Programming languages and their definition
Programming languages and their definition
Introduction to higher order categorical logic
Introduction to higher order categorical logic
Notions of computation and monads
Information and Computation
Handbook of logic in computer science (vol. 3)
Algorithms on Trees and Graphs
Algorithms on Trees and Graphs
Theoretical Computer Science
Mathematical Structures in Computer Science
Compactly generated domain theory
Mathematical Structures in Computer Science
Programming in Haskell
A Convenient Category of Domains
Electronic Notes in Theoretical Computer Science (ENTCS)
Infinite sets that admit fast exhaustive search
LICS '07 Proceedings of the 22nd Annual IEEE Symposium on Logic in Computer Science
Algorithmic Game Theory
Understanding and using spector's bar recursive interpretation of classical analysis
CiE'06 Proceedings of the Second conference on Computability in Europe: logical Approaches to Computational Barriers
What sequential games, the tychonoff theorem and the double-negation shift have in common
Proceedings of the third ACM SIGPLAN workshop on Mathematically structured functional programming
Computational interpretations of analysis via products of selection functions
CiE'10 Proceedings of the Programs, proofs, process and 6th international conference on Computability in Europe
The Peirce translation and the double negation shift
CiE'10 Proceedings of the Programs, proofs, process and 6th international conference on Computability in Europe
APLAS'11 Proceedings of the 9th Asian conference on Programming Languages and Systems
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Bar recursion arises in constructive mathematics, logic, proof theory and higher-type computability theory. We explain bar recursion in terms of sequential games, and show how it can be naturally understood as a generalisation of the principle of backward induction that arises in game theory. In summary, bar recursion calculates optimal plays and optimal strategies, which, for particular games of interest, amount to equilibria. We consider finite games and continuous countably infinite games, and relate the two. The above development is followed by a conceptual explanation of how the finite version of the main form of bar recursion considered here arises from a strong monad of selections functions that can be defined in any cartesian closed category. Finite bar recursion turns out to be a well-known morphism available in any strong monad, specialised to the selection monad.