A DSL for Integer Range Reasoning: Partition, Interval and Mapping Diagrams

Johannes Eriksson, Masoumeh Parsa

    Research output: Chapter in Book/Conference proceedingConference contributionScientificpeer-review


    Expressing linear integer constraints and assertions over integer ranges—as becomes necessary when reasoning about arrays—in a legible and succinct form poses a challenge for deductive program verification. Even simple assertions, such as integer predicates quantified over finite ranges, become quite verbose when given in basic first-order logic syntax. In this paper, we propose a domain-specific language (DSL) for assertions over integer ranges based on Reynolds’s interval and partition diagrams, two diagrammatic notations designed to integrate well into linear textual content such as specifications, program annotations, and proofs. We extend intervalf diagrams to the more general concept of mapping diagrams, representing partial functions from disjoint integer intervals. A subset of mapping diagrams, colorings, provide a compact notation for selecting integer intervals that we intend to constrain, and an intuitive new construct, the legend, allows connecting colorings to first-order integer predicates. Reynolds’s diagrams have not been supported widely by verification tools. We implement the syntax and semantics of partition and mapping diagrams as a DSL and theory extension to the Why3 program verifier. We illustrate the approach with examples of verified programs specified with colorings and legends. This work aims to extend the verification toolbox with a lightweight, intuitive DSL for array and integer range specifications.
    Original languageEnglish
    Title of host publicationPractical Aspects of Declarative Languages
    ISBN (Print)978-3-030-39196-6
    Publication statusPublished - 2020
    MoE publication typeA4 Article in a conference publication

    Publication series

    NameLecture Notes in Computer Science


    Dive into the research topics of 'A DSL for Integer Range Reasoning: Partition, Interval and Mapping Diagrams'. Together they form a unique fingerprint.

    Cite this