Continuous Functions on Final Coalgebras

Ghani, Neil; Hancock, Peter; Pattinson, Dirk

doi:10.1016/j.entcs.2006.06.009

Cited by 17 publications

(21 citation statements)

References 4 publications

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“…The special case where m = 0 interprets a tree in C n as an n-ary stream transformer. The special case n = m = 1 was treated in [GHP06], however, without applications to exact real number computation. In [GHP06], the program was 'guessed' and then verified, whereas we extracted the program from a proving making verification unnecessary.…”

Section: Coinductive Definition Of Uniform Continuitymentioning

confidence: 99%

“…Since the representing tree is a pure data structure (without function component) a lazy programming language, like Haskell, will memoise computations which may improve performance in certain situations. A similar representation of stream transformers has been studied in [GHP06].…”

Section: Introductionmentioning

confidence: 99%

“…The extracted algorithms are represented by finitely branching non-wellfounded trees which, if executed in a lazy programming language, give rise to memoised algorithms. These trees turn out to be a generalisation of the data structure studied in [GHP06], and the extracted program from the proof of closure under composition is a generalisation of the tree composing program defined in [GHP06].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

From Coinductive Proofs to Exact Real Arithmetic

Berger

2009

Computer Science Logic

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Abstract. We give a coinductive characterisation of the set of continuous functions defined on a compact real interval, and extract certified programs that construct and combine exact real number algorithms with respect to the binary signed digit representation of real numbers. The data type corresponding to the coinductive definition of continuous functions consists of finitely branching non-wellfounded trees describing when the algorithm writes and reads digits. This is a pilot study in using proof-theoretic methods for obtaining certified algorithms in exact real arithmetic.

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Section: Coinductive Definition Of Uniform Continuitymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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From Coinductive Proofs to Exact Real Arithmetic

Berger

2009

Computer Science Logic

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“…For our type-0 representation of uniformly continuous functions we adopt socalled read-write machines [3] or stream processors [11,12]. These are W-cototal R W -total ideals where…”

Section: Data Types Of Uniformly Continuous Functionsmentioning

confidence: 99%

“…Related work Nested definitions are used by Ghani, Hancock and Pattinson [11,12] to define uniformly continuous functions. They are also studied by Bird and Meertens [6] from a purely programming perspective.…”

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confidence: 99%

Program Extraction from Nested Definitions

Miyamoto

Forsberg

Schwichtenberg

2013

Interactive Theorem Proving

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Abstract. Minlog is a proof assistant which automatically extracts computational content in an extension of Gödel's T from formalized proofs. We report on extending Minlog to deal with predicates defined using a particular combination of induction and coinduction, via so-called nested definitions. In order to increase the efficiency of the extracted programs, we have also implemented a feature to translate terms into Haskell programs. To illustrate our theory and implementation, a formalisation of a theory of uniformly continuous functions due to Berger is presented.

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Mixed Inductive/Coinductive Types and Strong Normalization

Abel¹

Programming Languages and Systems

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Abstract. We introduce the concept of guarded saturated sets, saturated sets of strongly normalizing terms closed under folding of corecursive functions. Using this tool, we can model equi-inductive and equicoinductive types with terminating recursion and corecursion principles. Two type systems are presented: Mendler (co)iteration and sized types. As an application we show that we can directly represent the mixed inductive/coinductive type of stream processors with associated recursive operations.

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Continuous Functions on Final Coalgebras

Cited by 17 publications

References 4 publications

From Coinductive Proofs to Exact Real Arithmetic

From Coinductive Proofs to Exact Real Arithmetic

Program Extraction from Nested Definitions

Mixed Inductive/Coinductive Types and Strong Normalization

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