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- Murdoch James Gabbay, Andrew M. Pitts
- Formal Aspects of Computing
- 2002

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… (More)

- Andrew M. Pitts
- TACS
- 2001

This paper formalises within first-order logic some common practices in computer science to do with representing and reasoning about syntactical structures involving lexically scoped binding constructs. It introduces Nominal Logic, a version of first-order many-sorted logic with equality containing primitives for renaming via name-swapping, for freshness of… (More)

- Andrew M. Pitts
- Inf. Comput.
- 1996

New tools are presented for reasoning about properties of recursively de-ned domains. We work within a general, category-theoretic framework for various notions of`relation' on domains and for actions of domain construc-tors on relations. Freyd's analysis of recursive types in terms of a property of mixed initiality//nality is transferred to a corresponding… (More)

- Andrew M. Pitts, Ian David Bede Stark
- MFCS
- 1993

The research reported in this paper is concerned with the problem of reasoning about properties of higher order functions involving state. It is motivated by the desire to identify what, if any, are the difficulties created purely by locality of state, independent of other properties such as side-effects, exceptional termination and non-termination due to… (More)

- Christian Urban, Andrew M. Pitts, Murdoch James Gabbay
- Theor. Comput. Sci.
- 2004

We present a generalisation of first-order unification to the practically important case of equations between terms involving binding operations. A substitution of terms for variables solves such an equation if it makes the equated terms α-equivalent, i.e. equal up to renaming bound names. For the applications we have in mind, we must consider the simple,… (More)

- Murdoch James Gabbay, Andrew M. Pitts
- LICS
- 1999

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, -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… (More)

- Andrew M. Pitts, Murdoch James Gabbay
- MPC
- 2000

Languages such as ML or Lisp permit the use of recursively defined function expressions with locally declared storage locations. Although this can be very convenient from a programming point of view it severely complicates the properties of program equivalence even for relatively simple fragments of such languages—such as the simply typed fragment of… (More)

- Andrew M. Pitts
- 1995

FreshML extends ML with elegant and practical constructs for declaring and manipulating syntactical data involving statically scoped binding operations. User-declared FreshML datatypes involving binders are concrete, in the sense that values of these types can be deconstructed by matching against patterns naming bound variables explicitly. This may have the… (More)