Notions of computation and monads

Notions of Computation and Monads

The λ-calculus is considered an useful mathematical tool in the study of programming languages, since programs can be identified with λ-terms. However, if one goes further and uses βη-conversion to prove equivalence of programs, then a gross simplification is introduced (programs are identified with total functions from values to values), that may jeopardise the applicability of theoretical res...

Notions of Computation Determine Monads

We model notions of computation using algebraic operations and equations. We show that these generate several of the monads of primary interest that have been used to model computational effects, with the striking omission of the continuations monad. We focus on semantics for global and local state, showing that taking operations and equations as primitive yields a mathematical relationship tha...

Notions of Bidirectional Computation and Entangled State Monads

Bidirectional transformations (bx) support principled consistency maintenance between data sources. Each data source corresponds to one perspective on a composite system, manifested by operations to ‘get’ and ‘set’ a view of the whole from that particular perspective. Bx are important in a wide range of settings, including databases, interactive applications, and model-driven development. We sh...

Notions of omputation and monads

Parameterised Notions of Computation

Moggi’s Computational Monads and Power et al ’s equivalent notion of Freyd category have captured a large range of computational effects present in programming languages. Examples include non-termination, non-determinism, exceptions, continuations, side-effects and input/output. We present generalisations of both computational monads and Freyd categories, which we call parameterised monads and ...