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|
(************************************************************************)
(* v * The Coq Proof Assistant / The Coq Development Team *)
(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2015 *)
(* \VV/ **************************************************************)
(* // * This file is distributed under the terms of the *)
(* * GNU Lesser General Public License Version 2.1 *)
(************************************************************************)
(*i camlp4deps: "grammar/grammar.cma" i*)
open Pp
open Genarg
open Extraargs
open Mod_subst
open Names
open Tacexpr
open Glob_ops
open Tactics
open Errors
open Util
open Evd
open Equality
open Misctypes
open Proofview.Notations
DECLARE PLUGIN "extratactics"
(**********************************************************************)
(* admit, replace, discriminate, injection, simplify_eq *)
(* cutrewrite, dependent rewrite *)
TACTIC EXTEND admit
[ "admit" ] -> [ admit_as_an_axiom ]
END
let replace_in_clause_maybe_by (sigma,c1) c2 cl tac =
Proofview.Unsafe.tclEVARS sigma <*>
(replace_in_clause_maybe_by c1 c2 cl)
(Option.map Tacinterp.eval_tactic tac)
let replace_term dir_opt (sigma,c) cl =
Proofview.Unsafe.tclEVARS sigma <*>
(replace_term dir_opt c) cl
TACTIC EXTEND replace
["replace" open_constr(c1) "with" constr(c2) clause(cl) by_arg_tac(tac) ]
-> [ replace_in_clause_maybe_by c1 c2 cl tac ]
END
TACTIC EXTEND replace_term_left
[ "replace" "->" open_constr(c) clause(cl) ]
-> [ replace_term (Some true) c cl ]
END
TACTIC EXTEND replace_term_right
[ "replace" "<-" open_constr(c) clause(cl) ]
-> [ replace_term (Some false) c cl ]
END
TACTIC EXTEND replace_term
[ "replace" open_constr(c) clause(cl) ]
-> [ replace_term None c cl ]
END
let induction_arg_of_quantified_hyp = function
| AnonHyp n -> None,ElimOnAnonHyp n
| NamedHyp id -> None,ElimOnIdent (Loc.ghost,id)
(* Versions *_main must come first!! so that "1" is interpreted as a
ElimOnAnonHyp and not as a "constr", and "id" is interpreted as a
ElimOnIdent and not as "constr" *)
let elimOnConstrWithHoles tac with_evars c =
Tacticals.New.tclWITHHOLES with_evars (tac with_evars)
c.sigma (Some (None,ElimOnConstr c.it))
TACTIC EXTEND simplify_eq_main
| [ "simplify_eq" constr_with_bindings(c) ] ->
[ elimOnConstrWithHoles dEq false c ]
END
TACTIC EXTEND simplify_eq
[ "simplify_eq" ] -> [ dEq false None ]
| [ "simplify_eq" quantified_hypothesis(h) ] ->
[ dEq false (Some (induction_arg_of_quantified_hyp h)) ]
END
TACTIC EXTEND esimplify_eq_main
| [ "esimplify_eq" constr_with_bindings(c) ] ->
[ elimOnConstrWithHoles dEq true c ]
END
TACTIC EXTEND esimplify_eq
| [ "esimplify_eq" ] -> [ dEq true None ]
| [ "esimplify_eq" quantified_hypothesis(h) ] ->
[ dEq true (Some (induction_arg_of_quantified_hyp h)) ]
END
let discr_main c = elimOnConstrWithHoles discr_tac false c
TACTIC EXTEND discriminate_main
| [ "discriminate" constr_with_bindings(c) ] ->
[ discr_main c ]
END
TACTIC EXTEND discriminate
| [ "discriminate" ] -> [ discr_tac false None ]
| [ "discriminate" quantified_hypothesis(h) ] ->
[ discr_tac false (Some (induction_arg_of_quantified_hyp h)) ]
END
TACTIC EXTEND ediscriminate_main
| [ "ediscriminate" constr_with_bindings(c) ] ->
[ elimOnConstrWithHoles discr_tac true c ]
END
TACTIC EXTEND ediscriminate
| [ "ediscriminate" ] -> [ discr_tac true None ]
| [ "ediscriminate" quantified_hypothesis(h) ] ->
[ discr_tac true (Some (induction_arg_of_quantified_hyp h)) ]
END
open Proofview.Notations
let discrHyp id =
Proofview.tclEVARMAP >>= fun sigma ->
discr_main {it = Term.mkVar id,NoBindings; sigma = sigma;}
let injection_main c =
elimOnConstrWithHoles (injClause None) false c
TACTIC EXTEND injection_main
| [ "injection" constr_with_bindings(c) ] ->
[ injection_main c ]
END
TACTIC EXTEND injection
| [ "injection" ] -> [ injClause None false None ]
| [ "injection" quantified_hypothesis(h) ] ->
[ injClause None false (Some (induction_arg_of_quantified_hyp h)) ]
END
TACTIC EXTEND einjection_main
