Much work in the area of compiler calculation has focused on pure languages. While this simplifies the reasoning, it reduces the applicability. In this article, we show how an existing compiler calculation methodology can be naturally extended to ...

Formally verified compilers and formally verified static analyzers are a solution to the problem that certain industries face when they have to demonstrate to authorities that the object code they run truly corresponds to its source code and that ...

Monads and comonads are important constructions from category theory which find widespread application in computer science and other related disciplines. Distributive laws allow these constructions to interact compositionally. Such laws are not ...

Notions of computation can be modelled by monads. Algebraic effects offer a characterization of monads in terms of algebraic operations and equational axioms, where operations are basic programming features, such as reading or updating the state, ...

Semiring-valued fuzzy sets represent fuzzy objects with new value set structures, which make it possible to unify part of new and frequently used fuzzy structures. The theory of semiring-valued fuzzy sets uses some basic tools of category theory ...

Functional logic languages are a high-level approach to programming by combining the most important declarative features. They abstract from small-step operational details so that programmers can concentrate on the logical aspects of an application. ...

Monadic computations built by interpreting, or handling, operations of a free monad are a compelling formalism for modeling language semantics and defining the behaviors of effectful systems. The resulting layered semantics offer the promise of modular ...

The framework of quantitative equational logic has been successfully applied to reason about algebras whose carriers are metric spaces and operations are nonexpansive. We extend this framework in two orthogonal directions: algebras endowed with ...

Probability theory can be studied synthetically as the computational effect embodied by a commutative monad. In the recently proposed Markov categories, one works with an abstraction of the Kleisli category and then defines deterministic morphisms ...

We describe the canonical weak distributive law $\delta :\mathcal{S}\mathcal{P}\to \mathcal{P}\mathcal{S}$ of the powerset monad $\mathcal{P}$ over the S-left-semimodule monad $\mathcal{S}$, for a class of semirings S. We show that the composition of $\mathcal{P}$ with $\mathcal{S}$ by means of such $\delta$ yields almost the monad of convex subsets ...$\mathcal{}$$\mathbb{}\mathcal{}$${\mathcal{}}_{}$

This paper extends the Dijkstra monad framework, designed for writing specifications over effectful programs using monadic effects, to handle termination sensitive specifications over interactive programs. We achieve this by introducing base ...

We describe a monadification process for attribute grammars for more concisely written attribute equations, closer to the style of inference rules used in traditional typing and evaluation specifications. Inference rules specifying, for example, a ...

We discuss the relationship between monads and their known generalisation, graded monads, which are especially useful for modelling computational effects equipped with a form of sequential composition. Specifically, we ask if a graded monad can be ...

We introduce and study functor-functor and monad-comonad interaction laws as mathematical objects to describe interaction of effectful computations with behaviors of effect-performing machines. Monad-comonad interaction laws are monoid objects of the ...

Interaction trees (ITrees) are a general-purpose data structure for representing the behaviors of recursive programs that interact with their environments. A coinductive variant of “free monads,” ITrees are built out of uninterpreted events and their ...

We propose the first framework for defining relational program logics for arbitrary monadic effects. The framework is embedded within a relational dependent type theory and is highly expressive. At the semantic level, we provide an algebraic presentation ...

We investigate the Eilenberg-Moore algebras of the extended probabilistic powerdomain monad Vw over the category TOP₀ of T0 topological spaces and continuous maps. We prove that every Vw-algebra in our setting is a weakly locally convex sober ...

We show how various Haskell language features that are related to ambient effects can be modeled in Coq. For this purpose we build on previous work that demonstrates how to reason about existing Haskell programs by translating them into monadic Coq ...

In applications with a complex structure of side effects, effects should be dealt with modularly: components should be programmed against abstract effect interfaces that other components can instantiate as required, and reusable effect patterns should ...

This paper proposes a general semantic framework for verifying programs with arbitrary monadic side-effects using Dijkstra monads, which we define as monad-like structures indexed by a specification monad. We prove that any monad morphism between a ...