Year: 2020
Type: article
Abstract: The present work achieves a mathematical, in particularsyntax-independent, formulation ofdynamicsandintensionalityof computation in terms ofgamesandstrategies. Specifically, we givegame semanticsof a higher-order programming language that distinguishes programmes with the same value yet different algorithms (or intensionality) and thehiding operationon strategies that precisely corresponds to the (small-step) operational semantics (or dynamics) of the language. Categorically, our games and strategies give rise to acartesian closed bicategory, and our game semantics forms an instance of a bicategorical generalisation of the standard interpretation of functional programming languages in cartesian closed categories. This work is intended to be a step towards a mathematical foundation of intensional and dynamic aspects of logic and computation; it should be applicable to a wide range of logics and computations.
Authors: Norihiro Yamada, Samson Abramsky
Institutions: University of Minnesota, University of Oxford
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Award: G5893358924
OpenAlex ID: W2895976765