A New Approach to Abstract Syntax Involving Binders (1999)
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| Venue: | In 14th Annual Symposium on Logic in Computer Science |
| Citations: | 127 - 14 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...
