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arXiv · 1309.0706

A Report on Realizability

Walter Ferrer Santos·Mauricio Guillermo·Octavio Malherbe
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Abstract

Besides recalling the basic definitions of Realizability Lattices, Abstract Krivine Structures, Ordered Combinatory Algebras and Tripos and reviewing its relationships, we propose a new foundational framework for realizability. Motivated by Streicher's paper "Krivine's Classical Realizability from a Categorical Perspective" [9], we define the concept of Krivine's Ordered Combinatory Algebras (kOKA) as a common platform that is strong enough to do both: categorical and computational semantics. The OCAs produced by Streicher from AKSs in [9] are particular cases of kOKAs.

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Walter Ferrer Santos, Mauricio Guillermo, Octavio Malherbe. 2013-09-30. A Report on Realizability. https://arxiv.org/abs/1309.0706

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