A New Approach to Abstract Syntax Involving Binders

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A New Approach to Abstract Syntax Involving Binders (1999)

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by Murdoch Gabbay , Andrew Pitts

Venue:	In 14th Annual Symposium on Logic in Computer Science
Citations:	177 - 20 self

BibTeX

@INPROCEEDINGS{Gabbay99anew,
    author = {Murdoch Gabbay and Andrew Pitts},
    title = {A New Approach to Abstract Syntax Involving Binders},
    booktitle = {In 14th Annual Symposium on Logic in Computer Science},
    year = {1999},
    pages = {214--224},
    publisher = {IEEE Computer Society Press}
}

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Abstract

Syntax Involving Binders Murdoch Gabbay Cambridge University DPMMS Cambridge CB2 1SB, UK M.J.Gabbay@cantab.com Andrew Pitts Cambridge University Computer Laboratory Cambridge CB2 3QG, UK ap@cl.cam.ac.uk Abstract The Fraenkel-Mostowski permutation model of set theory with atoms (FM-sets) can serve as the semantic basis of meta-logics for specifying and reasoning about formal systems involving name binding, ff-conversion, capture avoiding substitution, and so on. We show that in FM-set theory one can express statements quantifying over `fresh' names and we use this to give a novel set-theoretic interpretation of name abstraction. Inductively defined FM-sets involving this name-abstraction set former (together with cartesian product and disjoint union) can correctly encode object-level syntax modulo ff-conversion. 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 n...

Keyphrases

abstract syntax involving binder new approach semantic basis object-level syntax modulo ff-conversion cartesian product fraenkel-mostowski permutation model name abstraction algebraic data type uk m.j.g formal system binding operator standard theory name binding novel set-theoretic interpretation fm-set theory

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