A Tutorial on Co-induction and Functional Programming (1994) [22 citations — 1 self]
http://www.dcs.ed.ac.uk/home/dts/aps/papers/gordon
http://www.dcs.ed.ac.uk/~dts/fps/papers/gordon.ps.
http://www.dcs.ed.ac.uk/home/dts/fps/papers/gordon
http://www.cl.cam.ac.uk/Research/Papers/adg/fp94.p
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author = {Andrew D. Gordon},
title = {A Tutorial on Co-induction and Functional Programming},
booktitle = {In Glasgow functional programming workshop},
year = {1994},
pages = {78--95},
publisher = {Springer}
}
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Abstract:
Co-induction is an important tool for reasoning about unbounded structures. This tutorial explains the foundations of co-induction, and shows how it justifies intuitive arguments about lazy streams, of central importance to lazy functional programmers. We explain from first principles a theory based on a new formulation of bisimilarity for functional programs, which coincides exactly with Morris-style contextual equivalence. We show how to prove properties of lazy streams by co-induction and derive Bird and Wadler's Take Lemma, a well-known proof technique for lazy streams. The aim of this paper is to explain why co-inductive definitions and proofs by co-induction are useful to functional programmers. Co-induction is dual to induction. To say a set is inductively defined just means it is the least solution of a certain form of inequation. For instance, the set of natural numbers N is the least solution (ordered by set inclusion, `) of the inequation f0g [ fS(x) j x 2 Xg ` X: (1) Th...
