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Commit 09722955 authored by Robbert Krebbers's avatar Robbert Krebbers
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Misc proof mode clean up.

parent 08212075
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Showing with 103 additions and 64 deletions
theories/proofmode/tactics.v
View file @ 09722955
......@@ -110,8 +110,9 @@ Tactic Notation "iClear" "(" ident_list(xs) ")" constr(Hs) :=
Tactic Notation "iExact" constr(H) :=
eapply tac_assumption with H _ _; (* (i:=H) *)
[env_reflexivity || fail "iExact:" H "not found"
|let P := match goal with |- FromAssumption _ ?P _ => P end in
apply _ || fail "iExact:" H ":" P "does not match goal"].
|apply _ ||
let P := match goal with |- FromAssumption _ ?P _ => P end in
fail "iExact:" H ":" P "does not match goal"].
Tactic Notation "iAssumptionCore" :=
let rec find Γ i P :=
......@@ -151,22 +152,26 @@ Tactic Notation "iExFalso" := apply tac_ex_falso.
Local Tactic Notation "iPersistent" constr(H) :=
eapply tac_persistent with _ H _ _ _; (* (i:=H) *)
[env_reflexivity || fail "iPersistent:" H "not found"
|let Q := match goal with |- IntoPersistentP ?Q _ => Q end in
apply _ || fail "iPersistent:" Q "not persistent"
|apply _ ||
let Q := match goal with |- IntoPersistentP ?Q _ => Q end in
fail "iPersistent:" Q "not persistent"
|env_reflexivity|].
Local Tactic Notation "iPure" constr(H) "as" simple_intropattern(pat) :=
eapply tac_pure with _ H _ _ _; (* (i:=H1) *)
[env_reflexivity || fail "iPure:" H "not found"
|let P := match goal with |- IntoPure ?P _ => P end in
apply _ || fail "iPure:" P "not pure"
|apply _ ||
let P := match goal with |- IntoPure ?P _ => P end in
fail "iPure:" P "not pure"
|intros pat].
Tactic Notation "iPureIntro" :=
iStartProof;
eapply tac_pure_intro;
[let P := match goal with |- FromPure ?P _ => P end in
apply _ || fail "iPureIntro:" P "not pure"|].
[apply _ ||
let P := match goal with |- FromPure ?P _ => P end in
fail "iPureIntro:" P "not pure"
|].
(** Framing *)
Local Ltac iFrameFinish :=
......@@ -184,8 +189,9 @@ Local Ltac iFramePure t :=
Local Ltac iFrameHyp H :=
eapply tac_frame with _ H _ _ _;
[env_reflexivity || fail "iFrame:" H "not found"
|let R := match goal with |- Frame _ ?R _ _ => R end in
apply _ || fail "iFrame: cannot frame" R
|apply _ ||
let R := match goal with |- Frame _ ?R _ _ => R end in
fail "iFrame: cannot frame" R
|iFrameFinish].
Local Ltac iFrameAnyPure :=
......@@ -268,11 +274,15 @@ Local Tactic Notation "iIntro" "(" simple_intropattern(x) ")" :=
try first
[(* (∀ _, _) *) apply tac_forall_intro
|(* (?P → _) *) eapply tac_impl_intro_pure;
[let P := match goal with |- IntoPure ?P _ => P end in
apply _ || fail "iIntro:" P "not pure"|]
[apply _ ||
let P := match goal with |- IntoPure ?P _ => P end in
fail "iIntro:" P "not pure"
|]
|(* (?P -∗ _) *) eapply tac_wand_intro_pure;
[let P := match goal with |- IntoPure ?P _ => P end in
apply _ || fail "iIntro:" P "not pure"|]
[apply _ ||
let P := match goal with |- IntoPure ?P _ => P end in
fail "iIntro:" P "not pure"
|]
|(* ⌜∀ _, _⌝ *) apply tac_pure_forall_intro
|(* ⌜_ → _⌝ *) apply tac_pure_impl_intro];
intros x.
......@@ -284,10 +294,12 @@ Local Tactic Notation "iIntro" constr(H) :=
eapply tac_impl_intro with _ H; (* (i:=H) *)
[reflexivity || fail 1 "iIntro: introducing" H
"into non-empty spatial context"
|env_reflexivity || fail "iIntro:" H "not fresh"|]
|env_reflexivity || fail "iIntro:" H "not fresh"
|]
| (* (_ -∗ _) *)
eapply tac_wand_intro with _ H; (* (i:=H) *)
[env_reflexivity || fail 1 "iIntro:" H "not fresh"|]
[env_reflexivity || fail 1 "iIntro:" H "not fresh"
|]
| fail 1 "iIntro: nothing to introduce" ].