| [ "einjection" constr_with_bindings(c) ] ->
[ elimOnConstrWithHoles (injClause None) true c ]
END
TACTIC EXTEND einjection
| [ "einjection" ] -> [ injClause None true None ]
| [ "einjection" quantified_hypothesis(h) ] -> [ injClause None true (Some (induction_arg_of_quantified_hyp h)) ]
END
TACTIC EXTEND injection_as_main
| [ "injection" constr_with_bindings(c) "as" simple_intropattern_list(ipat)] ->
[ elimOnConstrWithHoles (injClause (Some ipat)) false c ]
END
TACTIC EXTEND injection_as
| [ "injection" "as" simple_intropattern_list(ipat)] ->
[ injClause (Some ipat) false None ]
| [ "injection" quantified_hypothesis(h) "as" simple_intropattern_list(ipat) ] ->
[ injClause (Some ipat) false (Some (induction_arg_of_quantified_hyp h)) ]
END
TACTIC EXTEND einjection_as_main
| [ "einjection" constr_with_bindings(c) "as" simple_intropattern_list(ipat)] ->
[ elimOnConstrWithHoles (injClause (Some ipat)) true c ]
END
TACTIC EXTEND einjection_as
| [ "einjection" "as" simple_intropattern_list(ipat)] ->
[ injClause (Some ipat) true None ]
| [ "einjection" quantified_hypothesis(h) "as" simple_intropattern_list(ipat) ] ->
[ injClause (Some ipat) true (Some (induction_arg_of_quantified_hyp h)) ]
END
let injHyp id =
Proofview.tclEVARMAP >>= fun sigma ->
injection_main { it = Term.mkVar id,NoBindings; sigma = sigma; }
TACTIC EXTEND dependent_rewrite
| [ "dependent" "rewrite" orient(b) constr(c) ] -> [ rewriteInConcl b c ]
| [ "dependent" "rewrite" orient(b) constr(c) "in" hyp(id) ]
-> [ rewriteInHyp b c id ]
END
(** To be deprecated?, "cutrewrite (t=u) as <-" is equivalent to
"replace u with t" or "enough (t=u) as <-" and
"cutrewrite (t=u) as ->" is equivalent to "enough (t=u) as ->". *)
TACTIC EXTEND cut_rewrite
| [ "cutrewrite" orient(b) constr(eqn) ] -> [ cutRewriteInConcl b eqn ]
| [ "cutrewrite" orient(b) constr(eqn) "in" hyp(id) ]
-> [ cutRewriteInHyp b eqn id ]
END
(**********************************************************************)
(* Decompose *)
TACTIC EXTEND decompose_sum
| [ "decompose" "sum" constr(c) ] -> [ Elim.h_decompose_or c ]
END
TACTIC EXTEND decompose_record
| [ "decompose" "record" constr(c) ] -> [ Elim.h_decompose_and c ]
END
(**********************************************************************)
(* Contradiction *)
open Contradiction
TACTIC EXTEND absurd
[ "absurd" constr(c) ] -> [ absurd c ]
END
let onSomeWithHoles tac = function
| None -> tac None
| Some c -> Proofview.Unsafe.tclEVARS c.sigma <*> tac (Some c.it)
TACTIC EXTEND contradiction
[ "contradiction" constr_with_bindings_opt(c) ] ->
[ onSomeWithHoles contradiction c ]
END
(**********************************************************************)
(* AutoRewrite *)
open Autorewrite
let pr_orient _prc _prlc _prt = function
| true -> Pp.mt ()
| false -> Pp.str " <-"
let pr_orient_string _prc _prlc _prt (orient, s) =
pr_orient _prc _prlc _prt orient ++ Pp.spc () ++ Pp.str s
ARGUMENT EXTEND orient_string TYPED AS (bool * string) PRINTED BY pr_orient_string
| [ orient(r) preident(i) ] -> [ r, i ]
END
TACTIC EXTEND autorewrite
| [ "autorewrite" "with" ne_preident_list(l) clause(cl) ] ->
[ auto_multi_rewrite l ( cl) ]
| [ "autorewrite" "with" ne_preident_list(l) clause(cl) "using" tactic(t) ] ->
[
auto_multi_rewrite_with (Tacinterp.eval_tactic t) l cl
]
END
TACTIC EXTEND autorewrite_star
| [ "autorewrite" "*" "with" ne_preident_list(l) clause(cl) ] ->
[ auto_multi_rewrite ~conds:AllMatches l cl ]
| [ "autorewrite" "*" "with" ne_preident_list(l) clause(cl) "using" tactic(t) ] ->
[ auto_multi_rewrite_with ~conds:AllMatches (Tacinterp.eval_tactic t) l cl ]
END
(**********************************************************************)
(* Rewrite star *)
let rewrite_star clause orient occs (sigma,c) (tac : glob_tactic_expr option) =
let tac' = Option.map (fun t -> Tacinterp.eval_tactic t, FirstSolved) tac in
Proofview.Unsafe.tclEVARS sigma <*>
general_rewrite_ebindings_clause clause orient occs ?tac:tac' true true (c,NoBindings) true
TACTIC EXTEND rewrite_star
