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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,...
We describe a sequent calculus μLJ with primitives for inductive and coinductive datatypes and equip it with reduction rules allowing a sound translation of Gödel’s system T. We introduce the notion of a μ-closed category, relying on a uniform interpretation of open μLJ formulas as strong functors. We show that any μ-closed category is a sound model for μLJ. We then turn to the construction of a concrete μ-closed category based on Hyland-Ong game semantics. The model relies on three main ingredients:...
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