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Monads have been employed in programming languages for modeling various language features, most importantly those that involve side effects. In particular, Haskell’s IO monad provides access to I/O operations and mutable variables, without compromising referential transparency. Cyclic definitions that involve monadic computations give rise to the concept of value-recursion, where the fixed-point computation takes place only over the values, without repeating or losing effects. In this paper, we...
Monads have been employed in programming languages for modeling
various language features, most importantly those that involve
side effects. In particular, Haskell's IO monad provides
access to I/O operations and mutable variables, without compromising
referential transparency. Cyclic definitions that involve monadic computations
give rise to the concept of value-recursion, where the fixed-point
computation takes place only over the values, without repeating or losing
effects. In this paper,...
As generalizations of separable and Frobenius algebras, separable and Frobenius monoidal Hom-algebras are introduced. They are all related to the Hom-Frobenius-separability equation (HFS-equation). We characterize these two Hom-algebraic structures by the same central element and different normalizing conditions, and the structure of these two types of monoidal Hom-algebras is studied. The Nakayama automorphisms of Frobenius monoidal Hom-algebras are considered.
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