| [ "rewrite" "*" orient(o) open_constr(c) "in" hyp(id) "at" occurrences(occ) by_arg_tac(tac) ] ->
[ rewrite_star (Some id) o (occurrences_of occ) c tac ]
| [ "rewrite" "*" orient(o) open_constr(c) "at" occurrences(occ) "in" hyp(id) by_arg_tac(tac) ] ->
[ rewrite_star (Some id) o (occurrences_of occ) c tac ]
| [ "rewrite" "*" orient(o) open_constr(c) "in" hyp(id) by_arg_tac(tac) ] ->
[ rewrite_star (Some id) o Locus.AllOccurrences c tac ]
| [ "rewrite" "*" orient(o) open_constr(c) "at" occurrences(occ) by_arg_tac(tac) ] ->
[ rewrite_star None o (occurrences_of occ) c tac ]
| [ "rewrite" "*" orient(o) open_constr(c) by_arg_tac(tac) ] ->
[ rewrite_star None o Locus.AllOccurrences c tac ]
END
(**********************************************************************)
(* Hint Rewrite *)
let add_rewrite_hint bases ort t lcsr =
let env = Global.env() and sigma = Evd.empty in
let poly = Flags.is_universe_polymorphism () in
let f ce =
let c, ctx = Constrintern.interp_constr env sigma ce in
let ctx =
if poly then
Evd.evar_universe_context_set ctx
else
let cstrs = Evd.evar_universe_context_constraints ctx in
(Global.add_constraints cstrs; Univ.ContextSet.empty)
in
Constrexpr_ops.constr_loc ce, (c, ctx), ort, t in
let eqs = List.map f lcsr in
let add_hints base = add_rew_rules base eqs in
List.iter add_hints bases
let classify_hint _ = Vernacexpr.VtSideff [], Vernacexpr.VtLater
VERNAC COMMAND EXTEND HintRewrite CLASSIFIED BY classify_hint
[ "Hint" "Rewrite" orient(o) ne_constr_list(l) ":" preident_list(bl) ] ->
[ add_rewrite_hint bl o None l ]
| [ "Hint" "Rewrite" orient(o) ne_constr_list(l) "using" tactic(t)
":" preident_list(bl) ] ->
[ add_rewrite_hint bl o (Some t) l ]
| [ "Hint" "Rewrite" orient(o) ne_constr_list(l) ] ->
[ add_rewrite_hint ["core"] o None l ]
| [ "Hint" "Rewrite" orient(o) ne_constr_list(l) "using" tactic(t) ] ->
[ add_rewrite_hint ["core"] o (Some t) l ]
END
(**********************************************************************)
(* Hint Resolve *)
open Term
open Vars
open Coqlib
let project_hint pri l2r r =
let gr = Smartlocate.global_with_alias r in
let env = Global.env() in
let sigma = Evd.from_env env in
let sigma, c = Evd.fresh_global env sigma gr in
let t = Retyping.get_type_of env sigma c in
let t =
Tacred.reduce_to_quantified_ref env sigma (Lazy.force coq_iff_ref) t in
let sign,ccl = decompose_prod_assum t in
let (a,b) = match snd (decompose_app ccl) with
| [a;b] -> (a,b)
| _ -> assert false in
let p =
if l2r then build_coq_iff_left_proj () else build_coq_iff_right_proj () in
let c = Reductionops.whd_beta Evd.empty (mkApp (c,Termops.extended_rel_vect 0 sign)) in
let c = it_mkLambda_or_LetIn
(mkApp (p,[|mkArrow a (lift 1 b);mkArrow b (lift 1 a);c|])) sign in
let id =
Nameops.add_suffix (Nametab.basename_of_global gr) ("_proj_" ^ (if l2r then "l2r" else "r2l"))
in
let ctx = Evd.universe_context_set sigma in
let c = Declare.declare_definition ~internal:Declare.KernelSilent id (c,ctx) in
(pri,false,true,Hints.PathAny, Hints.IsGlobRef (Globnames.ConstRef c))
let add_hints_iff l2r lc n bl =
Hints.add_hints true bl
(Hints.HintsResolveEntry (List.map (project_hint n l2r) lc))
VERNAC COMMAND EXTEND HintResolveIffLR CLASSIFIED AS SIDEFF
[ "Hint" "Resolve" "->" ne_global_list(lc) natural_opt(n)
":" preident_list(bl) ] ->
[ add_hints_iff true lc n bl ]
| [ "Hint" "Resolve" "->" ne_global_list(lc) natural_opt(n) ] ->
[ add_hints_iff true lc n ["core"] ]
END
VERNAC COMMAND EXTEND HintResolveIffRL CLASSIFIED AS SIDEFF
[ "Hint" "Resolve" "<-" ne_global_list(lc) natural_opt(n)
":" preident_list(bl) ] ->
[ add_hints_iff false lc n bl ]
| [ "Hint" "Resolve" "<-" ne_global_list(lc) natural_opt(n) ] ->
[ add_hints_iff false lc n ["core"] ]
END
(**********************************************************************)
(* Refine *)
let refine_tac {Glob_term.closure=closure;term=term} =
Proofview.Goal.nf_enter begin fun gl ->
let concl = Proofview.Goal.concl gl in
let env = Proofview.Goal.env gl in
let flags = Pretyping.all_no_fail_flags in
