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Notions of Computation and Monads (1989) [556 citations — 15 self]

by Eugenio Moggi
Information and Computation
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Abstract:

The lambda-calculus is considered an useful mathematical tool in the study of programming languages, since programs can be identified with lambda-terms. However, if one goes further and uses beta eta-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.

Citations

346 Computational lambda calculus and monads – Moggi - 1989
270 Denotational semantics: A Methodology for Language Development – Schmidt - 1986
240 Categories for the Working Mathematician – MacLane - 1972
225 Call-by-name, call-by-value, and the -calculus – Plotkin - 1975
208 Basic concepts of enriched category theory, London Mathematical Society Lecture Note Series 64 – Kelly - 1982
138 Call-by-name, call-by-value, and the λ-calculus – Plotkin - 1975
135 Toposes, triples and theories – Barr, Wells - 1984
134 An abstract view of programming languages – Moggi - 1989
134 The category-theoretic solution of recursive domain equations – Smyth, Plotkin - 1982
132 Action Semantics – Mosses - 1992
129 Semantic domains – Gunter, Scott - 1990
127 Higherorder modules and the phase distinction – Harper, Mitchell, et al. - 1990
103 Introduction to Higher-Order Categorical Logic – Lambek, Scott - 1986
85 Linear logic, -autonomous categories and cofree coalgebras – Seely - 1989
82 The linear abstract machine – Lafont - 1988
66 Edinburgh LCF: A Mechanical Logic – Gordon, Milner, et al. - 1979
62 The formal theory of monads – Street - 1972
49 Programming with Continuations – Friedman, Haynes, et al. - 1984
44 Identity and existence in intuitionistic logic – Scott - 1979
40 The theory of constructions : Categorical semantics and topos-theoretic models – Hyland, Pitts - 1988
38 Continuity and effectiveness in topoi – Rosolini - 1986
37 A type-theoretic alternative to – Scott - 1993
33 A syntactic theory of sequential state – Felleisen, Friedman - 1989
33 Strong functors and monoidal monads – Kock - 1972
32 Partial objects in constructive type theory – Constable, Smith - 1987
27 Doctrines in categorical logic – Kock, Reyes - 1977
26 The Partial Lambda-Calculus – Moggi - 1988
26 First order categorical logic – Makkai, Reyes - 1977
25 Algebraic Theories, volume 26 of Graduate Texts in Mathematics – Manes - 1976
24 A category-theoretic account of program modules – Moggi - 1989
24 Programming, transforming, and proving with function abstractions and memories – Mason, Talcott - 1989
24 Denotational semantics with partial functions – Plotkin - 1985
21 Relating theories of the -calculus – Scott - 1980
20 Computational foundations of basic recursive function theory – Constable, Smith - 1988
17 The Logic of Topoi – Fourman - 1977
16 Continuity and eectiveness in topoi – Rosolini - 1986
12 Verification of programs that destructively manipulate data – Mason - 1988
10 Categories of Partial Morphisms and the partial lambda-calculus – Moggi - 1985
10 New foundations for Fixpoint Computations – Crole, Pitts - 1990
9 Relating theories of the λ-calculus – Scott - 1980
8 A sound and complete axiomatization of operational equivalence between programs with memory – Mason, Talcott - 1989
6 Syntactic Aspects of the Non-deterministic Lambda Calculus – Sharma - 1984
3 Indexed Categories and their Applications – Johnstone, Pare - 1978
2 New foundations for computations – Crole, Pitts - 1990
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