# Notions of Computation and Monads

@article{Moggi1991NotionsOC,
author={Eugenio Moggi},
journal={Inf. Comput.},
year={1991},
volume={93},
pages={55-92}
}
• E. Moggi
• Published 1 July 1991
• Computer Science
• Inf. Comput.
1,836 Citations

## Tables from this paper

• Computer Science, Mathematics
• 2005
Using the notion of module over a monad, a category of exponential monads is built, which can be understood as the category of lambda-calculi, and it is proved that it has an initial object (the pure untypedlambda-calculus).
Adequacy for Infinitary Algebraic Effects (Abstract)
Moggi endowed the computational λ-calculus with an effect-oriented denotational semantics by taking the denotations of terms to be morphisms in the Kleisli category of the monad.
A typed, algebraic, computational lambda-calculus†
• B. Valiron
• Mathematics
Mathematical Structures in Computer Science
• 2013
This paper develops a categorical analysis of a general simply typed lambda-calculus endowed with the structure of a module and develops various concrete models for both the case without fixpoints and for the case with them.
• Mathematics
FoSSaCS
• 2001
This work considers call-by-value PCF with-- and without--recursion, an extension of λc with arithmetic, and proves general adequacy theorems, and illustrates these with two examples: nond determinism and probabilistic nondeterminism.
• Mathematics
FoSSaCS
• 2002
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.
Semantics for Algebraic Operations
• Mathematics, Computer Science
MFPS
• 2001
Notion of strong monad in computing
• Kruna Ratkovic
• Mathematics
2018 23rd International Scientific-Professional Conference on Information Technology (IT)
• 2018
This survey gives a brief introduction of the notion of a strong monad in a categorical framework together with some illustrative examples in the theory of computation.
Instances of Computational Effects: An Algebraic Perspective
• S. Staton
• Mathematics
2013 28th Annual ACM/IEEE Symposium on Logic in Computer Science
• 2013
A syntactic framework with variable binding is developed that allows us to describe equations between programs while taking into account the idea that there may be different instances of a particular computational effect.
Semantics of a Typed Algebraic Lambda-Calculus
This paper proposes a semantic analysis of a general simply-typed lambda-calculus endowed with a structure of vector space and sketches an algebraic vectorial PCF and its possible denotational interpretations.
Unifying Theories of Programming with Monads
A simple functional programming approach to the combination of probabilistic and nondeterministic choice in program calculi is presented, based on algebraic theories of computational effects, which makes use of the powerful abstraction facilities of modern functional languages.

## References

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• Computer Science
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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.
New foundations for fixpoint computations
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[1990] Proceedings. Fifth Annual IEEE Symposium on Logic in Computer Science
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A novel higher-order typed constructive predicate logic for fixpoint computations which exploits the categorical semantics of computations introduced by E. Moggi (1989) and contains a strong version
A category-theoretic account of program modules
• E. Moggi
• Computer Science
Mathematical Structures in Computer Science
• 1991
It is illustrated how ML can be extended to support higher order modules, by developing a category-theoretic semantics for a calculus of modules with dependent types.
Computational foundations of basic recursive function theory
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The purpose of the present paper is to set up a categorical framework in which the known techniques for solving equations find a natural place, generalizing from least fixed-points of continuous functions over cpos to initial ones of continuous functors over $\omega$-categories.