let tycon = Pretyping.OfType concl in
let lvar = { Pretyping.empty_lvar with
Pretyping.ltac_constrs = closure.Glob_term.typed;
Pretyping.ltac_uconstrs = closure.Glob_term.untyped;
Pretyping.ltac_idents = closure.Glob_term.idents;
} in
let update evd = Pretyping.understand_ltac flags env evd lvar tycon term in
Tactics.New.refine ~unsafe:false update
end
TACTIC EXTEND refine
[ "refine" uconstr(c) ] -> [ refine_tac c ]
END
(**********************************************************************)
(* Inversion lemmas (Leminv) *)
open Inv
open Leminv
let seff id = Vernacexpr.VtSideff [id], Vernacexpr.VtLater
VERNAC COMMAND EXTEND DeriveInversionClear
| [ "Derive" "Inversion_clear" ident(na) "with" constr(c) "Sort" sort(s) ]
=> [ seff na ]
-> [ add_inversion_lemma_exn na c s false inv_clear_tac ]
| [ "Derive" "Inversion_clear" ident(na) "with" constr(c) ] => [ seff na ]
-> [ add_inversion_lemma_exn na c GProp false inv_clear_tac ]
END
open Term
VERNAC COMMAND EXTEND DeriveInversion
| [ "Derive" "Inversion" ident(na) "with" constr(c) "Sort" sort(s) ]
=> [ seff na ]
-> [ add_inversion_lemma_exn na c s false inv_tac ]
| [ "Derive" "Inversion" ident(na) "with" constr(c) ] => [ seff na ]
-> [ add_inversion_lemma_exn na c GProp false inv_tac ]
END
VERNAC COMMAND EXTEND DeriveDependentInversion
| [ "Derive" "Dependent" "Inversion" ident(na) "with" constr(c) "Sort" sort(s) ]
=> [ seff na ]
-> [ add_inversion_lemma_exn na c s true dinv_tac ]
END
VERNAC COMMAND EXTEND DeriveDependentInversionClear
| [ "Derive" "Dependent" "Inversion_clear" ident(na) "with" constr(c) "Sort" sort(s) ]
=> [ seff na ]
-> [ add_inversion_lemma_exn na c s true dinv_clear_tac ]
END
(**********************************************************************)
(* Subst *)
TACTIC EXTEND subst
| [ "subst" ne_var_list(l) ] -> [ subst l ]
| [ "subst" ] -> [ subst_all () ]
END
let simple_subst_tactic_flags =
{ only_leibniz = true; rewrite_dependent_proof = false }
TACTIC EXTEND simple_subst
| [ "simple" "subst" ] -> [ subst_all ~flags:simple_subst_tactic_flags () ]
END
open Evar_tactics
(**********************************************************************)
(* Evar creation *)
(* TODO: add support for some test similar to g_constr.name_colon so that
expressions like "evar (list A)" do not raise a syntax error *)
TACTIC EXTEND evar
[ "evar" "(" ident(id) ":" lconstr(typ) ")" ] -> [ let_evar (Name id) typ ]
| [ "evar" constr(typ) ] -> [ let_evar Anonymous typ ]
END
open Tacticals
TACTIC EXTEND instantiate
[ "instantiate" "(" ident(id) ":=" lglob(c) ")" ] ->
[ Tacticals.New.tclTHEN (instantiate_tac_by_name id c) Proofview.V82.nf_evar_goals ]
| [ "instantiate" "(" integer(i) ":=" lglob(c) ")" hloc(hl) ] ->
[ Tacticals.New.tclTHEN (instantiate_tac i c hl) Proofview.V82.nf_evar_goals ]
| [ "instantiate" ] -> [ Proofview.V82.nf_evar_goals ]
END
(**********************************************************************)
(** Nijmegen "step" tactic for setoid rewriting *)
open Tactics
open Glob_term
open Libobject
open Lib
(* Registered lemmas are expected to be of the form
x R y -> y == z -> x R z (in the right table)
x R y -> x == z -> z R y (in the left table)
*)
let transitivity_right_table = Summary.ref [] ~name:"transitivity-steps-r"
let transitivity_left_table = Summary.ref [] ~name:"transitivity-steps-l"
(* [step] tries to apply a rewriting lemma; then apply [tac] intended to
complete to proof of the last hypothesis (assumed to state an equality) *)
let step left x tac =
let l =
List.map (fun lem ->
Tacticals.New.tclTHENLAST
(apply_with_bindings (lem, ImplicitBindings [x]))
tac)
!(if left then transitivity_left_table else transitivity_right_table)
in
Tacticals.New.tclFIRST l
(* Main function to push lemmas in persistent environment *)
let cache_transitivity_lemma (_,(left,lem)) =
if left then
transitivity_left_table := lem :: !transitivity_left_table
else
transitivity_right_table := lem :: !transitivity_right_table
let subst_transitivity_lemma (subst,(b,ref)) = (b,subst_mps subst ref)
