Source file tac2stdlib.ml
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open Names
open Genredexpr
open Tac2expr
open Tac2val
open Tac2ffi
open Tac2types
open Tac2extffi
open Proofview.Notations
module Value = Tac2ffi
(** Make a representation with a dummy from function *)
let make_to_repr f = Tac2ffi.make_repr (fun _ -> assert false) f
let return x = Proofview.tclUNIT x
let thaw f = f ()
let uthaw r f = Tac2ffi.to_fun1 Tac2ffi.of_unit (repr_to r) f ()
let to_name c = match Value.to_option Value.to_ident c with
| None -> Anonymous
| Some id -> Name id
let name = make_to_repr to_name
let to_occurrences = function
| ValInt 0 -> AllOccurrences
| ValBlk (0, [| vl |]) -> AllOccurrencesBut (Value.to_list Value.to_int vl)
| ValInt 1 -> NoOccurrences
| ValBlk (1, [| vl |]) -> OnlyOccurrences (Value.to_list Value.to_int vl)
| _ -> assert false
let occurrences = make_to_repr to_occurrences
let to_hyp_location_flag v = match Value.to_int v with
| 0 -> InHyp
| 1 -> InHypTypeOnly
| 2 -> InHypValueOnly
| _ -> assert false
let to_clause v = match Value.to_tuple v with
| [| hyps; concl |] ->
let cast v = match Value.to_tuple v with
| [| hyp; occ; flag |] ->
(Value.to_ident hyp, to_occurrences occ, to_hyp_location_flag flag)
| _ -> assert false
in
let hyps = Value.to_option (fun h -> Value.to_list cast h) hyps in
{ onhyps = hyps; concl_occs = to_occurrences concl; }
| _ -> assert false
let clause = make_to_repr to_clause
let to_red_strength = function
| ValInt 0 -> Norm
| ValInt 1 -> Head
| _ -> assert false
let to_red_flag v : Tac2types.red_flag = match Value.to_tuple v with
| [| strength; beta; iota; fix; cofix; zeta; delta; const |] ->
{
rStrength = to_red_strength strength;
rBeta = Value.to_bool beta;
rMatch = Value.to_bool iota;
rFix = Value.to_bool fix;
rCofix = Value.to_bool cofix;
rZeta = Value.to_bool zeta;
rDelta = Value.to_bool delta;
rConst = Value.to_list Value.to_reference const;
}
| _ -> assert false
let red_flags = make_to_repr to_red_flag
let constr_with_occs = pair constr occurrences
let reference_with_occs = pair reference occurrences
let to_red_context = to_option (to_pair to_pattern to_occurrences)
let red_context = make_to_repr to_red_context
let rec to_intro_pattern v = match Value.to_block v with
| (0, [| b |]) -> IntroForthcoming (Value.to_bool b)
| (1, [| pat |]) -> IntroNaming (to_intro_pattern_naming pat)
| (2, [| act |]) -> IntroAction (to_intro_pattern_action act)
| _ -> assert false
and to_intro_pattern_naming = function
| ValBlk (0, [| id |]) -> IntroIdentifier (Value.to_ident id)
| ValBlk (1, [| id |]) -> IntroFresh (Value.to_ident id)
| ValInt 0 -> IntroAnonymous
| _ -> assert false
and to_intro_pattern_action = function
| ValInt 0 -> IntroWildcard
| ValBlk (0, [| op |]) -> IntroOrAndPattern (to_or_and_intro_pattern op)
| ValBlk (1, [| inj |]) ->
let map ipat = to_intro_pattern ipat in
IntroInjection (Value.to_list map inj)
| ValBlk (2, [| c; ipat |]) ->
let c = Value.to_fun1 Value.of_unit Value.to_constr c in
IntroApplyOn (c, to_intro_pattern ipat)
| ValBlk (3, [| b |]) -> IntroRewrite (Value.to_bool b)
| _ -> assert false
and to_or_and_intro_pattern v = match Value.to_block v with
| (0, [| ill |]) ->
IntroOrPattern (Value.to_list to_intro_patterns ill)
| (1, [| il |]) ->
IntroAndPattern (to_intro_patterns il)
| _ -> assert false
and to_intro_patterns il =
Value.to_list to_intro_pattern il
let rec of_intro_pattern = function
| IntroForthcoming b -> of_block (0, [|of_bool b|])
| IntroNaming pat -> of_block (1, [|of_intro_pattern_naming pat|])
| IntroAction act -> of_block (2, [|of_intro_pattern_action act|])
and of_intro_pattern_naming = function
| IntroIdentifier id -> of_block (0, [|of_ident id|])
