Related papers: Localisable Monads
In the study of computational effects, it is important to consider the notion of computational effects with parameters. The need of such a notion arises when, for example, statically estimating the range of effects caused by a program, or…
Monads are a useful tool for structuring effectful features of computation such as state, non-determinism, and continuations. In the last decade, several generalisations of monads have been suggested which provide a more fine-grained model…
Monads in category theory are algebraic structures that can be used to model computational effects in programming languages. We show how the notion of "centre", and more generally "centrality", i.e. the property for an effect to commute…
Graded monads refine traditional monads using effect annotations in order to describe quantitatively the computational effects that a program can generate. They have been successfully applied to a variety of formal systems for reasoning…
Monads provide a simple and concise interface to user-defined computational effects in functional programming languages. This enables equational reasoning about effects, abstraction over monadic interfaces and the development of monad…
Monads are a popular tool for the working functional programmer to structure effectful computations. This paper presents polymonads, a generalization of monads. Polymonads give the familiar monadic bind the more general type forall a,b. L a…
This thesis revolves around an area of computer science called "semantics". We work with operational semantics, equational theories, and denotational semantics. The first contribution of this thesis is a study of the commutativity of…
Type-and-effect systems incorporate information about the computational effects, e.g., state mutation, probabilistic choice, or I/O, a program phrase may invoke alongside its return value. A semantics for type-and-effect systems involves a…
Free monads (and their variants) have become a popular general-purpose tool for representing the semantics of effectful programs in proof assistants. These data structures support the compositional definition of semantics parameterized by…
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…
The modern theory of functional programming languages uses monads for encoding computational side-effects and side-contexts, beyond bare-bone program logic. Even though quantum computing is intrinsically side-effectful (as in quantum…
Partial Combinatory Algebras (PCAs) provide a foundational model of the untyped $\lambda$-calculus and serve as the basis for many notions of computability, such as realizability theory. However, PCAs support a very limited notion of…
Computational effects are commonly modelled by monads, but often a monad can be presented by an algebraic theory of operations and equations. This talk is about monads and algebraic theories for languages for inference, and their…
It is well established that equational algebraic theories, and the monads they generate, can be used to encode computational effects. An important insight of Power and Shkaravska is that comodels of an algebraic theory T -- i.e., models in…
We develop the theory of strong and commutative monads in the 2-dimensional setting of bicategories. This provides a framework for the analysis of effects in many recent models which form bicategories and not categories, such as those based…
One can perform equational reasoning about computational effects with a purely functional programming language thanks to monads. Even though equational reasoning for effectful programs is desirable, it is not yet mainstream. This is partly…
This paper presents equational-based logics for proving first order properties of programming languages involving effects. We propose two dual inference system patterns that can be instanciated with monads or comonads in order to be used…
We introduce the abstract notions of "monadic operational semantics", a small-step semantics where computational effects are modularly modeled by a monad, and "type-and-effect system", including "effect types" whose interpretation lifts…
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…
The original purpose of component-based development was to provide techniques to master complex software, through composition, reuse and parametrisation. However, such systems are rapidly moving towards a level in which software becomes…