let inTransitivity : bool * constr -> obj =
declare_object {(default_object "TRANSITIVITY-STEPS") with
cache_function = cache_transitivity_lemma;
open_function = (fun i o -> if Int.equal i 1 then cache_transitivity_lemma o);
subst_function = subst_transitivity_lemma;
classify_function = (fun o -> Substitute o) }
(* Main entry points *)
let add_transitivity_lemma left lem =
let lem',ctx (*FIXME*) = Constrintern.interp_constr (Global.env ()) Evd.empty lem in
add_anonymous_leaf (inTransitivity (left,lem'))
(* Vernacular syntax *)
TACTIC EXTEND stepl
| ["stepl" constr(c) "by" tactic(tac) ] -> [ step true c (Tacinterp.eval_tactic tac) ]
| ["stepl" constr(c) ] -> [ step true c (Proofview.tclUNIT ()) ]
END
TACTIC EXTEND stepr
| ["stepr" constr(c) "by" tactic(tac) ] -> [ step false c (Tacinterp.eval_tactic tac) ]
| ["stepr" constr(c) ] -> [ step false c (Proofview.tclUNIT ()) ]
END
VERNAC COMMAND EXTEND AddStepl CLASSIFIED AS SIDEFF
| [ "Declare" "Left" "Step" constr(t) ] ->
[ add_transitivity_lemma true t ]
END
VERNAC COMMAND EXTEND AddStepr CLASSIFIED AS SIDEFF
| [ "Declare" "Right" "Step" constr(t) ] ->
[ add_transitivity_lemma false t ]
END
VERNAC COMMAND EXTEND ImplicitTactic CLASSIFIED AS SIDEFF
| [ "Declare" "Implicit" "Tactic" tactic(tac) ] ->
[ Pfedit.declare_implicit_tactic (Tacinterp.interp tac) ]
| [ "Clear" "Implicit" "Tactic" ] ->
[ Pfedit.clear_implicit_tactic () ]
END
(**********************************************************************)
(*spiwack : Vernac commands for retroknowledge *)
VERNAC COMMAND EXTEND RetroknowledgeRegister CLASSIFIED AS SIDEFF
| [ "Register" constr(c) "as" retroknowledge_field(f) "by" constr(b)] ->
[ let tc,ctx = Constrintern.interp_constr (Global.env ()) Evd.empty c in
let tb,ctx(*FIXME*) = Constrintern.interp_constr (Global.env ()) Evd.empty b in
Global.register f tc tb ]
END
(**********************************************************************)
(* sozeau: abs/gen for induction on instantiated dependent inductives, using "Ford" induction as
defined by Conor McBride *)
TACTIC EXTEND generalize_eqs
| ["generalize_eqs" hyp(id) ] -> [ abstract_generalize ~generalize_vars:false id ]
END
TACTIC EXTEND dep_generalize_eqs
| ["dependent" "generalize_eqs" hyp(id) ] -> [ abstract_generalize ~generalize_vars:false ~force_dep:true id ]
END
TACTIC EXTEND generalize_eqs_vars
| ["generalize_eqs_vars" hyp(id) ] -> [ abstract_generalize ~generalize_vars:true id ]
END
TACTIC EXTEND dep_generalize_eqs_vars
| ["dependent" "generalize_eqs_vars" hyp(id) ] -> [ abstract_generalize ~force_dep:true ~generalize_vars:true id ]
END
(** Tactic to automatically simplify hypotheses of the form [Π Δ, x_i = t_i -> T]
where [t_i] is closed w.r.t. Δ. Such hypotheses are automatically generated
during dependent induction. For internal use. *)
TACTIC EXTEND specialize_eqs
[ "specialize_eqs" hyp(id) ] -> [ Proofview.V82.tactic (specialize_eqs id) ]
END
(**********************************************************************)
(* A tactic that considers a given occurrence of [c] in [t] and *)
(* abstract the minimal set of all the occurrences of [c] so that the *)
(* abstraction [fun x -> t[x/c]] is well-typed *)
(* *)
(* Contributed by Chung-Kil Hur (Winter 2009) *)
(**********************************************************************)
let subst_var_with_hole occ tid t =
let occref = if occ > 0 then ref occ else Find_subterm.error_invalid_occurrence [occ] in
let locref = ref 0 in
let rec substrec = function
| GVar (_,id) as x ->
if Id.equal id tid
then
(decr occref;
if Int.equal !occref 0 then x
else
(incr locref;
GHole (Loc.make_loc (!locref,0),
Evar_kinds.QuestionMark(Evar_kinds.Define true),
Misctypes.IntroAnonymous, None)))
else x
| c -> map_glob_constr_left_to_right substrec c in
let t' = substrec t
in
if !occref > 0 then Find_subterm.error_invalid_occurrence [occ] else t'
let subst_hole_with_term occ tc t =
let locref = ref 0 in
let occref = ref occ in
let rec substrec = function
