## Staff -KATSUMATA, Shin-ya-

Name

**KATSUMATA, Shin-ya**
Position
Assistant Professor

E-Mail
sinya (email address: add @kurims.kyoto-u.ac.jp)

Research

Shin-ya Katsumata is working on the semantics of programming
languages. His current research interests are the following.

I) He is working on relational models of programming languages with computational effects. He especially studies a method to construct logical relations for monads based on Lindley and Stark's TT-lifting. The unique feature of this method is flexibility: it takes a wide class of parameters, and by varying them we can derive many different and useful logical relations for monads. Exploiting this flexibility, he obtained several results about the semantics of the lambda calculus and computational effects: 1) a solution to the definability problem of the lambda calculus with coproducts in any bi-CCC. 2) a simple, yet general conditions to establish relationships between monadic semantics of functional languages with computational effects. 3) a characterisation of the class of preorders on monads, and their enumeration (joint work with Tetsuya Sato).

II) He studies attribute grammars from a categorical perspective. One contribution is to give a new categorical formulation of attribute grammars as first-order algebras in the compact closed category obtained by Joyal et al's Int construction on a traced symmetric monoidal category. He also gives a functorial characterisation of Ganzinger and Giegerich's descriptional composition.

III) Effect systems are a type theoretic framework to statically estimate side effects caused by programs. Since the unification of monadic types and effect annotations, several semantic structures for the effect-annotated monadic types were introduced. In [1], he proposed to use a generalisation of monads with grades for the denotational semantics of effect-annotated monadic types. In a recent joint work with Fujii (Univ. of Tokyo) and Melliès (Univ. Paris Denis Diderot), we gave Eilenberg-Moore and Kleisli resolutions of graded monads.

[1] Shin-ya Katsumata. Parametric Effect Monads and Semantics of Effect Systems. In Proc. POPL '14, pp. 633-645, ACM, 2014.

I) He is working on relational models of programming languages with computational effects. He especially studies a method to construct logical relations for monads based on Lindley and Stark's TT-lifting. The unique feature of this method is flexibility: it takes a wide class of parameters, and by varying them we can derive many different and useful logical relations for monads. Exploiting this flexibility, he obtained several results about the semantics of the lambda calculus and computational effects: 1) a solution to the definability problem of the lambda calculus with coproducts in any bi-CCC. 2) a simple, yet general conditions to establish relationships between monadic semantics of functional languages with computational effects. 3) a characterisation of the class of preorders on monads, and their enumeration (joint work with Tetsuya Sato).

II) He studies attribute grammars from a categorical perspective. One contribution is to give a new categorical formulation of attribute grammars as first-order algebras in the compact closed category obtained by Joyal et al's Int construction on a traced symmetric monoidal category. He also gives a functorial characterisation of Ganzinger and Giegerich's descriptional composition.

III) Effect systems are a type theoretic framework to statically estimate side effects caused by programs. Since the unification of monadic types and effect annotations, several semantic structures for the effect-annotated monadic types were introduced. In [1], he proposed to use a generalisation of monads with grades for the denotational semantics of effect-annotated monadic types. In a recent joint work with Fujii (Univ. of Tokyo) and Melliès (Univ. Paris Denis Diderot), we gave Eilenberg-Moore and Kleisli resolutions of graded monads.

[1] Shin-ya Katsumata. Parametric Effect Monads and Semantics of Effect Systems. In Proc. POPL '14, pp. 633-645, ACM, 2014.