Andrew M. Pitts

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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)
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)
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)
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)
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)
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)