Monoidal logics are logics that can be seen as specific instances of monoidal categories. They are constructed using specific rules and axiom schemata that allow to make explicit the monoidal structure of the logics. Among monoidal logics, we find Cartesian logics, which are instances of Cartesian categories. As it happens, many paradoxes in epistemic, deontic and action logics can be related t...

Wadler and Thiemann unified type-and-effect systems with monadic semantics via a syntactic correspondence and soundness results with respect to an operational semantics. They conjecture that a general, “coherent” denotational semantics can be given to unify effect systems with a monadic-style semantics. We provide such a semantics based on the novel structure of an indexed monad, which we intro...

A tension in language design has been between simple semantics on the one hand, and rich possibilities for side-effects, exception handling and so on on the other. The introduction of monads has made a large step towards reconciling these alternatives. First proposed by Moggi as a way of structuring semantic descriptions, they were adopted by Wadler to structure Haskell programs. Monads have be...

Language-based approaches to security typically use static type systems to control information flow, relying on type inference to distinguish secure programs from insecure ones. This paper advocates a novel approach to language-based security: by structuring software with monads (a form of abstract data type for effects), we are able to maintain separation of effects by construction. The thesis...

The formal theory of monads, originally introduced by Street in [22] and developed further by Lack and Street [17] provides a mathematically efficient treatment of several aspects of the theory of monads [1]. For example, it exhibits a universal property of the category of algebras for a monad and provides a clear explanation for Beck’s axioms for a distributive law [2]. Over the past few years...