tests.v 4.55 KB
Newer Older
Ralf Jung's avatar
Ralf Jung committed
1
(** This file is essentially a bunch of testcases. *)
Ralf Jung's avatar
Ralf Jung committed
2
Require Import program_logic.upred.
Ralf Jung's avatar
Ralf Jung committed
3
Require Import heap_lang.lifting heap_lang.sugar.
4
Import heap_lang uPred notations.
Ralf Jung's avatar
Ralf Jung committed
5 6

Module LangTests.
7 8
  Definition add := (21 + 21)%L.
  Goal  σ, prim_step add σ 42 σ None.
9
  Proof. intros; do_step done. Qed.
10
  (* FIXME RJ why do I need the %L ? *)
Ralf Jung's avatar
Ralf Jung committed
11 12
  Definition rec : expr := (rec:: #0 #1)%L. (* fix f x => f x *)
  Definition rec_app : expr := rec 0.
Ralf Jung's avatar
Ralf Jung committed
13
  Goal  σ, prim_step rec_app σ rec_app σ None.
14 15
  Proof. Set Printing All. intros; do_step done. Qed.
  Definition lam : expr := (λ: #0 + 21)%L.
16
  Goal  σ, prim_step (App lam (LitNat 21)) σ add σ None.
17
  Proof. intros; do_step done. Qed.
Ralf Jung's avatar
Ralf Jung committed
18 19
End LangTests.

20
Module LiftingTests.
21 22
  Context {Σ : iFunctor}.
  Implicit Types P : iProp heap_lang Σ.
23
  Implicit Types Q : val  iProp heap_lang Σ.
24

25
  (* FIXME: Fix levels so that we do not need the parenthesis here. *)
26
  Definition e  : expr := (let: ref 1 in #0 <- !#0 + 1; !#0)%L.
Ralf Jung's avatar
Ralf Jung committed
27
  Goal  σ E, (ownP σ : iProp heap_lang Σ)  (wp E e (λ v, (v = 2))).
28 29
  Proof.
    move=> σ E. rewrite /e.
30
    rewrite -wp_let. rewrite -wp_alloc_pst; last done.
31 32 33
    apply sep_intro_True_r; first done.
    rewrite -later_intro. apply forall_intro=>l.
    apply wand_intro_l. rewrite right_id. apply const_elim_l; move=>_.
34
    rewrite -later_intro. asimpl.
35 36
    (* TODO RJ: If you go here, you can see how the sugar does not print
       all so nicely. *)
37 38 39
    rewrite -(wp_bindi (SeqCtx (Load (Loc _)))).
    rewrite -(wp_bindi (StoreRCtx (LocV _))).
    rewrite -(wp_bindi (PlusLCtx _)).
40
    rewrite -wp_load_pst; first (apply sep_intro_True_r; first done); last first.
41
    { by rewrite lookup_insert. } (* RJ FIXME: figure out why apply and eapply fail. *)
42
    rewrite -later_intro. apply wand_intro_l. rewrite right_id.
Ralf Jung's avatar
Ralf Jung committed
43
    rewrite -wp_plus -later_intro.
44
    rewrite -wp_store_pst; first (apply sep_intro_True_r; first done); last first.
45 46
    { by rewrite lookup_insert. }
    { done. }
47
    rewrite -later_intro. apply wand_intro_l. rewrite right_id.
48
    rewrite -wp_lam // -later_intro. asimpl.
49
    rewrite -wp_load_pst; first (apply sep_intro_True_r; first done); last first.
50
    { by rewrite lookup_insert. }
51
    rewrite -later_intro. apply wand_intro_l. rewrite right_id.
52 53
    by apply const_intro.
  Qed.
54

Ralf Jung's avatar
Ralf Jung committed
55 56 57
  (* TODO: once asimpl preserves notation, we don't need
     FindPred' anymore. *)
  (* FIXME: fix notation so that we do not need parenthesis or %L *)
58 59 60 61 62 63
  Definition FindPred' n1 Sn1 n2 f : expr :=
    if Sn1 < n2 then f Sn1 else n1.
  Definition FindPred n2 : expr :=
    rec:: (let: #1 + 1 in FindPred' #2 #0 n2.[ren(+3)] #1)%L.
  Definition Pred : expr :=
    λ: (if #0  0 then 0 else FindPred #0 0)%L.
Ralf Jung's avatar
Ralf Jung committed
64

65
  Lemma FindPred_spec n1 n2 E Q :
Ralf Jung's avatar
Ralf Jung committed
66 67
    ((n1 < n2)  Q (pred n2)) 
       wp E (FindPred n2 n1) Q.
68 69 70 71 72 73 74 75
  Proof.
    revert n1. apply löb_all_1=>n1.
    rewrite -wp_rec //. asimpl.
    (* Get rid of the ▷ in the premise. *)
    etransitivity; first (etransitivity; last eapply equiv_spec, later_and).
    { apply and_mono; first done. by rewrite -later_intro. }
    apply later_mono.
    (* Go on. *)
Ralf Jung's avatar
Ralf Jung committed
76
    rewrite -(wp_let _ _ (FindPred' n1 #0 n2 (FindPred n2))).
77
    rewrite -wp_plus. asimpl.
78
    rewrite -(wp_bindi (CaseCtx _ _)).
79
    rewrite -!later_intro /=.
80
    apply wp_lt; intros Hn12.
81
    * (* TODO RJ: It would be better if we could use wp_if_true here
82 83 84
         (and below). But we cannot, because the substitutions in there
         got already unfolded. *)
      rewrite -wp_case_inl //.
85
      rewrite -!later_intro. asimpl.
86
      rewrite (forall_elim (S n1)).
87 88 89
      eapply impl_elim; first by eapply and_elim_l. apply and_intro.
      + apply const_intro; omega.
      + by rewrite !and_elim_r.
90
    * rewrite -wp_case_inr //.
91
      rewrite -!later_intro -wp_value' //.
92
      rewrite and_elim_r. apply const_elim_l=>Hle.
Ralf Jung's avatar
Ralf Jung committed
93
      by replace n1 with (pred n2) by omega.
94 95 96
  Qed.

  Lemma Pred_spec n E Q :
Ralf Jung's avatar
Ralf Jung committed
97
    Q (pred n)  wp E (Pred n) Q.
98 99
  Proof.
    rewrite -wp_lam //. asimpl.
100
    rewrite -(wp_bindi (CaseCtx _ _)).
101
    apply later_mono, wp_le=> Hn.
Ralf Jung's avatar
Ralf Jung committed
102 103
    - rewrite -wp_case_inl //.
      rewrite -!later_intro -wp_value' //.
Ralf Jung's avatar
Ralf Jung committed
104
      by replace n with 0 by omega.
Ralf Jung's avatar
Ralf Jung committed
105
    - rewrite -wp_case_inr //.
106
      rewrite -!later_intro -FindPred_spec.
Ralf Jung's avatar
Ralf Jung committed
107
      auto using and_intro, const_intro with omega.
108
  Qed.
Ralf Jung's avatar
Ralf Jung committed
109

110
  Goal  E,
111
    True  wp (Σ:=Σ) E (let: Pred 42 in Pred #0) (λ v, (v = 40)).
Ralf Jung's avatar
Ralf Jung committed
112 113 114 115 116
  Proof.
    intros E. rewrite -wp_let. rewrite -Pred_spec -!later_intro.
    asimpl. (* TODO RJ: Can we somehow make it so that Pred gets folded again? *)
    rewrite -Pred_spec -later_intro. by apply const_intro.
  Qed.
117
End LiftingTests.