| IntroFresh id -> of_block (1, [|of_ident id|])
| IntroAnonymous -> of_int 0
and of_intro_pattern_action = function
| IntroWildcard -> of_int 0
| IntroOrAndPattern op -> of_block (0, [|of_or_and_intro_pattern op|])
| IntroInjection inj -> of_block (1, [|of_list of_intro_pattern inj|])
| IntroApplyOn (c, ipat) ->
let c = repr_of (fun1 unit constr) c in
of_block (2, [|c; of_intro_pattern ipat|])
| IntroRewrite b -> of_block (3, [|of_bool b|])
and of_or_and_intro_pattern = function
| IntroOrPattern ill -> of_block (0, [|of_list of_intro_patterns ill|])
| IntroAndPattern il -> of_block (1, [|of_intro_patterns il|])
and of_intro_patterns il = of_list of_intro_pattern il
let intro_pattern = make_repr of_intro_pattern to_intro_pattern
let intro_patterns = make_repr of_intro_patterns to_intro_patterns
let to_destruction_arg v = match Value.to_block v with
| (0, [| c |]) ->
let c = uthaw constr_with_bindings c in
ElimOnConstr c
| (1, [| id |]) -> ElimOnIdent (Value.to_ident id)
| (2, [| n |]) -> ElimOnAnonHyp (Value.to_int n)
| _ -> assert false
let destruction_arg = make_to_repr to_destruction_arg
let to_induction_clause v = match Value.to_tuple v with
| [| arg; eqn; as_; in_ |] ->
let arg = to_destruction_arg arg in
let eqn = Value.to_option to_intro_pattern_naming eqn in
let as_ = Value.to_option to_or_and_intro_pattern as_ in
let in_ = Value.to_option to_clause in_ in
(arg, eqn, as_, in_)
| _ ->
assert false
let induction_clause = make_to_repr to_induction_clause
let to_assertion v = match Value.to_block v with
| (0, [| ipat; t; tac |]) ->
let to_tac t = Value.to_fun1 Value.of_unit Value.to_unit t in
let ipat = Value.to_option to_intro_pattern ipat in
let t = Value.to_constr t in
let tac = Value.to_option to_tac tac in
AssertType (ipat, t, tac)
| (1, [| id; c |]) ->
AssertValue (Value.to_ident id, Value.to_constr c)
| _ -> assert false
let assertion = make_to_repr to_assertion
let to_multi = function
| ValBlk (0, [| n |]) -> Precisely (Value.to_int n)
| ValBlk (1, [| n |]) -> UpTo (Value.to_int n)
| ValInt 0 -> RepeatStar
| ValInt 1 -> RepeatPlus
| _ -> assert false
let to_rewriting v = match Value.to_tuple v with
| [| orient; repeat; c |] ->
let orient = Value.to_option Value.to_bool orient in
let repeat = to_multi repeat in
let c = uthaw constr_with_bindings c in
(orient, repeat, c)
| _ -> assert false
let rewriting = make_to_repr to_rewriting
let to_debug v = match Value.to_int v with
| 0 -> Hints.Off
| 1 -> Hints.Info
| 2 -> Hints.Debug
| _ -> assert false
let debug = make_to_repr to_debug
let to_strategy v = match Value.to_int v with
| 0 -> Class_tactics.Bfs
| 1 -> Class_tactics.Dfs
| _ -> assert false
let strategy = make_to_repr to_strategy
let to_inversion_kind v = match Value.to_int v with
| 0 -> Inv.SimpleInversion
| 1 -> Inv.FullInversion
| 2 -> Inv.FullInversionClear
| _ -> assert false
let inversion_kind = make_to_repr to_inversion_kind
let to_move_location = function
| ValInt 0 -> Logic.MoveFirst
| ValInt 1 -> Logic.MoveLast
| ValBlk (0, [|id|]) -> Logic.MoveAfter (Value.to_ident id)
| ValBlk (1, [|id|]) -> Logic.MoveBefore (Value.to_ident id)
| _ -> assert false
let move_location = make_to_repr to_move_location
let to_generalize_arg v = match Value.to_tuple v with
| [| c; occs; na |] ->
(Value.to_constr c, to_occurrences occs, to_name na)
| _ -> assert false
let generalize_arg = make_to_repr to_generalize_arg
(** Standard tactics sharing their implementation with Ltac1 *)
open Tac2externals
let define s =
define { mltac_plugin = "rocq-runtime.plugins.ltac2"; mltac_tactic = s }
(** Tactics from Tacexpr *)
let () =
define "tac_intros"
(bool @-> intro_patterns @-> tac unit)
Tac2tactics.intros_patterns
let () =
