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Game semantics has provided adequate models for a variety of programming languages, in which types are interpreted as two-player games and programs as strategies. Melli`es (2018) suggested that such categories of games and strategies may be obtained as instances of a simple abstract construction on weak double categories. However, in the particular case of simple games, his construction slightly differs from the standard category. We refine the abstract construction using factorisation systems, and show that the new construction yields the standard category of simple games and strategies. Another perhaps surprising instance is Days convolution monoidal structure on the category of presheaves over a strict monoidal category.
Game semantics is a denotational semantics presenting compositionally the computational behaviour of various kinds of effectful programs. One of its celebrated achievement is to have obtained full abstraction results for programming languages with a
Game semantics is a rich and successful class of denotational models for programming languages. Most game models feature a rather intuitive setup, yet surprisingly difficult proofs of such basic results as associativity of composition of strategies.
Types in logic programming have focused on conservative approximations of program semantics by regular types, on one hand, and on type systems based on a prescriptive semantics defined for typed programs, on the other. In this paper, we define a new
The optimization phase of a compiler is responsible for transforming an intermediate representation (IR) of a program into a more efficient form. Modern optimizers, such as that used in the GraalVM compiler, use an IR consisting of a sophisticated gr
We propose a semantics for permutation equivalence in higher-order rewriting. This semantics takes place in cartesian closed 2-categories, and is proved sound and complete.