dart / sdk.git / 5c90b1fd98e767702357faa561193777527bd9c6 / . / pkg / kernel / coq / CommonTactics.v

(* Copyright (c) 2017, the Dart project authors. Please see the AUTHORS file | |

* for details. All rights reserved. Use of this source code is governed by a | |

* BSD-style license that can be found in the LICENSE file. *) | |

Require Import Common. | |

Require Export CpdtTactics. | |

Import OptionMonad. | |

Ltac extract E x y := set (x := E); assert (y : E = x); [auto|rewrite y in *]. | |

Ltac force_expr E H := | |

let v1 := fresh in | |

let v2 := fresh in | |

extract E v1 v2; destruct v1; [idtac|simpl in H; contradict H; congruence]. | |

Lemma bind_some : forall A B x f, @opt_bind A B (Some x) f = f x. | |

Proof. | |

auto. | |

Qed. | |

Lemma simpl_if : forall A (e1 e2 : A), (if true then e1 else e2) = e1. | |

auto. | |

Qed. | |

(* remember (expression_type CE (NatMap.add v s TE) arg) as EXP. *) | |

(* destruct EXP; [rewrite bind_some in H1|simpl in H1; contradict H1; congruence]. *) | |

Ltac force_option := | |

match goal with | |

| [ H : (opt_bind ?y (fun x => ?z)) = Some ?w |- _ ] => | |

force_expr y H; rewrite bind_some in H | |

| [ H : (if ?cond then ?x else None) = Some ?w |- _ ] => | |

force_expr cond H; rewrite simpl_if in H | |

| [ H : (match ?x with _ => _ end) = Some ?w |- _ ] => | |

force_expr x H | |

end. | |

Ltac force_options := repeat force_option. | |

Inductive ltac_no_arg : Set := | |

| Ltac_No_Arg : ltac_no_arg. | |

Ltac extract_head_2 term H varid eqid := | |

match type of H with | |

| context[term ?X] => extract_head_2 (term X) H varid eqid | |

| context[term] => remember term as varid eqn:eqid | |

end. | |

Ltac extract_head_1 term H varid := let eqid := fresh varid "Eq" in extract_head_2 term H varid eqid. | |

Ltac extract_head_0 term H := let varid := fresh H in extract_head_1 term H varid. | |

Ltac extract_head_goal_2 term varid eqid := | |

match goal with | |

| [ |- context[term ?X] ] => extract_head_goal_2 (term X) varid eqid | |

| [ |- context[term] ] => remember term as varid eqn:eqid | |

end. | |

Ltac extract_head_goal_1 term varid := let eqid := fresh varid "Eq" in extract_head_goal_2 term varid eqid. | |

Ltac extract_head_goal_0 term := let varid := fresh "G" in extract_head_goal_1 term varid. | |

Tactic Notation "extract_head" constr(term) "in" constr(H) := extract_head_0 term H. | |

Tactic Notation "extract_head" constr(term) "in" constr(H) "as" ident(name) := extract_head_1 term H name. | |

Tactic Notation "extract_head" constr(term) "in" constr(H) "as" ident(name) "," ident(name2) := extract_head_2 term H name name2. | |

Tactic Notation "extract_head" constr(term) := extract_head_goal_0 term. | |

Tactic Notation "extract_head" constr(term) "as" ident(name) := extract_head_goal_1 term name. | |

Tactic Notation "extract_head" constr(term) "as" ident(name) "," ident(name2) := extract_head_goal_2 term name name2. | |

Ltac continue_with H := | |

match type of H with | |

| ?X -> ?Y => | |

let K := fresh H in | |

let H' := fresh H in | |

assert (X) as K; [idtac|pose proof (H K) as H'] | |

end. |