By considering the meaning of programs using mathematical structures such as categories, we can discuss properties of programs mathematically. In particular, it is important to understand computational effects such as program input/output, errors, and memory reading/writing mathematically. In this talk, we start by treating various algebraic structures in a unified manner in terms of category theory. By doing so, we observe that monads can be obtained naturally, and use them to interpret programs. Finally, we introduce an idea for extending algebraic structures and their applications to programs.

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