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

Ulrich Berger, Kenji Miyamoto, Helmut Schwichtenberg, Monika Seisenberger
2011 Lecture Notes in Computer Science  
Case Study on Translator • Theorem: if rational 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  ... 
doi:10.1007/978-3-642-22944-2_29 fatcat:a52xuqzngjhxrirrqfleudyxgm

Constructive analysis, types and exact real numbers

HERMAN GEUVERS, MILAD NIQUI, BAS SPITTERS, FREEK WIEDIJK
2007 Mathematical Structures in Computer Science  
We then put these models in 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  ... 
doi:10.1017/s0960129506005834 fatcat:kdehtcealnbszcfuszmcbzpdhu