| GHole (_,Evar_kinds.QuestionMark(Evar_kinds.Define true),Misctypes.IntroAnonymous,s) ->
decr occref;
if Int.equal !occref 0 then tc
else
(incr locref;
GHole (Loc.make_loc (!locref,0),
Evar_kinds.QuestionMark(Evar_kinds.Define true),Misctypes.IntroAnonymous,s))
| c -> map_glob_constr_left_to_right substrec c
in
substrec t
open Tacmach
let out_arg = function
| ArgVar _ -> anomaly (Pp.str "Unevaluated or_var variable")
| ArgArg x -> x
let hResolve id c occ t =
Proofview.Goal.nf_enter begin fun gl ->
let sigma = Proofview.Goal.sigma gl in
let env = Termops.clear_named_body id (Proofview.Goal.env gl) in
let concl = Proofview.Goal.concl gl in
let env_ids = Termops.ids_of_context env in
let c_raw = Detyping.detype true env_ids env sigma c in
let t_raw = Detyping.detype true env_ids env sigma t in
let rec resolve_hole t_hole =
try
Pretyping.understand env sigma t_hole
with
| Pretype_errors.PretypeError (_,_,Pretype_errors.UnsolvableImplicit _) as e ->
let (e, info) = Errors.push e in
let loc = match Loc.get_loc info with None -> Loc.ghost | Some loc -> loc in
resolve_hole (subst_hole_with_term (fst (Loc.unloc loc)) c_raw t_hole)
in
let t_constr,ctx = resolve_hole (subst_var_with_hole occ id t_raw) in
let sigma = Evd.merge_universe_context sigma ctx in
let t_constr_type = Retyping.get_type_of env sigma t_constr in
Tacticals.New.tclTHEN
(Proofview.Unsafe.tclEVARS sigma)
(change_concl (mkLetIn (Anonymous,t_constr,t_constr_type,concl)))
end
let hResolve_auto id c t =
let rec resolve_auto n =
try
hResolve id c n t
with
| UserError _ as e -> raise e
| e when Errors.noncritical e -> resolve_auto (n+1)
in
resolve_auto 1
TACTIC EXTEND hresolve_core
| [ "hresolve_core" "(" ident(id) ":=" constr(c) ")" "at" int_or_var(occ) "in" constr(t) ] -> [ hResolve id c (out_arg occ) t ]
| [ "hresolve_core" "(" ident(id) ":=" constr(c) ")" "in" constr(t) ] -> [ hResolve_auto id c t ]
END
(**
hget_evar
*)
let hget_evar n =
Proofview.Goal.nf_enter begin fun gl ->
let sigma = Proofview.Goal.sigma gl in
let concl = Proofview.Goal.concl gl in
let evl = evar_list concl in
if List.length evl < n then
error "Not enough uninstantiated existential variables.";
if n <= 0 then error "Incorrect existential variable index.";
let ev = List.nth evl (n-1) in
let ev_type = existential_type sigma ev in
change_concl (mkLetIn (Anonymous,mkEvar ev,ev_type,concl))
end
TACTIC EXTEND hget_evar
| [ "hget_evar" int_or_var(n) ] -> [ hget_evar (out_arg n) ]
END
(**********************************************************************)
(**********************************************************************)
(* A tactic that reduces one match t with ... by doing destruct t. *)
(* if t is not a variable, the tactic does *)
(* case_eq t;intros ... heq;rewrite heq in *|-. (but heq itself is *)
(* preserved). *)
(* Contributed by Julien Forest and Pierre Courtieu (july 2010) *)
(**********************************************************************)
exception Found of unit Proofview.tactic
let rewrite_except h =
Proofview.Goal.nf_enter begin fun gl ->
let hyps = Tacmach.New.pf_ids_of_hyps gl in
Tacticals.New.tclMAP (fun id -> if Id.equal id h then Proofview.tclUNIT () else
Tacticals.New.tclTRY (Equality.general_rewrite_in true Locus.AllOccurrences true true id (mkVar h) false))
hyps
end
let refl_equal =
let coq_base_constant s =
Coqlib.gen_constant_in_modules "RecursiveDefinition"
(Coqlib.init_modules @ [["Coq";"Arith";"Le"];["Coq";"Arith";"Lt"]]) s in
function () -> (coq_base_constant "eq_refl")
(* This is simply an implementation of the case_eq tactic. this code
should be replaced by a call to the tactic but I don't know how to
call it before it is defined. *)
let mkCaseEq a : unit Proofview.tactic =
Proofview.Goal.nf_enter begin fun gl ->
let type_of_a = Tacmach.New.of_old (fun g -> Tacmach.pf_type_of g a) gl in
Tacticals.New.tclTHENLIST
[Proofview.V82.tactic (Tactics.Simple.generalize [mkApp(delayed_force refl_equal, [| type_of_a; a|])]);
Proofview.Goal.nf_enter begin fun gl ->
let concl = Proofview.Goal.concl gl in