define "tac_apply"
(bool @-> bool @-> list (thunk constr_with_bindings) @->
option (pair ident (option intro_pattern)) @-> tac unit)
Tac2tactics.apply
let () =
define "tac_elim"
(bool @-> constr_with_bindings @-> option constr_with_bindings @-> tac unit)
Tac2tactics.elim
let () =
define "tac_case"
(bool @-> constr_with_bindings @-> tac unit)
Tac2tactics.general_case_analysis
let () =
define "tac_generalize"
(list generalize_arg @-> tac unit)
Tac2tactics.generalize
let () =
define "tac_assert"
(assertion @-> tac unit)
Tac2tactics.assert_
let tac_enough c tac ipat =
let tac = Option.map (fun o -> Option.map (fun f -> thaw f) o) tac in
Tac2tactics.forward false tac ipat c
let () =
define "tac_enough"
(constr @-> option (option (thunk unit)) @-> option intro_pattern @-> tac unit)
tac_enough
let tac_pose na c = Tactics.letin_tac None na c None Locusops.nowhere
let () =
define "tac_pose"
(name @-> constr @-> tac unit)
tac_pose
let tac_set ev p cl =
Proofview.tclEVARMAP >>= fun sigma ->
thaw p >>= fun (na, c) ->
Tac2tactics.letin_pat_tac ev None na (Some sigma, c) cl
let () =
define "tac_set"
(bool @-> thunk (pair name constr) @-> clause @-> tac unit)
tac_set
let tac_remember ev na c eqpat cl =
let eqpat = Option.default (IntroNaming IntroAnonymous) eqpat in
match eqpat with
| IntroNaming eqpat ->
Proofview.tclEVARMAP >>= fun sigma ->
thaw c >>= fun c ->
Tac2tactics.letin_pat_tac ev (Some (true, eqpat)) na (Some sigma, c) cl
| _ ->
Tacticals.tclZEROMSG (Pp.str "Invalid pattern for remember")
let () =
define "tac_remember"
(bool @-> name @-> thunk constr @-> option intro_pattern @-> clause @-> tac unit)
tac_remember
let () =
define "tac_destruct"
(bool @-> list induction_clause @-> option constr_with_bindings @-> tac unit)
(Tac2tactics.induction_destruct false)
let () =
define "tac_induction"
(bool @-> list induction_clause @-> option constr_with_bindings @-> tac unit)
(Tac2tactics.induction_destruct true)
let () = define "tac_exfalso" (unit @-> tac unit) @@ fun () ->
Tactics.exfalso
(** Reductions *)
let () =
define "reduce_in"
(reduction @-> clause @-> tac unit)
Tac2tactics.reduce_in
let () =
define "reduce_constr"
(reduction @-> constr @-> tac constr)
Tac2tactics.reduce_constr
let () = define "red"
(ret reduction)
Red
let () = define "hnf"
(ret reduction)
Hnf
let () =
define "simpl"
(red_flags @-> red_context @-> tac reduction)
Tac2tactics.simpl
let () =
define "cbv"
(red_flags @-> tac reduction)
Tac2tactics.cbv
let () =
define "cbn"
(red_flags @-> tac reduction)
Tac2tactics.cbn
let () =
define "lazy"
(red_flags @-> tac reduction)
Tac2tactics.lazy_
let () =
define "unfold"
(list reference_with_occs @-> tac reduction)
Tac2tactics.unfold
let () =
define "fold"
(list constr @-> ret reduction)
(fun cs -> Fold cs)
let () =
define "pattern"
(list constr_with_occs @-> ret reduction)
Tac2tactics.pattern
let () =
define "vm"
(red_context @-> ret reduction)
Tac2tactics.vm
let () =
define "native"
(red_context @-> ret reduction)
Tac2tactics.native
(** Rewritings *)
let () =
define "tac_change"
(option pattern @-> fun1 (array constr) constr @-> clause @-> tac unit)
Tac2tactics.change
let () =
define "tac_rewrite"
(bool @-> list rewriting @-> clause @-> option (thunk unit) @-> tac unit)
Tac2tactics.rewrite
let () =
define "tac_setoid_rewrite"
(bool @-> uthaw constr_with_bindings @--> occurrences @-> option ident @-> tac unit)
Tac2tactics.setoid_rewrite
let () =
define "tac_rewrite_strat"
(rewstrategy @-> option ident @-> tac unit)
Tac2tactics.rewrite_strat
let () =
define "rewstrat_id"
(ret rewstrategy)
Rewrite.Strategies.id
let () =
define "rewstrat_fail"
(ret rewstrategy)
Rewrite.Strategies.fail
let () =
define "rewstrat_refl"
