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Functional big-step semantics

Authors

Scott Owens, Magnus Myreen, Ramana Kumar and Yong Kiam Tan

University of Kent

Chalmers University of Technology

NICTA

ASTAR

Abstract

When doing an interactive proof about a piece of software, it is important that the underlying programming language's semantics does not make the proof unnecessarily difficult or unwieldy. Both small-step and big-step semantics are commonly used, and the latter is typically given by an inductively defined relation. In this paper, we consider an alternative: using a recursive function akin to an interpreter for the language. The advantages include a better induction theorem, less duplication, accessibility to ordinary functional programmers, and the ease of doing symbolic simulation in proofs via rewriting. We believe that this style of semantics is well suited for compiler verification, including proofs of divergence preservation. We do not claim the invention of this style of semantics: our contribution here is to clarify its value, and to explain how it supports several language features that might appear to require a relational or small-step approach. We illustrate the technique on a simple imperative language with C-like for-loops and a break statement, and compare it to a variety of other approaches. We also provide ML and lambda-calculus based examples to illustrate its generality.

BibTeX Entry

  @inproceedings{Owens_MKT_16,
    doi              = {10.1007/978-3-662-49498-1_23},
    author           = {Owens, Scott and Myreen, Magnus and Kumar, Ramana and Tan, Yong Kiam},
    month            = apr,
    year             = {2016},
    keywords         = {cakeml},
    title            = {Functional Big-Step Semantics},
    booktitle        = {European Symposium on Programming},
    pages            = {27},
    address          = {Eindhoven, The Netherlands}
  }

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