Topic
Distributive law between monads
About: Distributive law between monads is a research topic. Over the lifetime, 95 publications have been published within this topic receiving 5303 citations.
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TL;DR: Calculi are introduced, based on a categorical semantics for computations, that provide a correct basis for proving equivalence of programs for a wide range of notions of computation.
Abstract: The λ-calculus is considered a 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 results. In this paper we introduce calculi, based on a categorical semantics for computations , that provide a correct basis for proving equivalence of programs for a wide range of notions of computation .
1,825 citations
05 Jun 1989
TL;DR: The author gives a calculus based on a categorical semantics for computations, which provides a correct basis for proving equivalence of programs, independent from any specific computational model.
Abstract: The lambda -calculus is considered a useful mathematical tool in the study of programming languages. However, if one uses beta eta -conversion to prove equivalence of programs, then a gross simplification is introduced. The author gives a calculus based on a categorical semantics for computations, which provides a correct basis for proving equivalence of programs, independent from any specific computational model. >
957 citations
TL;DR: In this article, the authors give an explicit description of the free completion EM ( K ) of a 2-category K under the Eilenberg-Moore construction, and demonstrate that much of the formal theory of monads can be deduced using only the universal property of this completion.
526 citations
08 Apr 2002
TL;DR: This work focuses on semantics for global and local state, showing that taking operations and equations as primitive yields a mathematical relationship that reflects their computational relationship.
Abstract: 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 that reflects their computational relationship.
318 citations
29 Sep 1998
TL;DR: This work shows that the type, region, and effect system of Talpin and Jouvelot carries over directly to an analogous system for monads, including a type and effect reconstruction algorithm.
Abstract: Gifford and others proposed an effect typing discipline to delimit the scope of computational effects within a program, while Moggi and others proposed monads for much the same purpose. Here we marry effects to monads, uniting two previously separate lines of research. In particular, we show that the type, region, and effect system of Talpin and Jouvelot carries over directly to an analogous system for monads, including a type and effect reconstruction algorithm. The same technique should allow one to transpose any effect systems into a corresponding monad system.
161 citations