(ret rewstrategy)
Rewrite.Strategies.refl
let () =
define "rewstrat_progress"
(rewstrategy @-> ret rewstrategy)
Rewrite.Strategies.progress
let () =
define "rewstrat_seq"
(rewstrategy @-> rewstrategy @-> ret rewstrategy)
Rewrite.Strategies.seq
let () =
define "rewstrat_seqs"
(list rewstrategy @-> ret rewstrategy)
Rewrite.Strategies.seqs
let () =
define "rewstrat_choice"
(rewstrategy @-> rewstrategy @-> ret rewstrategy)
Rewrite.Strategies.choice
let () =
define "rewstrat_choices"
(list rewstrategy @-> ret rewstrategy)
Rewrite.Strategies.choices
let () =
define "rewstrat_try"
(rewstrategy @-> ret rewstrategy)
Rewrite.Strategies.try_
let () =
define "rewstrat_fix"
(closure @-> tac rewstrategy)
Tac2tactics.RewriteStrats.fix
let () =
define "rewstrat_any"
(rewstrategy @-> ret rewstrategy)
Rewrite.Strategies.any
let () =
define "rewstrat_repeat"
(rewstrategy @-> ret rewstrategy)
Rewrite.Strategies.repeat
let () =
define "rewstrat_one_subterm"
(rewstrategy @-> ret rewstrategy)
Rewrite.Strategies.one_subterm
let () =
define "rewstrat_all_subterms"
(rewstrategy @-> ret rewstrategy)
Rewrite.Strategies.all_subterms
let () =
define "rewstrat_bottomup"
(rewstrategy @-> ret rewstrategy)
Rewrite.Strategies.bottomup
let () =
define "rewstrat_topdown"
(rewstrategy @-> ret rewstrategy)
Rewrite.Strategies.topdown
let () =
define "rewstrat_innermost"
(rewstrategy @-> ret rewstrategy)
Rewrite.Strategies.innermost
let () =
define "rewstrat_outermost"
(rewstrategy @-> ret rewstrategy)
Rewrite.Strategies.outermost
let () =
define "rewstrat_hints"
(ident @-> ret rewstrategy)
Tac2tactics.RewriteStrats.hints
let () =
define "rewstrat_old_hints"
(ident @-> ret rewstrategy)
Tac2tactics.RewriteStrats.old_hints
let () =
define "rewstrat_one_lemma"
(preterm @-> bool @-> ret rewstrategy)
Tac2tactics.RewriteStrats.one_lemma
let () =
define "rewstrat_lemmas"
(list preterm @-> ret rewstrategy)
Tac2tactics.RewriteStrats.lemmas
let () =
define "rewstrat_fold"
(constr @-> ret rewstrategy)
Rewrite.Strategies.fold
let () =
define "rewstrat_eval"
(reduction @-> ret rewstrategy)
Rewrite.Strategies.reduce
let () =
define "tac_inversion"
(inversion_kind @-> destruction_arg @-> option intro_pattern @->
option (list ident) @-> tac unit)
Tac2tactics.inversion
(** Tactics from coretactics *)
let () =
define "tac_reflexivity" (unit @-> tac unit) (fun _ -> Tactics.intros_reflexivity)
let () =
define "tac_move" (ident @-> move_location @-> tac unit) Tactics.move_hyp
let tac_intro id mv =
let mv = Option.default Logic.MoveLast mv in
Tactics.intro_move id mv
let () =
define "tac_intro" (option ident @-> option move_location @-> tac unit) tac_intro
let () =
define "tac_assumption" (unit @-> tac unit) (fun _ -> Tactics.assumption)
let () =
define "tac_eassumption" (unit @-> tac unit) (fun _ -> Eauto.e_assumption)
let () =
define "tac_transitivity" (constr @-> tac unit)
(fun c -> Tactics.intros_transitivity (Some c))
let () =
define "tac_etransitivity" (unit @-> tac unit)
(fun _ -> Tactics.intros_transitivity None)
let () =
define "tac_cut" (constr @-> tac unit) Tactics.cut
let () =
define "tac_left" (bool @-> bindings @-> tac unit) Tac2tactics.left_with_bindings
let () =
define "tac_right" (bool @-> bindings @-> tac unit) Tac2tactics.right_with_bindings
let () =
define "tac_introsuntil" (qhyp @-> tac unit) Tactics.intros_until
let () =
define "tac_exactnocheck" (constr @-> tac unit) Tactics.exact_no_check
let () =
define "tac_vmcastnocheck" (constr @-> tac unit) Tactics.vm_cast_no_check
let () =
define "tac_nativecastnocheck" (constr @-> tac unit) Tactics.native_cast_no_check
let () =
define "tac_constructor" (bool @-> tac unit) (fun ev -> Tactics.any_constructor ev None)
let () =
