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Representations of Stream Processors Using Nested Fixed Points

Neil Ghani ; Peter Hancock ; Dirk Pattinson.

We define representations of continuous functions on infinite streams of discrete values, both in the case of discrete-valued functions, and in the case of stream-valued functions. We define also an operation on the representations of two continuous functions between streams that yields a&nbsp;[&hellip;]

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Generic Fibrational Induction

Neil Ghani ; Patricia Johann ; Clement Fumex.

This paper provides an induction rule that can be used to prove properties of data structures whose types are inductive, i.e., are carriers of initial algebras of functors. Our results are semantic in nature and are inspired by Hermida and Jacobs' elegant algebraic formulation of induction for&nbsp;[&hellip;]

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Refining Inductive Types

Robert Atkey ; Patricia Johann ; Neil Ghani.

Dependently typed programming languages allow sophisticated properties of data to be expressed within the type system. Of particular use in dependently typed programming are indexed types that refine data by computationally useful information. For example, the N-indexed type of vectors refines lists&nbsp;[&hellip;]

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