Local Tactic Notation "iIntro" "#" constr(H) :=
......@@ -295,14 +307,18 @@ Local Tactic Notation "iIntro" "#" constr(H) :=
first
[ (* (?P → _) *)
eapply tac_impl_intro_persistent with _ H _; (* (i:=H) *)
[let P := match goal with |- IntoPersistentP ?P _ => P end in
apply _ || fail 1 "iIntro: " P " not persistent"
|env_reflexivity || fail 1 "iIntro:" H "not fresh"|]
[apply _ ||
let P := match goal with |- IntoPersistentP ?P _ => P end in
fail 1 "iIntro: " P " not persistent"
|env_reflexivity || fail 1 "iIntro:" H "not fresh"
|]
| (* (?P -∗ _) *)
eapply tac_wand_intro_persistent with _ H _; (* (i:=H) *)
[let P := match goal with |- IntoPersistentP ?P _ => P end in
apply _ || fail 1 "iIntro: " P " not persistent"
|env_reflexivity || fail 1 "iIntro:" H "not fresh"|]
[apply _ ||
let P := match goal with |- IntoPersistentP ?P _ => P end in
fail 1 "iIntro: " P " not persistent"
|env_reflexivity || fail 1 "iIntro:" H "not fresh"
|]
| fail 1 "iIntro: nothing to introduce" ].
Local Tactic Notation "iIntro" "_" :=
......@@ -346,16 +362,18 @@ Local Tactic Notation "iSpecializeArgs" constr(H) open_constr(xs) :=
| hcons ?x ?xs =>
eapply tac_forall_specialize with _ H _ _ _; (* (i:=H) (a:=x) *)
[env_reflexivity || fail 1 "iSpecialize:" H "not found"
|let P := match goal with |- IntoForall ?P _ => P end in
apply _ || fail 1 "iSpecialize: cannot instantiate" P "with" x
|apply _ ||
let P := match goal with |- IntoForall ?P _ => P end in
fail 1 "iSpecialize: cannot instantiate" P "with" x
|exists x; split; [env_reflexivity|go xs]]
end in
go xs.
Local Tactic Notation "iSpecializePat" constr(H) constr(pat) :=
let solve_to_wand H1 :=
apply _ ||
let P := match goal with |- IntoWand ?P _ _ => P end in
apply _ || fail "iSpecialize:" P "not an implication/wand" in
fail "iSpecialize:" P "not an implication/wand" in
let rec go H1 pats :=
lazymatch pats with
| [] => idtac
......@@ -366,16 +384,18 @@ Local Tactic Notation "iSpecializePat" constr(H) constr(pat) :=
eapply tac_specialize with _ _ H2 _ H1 _ _ _ _; (* (j:=H1) (i:=H2) *)
[env_reflexivity || fail "iSpecialize:" H2 "not found"
|env_reflexivity || fail "iSpecialize:" H1 "not found"
|let P := match goal with |- IntoWand ?P ?Q _ => P end in
|apply _ ||
let P := match goal with |- IntoWand ?P ?Q _ => P end in
let Q := match goal with |- IntoWand ?P ?Q _ => Q end in
apply _ || fail "iSpecialize: cannot instantiate" P "with" Q
fail "iSpecialize: cannot instantiate" P "with" Q
|env_reflexivity|go H1 pats]
| SPureGoal ?d :: ?pats =>
eapply tac_specialize_assert_pure with _ H1 _ _ _ _ _;
[env_reflexivity || fail "iSpecialize:" H1 "not found"
|solve_to_wand H1
|let Q := match goal with |- FromPure ?Q _ => Q end in
apply _ || fail "iSpecialize:" Q "not pure"
|apply _ ||
let Q := match goal with |- FromPure ?Q _ => Q end in
fail "iSpecialize:" Q "not pure"
|env_reflexivity
|done_if d (*goal*)
|go H1 pats]
......@@ -383,8 +403,9 @@ Local Tactic Notation "iSpecializePat" constr(H) constr(pat) :=
eapply tac_specialize_assert_persistent with _ _ H1 _ _ _ _;
[env_reflexivity || fail "iSpecialize:" H1 "not found"
|solve_to_wand H1
|let Q := match goal with |- PersistentP ?Q => Q end in
apply _ || fail "iSpecialize:" Q "not persistent"
|apply _ ||
let Q := match goal with |- PersistentP ?Q => Q end in
fail "iSpecialize:" Q "not persistent"
|env_reflexivity
|iFrame Hs_frame; done_if d (*goal*)
|go H1 pats]
......@@ -406,8 +427,9 @@ Local Tactic Notation "iSpecializePat" constr(H) constr(pat) :=
eapply tac_specialize_assert_persistent with _ _ H1 _ _ _ _;
[env_reflexivity || fail "iSpecialize:" H1 "not found"
|solve_to_wand H1
|let Q := match goal with |- PersistentP ?Q => Q end in
apply _ || fail "iSpecialize:" Q "not persistent"
|apply _ ||
let Q := match goal with |- PersistentP ?Q => Q end in
fail "iSpecialize:" Q "not persistent"
|env_reflexivity
|solve [iFrame "∗ #"]
|go H1 pats]
......@@ -419,8 +441,8 @@ Local Tactic Notation "iSpecializePat" constr(H) constr(pat) :=
| GSpatial => apply elim_modal_dummy
| GModal => apply _ || fail "iSpecialize: goal not a modality"
end
|iFrame "∗ #"; apply tac_unlock
|| fail "iSpecialize: premise cannot be solved by framing"
|iFrame "∗ #"; apply tac_unlock ||
fail "iSpecialize: premise cannot be solved by framing"
|reflexivity]; iIntro H1; go H1 pats
end in let pats := spec_pat.parse pat in go H pats.
