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Minlog - A Tool for Program Extraction Supporting Algebras and Coalgebras
[chapter]

2011
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Lecture Notes in Computer Science
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Case Study on Translator • Theorem: if rational

doi:10.1007/978-3-642-22944-2_29
fatcat:a52xuqzngjhxrirrqfleudyxgm
*a*∈ [−1, 1],*a*is approximable in SDS. • Proof by coinduction •*Extracting**a**program*from the proof • Experiments We describe the theorem in the following ... Examples of Free*Algebras*Totality*and*Cototality Total ideals of*a*base type are in*a*finite constructor expression. • True, False • 0, S(S(S0)) • Nil, L::R: Cototal ideals of*a*base type are total ...*Program**Extraction*via Realizability Interpretation • Decoration of Logical Connectives • → c , → nc , ∀ c , ∀ nc • c stands*for*computational, nc*for*non-computational • Logically same, Computationally ...##
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Constructive analysis, types and exact real numbers

2007
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Mathematical Structures in Computer Science
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We then put these models in

doi:10.1017/s0960129506005834
fatcat:kdehtcealnbszcfuszmcbzpdhu
*a*uniform framework using realisability, opening the door*for*the use of type theoretic*and**coalgebraic*constructions both in computing*and*reasoning about these computations ... We will present some of the problems*and*solutions of exact real arithmetic varying from concrete implementations, representation*and*algorithms to various models*for*real computation. ... Note that to be able to do*program**extraction*in*a*proof assistant, the logic of the assistant does not need to be constructive: Isabelle/HOL is based on*a*classical logic, but it*supports**program**extraction*...