Commit 88e31976 authored by Robbert Krebbers's avatar Robbert Krebbers

Merge branch 'haidang/coq-stdpp-hai/QpCountable'

parents ee6200b4 8f7f211d
(* Copyright (c) 2012-2017, Coq-std++ developers. *)
(* This file is distributed under the terms of the BSD license. *)
From stdpp Require Export list.
From Coq.QArith Require Import QArith_base Qcanon.
From stdpp Require Export list numbers.
Set Default Proof Using "Type".
Local Open Scope positive.
......@@ -83,14 +84,14 @@ Qed.
(** * Instances *)
(** ** Injection *)
Section injective_countable.
Section inj_countable.
Context `{Countable A, EqDecision B}.
Context (f : B A) (g : A option B) (fg : x, g (f x) = Some x).
Program Instance injective_countable : Countable B :=
Program Instance inj_countable : Countable B :=
{| encode y := encode (f y); decode p := x decode p; g x |}.
Next Obligation. intros y; simpl; rewrite decode_encode; eauto. Qed.
End injective_countable.
End inj_countable.
(** ** Option *)
Program Instance option_countable `{Countable A} : Countable (option A) := {|
......@@ -256,7 +257,8 @@ Program Instance N_countable : Countable N := {|
decode p := if decide (p = 1) then Some 0%N else Some (Npos (Pos.pred p))
|}.
Next Obligation.
by intros [|p];simpl;[|rewrite decide_False,Pos.pred_succ by (by destruct p)].
intros [|p]; simpl; [done|].
by rewrite decide_False, Pos.pred_succ by (by destruct p).
Qed.
Program Instance Z_countable : Countable Z := {|
encode x := match x with Z0 => 1 | Zpos p => p~0 | Zneg p => p~1 end;
......@@ -268,3 +270,20 @@ Program Instance nat_countable : Countable nat :=
Next Obligation.
by intros x; lazy beta; rewrite decode_encode; csimpl; rewrite Nat2N.id.
Qed.
Global Program Instance Qc_countable : Countable Qc :=
inj_countable
(λ p : Qc, let 'Qcmake (x # y) _ := p return _ in (x,y))
(λ q : Z * positive, let '(x,y) := q return _ in Some (Q2Qc (x # y))) _.
Next Obligation.
intros [[x y] Hcan]. f_equal. apply Qc_is_canon. simpl. by rewrite Hcan.
Qed.
Global Program Instance Qp_countable : Countable Qp :=
inj_countable
Qp_car
(λ p : Qc, guard (0 < p)%Qc as Hp; Some (mk_Qp p Hp)) _.
Next Obligation.
intros [p Hp]. unfold mguard, option_guard; simpl.
case_match; [|done]. f_equal. by apply Qp_eq.
Qed.
......@@ -200,3 +200,7 @@ Lemma not_and_l_alt {P Q : Prop} `{Decision P} : ¬(P ∧ Q) ↔ ¬P ∨ (¬Q
Proof. destruct (decide P); tauto. Qed.
Lemma not_and_r_alt {P Q : Prop} `{Decision Q} : ¬(P Q) (¬P Q) ¬Q.
Proof. destruct (decide Q); tauto. Qed.
Program Definition inj_eq_dec `{EqDecision A} {B} (f : B A)
`{!Inj (=) (=) f} : EqDecision B := λ x y, cast_if (decide (f x = f y)).
Solve Obligations with firstorder congruence.
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