(* $Id$ *)
-open ProofEngineHelpers
open ProofEngineTypes
exception TheTypeOfTheCurrentGoalIsAMetaICannotChooseTheRightElimiantionPrinciple
exception NotAnInductiveTypeToEliminate
exception WrongUriToVariable of string
+exception NotAnEliminator
(* lambda_abstract newmeta ty *)
(* returns a triple [bo],[context],[ty'] where *)
(* howmany = -1 means Intros, howmany > 0 means Intros n *)
let lambda_abstract ?(howmany=(-1)) metasenv context newmeta ty mk_fresh_name =
let module C = Cic in
- let rec collect_context context howmany ty =
+ let rec collect_context context howmany do_whd ty =
match howmany with
| 0 ->
let irl =
context, ty, (C.Meta (newmeta,irl))
| _ ->
match ty with
- C.Cast (te,_) -> collect_context context howmany te
+ 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 (context',ty,bo) =
- collect_context ((Some (n',(C.Decl s)))::context) (howmany - 1) 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) ->
let (context',ty,bo) =
- collect_context ((Some (n,(C.Def (s,None))))::context) (howmany - 1) t
+ collect_context ((Some (n,(C.Def (s,None))))::context) (howmany - 1) do_whd t
in
(context',ty,C.LetIn(n,s,bo))
| _ as t ->
CicMkImplicit.identity_relocation_list_for_metavariable context
in
context, t, (C.Meta (newmeta,irl))
- else
+ else if do_whd then
+ 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"))
in
- collect_context context howmany ty
+ collect_context context howmany true ty
let eta_expand metasenv context t arg =
let module T = CicTypeChecker in
let new_metasenv_and_unify_and_t newmeta' metasenv' context term' ty termty goal_arity =
let (consthead,newmetasenv,arguments,_) =
- saturate_term newmeta' metasenv' context termty goal_arity in
+ TermUtil.saturate_term newmeta' metasenv' context termty
+ goal_arity in
let subst,newmetasenv',_ =
CicUnification.fo_unif newmetasenv context consthead ty CicUniv.empty_ugraph
in
Cic.Prod (n,s,t) -> 1 + count_prods (Some (n,Cic.Decl s)::context) t
| _ -> 0
-let apply_tac_verbose_with_subst ~term (proof, goal) =
+let apply_with_subst ~term ~subst ~maxmeta (proof, goal) =
(* Assumption: The term "term" must be closed in the current context *)
let module T = CicTypeChecker in
let module R = CicReduction in
let module C = Cic in
- let (_,metasenv,_,_) = proof in
+ let (_,metasenv,_,_, _) = proof in
let metano,context,ty = CicUtil.lookup_meta goal metasenv in
- let newmeta = new_meta_of_proof ~proof in
+ let newmeta = max (CicMkImplicit.new_meta metasenv subst) maxmeta in
let exp_named_subst_diff,newmeta',newmetasenvfragment,term' =
match term with
C.Var (uri,exp_named_subst) ->
CicMetaSubst.apply_subst ((metano,(context,bo',Cic.Implicit None))::subst)
in
let (newproof, newmetasenv''') =
- subst_meta_and_metasenv_in_proof proof metano subst_in newmetasenv''
+ ProofEngineHelpers.subst_meta_and_metasenv_in_proof proof metano subst_in
+ newmetasenv''
in
- (((metano,(context,bo',Cic.Implicit None))::subst)(* subst_in *), (* ALB *)
- (newproof,
- List.map (function (i,_,_) -> i) new_uninstantiatedmetas))
+ let subst = ((metano,(context,bo',Cic.Implicit None))::subst) in
+ subst,
+ (newproof, List.map (function (i,_,_) -> i) new_uninstantiatedmetas),
+ max maxmeta (CicMkImplicit.new_meta newmetasenv''' subst)
(* ALB *)
-let apply_tac_verbose_with_subst ~term status =
+let apply_with_subst ~term ?(subst=[]) ?(maxmeta=0) status =
try
(* apply_tac_verbose ~term status *)
- apply_tac_verbose_with_subst ~term status
+ apply_with_subst ~term ~subst ~maxmeta status
(* TODO cacciare anche altre eccezioni? *)
with
| CicUnification.UnificationFailure msg
- | CicTypeChecker.TypeCheckerFailure msg ->
- raise (Fail msg)
+ | CicTypeChecker.TypeCheckerFailure msg -> raise (Fail msg)
(* ALB *)
let apply_tac_verbose ~term status =
- let subst, status = apply_tac_verbose_with_subst ~term status in
+ let subst, status, _ = apply_with_subst ~term status in
(CicMetaSubst.apply_subst subst), status
let apply_tac ~term status = snd (apply_tac_verbose ~term status)
=
let module C = Cic in
let module R = CicReduction in
- let (_,metasenv,_,_) = proof in
+ let (_,metasenv,_,_, _) = proof in
let metano,context,ty = CicUtil.lookup_meta goal metasenv in
- let newmeta = new_meta_of_proof ~proof in
+ let newmeta = ProofEngineHelpers.new_meta_of_proof ~proof in
let (context',ty',bo') =
lambda_abstract ?howmany metasenv context newmeta ty mk_fresh_name_callback
in
let (newproof, _) =
