## Coalgebraic Theories of Sequences in PVS (1998)

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### BibTeX

@MISC{Hensel98coalgebraictheories,

author = {Ulrich Hensel and Bart Jacobs},

title = {Coalgebraic Theories of Sequences in PVS},

year = {1998}

}

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### Abstract

This paper explains the setting of an extensive formalisation of the theory of sequences (finite and infinite lists of elements of some data type) in the Prototype Verification System pvs. This formalisation is based on the characterisation of sequences as a final coalgebra, which is used as an axiom. The resulting theories comprise standard operations on sequences like composition (or concatenation), filtering, flattening, and their properties. They also involve the prefix ordering and proofs that sequences form an algebraic complete partial order. The finality axiom gives rise to various reasoning principles, like bisimulation, simulation, invariance, and induction for admissible predicates. Most of the proofs of equality statements are based on bisimulations, and most of the proofs of prefix order statements use simulations. Some significant aspects of these theories are described in detail. This coalgebraic formalisation of sequences is presented as a concrete example that shows t...