cases_tac ~term)
+ let reorder_pattern ((proof, goal) as status) =
+ let _,metasenv,_,_,_,_ = proof in
+ let conjecture = CicUtil.lookup_meta goal metasenv in
+ let _,context,_ = conjecture in
+ let pattern = ProofEngineHelpers.sort_pattern_hyps context pattern in
+ PET.apply_tactic
+ (Tacticals.then_ ~start:(generalize_pattern_tac pattern)
+ ~continuation:(PET.mk_tactic (cases_tac pattern))) status
+ in
+ PET.mk_tactic reorder_pattern
;;
[ReductionTactics.simpl_tac
~pattern:(ProofEngineTypes.conclusion_pattern None)])
;;
-
-(* FG: insetrts a "hole" in the context (derived from letin_tac) *)
-
-let letout_tac =
- let mk_fresh_name_callback = FreshNamesGenerator.mk_fresh_name ~subst:[] in
- let term = C.Sort C.Set in
- let letout_tac (proof, goal) =
- let curi, metasenv, pbo, pty, attrs = proof in
- let metano, context, ty = CicUtil.lookup_meta goal metasenv in
- let newmeta = ProofEngineHelpers.new_meta_of_proof ~proof in
- let fresh_name = mk_fresh_name_callback metasenv context (Cic.Name "hole") ~typ:term in
- let context_for_newmeta = None :: context in
- let irl = CicMkImplicit.identity_relocation_list_for_metavariable context_for_newmeta in
- let newmetaty = CicSubstitution.lift 1 ty in
- let bo' = C.LetIn (fresh_name, term, C.Meta (newmeta,irl)) in
- let newproof, _ = ProofEngineHelpers.subst_meta_in_proof proof metano bo'[newmeta,context_for_newmeta,newmetaty] in
- newproof, [newmeta]
- in
- mk_tactic letout_tac
projects / helm.git / blobdiff