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CompilerCorrectness: a running example program to optimize

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Adam Chlipala 2017-03-19 14:29:56 -04:00
parent 7cebd4bfba
commit dd7ce9f869
2 changed files with 69 additions and 0 deletions
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68
CompilerCorrectness.v
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@ -124,6 +124,66 @@ Definition traceEquivalence (vc1 vc2 : valuation * cmd) :=
vc1 <| vc2 /\ vc2 <| vc1. vc1 <| vc2 /\ vc2 <| vc1.
Infix "=|" := traceEquivalence (at level 70). Infix "=|" := traceEquivalence (at level 70).
Definition daysPerWeek := 7.
Definition weeksPerMonth := 4.
Definition daysPerMonth := (daysPerWeek * weeksPerMonth)%arith.
Example month_boundaries_in_days :=
"acc" <- 0;;
while 1 loop
when daysPerMonth then
"acc" <- "acc" + daysPerMonth;;
Output "acc"
else
(* Oh no! We must have calculated it wrong, since we got zero! *)
Skip
done
done.
Hint Extern 1 (interp _ _ = _) => simplify; congruence.
Hint Extern 1 (interp _ _ <> _) => simplify; congruence.
Theorem first_few_values :
generate ($0, month_boundaries_in_days) [28; 56].
Proof.
unfold month_boundaries_in_days.
eapply GenSilent.
eapply CStep with (C := CSeq Hole _); eauto.
eapply GenSilent.
eapply CStep with (C := Hole); eauto.
eapply GenSilent.
eapply CStep with (C := Hole); eauto.
eapply GenSilent.
eapply CStep with (C := CSeq Hole _); eauto.
eapply GenSilent.
eapply CStep with (C := CSeq (CSeq Hole _) _); eauto.
eapply GenSilent.
eapply CStep with (C := CSeq Hole _); eauto.
eapply GenOutput.
eapply CStep with (C := CSeq Hole _); eauto.
replace 28 with (interp "acc"
($0 $+ ("acc", interp 0 $0)
$+ ("acc", interp ("acc" + daysPerMonth)%arith ($0 $+ ("acc", interp 0 $0))))); eauto.
eapply GenSilent.
eapply CStep with (C := Hole); eauto.
eapply GenSilent.
eapply CStep with (C := Hole); eauto.
eapply GenSilent.
eapply CStep with (C := CSeq Hole _); eauto.
eapply GenSilent.
eapply CStep with (C := CSeq (CSeq Hole _) _); eauto.
eapply GenSilent.
eapply CStep with (C := CSeq Hole _); eauto.
eapply GenOutput.
eapply CStep with (C := CSeq Hole _); eauto.
replace 56 with (interp "acc"
($0 $+ ("acc", interp 0 $0) $+ ("acc",
interp ("acc" + daysPerMonth)%arith ($0 $+ ("acc", interp 0 $0))) $+ ("acc",
interp ("acc" + daysPerMonth)%arith
($0 $+ ("acc", interp 0 $0) $+ ("acc",
interp ("acc" + daysPerMonth)%arith ($0 $+ ("acc", interp 0 $0))))))); eauto.
constructor.
Qed.
(** * Basic Simulation Arguments and Optimizing Expressions *) (** * Basic Simulation Arguments and Optimizing Expressions *)
@ -174,6 +234,8 @@ Fixpoint cfoldExprs (c : cmd) : cmd :=
| Output e => Output (cfoldArith e) | Output e => Output (cfoldArith e)
end. end.
Compute cfoldExprs month_boundaries_in_days.
Theorem skip_or_step : forall v c, Theorem skip_or_step : forall v c,
c = Skip c = Skip
\/ exists v' l c', cstep (v, c) l (v', c'). \/ exists v' l c', cstep (v, c) l (v', c').
@ -376,6 +438,8 @@ Fixpoint cfold (c : cmd) : cmd :=
| Output e => Output (cfoldArith e) | Output e => Output (cfoldArith e)
end. end.
Compute cfold month_boundaries_in_days.
Notation silent_cstep := (fun a b => cstep a None b). Notation silent_cstep := (fun a b => cstep a None b).
Lemma silent_generate_fwd : forall ns vc vc', Lemma silent_generate_fwd : forall ns vc vc',
@ -722,6 +786,8 @@ Fixpoint noUnderscore (c : cmd) : bool :=
| Output e => noUnderscoreArith e | Output e => noUnderscoreArith e
end. end.
Compute noUnderscore month_boundaries_in_days.
Fixpoint flattenArith (tempCount : nat) (dst : var) (e : arith) : nat * cmd := Fixpoint flattenArith (tempCount : nat) (dst : var) (e : arith) : nat * cmd :=
match e with match e with
| Const _ | Const _
@ -756,6 +822,8 @@ Fixpoint flatten (c : cmd) : cmd :=
| Output _ => c | Output _ => c
end. end.
Compute flatten month_boundaries_in_days.
Section simulation_multiple. Section simulation_multiple.
Variable R : valuation * cmd -> valuation * cmd -> Prop. Variable R : valuation * cmd -> valuation * cmd -> Prop.

1
_CoqProject
View file

@ -29,6 +29,7 @@ OperationalSemantics.v
LogicProgramming.v LogicProgramming.v
LogicProgramming_template.v LogicProgramming_template.v
AbstractInterpretation.v AbstractInterpretation.v
CompilerCorrectness.v
LambdaCalculusAndTypeSoundness_template.v LambdaCalculusAndTypeSoundness_template.v
LambdaCalculusAndTypeSoundness.v LambdaCalculusAndTypeSoundness.v
TypesAndMutation.v TypesAndMutation.v