Presburger Arithmetic and Its Use in Verification

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APPENDIX B. SOURCE CODE OF EXPERIMENTS B.6 OmegaTest.fs ï»¿module OmegaTest open Microsoft.FSharp.Collections open Utilities open Term // Input: a list of conjunctions and a list of disjunction pairs. // Output: do cartesian products on the input. let cartesian (cons, diss) = let rec cartesianUtil = function |[]−> [cons] | L::Ls −> cartesianUtil Ls |> List.collect (fun C −> L |> List.map (fun x −> x::C)) cartesianUtil diss exception OmegaTestFail type CoeffTerm = struct val coeff: int val term: Term new (c, t) ={coeff = c; term = t} end // Product all pairs of opposite literals let merge(outs, lowers: CoeffTerm list, uppers: CoeffTerm list) = let ins =[for l in lowers do for u in uppers do if l.coeff =1||u.coeff =1then yield ((l.coeff ∗∗ u.term ++ u.coeff ∗∗ l.term) −− One) else raise OmegaTestFail] ins@outs let project(x, fs) = let outs = List.filter (fun t −> findCoeff(t, x) =0)fs let lowers =[ for t in fs do let c = findCoeff(t, x) if c >0then yield CoeffTerm(c, t) ] let uppers =[ for t in fs do let c = findCoeff(t, x) if c
B.6. OMEGATEST.FS else merge(outs, lowers, uppers) let omegaTest(xs, fs) = let rec omegaTestUtil(xs, fs) = match xs with |[]−> xs, fs | x::xs’−> try omegaTestUtil(xs’, project(x, fs)) with OmegaTestFail −> xs, fs omegaTestUtil(xs, fs) let resolve(xs, tll) = printfn "Resolving␣%i␣Omega␣Tests" (List.length tll) List.map (fun tl −> omegaTest(xs, tl)) tll let resolveParallel(xs, tll) = printfn "Resolving␣%i␣Omega␣Tests" (List.length tll) List.ofSeq (PSeq.map (fun tl −> omegaTest(xs, tl)) tll) 87
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Presburger Arithmetic and Its Use i
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Abstract Today, when every computer
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Preface The thesis is a part of the
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List of Abbreviations CPU DAG DC DN
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5.2 Simplification of Presburger fo
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CHAPTER 1. INTRODUCTION functional
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Chapter 2 Multicore parallelism on
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2.1. MULTICORE PARALLELISM: A BRIEF
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2.2. MULTICORE PARALLELISM ON .NET
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Chapter 3 Functional paradigm and m
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3.1. PARALLEL FUNCTIONAL ALGORITHMS
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3.2. SOME PITFALLS OF FUNCTIONAL PA
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3.2. SOME PITFALLS OF FUNCTIONAL PA
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Chapter 4 Theory of Presburger Arit
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4.2. DECISION PROCEDURES FOR PRESBU
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Page 45 and 46: Chapter 5 Duration Calculus and Pre
Page 47 and 48: 5.1. DURATION CALCULUS AND SIDE-CON
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Page 71 and 72: Chapter 8 Conclusions In this work,
Page 73 and 74: References [1] Nikolaj Bjørner. Li
Page 75: [28] C. R. Reddy and D. W. Loveland
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Page 82 and 83: APPENDIX B. SOURCE CODE OF EXPERIME
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