let env = Proofview.Goal.env gl in
change_concl
(snd (Tacred.pattern_occs [Locus.OnlyOccurrences [1], a] env Evd.empty concl))
end;
simplest_case a]
end
let case_eq_intros_rewrite x =
Proofview.Goal.nf_enter begin fun gl ->
let n = nb_prod (Proofview.Goal.concl gl) in
(* Pp.msgnl (Printer.pr_lconstr x); *)
Tacticals.New.tclTHENLIST [
mkCaseEq x;
Proofview.Goal.nf_enter begin fun gl ->
let concl = Proofview.Goal.concl gl in
let hyps = Tacmach.New.pf_ids_of_hyps gl in
let n' = nb_prod concl in
let h = Tacmach.New.of_old (fun g -> fresh_id hyps (Id.of_string "heq") g) gl in
Tacticals.New.tclTHENLIST [
Tacticals.New.tclDO (n'-n-1) intro;
introduction h;
rewrite_except h]
end
]
end
let rec find_a_destructable_match t =
match kind_of_term t with
| Case (_,_,x,_) when closed0 x ->
if isVar x then
(* TODO check there is no rel n. *)
raise (Found (Tacinterp.eval_tactic(<:tactic<destruct x>>)))
else
(* let _ = Pp.msgnl (Printer.pr_lconstr x) in *)
raise (Found (case_eq_intros_rewrite x))
| _ -> iter_constr find_a_destructable_match t
let destauto t =
try find_a_destructable_match t;
Proofview.tclZERO (UserError ("", str"No destructable match found"))
with Found tac -> tac
let destauto_in id =
Proofview.Goal.nf_enter begin fun gl ->
let ctype = Tacmach.New.of_old (fun g -> Tacmach.pf_type_of g (mkVar id)) gl in
(* Pp.msgnl (Printer.pr_lconstr (mkVar id)); *)
(* Pp.msgnl (Printer.pr_lconstr (ctype)); *)
destauto ctype
end
TACTIC EXTEND destauto
| [ "destauto" ] -> [ Proofview.Goal.nf_enter (fun gl -> destauto (Proofview.Goal.concl gl)) ]
| [ "destauto" "in" hyp(id) ] -> [ destauto_in id ]
END
(* ********************************************************************* *)
let eq_constr x y =
Proofview.Goal.enter (fun gl ->
let evd = Proofview.Goal.sigma gl in
if Evd.eq_constr_univs_test evd x y then Proofview.tclUNIT ()
else Tacticals.New.tclFAIL 0 (str "Not equal"))
TACTIC EXTEND constr_eq
| [ "constr_eq" constr(x) constr(y) ] -> [ eq_constr x y ]
END
TACTIC EXTEND constr_eq_nounivs
| [ "constr_eq_nounivs" constr(x) constr(y) ] -> [
if eq_constr_nounivs x y then Proofview.tclUNIT () else Tacticals.New.tclFAIL 0 (str "Not equal") ]
END
TACTIC EXTEND is_evar
| [ "is_evar" constr(x) ] ->
[ match kind_of_term x with
| Evar _ -> Proofview.tclUNIT ()
| _ -> Tacticals.New.tclFAIL 0 (str "Not an evar")
]
END
let rec has_evar x =
match kind_of_term x with
| Evar _ -> true
| Rel _ | Var _ | Meta _ | Sort _ | Const _ | Ind _ | Construct _ ->
false
| Cast (t1, _, t2) | Prod (_, t1, t2) | Lambda (_, t1, t2) ->
has_evar t1 || has_evar t2
| LetIn (_, t1, t2, t3) ->
has_evar t1 || has_evar t2 || has_evar t3
| App (t1, ts) ->
has_evar t1 || has_evar_array ts
| Case (_, t1, t2, ts) ->
has_evar t1 || has_evar t2 || has_evar_array ts
| Fix ((_, tr)) | CoFix ((_, tr)) ->
has_evar_prec tr
| Proj (p, c) -> has_evar c
and has_evar_array x =
Array.exists has_evar x
and has_evar_prec (_, ts1, ts2) =
Array.exists has_evar ts1 || Array.exists has_evar ts2
TACTIC EXTEND has_evar
| [ "has_evar" constr(x) ] ->
[ if has_evar x then Proofview.tclUNIT () else Tacticals.New.tclFAIL 0 (str "No evars") ]
END
TACTIC EXTEND is_hyp
| [ "is_var" constr(x) ] ->
[ match kind_of_term x with
| Var _ -> Proofview.tclUNIT ()
| _ -> Tacticals.New.tclFAIL 0 (str "Not a variable or hypothesis") ]
END
TACTIC EXTEND is_fix
| [ "is_fix" constr(x) ] ->
[ match kind_of_term x with
| Fix _ -> Proofview.tclUNIT ()
| _ -> Tacticals.New.tclFAIL 0 (Pp.str "not a fix definition") ]
END;;
TACTIC EXTEND is_cofix
| [ "is_cofix" constr(x) ] ->
[ match kind_of_term x with
| CoFix _ -> Proofview.tclUNIT ()
| _ -> Tacticals.New.tclFAIL 0 (Pp.str "not a cofix definition") ]
END;;
(* Command to grab the evars left unresolved at the end of a proof. *)
(* spiwack: I put it in extratactics because it is somewhat tied with
the semantics of the LCF-style tactics, hence with the classic tactic
mode. *)
VERNAC COMMAND EXTEND GrabEvars
[ "Grab" "Existential" "Variables" ]
=> [ Vernacexpr.VtProofStep false, Vernacexpr.VtLater ]