define "tac_constructorn" (bool @-> int @-> bindings @-> tac unit)
(fun ev n bnd -> Tac2tactics.constructor_tac ev None n bnd)
let () =
define "tac_specialize"
(constr_with_bindings @-> option intro_pattern @-> tac unit)
Tac2tactics.specialize
let () =
define "tac_symmetry" (clause @-> tac unit) Tac2tactics.symmetry
let () =
define "tac_split" (bool @-> bindings @-> tac unit) Tac2tactics.split_with_bindings
let () =
define "tac_rename" (list (pair ident ident) @-> tac unit) Tactics.rename_hyp
let () =
define "tac_revert" (list ident @-> tac unit) Generalize.revert
let () =
define "tac_admit" (unit @-> tac unit) (fun _ -> Proofview.give_up)
let () =
define "tac_fix" (ident @-> int @-> tac unit) Tactics.fix
let () =
define "tac_cofix" (ident @-> tac unit) Tactics.cofix
let () =
define "tac_clear" (list ident @-> tac unit) Tactics.clear
let () =
define "tac_keep" (list ident @-> tac unit) Tactics.keep
let () =
define "tac_clearbody" (list ident @-> tac unit) Tactics.clear_body
(** Tactics from extratactics *)
let () =
define "tac_discriminate"
(bool @-> option destruction_arg @-> tac unit)
Tac2tactics.discriminate
let () =
define "tac_injection"
(bool @-> option intro_patterns @-> option destruction_arg @-> tac unit)
Tac2tactics.injection
let () =
define "tac_absurd" (constr @-> tac unit) Contradiction.absurd
let () =
define "tac_contradiction"
(option constr_with_bindings @-> tac unit)
Tac2tactics.contradiction
let () =
define "tac_autorewrite"
(bool @-> option (thunk unit) @-> list ident @-> clause @-> tac unit)
(fun all by ids cl -> Tac2tactics.autorewrite ~all by ids cl)
let () =
define "tac_subst" (list ident @-> tac unit) Equality.subst
let () =
define "tac_substall"
(unit @-> tac unit)
(fun _ -> return () >>= fun () -> Equality.subst_all ())
(** Auto *)
let () =
define "tac_trivial"
(debug @-> list reference @-> option (list ident) @-> tac unit)
Tac2tactics.trivial
let () =
define "tac_eauto"
(debug @-> option int @-> list reference @-> option (list ident) @-> tac unit)
Tac2tactics.eauto
let () =
define "tac_auto"
(debug @-> option int @-> list reference @-> option (list ident) @-> tac unit)
Tac2tactics.auto
let () =
define "tac_typeclasses_eauto"
(option strategy @-> option int @-> option (list ident) @-> tac unit)
Tac2tactics.typeclasses_eauto
let () =
define "tac_resolve_tc" (constr @-> tac unit) Class_tactics.resolve_tc
let () =
define "tac_unify" (constr @-> constr @-> tac unit) Tac2tactics.unify
(** Tactics for [Ltac2/TransparentState.v]. *)
let () =
define "current_transparent_state"
(unit @-> tac transparent_state)
Tac2tactics.current_transparent_state
let () =
define "full_transparent_state" (ret transparent_state) TransparentState.full
let () =
define "empty_transparent_state" (ret transparent_state) TransparentState.empty
(** Tactics around Evarconv unification (in [Ltac2/Unification.v]). *)
let to_conv_pb v = match Tac2ffi.to_int v with
| 0 -> Conversion.CONV
| 1 -> Conversion.CUMUL
| _ -> assert false
let () =
define "infer_conv" (to_conv_pb @--> transparent_state @-> constr @-> constr @-> tac bool) @@ fun pb ts c1 c2 ->
Tac2core.pf_apply @@ fun env sigma ->
match Reductionops.infer_conv ~pb ~ts env sigma c1 c2 with
| Some sigma -> Proofview.Unsafe.tclEVARS sigma <*> return true
| None -> return false
let () =
define "evarconv_unify"
(transparent_state @-> constr @-> constr @-> tac unit)
Tac2tactics.evarconv_unify
let () =
define "congruence"
(option int @-> option (list constr) @-> tac unit)
Tac2tactics.congruence
let () =
define "simple_congruence"
(option int @-> option (list constr) @-> tac unit)
Tac2tactics.simple_congruence
let () = define "f_equal" (unit @-> tac unit) @@ fun () ->
Tac2tactics.f_equal