- subst_meta_in_proof proof metano bo' [newmeta,context',ty']
+ ProofEngineHelpers.subst_meta_in_proof proof metano bo'
+ [newmeta,context',ty']
in
(newproof, [newmeta])
in
term (proof, goal)
=
let module C = Cic in
- let curi,metasenv,pbo,pty = proof in
+ let curi,metasenv,pbo,pty, attrs = proof in
let metano,context,ty = CicUtil.lookup_meta goal metasenv in
- let newmeta1 = new_meta_of_proof ~proof in
+ let newmeta1 = ProofEngineHelpers.new_meta_of_proof ~proof in
let newmeta2 = newmeta1 + 1 in
let fresh_name =
mk_fresh_name_callback metasenv context (Cic.Name "Hcut") ~typ:term in
C.Meta (newmeta2,irl2)]
in
let (newproof, _) =
- subst_meta_in_proof proof metano bo'
+ ProofEngineHelpers.subst_meta_in_proof proof metano bo'
[newmeta2,context,term; newmeta1,context_for_newmeta1,newmeta1ty];
in
(newproof, [newmeta1 ; newmeta2])
term (proof, goal)
=
let module C = Cic in
- let curi,metasenv,pbo,pty = proof in
+ let curi,metasenv,pbo,pty, attrs = proof in
+ (* occur check *)
+ let occur i t =
+ let m = CicUtil.metas_of_term t in
+ List.exists (fun (j,_) -> i=j) m
+ in
let metano,context,ty = CicUtil.lookup_meta goal metasenv in
- let _,_ = (* TASSI: FIXME *)
+ if occur metano term then
+ 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 newmeta = new_meta_of_proof ~proof 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 =
let newmetaty = CicSubstitution.lift 1 ty in
let bo' = C.LetIn (fresh_name,term,C.Meta (newmeta,irl)) in
let (newproof, _) =
- subst_meta_in_proof
+ ProofEngineHelpers.subst_meta_in_proof
proof metano bo'[newmeta,context_for_newmeta,newmetaty]
in
(newproof, [newmeta])
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 (_,metasenv,_,_, _) = proof in
let metano,context,ty = CicUtil.lookup_meta goal metasenv in
let module T = CicTypeChecker in
let module R = CicReduction in
if b then
begin
let (newproof, metasenv') =
- subst_meta_in_proof proof metano term [] in
+ ProofEngineHelpers.subst_meta_in_proof proof metano term [] in
(newproof, [])
end
else
mk_tactic (exact_tac ~term)
(* not really "primitive" tactics .... *)
-let elim_tac ~term =
- let elim_tac ~term (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) = 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
+
+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 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) =
- ProofEngineHelpers.saturate_term
+ 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 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"
in
U.uri_of_string (buri ^ "/" ^ name ^ ext ^ ".con")
in
- let eliminator_ref = C.Const (eliminator_uri,exp_named_subst) 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 eliminator_ref = match using with
+ | None -> C.Const (eliminator_uri,exp_named_subst)
+ | Some t -> t
+ in
+ 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 refined_term,_,metasenv'',_ =
+ 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,_refined_termty,metasenv'',_ugraph =
CicRefine.type_of_aux' metasenv' context term_to_refine
- CicUniv.empty_ugraph
+ ugraph
in
let new_goals =
ProofEngineHelpers.compare_metasenvs
~oldmetasenv:metasenv ~newmetasenv:metasenv''
in
- let proof' = curi,metasenv'',proofbo,proofty 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 =
- let (_,metasenv''',_,_) = proof'' in
+ let (_,metasenv''',_,_, _) = proof'' in
List.filter
(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 ~term)
+ 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 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,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 _,_,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
+ 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 replace = ProofEngineReduction.replace_lifting
+ ~equality:(CicUtil.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
+ 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 ~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 ~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
let letout_tac (proof, goal) =
- let curi, metasenv, pbo, pty = proof in
+ let curi, metasenv, pbo, pty, attrs = proof in
let metano, context, ty = CicUtil.lookup_meta goal metasenv in
- let newmeta = new_meta_of_proof ~proof 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, _ = subst_meta_in_proof proof metano bo'[newmeta,context_for_newmeta,newmetaty] 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