......@@ -447,8 +469,9 @@ Tactic Notation "iSpecializeCore" open_constr(t) "as" constr(p) :=
eapply tac_specialize_persistent_helper with _ H _ _ _;
[env_reflexivity || fail "iSpecialize:" H "not found"
|iSpecializeArgs H xs; iSpecializePat H pat; last (iExact H)
|let Q := match goal with |- PersistentP ?Q => Q end in
apply _ || fail "iSpecialize:" Q "not persistent"
|apply _ ||
let Q := match goal with |- PersistentP ?Q => Q end in
fail "iSpecialize:" Q "not persistent"
|env_reflexivity|(* goal *)]
| false => iSpecializeArgs H xs; iSpecializePat H pat
end
......@@ -611,21 +634,27 @@ Tactic Notation "iRevert" "(" ident(x1) ident(x2) ident(x3) ident(x4)
Tactic Notation "iLeft" :=
iStartProof;
eapply tac_or_l;
[let P := match goal with |- FromOr ?P _ _ => P end in
apply _ || fail "iLeft:" P "not a disjunction"|].
[apply _ ||
let P := match goal with |- FromOr ?P _ _ => P end in
fail "iLeft:" P "not a disjunction"
|].
Tactic Notation "iRight" :=
iStartProof;
eapply tac_or_r;
[let P := match goal with |- FromOr ?P _ _ => P end in
apply _ || fail "iRight:" P "not a disjunction"|].
[apply _ ||
let P := match goal with |- FromOr ?P _ _ => P end in
fail "iRight:" P "not a disjunction"
|].
Local Tactic Notation "iOrDestruct" constr(H) "as" constr(H1) constr(H2) :=
eapply tac_or_destruct with _ _ H _ H1 H2 _ _ _; (* (i:=H) (j1:=H1) (j2:=H2) *)
[env_reflexivity || fail "iOrDestruct:" H "not found"
|let P := match goal with |- IntoOr ?P _ _ => P end in
apply _ || fail "iOrDestruct: cannot destruct" P
|apply _ ||
let P := match goal with |- IntoOr ?P _ _ => P end in
fail "iOrDestruct: cannot destruct" P
|env_reflexivity || fail "iOrDestruct:" H1 "not fresh"
|env_reflexivity || fail "iOrDestruct:" H2 "not fresh"| |].
|env_reflexivity || fail "iOrDestruct:" H2 "not fresh"
| |].
(** * Conjunction and separating conjunction *)
Tactic Notation "iSplit" :=
......@@ -633,24 +662,27 @@ Tactic Notation "iSplit" :=
lazymatch goal with
| |- _ ⊢ _ =>
eapply tac_and_split;
[let P := match goal with |- FromAnd ?P _ _ => P end in
apply _ || fail "iSplit:" P "not a conjunction"| |]
[apply _ ||
let P := match goal with |- FromAnd ?P _ _ => P end in
fail "iSplit:" P "not a conjunction"| |]
end.
Tactic Notation "iSplitL" constr(Hs) :=
iStartProof;
let Hs := words Hs in
eapply tac_sep_split with _ _ false Hs _ _; (* (js:=Hs) *)
[let P := match goal with |- FromSep ?P _ _ => P end in
apply _ || fail "iSplitL:" P "not a separating conjunction"
[apply _ ||
let P := match goal with |- FromSep ?P _ _ => P end in
fail "iSplitL:" P "not a separating conjunction"
|env_reflexivity || fail "iSplitL: hypotheses" Hs
"not found in the context"| |].
Tactic Notation "iSplitR" constr(Hs) :=
iStartProof;
let Hs := words Hs in
eapply tac_sep_split with _ _ true Hs _ _; (* (js:=Hs) *)
[let P := match goal with |- FromSep ?P _ _ => P end in
apply _ || fail "iSplitR:" P "not a separating conjunction"
[apply _ ||
let P := match goal with |- FromSep ?P _ _ => P end in
fail "iSplitR:" P "not a separating conjunction"
|env_reflexivity || fail "iSplitR: hypotheses" Hs
"not found in the context"| |].