-> [ Proof_global.simple_with_current_proof (fun _ p -> Proof.V82.grab_evars p) ]
END
(* Shelves all the goals under focus. *)
TACTIC EXTEND shelve
| [ "shelve" ] ->
[ Proofview.shelve ]
END
(* Shelves the unifiable goals under focus, i.e. the goals which
appear in other goals under focus (the unfocused goals are not
considered). *)
TACTIC EXTEND shelve_unifiable
| [ "shelve_unifiable" ] ->
[ Proofview.shelve_unifiable ]
END
(* Command to add every unshelved variables to the focus *)
VERNAC COMMAND EXTEND Unshelve
[ "Unshelve" ]
=> [ Vernacexpr.VtProofStep false, Vernacexpr.VtLater ]
-> [ Proof_global.simple_with_current_proof (fun _ p -> Proof.unshelve p) ]
END
(* Gives up on the goals under focus: the goals are considered solved,
but the proof cannot be closed until the user goes back and solve
these goals. *)
TACTIC EXTEND give_up
| [ "give_up" ] ->
[ Proofview.give_up ]
END
(* cycles [n] goals *)
TACTIC EXTEND cycle
| [ "cycle" int_or_var(n) ] -> [ Proofview.cycle (out_arg n) ]
END
(* swaps goals number [i] and [j] *)
TACTIC EXTEND swap
| [ "swap" int_or_var(i) int_or_var(j) ] -> [ Proofview.swap (out_arg i) (out_arg j) ]
END
(* reverses the list of focused goals *)
TACTIC EXTEND revgoals
| [ "revgoals" ] -> [ Proofview.revgoals ]
END
type cmp =
| Eq
| Lt | Le
| Gt | Ge
type 'i test =
| Test of cmp * 'i * 'i
let wit_cmp : (cmp,cmp,cmp) Genarg.genarg_type = Genarg.make0 None "cmp"
let wit_test : (int or_var test,int or_var test,int test) Genarg.genarg_type =
Genarg.make0 None "tactest"
let pr_cmp = function
| Eq -> Pp.str"="
| Lt -> Pp.str"<"
| Le -> Pp.str"<="
| Gt -> Pp.str">"
| Ge -> Pp.str">="
let pr_cmp' _prc _prlc _prt = pr_cmp
let pr_test_gen f (Test(c,x,y)) =
Pp.(f x ++ pr_cmp c ++ f y)
let pr_test = pr_test_gen (Pptactic.pr_or_var Pp.int)
let pr_test' _prc _prlc _prt = pr_test
let pr_itest = pr_test_gen Pp.int
let pr_itest' _prc _prlc _prt = pr_itest
ARGUMENT EXTEND comparison TYPED AS cmp PRINTED BY pr_cmp'
| [ "=" ] -> [ Eq ]
| [ "<" ] -> [ Lt ]
| [ "<=" ] -> [ Le ]
| [ ">" ] -> [ Gt ]
| [ ">=" ] -> [ Ge ]
END
let interp_test ist gls = function
| Test (c,x,y) ->
project gls ,
Test(c,Tacinterp.interp_int_or_var ist x,Tacinterp.interp_int_or_var ist y)
ARGUMENT EXTEND test
PRINTED BY pr_itest'
INTERPRETED BY interp_test
RAW_TYPED AS test
RAW_PRINTED BY pr_test'
GLOB_TYPED AS test
GLOB_PRINTED BY pr_test'
| [ int_or_var(x) comparison(c) int_or_var(y) ] -> [ Test(c,x,y) ]
END
let interp_cmp = function
| Eq -> Int.equal
| Lt -> ((<):int->int->bool)
| Le -> ((<=):int->int->bool)
| Gt -> ((>):int->int->bool)
| Ge -> ((>=):int->int->bool)
let run_test = function
| Test(c,x,y) -> interp_cmp c x y
let guard tst =
if run_test tst then
Proofview.tclUNIT ()
else
let msg = Pp.(str"Condition not satisfied:"++ws 1++(pr_itest tst)) in
Proofview.tclZERO (Errors.UserError("guard",msg))
TACTIC EXTEND guard
| [ "guard" test(tst) ] -> [ guard tst ]
END
let decompose l c =
Proofview.Goal.enter begin fun gl ->
let to_ind c =
if isInd c then Univ.out_punivs (destInd c)
else error "not an inductive type"
in
let l = List.map to_ind l in
Elim.h_decompose l c
end
TACTIC EXTEND decompose
| [ "decompose" "[" ne_constr_list(l) "]" constr(c) ] -> [ decompose l c ]
END
(** library/keys *)
VERNAC COMMAND EXTEND Declare_keys CLASSIFIED AS SIDEFF
| [ "Declare" "Equivalent" "Keys" constr(c) constr(c') ] -> [
let it c = snd (Constrintern.interp_open_constr (Global.env ()) Evd.empty c) in
let k1 = Keys.constr_key (it c) in
let k2 = Keys.constr_key (it c') in
match k1, k2 with
| Some k1, Some k2 -> Keys.declare_equiv_keys k1 k2
| _ -> () ]
END
VERNAC COMMAND EXTEND Print_keys CLASSIFIED AS QUERY
| [ "Print" "Equivalent" "Keys" ] -> [ msg_info (Keys.pr_keys Printer.pr_global) ]
END
VERNAC COMMAND EXTEND OptimizeProof
| [ "Optimize" "Proof" ] => [ Vernac_classifier.classify_as_proofstep ] ->
[ Proof_global.compact_the_proof () ]
| [ "Optimize" "Heap" ] => [ Vernac_classifier.classify_as_proofstep ] ->
[ Gc.compact () ]
END
|