A new approach to abstract syntax with variable binding

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A new approach to abstract syntax with variable binding (2002)

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by Murdoch J. Gabbay , Andrew M. Pitts

Venue:	Formal Aspects of Computing
Citations:	287 - 63 self

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@ARTICLE{Gabbay02anew,
    author = {Murdoch J. Gabbay and Andrew M. Pitts},
    title = {A new approach to abstract syntax with variable binding},
    journal = {Formal Aspects of Computing},
    year = {2002},
    volume = {13},
    pages = {341--363}
}

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Abstract

Abstract. The permutation model of set theory with atoms (FM-sets), devised by Fraenkel and Mostowski in the 1930s, supports notions of ‘name-abstraction ’ and ‘fresh name ’ that provide a new way to represent, compute with, and reason about the syntax of formal systems involving variable-binding operations. Inductively defined FM-sets involving the name-abstraction set former (together with Cartesian product and disjoint union) can correctly encode syntax modulo renaming of bound variables. In this way, the standard theory of algebraic data types can be extended to encompass signatures involving binding operators. In particular, there is an associated notion of structural recursion for defining syntax-manipulating functions (such as capture avoiding substitution, set of free variables, etc.) and a notion of proof by structural induction, both of which remain pleasingly close to informal practice in computer science. 1.

Keyphrases

variable binding new approach cartesian product structural induction variable-binding operation bound variable standard theory support notion algebraic data type formal system syntax modulo renaming fresh name structural recursion associated notion computer science informal practice free variable syntax-manipulating function new way permutation model binding operator

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