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Coinduction in Coq
 Lecture Notes of TYPES Summer School 2005, Sweden, Volume II
, 2005
"... When providing a collection of constructors to define an inductive type, we actually also define a dual operation: a destructor. This destructor is always defined using the same structure of patternmatching, so that we have a tendency to forget that we do extend the “patternmatching ” capability w ..."
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Cited by 4 (0 self)
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definitions are functions that consume elements of the inductive type. The discipline of structural recursion imposes that recursive calls consume data that is obtained through the destructor. The inductive type uses the constructors and destructors in a specific way. Coinductive
An exercise in coinduction: Moessner’s theorem
"... We present a coinductive proof of Moessner’s theorem. This theorem describes the construction of the stream (1 n, 2 n, 3 n,...) (for n ≥ 1) out of the stream of natural numbers by repeatedly dropping and summing elements. Our formalisation consists of a direct translation of the operational descript ..."
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We present a coinductive proof of Moessner’s theorem. This theorem describes the construction of the stream (1 n, 2 n, 3 n,...) (for n ≥ 1) out of the stream of natural numbers by repeatedly dropping and summing elements. Our formalisation consists of a direct translation of the operational
Domain Theory
 Handbook of Logic in Computer Science
, 1994
"... Least fixpoints as meanings of recursive definitions. ..."
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Cited by 546 (25 self)
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Least fixpoints as meanings of recursive definitions.
A Tutorial on (Co)Algebras and (Co)Induction
 EATCS Bulletin
, 1997
"... . Algebraic structures which are generated by a collection of constructors like natural numbers (generated by a zero and a successor) or finite lists and trees are of wellestablished importance in computer science. Formally, they are initial algebras. Induction is used both as a definition pr ..."
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Cited by 269 (36 self)
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of various kinds. Such coalgebraic systems are common in computer science. And "coinduction" is the appropriate te...
A Tutorial on [Co]Inductive Types in Coq
, 1998
"... This document 1 is an introduction to the definition and use of inductive and coinductive types in the Coq proof environment. It explains how types like natural numbers and infinite streams are defined in Coq, and the kind of proof techniques that can be used to reason about them (case analysis, in ..."
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This document 1 is an introduction to the definition and use of inductive and coinductive types in the Coq proof environment. It explains how types like natural numbers and infinite streams are defined in Coq, and the kind of proof techniques that can be used to reason about them (case analysis
Automata and coinduction (an exercise in coalgebra
 LNCS
, 1998
"... The classical theory of deterministic automata is presented in terms of the notions of homomorphism and bisimulation, which are the cornerstones of the theory of (universal) coalgebra. This leads to a transparent and uniform presentation of automata theory and yields some new insights, amongst which ..."
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Cited by 86 (19 self)
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which coinduction proof methods for language equality and language inclusion. At the same time, the present treatment of automata theory may serve as an introduction to coalgebra.
Formal certification of a compiler backend, or: programming a compiler with a proof assistant
 IN PROC. 33RD ACM SYMPOSIUM ON PRINCIPLES OF PROGRAMMING LANGUAGES (POPL ’06
, 2006
"... This paper reports on the development and formal certification (proof of semantic preservation) of a compiler from Cminor (a Clike imperative language) to PowerPC assembly code, using the Coq proof assistant both for programming the compiler and for proving its correctness. Such a certified compile ..."
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This paper reports on the development and formal certification (proof of semantic preservation) of a compiler from Cminor (a Clike imperative language) to PowerPC assembly code, using the Coq proof assistant both for programming the compiler and for proving its correctness. Such a certified
Hardware Verification using coinduction in COQ
 In Proceedings of the International Conference on Theorem Proving in HigherOrder Logics
, 1999
"... . This paper presents a toolbox implemented in Coq and dedicated to the specification and verification of synchronous sequential devices. The use of Coq coinductive types underpins our methodology and leads to elegant and uniform descriptions of the circuits and their behaviours as well as clea ..."
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. This paper presents a toolbox implemented in Coq and dedicated to the specification and verification of synchronous sequential devices. The use of Coq coinductive types underpins our methodology and leads to elegant and uniform descriptions of the circuits and their behaviours as well
Results 1  10
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2,997