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Diffstat (limited to 'lib/OptionMonad.v')
-rw-r--r-- | lib/OptionMonad.v | 76 |
1 files changed, 76 insertions, 0 deletions
diff --git a/lib/OptionMonad.v b/lib/OptionMonad.v new file mode 100644 index 00000000..f3566d5c --- /dev/null +++ b/lib/OptionMonad.v @@ -0,0 +1,76 @@ +(* Declare Scope option_monad_scope. *) + +Notation "'SOME' X <- A 'IN' B" := (match A with Some X => B | None => None end) + (at level 200, X ident, A at level 100, B at level 200) + : option_monad_scope. + +Notation "'ASSERT' A 'IN' B" := (if A then B else None) + (at level 200, A at level 100, B at level 200) + : option_monad_scope. + +Local Open Scope option_monad_scope. + + +(** Simple tactics for option-monad *) + +Ltac deepest_match exp := + match exp with + | context f [match ?expr with | _ => _ end] => ltac: (deepest_match expr) + | _ => exp + end. + +Ltac autodestruct := + let EQ := fresh "EQ" in + match goal with + | |- context f [match ?expr with | _ => _ end] => + let t := ltac: (deepest_match expr) in + destruct t eqn:EQ; generalize EQ; clear EQ; congruence || trivial + end. + +(* deprecated version of "autodestruct". the new one seems a better replacement +Ltac dummy_autodestruct := + let EQ := fresh "EQ" in + match goal with + | |- context f [match ?expr with | _ => _ end] => destruct expr eqn:EQ; generalize EQ; clear EQ; congruence || trivial + end. +*) + +Lemma destruct_SOME A B (P: option B -> Prop) (e: option A) (f: A -> option B): + (forall x, e = Some x -> P (f x)) -> (e = None -> P None) -> (P (SOME x <- e IN f x)). +Proof. + intros; destruct e; simpl; auto. +Qed. + +Lemma destruct_ASSERT B (P: option B -> Prop) (e: bool) (x: option B): + (e = true -> P x) -> (e = false -> P None) -> (P (ASSERT e IN x)). +Proof. + intros; destruct e; simpl; auto. +Qed. + +Ltac inversion_SOME x := + try (eapply destruct_SOME; [ let x := fresh x in intro x | simpl; try congruence ]). + +Ltac inversion_ASSERT := + try (eapply destruct_ASSERT; [ idtac | simpl; try congruence ]). + +Ltac simplify_someHyp := + match goal with + | H: None = Some _ |- _ => inversion H; clear H; subst + | H: Some _ = None |- _ => inversion H; clear H; subst + | H: ?t = ?t |- _ => clear H + | H: Some _ = Some _ |- _ => inversion H; clear H; subst + | H: Some _ <> None |- _ => clear H + | H: None <> Some _ |- _ => clear H + | H: _ = Some _ |- _ => (try rewrite !H in * |- *); generalize H; clear H + | H: _ = None |- _ => (try rewrite !H in * |- *); generalize H; clear H + | H: None = _ |- _ => (try rewrite <- !H in * |- *); generalize H; clear H + end. + +Ltac simplify_someHyps := + repeat (simplify_someHyp; simpl in * |- *). + +Ltac try_simplify_someHyps := + try (intros; simplify_someHyps; eauto). + +Ltac simplify_option := repeat (try_simplify_someHyps; autodestruct); try_simplify_someHyps. + |