......@@ -660,15 +692,17 @@ Tactic Notation "iSplitR" := iSplitL "".
Local Tactic Notation "iAndDestruct" constr(H) "as" constr(H1) constr(H2) :=
eapply tac_and_destruct with _ H _ H1 H2 _ _ _; (* (i:=H) (j1:=H1) (j2:=H2) *)
[env_reflexivity || fail "iAndDestruct:" H "not found"
|let P := match goal with |- IntoAnd _ ?P _ _ => P end in
apply _ || fail "iAndDestruct: cannot destruct" P
|apply _ ||
let P := match goal with |- IntoAnd _ ?P _ _ => P end in
fail "iAndDestruct: cannot destruct" P
|env_reflexivity || fail "iAndDestruct:" H1 "or" H2 " not fresh"|].
Local Tactic Notation "iAndDestructChoice" constr(H) "as" constr(lr) constr(H') :=
eapply tac_and_destruct_choice with _ H _ lr H' _ _ _;
[env_reflexivity || fail "iAndDestructChoice:" H "not found"
|let P := match goal with |- IntoAnd _ ?P _ _ => P end in
apply _ || fail "iAndDestructChoice: cannot destruct" P
|apply _ ||
let P := match goal with |- IntoAnd _ ?P _ _ => P end in
fail "iAndDestructChoice: cannot destruct" P
|env_reflexivity || fail "iAndDestructChoice:" H' " not fresh"|].
(** * Combinining hypotheses *)
......@@ -686,8 +720,9 @@ Tactic Notation "iCombine" constr(H1) constr(H2) "as" constr(H) :=
Tactic Notation "iExists" uconstr(x1) :=
iStartProof;
eapply tac_exist;
[let P := match goal with |- FromExist ?P _ => P end in
apply _ || fail "iExists:" P "not an existential"
[apply _ ||
let P := match goal with |- FromExist ?P _ => P end in
fail "iExists:" P "not an existential"
|cbv beta; eexists x1].
Tactic Notation "iExists" uconstr(x1) "," uconstr(x2) :=
......@@ -715,8 +750,9 @@ Local Tactic Notation "iExistDestruct" constr(H)
"as" simple_intropattern(x) constr(Hx) :=
eapply tac_exist_destruct with H _ Hx _ _; (* (i:=H) (j:=Hx) *)
[env_reflexivity || fail "iExistDestruct:" H "not found"
|let P := match goal with |- IntoExist ?P _ => P end in
apply _ || fail "iExistDestruct: cannot destruct" P|];
|apply _ ||
let P := match goal with |- IntoExist ?P _ => P end in
fail "iExistDestruct: cannot destruct" P|];
let y := fresh in
intros y; eexists; split;
[env_reflexivity || fail "iExistDestruct:" Hx "not fresh"
......@@ -747,15 +783,17 @@ Tactic Notation "iNext":= iNext _.
Tactic Notation "iModIntro" :=
iStartProof;
eapply tac_modal_intro;
[let P := match goal with |- FromModal ?P _ => P end in
apply _ || fail "iModIntro:" P "not a modality"|].
[apply _ ||
let P := match goal with |- FromModal ?P _ => P end in
fail "iModIntro:" P "not a modality"|].
Tactic Notation "iModCore" constr(H) :=
eapply tac_modal_elim with _ H _ _ _ _;
[env_reflexivity || fail "iMod:" H "not found"
|let P := match goal with |- ElimModal ?P _ _ _ => P end in
|apply _ ||
let P := match goal with |- ElimModal ?P _ _ _ => P end in
let Q := match goal with |- ElimModal _ _ ?Q _ => Q end in
apply _ || fail "iMod: cannot eliminate modality " P "in" Q
fail "iMod: cannot eliminate modality " P "in" Q
|env_reflexivity|].
(** * Basic destruct tactic *)
......@@ -1386,8 +1424,9 @@ Local Tactic Notation "iRewriteCore" constr(lr) open_constr(lem) "in" constr(H)
eapply (tac_rewrite_in _ Heq _ _ H _ _ lr);
[env_reflexivity || fail "iRewrite:" Heq "not found"
|env_reflexivity || fail "iRewrite:" H "not found"
|let P := match goal with |- ?P ⊢ _ => P end in
apply: reflexivity || fail "iRewrite:" P "not an equality"
|apply: reflexivity ||
let P := match goal with |- ?P ⊢ _ => P end in
fail "iRewrite:" P "not an equality"
|iRewriteFindPred
|intros ??? ->; reflexivity
|env_reflexivity|lazy beta; iClear Heq]).
......
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