Parametric Higher-Order Abstract Syntax for Mechanized Semantics

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Parametric Higher-Order Abstract Syntax for Mechanized Semantics (2008)

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by Adam Chlipala

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42 - 2 self

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@MISC{Chlipala08parametrichigher-order,
    author = {Adam Chlipala},
    title = {Parametric Higher-Order Abstract Syntax for Mechanized Semantics},
    year = {2008}
}

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Abstract

We present parametric higher-order abstract syntax (PHOAS), a new approach to formalizing the syntax of programming languages in computer proof assistants based on type theory. Like higherorder abstract syntax (HOAS), PHOAS uses the meta language’s binding constructs to represent the object language’s binding constructs. Unlike HOAS, PHOAS types are definable in generalpurpose type theories that support traditional functional programming, like Coq’s Calculus of Inductive Constructions. We walk through how Coq can be used to develop certified, executable program transformations over several statically-typed functional programming languages formalized with PHOAS; that is, each transformation has a machine-checked proof of type preservation and semantic preservation. Our examples include CPS translation and closure conversion for simply-typed lambda calculus, CPS translation for System F, and translation from a language with ML-style pattern matching to a simpler language with no variable-arity binding constructs. By avoiding the syntactic hassle associated with first-order representation techniques, we achieve a very high degree of proof automation.

Keyphrases

mechanized semantics parametric higher-order abstract syntax cps translation object language simpler language simply-typed lambda calculus new approach computer proof assistant ml-style pattern inductive construction high degree generalpurpose type theory phoas type semantic preservation binding construct executable program transformation traditional functional programming machine-checked proof variable-arity binding construct syntactic hassle meta language present parametric higher-order abstract syntax type preservation proof automation higherorder abstract syntax type theory several statically-typed functional programming language closure conversion first-order representation technique

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