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47
Practical Coinduction
, 2012
"... Induction is a wellestablished proof principle that is taught in most undergraduate programs in mathematics and computer science. In computer science, it is used primarily to reason about inductivelydefined datatypes such as finite lists, finite trees, and the natural numbers. Coinduction is the d ..."
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Cited by 1 (0 self)
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Induction is a wellestablished proof principle that is taught in most undergraduate programs in mathematics and computer science. In computer science, it is used primarily to reason about inductivelydefined datatypes such as finite lists, finite trees, and the natural numbers. Coinduction
Induction and Recursion on Datatypes
, 1995
"... this paper we introduce a notion of induction over an arbitrary datatype and go on to show how the notion is used to establish unicity of a certain (broad) class of equations. Our overall goal is to develop a calculational theory of mathematical induction. That is we want to be able to calculate rel ..."
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Cited by 17 (7 self)
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developed in this paper is general and not specific to any particular datatype. We define a notion of F reductivity (so called in order to avoid confusion with existing notions of inductivity), where F stands for a "relator", and show that F reductive relations always exist, whatever the value
Residual theory in λcalculus: A formal development
 Journal of Functional Programming
, 1994
"... Abstract. We present the complete development, in Gallina, of the residual theory of βreduction in pure λcalculus. The main result is the Prism Theorem, and its corollary Lévy’s Cube Lemma, a strong form of the parallelmoves lemma, itself a key step towards the confluence theorem and its usual co ..."
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Cited by 23 (2 self)
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calculus with recursive definitions, inductively defined datatypes, and inductive predicate definitions reminiscent of logic programming. The development presented here was fully checked in the current distribution version Coq V5.8. We just state the lemmas in the order in which they are proved, omitting
Datatype Generic Programming in F#
"... Datatype generic programming enables programmers to define functions by induction over the structure of types on which these functions operate. This paper presents a library for datatype generic programming in F#, built on top of the.NET reflection mechanism. The generic functions defined using thi ..."
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Datatype generic programming enables programmers to define functions by induction over the structure of types on which these functions operate. This paper presents a library for datatype generic programming in F#, built on top of the.NET reflection mechanism. The generic functions defined using
PolyP  a polytypic programming language extension
 POPL '97: The 24th ACM SIGPLANSIGACT Symposium on Principles of Programming Languages
, 1997
"... Many functions have to be written over and over again for different datatypes, either because datatypes change during the development of programs, or because functions with similar functionality are needed on different datatypes. Examples of such functions are pretty printers, debuggers, equality fu ..."
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Cited by 188 (32 self)
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functions, unifiers, pattern matchers, rewriting functions, etc. Such functions are called polytypic functions. A polytypic function is a function that is defined by induction on the structure of userdefined datatypes. This paper extends a functional language (a subset of Haskell) with a construct
Iteration and Coiteration Schemes for HigherOrder and Nested Datatypes
"... This article studies the implementation of inductive and coinductive constructors of higher kinds (higherorder nested datatypes) in typed term rewriting, with emphasis on the choice of the iteration and coiteration constructions to support as primitive. We propose and compare several wellbehaved e ..."
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This article studies the implementation of inductive and coinductive constructors of higher kinds (higherorder nested datatypes) in typed term rewriting, with emphasis on the choice of the iteration and coiteration constructions to support as primitive. We propose and compare several well
A Coinduction Principle for Recursively Defined Domains
 THEORETICAL COMPUTER SCIENCE
, 1992
"... This paper establishes a new property of predomains recursively defined using the cartesian product, disjoint union, partial function space and convex powerdomain constructors. We prove that the partial order on such a recursive predomain D is the greatest fixed point of a certain monotone operator ..."
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Cited by 43 (3 self)
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, whereas in the second case they are his applicative bisimulations. The coinduction principle also provides an apparently useful tool for reasoning about equality of elements of recursively defined datatypes in (strict or lazy) higher order functional programming languages.
Verification of Programs on Truly Nested Datatypes in Intensional Type Theory
"... Nested datatypes are families of datatypes that are indexed over all types such that the constructors may relate different family members (unlike the homogeneous lists). Moreover, even the family name may be involved in the expression that gives the index the argument type of the constructor refers ..."
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by polymorphic typing. And they are generic in the sense that no specific syntactic form of the underlying datatype “functor ” is required. However, there have not been induction principles for the verification of the programs thus obtained although they are wellknown in the usual model of initial algebras
Defining Inductive Operators using Distances over Lists ∗
"... Instancebased learning is one of the most widelyused paradigms in the field of automatic induction. Several reasons back its popularity, among them, we must stand out its capability to cope with different data representations: these methods are designed on the basis of a similarity principle (simi ..."
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Cited by 1 (0 self)
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Instancebased learning is one of the most widelyused paradigms in the field of automatic induction. Several reasons back its popularity, among them, we must stand out its capability to cope with different data representations: these methods are designed on the basis of a similarity principle
Relational Properties of Domains
 Information and Computation
, 1996
"... New tools are presented for reasoning about properties of recursively defined domains. We work within a general, categorytheoretic framework for various notions of `relation' on domains and for actions of domain constructors on relations. Freyd's analysis of recursive types in terms of a ..."
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Cited by 115 (6 self)
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semantics for functional programming languages with userdeclared datatypes. We show how the initiality/finality property of invariant relations can be specialized to yield an induction principle for admissible subsets of recursively defined domains, generalizing the principle of structural induction
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