Inÿnite trees form a free completely iterative theory over any given signature—this fact, proved by Elgot, Bloom and Tindell, turns out to be a special case of a much more general categorical result exhibited in the present paper. We prove that whenever an endofunctor H of a category has ÿnal coalgebras for all functors H () + X , then those coalgebras, TX… (More)
Rippling is a radically new technique for the automation of mathematical reasoning. It is widely applicable whenever a goal is to be proved from one or more syntactically similar givens. The goal is manipulated to resemble the givens more closely, so that they can be used in its proof. The goal is annotated to indicate which subexpressions are to be moved… (More)
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Introduction The original motivation 1 for the work described in this paper was to determine the proof theoretic strength of the type theories implemented in the proof development systems Lego and Coq, Luo and Pollack 92, Barras et al 96]. These type theories combine the impredicative type of propositions 2 , from the calculus of constructions, Coquand 90],… (More)
We describe the nal universe approach to the character-isation of semantic universes and illustrate it by giving char-acterisations of the universes of CCS and CSP processes.
We present a generalisation of the type-theoretic interpretation of constructive set theory into Martin-Löf type theory. The original interpretation treated logic in Martin-Löf type theory via the propositions-as-types interpretation. The generalisation involves replacing Martin-Löf type theory with a new type theory in which logic is treated as primitive.… (More)