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Game Semantics for Martin-Löf Type Theory
Norihiro Yamada
We present a new game semantics for Martin-Löf type theory (MLTT), our aim is to give a mathematical and intensional explanation of MLTT. Specifically, we propose a category with f…
Game-theoretic Interpretation of Type Theory Part II: Uniqueness of Identity Proofs and Univalence
Norihiro Yamada
In the present paper, based on the previous work (Part I), we present a game semantics for the intensional variant of intuitionistic type theory that refutes the principle of uniqu…
Game-theoretic Interpretation of Intuitionistic Type Theory
Norihiro Yamada
We present a game semantics for intuitionistic type theory. Specifically, we propose categories with families of a new variant of games and strategies for both extensional and inte…
Dynamic Game Semantics
Norihiro Yamada, Samson Abramsky
The present paper gives a mathematical, in particular, syntax-independent, formulation of intensionality and dynamics of computation in terms of games and strategies. Specifically,…