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share/popl08-tutorial-Fsub/AdditionalTactics.v.crashcoqide

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+(** A library of additional tactics. *)
+
+Require Export String.
+Open Scope string_scope.
+
+
+(* *********************************************************************** *)
+(** * Extensions of the standard library *)
+
+(** "[remember c as x in |-]" replaces the term [c] by the identifier
+    [x] in the conclusion of the current goal and introduces the
+    hypothesis [x=c] into the context.  This tactic differs from a
+    similar one in the standard library in that the replacmement is
+    made only in the conclusion of the goal; the context is left
+    unchanged. *)
+
+Tactic Notation "remember" constr(c) "as" ident(x) "in" "|-" :=
+  let x := fresh x in
+  let H := fresh "Heq" x in
+  (set (x := c); assert (H : x = c) by reflexivity; clearbody x).
+
+(** "[unsimpl E]" replaces all occurence of [X] by [E], where [X] is
+    the result that tactic [simpl] would give when used to evaluate
+    [E]. *)
+
+Tactic Notation "unsimpl" constr(E) :=
+  let F := (eval simpl in E) in change F with E.
+
+(** The following tactic calls the [apply] tactic with the first
+    hypothesis that succeeds, "first" meaning the hypothesis that
+    comes earlist in the context (i.e., higher up in the list). *)
+
+Ltac apply_first_hyp :=
+  match reverse goal with
+    | H : _ |- _ => apply H
+  end.
+
+
+(* *********************************************************************** *)
+(** * Variations on [auto] *)
+
+(** The [auto*] and [eauto*] tactics are intended to be "stronger"
+    versions of the [auto] and [eauto] tactics.  Similar to [auto] and
+    [eauto], they each take an optional "depth" argument.  Note that
+    if we declare these tactics using a single string, e.g., "auto*",
+    then the resulting tactics are unusable since they fail to
+    parse. *)
+
+Tactic Notation "auto" "*" :=
+  try solve [ congruence | auto | intuition auto ].
+
+Tactic Notation "auto" "*" integer(n) :=
+  try solve [ congruence | auto n | intuition (auto n) ].
+
+Tactic Notation "eauto" "*" :=
+  try solve [ congruence | eauto | intuition eauto ].
+
+Tactic Notation "eauto" "*" integer(n) :=
+  try solve [ congruence | eauto n | intuition (eauto n) ].
+
+
+(* *********************************************************************** *)
+(** * Delineating cases in proofs *)
+
+(** This section was taken from the POPLmark Wiki
+    ( http://alliance.seas.upenn.edu/~plclub/cgi-bin/poplmark/ ). *)
+
+(** ** Tactic definitions *)
+
+Ltac move_to_top x :=
+  match reverse goal with
+  | H : _ |- _ => try move x after H
+  end.
+
+Tactic Notation "assert_eq" ident(x) constr(v) :=
+  let H := fresh in
+  assert (x = v) as H by reflexivity;
+  clear H.
+
+Tactic Notation "Case_aux" ident(x) constr(name) :=
+  first [
+    set (x := name); move_to_top x
+  | assert_eq x name
+  | fail 1 "because we are working on a different case." ].
+
+Ltac Case name := Case_aux case name.
+Ltac SCase name := Case_aux subcase name.
+Ltac SSCase name := Case_aux subsubcase name.
+
+(** ** Example
+
+    One mode of use for the above tactics is to wrap Coq's [induction]
+    tactic such that automatically inserts "case" markers into each
+    branch of the proof.  For example:
+
+<<
+ Tactic Notation "induction" "nat" ident(n) :=
+   induction n; [ Case "O" | Case "S" ].
+ Tactic Notation "sub" "induction" "nat" ident(n) :=
+   induction n; [ SCase "O" | SCase "S" ].
+ Tactic Notation "sub" "sub" "induction" "nat" ident(n) :=
+   induction n; [ SSCase "O" | SSCase "S" ].
+>>
+
+    If you use such customized versions of the induction tactics, then
+    the [Case] tactic will verify that you are working on the case
+    that you think you are.  You may also use the [Case] tactic with
+    the standard version of [induction], in which case no verification
+    is done. *)