Parametric Higher-Order Abstract Syntax for Mechanized Semantics

Parametric Higher-Order Abstract Syntax for Mechanized Semantics

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by Adam Chlipala

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TITLE	Parametric Higher-Order Abstract Syntax for Mechanized Semantics	SVM HeaderParse 0.2
AUTHOR NAME	Adam Chlipala	SVM HeaderParse 0.2
AUTHOR AFFIL	Harvard University, Cambridge, MA	SVM HeaderParse 0.2
AUTHOR ADDR	USA	SVM HeaderParse 0.2
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. Categories and Subject Descriptors F.3.1 [Logics and meanings	SVM HeaderParse 0.2
CITATIONS	33 found	ParsCit 1.0