## 1,836 Citations

MODULES OVER MONADS, MONADIC SYNTAX AND THE CATEGORY OF UNTYPED LAMBDA-CALCULI

- 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)

- Computer ScienceCALCO
- 2009

Moggi endowed the computational Î»-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-calculusâ€

- MathematicsMathematical 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.

Adequacy for Algebraic Effects

- MathematicsFoSSaCS
- 2001

This work considers call-by-value PCF with-- and without--recursion, an extension of Î»c with arithmetic, and proves general adequacy theorems, and illustrates these with two examples: nond determinism and probabilistic nondeterminism.

Notions of Computation Determine Monads

- MathematicsFoSSaCS
- 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.

Notion of strong monad in computing

- Mathematics2018 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

- Mathematics2013 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

- Computer ScienceDCM
- 2010

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

- Computer ScienceUTP
- 2012

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

SHOWING 1-10 OF 60 REFERENCES

Computational lambda-calculus and monads

- Computer Science[1989] Proceedings. Fourth Annual Symposium on Logic in Computer Science
- 1989

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

- Computer Science[1990] Proceedings. Fifth Annual IEEE Symposium on Logic in Computer Science
- 1990

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 versionâ€¦

A category-theoretic account of program modules

- Computer ScienceMathematical 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

- Mathematics[1988] Proceedings. Third Annual Information Symposium on Logic in Computer Science
- 1988

The category-theoretic solution of recursive domain equations

- Mathematics18th Annual Symposium on Foundations of Computer Science (sfcs 1977)
- 1977

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.

Strong functors and monoidal monads

- Mathematics
- 1972

In [4] we proved that a commutative monad on a symmetric monoidal closed category carries the structure of a symmetric monoidal monad ([4], Theorem 3.2). We here prove the converse, so that, takenâ€¦

Verification of Programs That Destructively Manipulate Data

- Computer ScienceSci. Comput. Program.
- 1988

The partial lambda calculus

- Mathematics
- 1988

This thesis investigates various formal systems for reasoning about partial functions or partial elements, with particular emphasis on lambda calculi for partial functions. Beeson's (intuitionistic)â€¦

Call-by-Name, Call-by-Value and the lambda-Calculus

- Computer ScienceTheor. Comput. Sci.
- 1975