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The Intensional Lambda Calculus
2007We introduce a natural deduction formulation for the Logic of Proofs, a refinement of modal logic S4 in which the assertion ? A is replaced by [[s]]Awhose intended reading is "s is a proof of A". A term calculus for this formulation yields a typed lambda calculus ? I that internalises intensionalinformation on howa term is computed.
Sergei N. Artëmov, Eduardo Bonelli
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Lambda calculus as a workflow model
Concurrency and Computation: Practice and Experience, 2008AbstractData‐oriented workflows are often used in scientific applications for executing a set of dependent tasks across multiple computers. We discuss how these can be modeled using lambda calculus, and how ideas from functional programming are applicable in the design of workflows.
Peter M. Kelly +2 more
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2005
The need to use position-dependent parameters often hampers the definition of flexible, extensible, and reusable abstractions for software composition. This observation has led us to explore the concept of forms, which are first-class extensible records and that, in combination with a small set of purely asymmetric operators, provide a core language to
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The need to use position-dependent parameters often hampers the definition of flexible, extensible, and reusable abstractions for software composition. This observation has led us to explore the concept of forms, which are first-class extensible records and that, in combination with a small set of purely asymmetric operators, provide a core language to
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Proceedings of the 2019 ACM SIGPLAN Workshop on Partial Evaluation and Program Manipulation, 2019
Closure calculus is simpler than pure lambda-calculus as it does not mention free variables or index manipulation, variable renaming, implicit substitution, or any other meta-theory. Further, all programs, even recursive ones, can be expressed as normal forms.
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Closure calculus is simpler than pure lambda-calculus as it does not mention free variables or index manipulation, variable renaming, implicit substitution, or any other meta-theory. Further, all programs, even recursive ones, can be expressed as normal forms.
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Stud Logica, 2007
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Marie-Renée Fleury, Myriam Quatrini
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zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Marie-Renée Fleury, Myriam Quatrini
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The lambda calculus is algebraic
Journal of Functional Programming, 2002This paper serves as a self-contained, tutorial introduction to combinatory models of the untyped lambda calculus. We focus particularly on the interpretation of free variables. We argue that free variables should not be interpreted as elements in a model, as is usually done, but as indeterminates.
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Atomic Lambda Calculus: A Typed Lambda-Calculus with Explicit Sharing [PDF]
2013 28th Annual ACM/IEEE Symposium on Logic in Computer Science, 2013 An explicit-sharing lambda-calculus is presented, based on a Curry-Howard-style interpretation of the deep inference proof formalism. Duplication of subterms during reduction proceeds `atomically', i.e. on individual constructors, similar to optimal graph reduction in the style of Lamping. The calculus preserves strong normalisation with respect to the
Tom Gundersen +2 more
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ACM Turing Centenary Celebration on - ACM-TURING '12, 2012
A very fast development in the early 1930s, following Hilbert's codification of Mathematical Logic, led to the Incompleteness Theorems, Computable Functions, Undecidability Theorems, and the general formulation of recursive Function Theory. The so-called Lambda Calculus played a key role.
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A very fast development in the early 1930s, following Hilbert's codification of Mathematical Logic, led to the Incompleteness Theorems, Computable Functions, Undecidability Theorems, and the general formulation of recursive Function Theory. The so-called Lambda Calculus played a key role.
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Boolean Algebras for Lambda Calculus
21st Annual IEEE Symposium on Logic in Computer Science (LICS'06), 2006In this paper we show that the Stone representation theorem for Boolean algebras can be generalized to combinatory algebras. In every combinatory algebra there is a Boolean algebra of central elements (playing the role of idempotent elements in rings), whose operations are defined by suitable combinators.
MANZONETTO G, SALIBRA, Antonino
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