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Set-theoretical models of λ-calculus: theories, expansions, isomorphisms
- G. Longo
- Mathematics, Computer ScienceAnn. Pure Appl. Log.
- 1 August 1983
A calculus for overloaded functions with subtyping
It is shown that this calculus provides a foundation for typed object-oriented languages which solves some of the problems of the standard record-based approach and provides a type-discipline for a relevant fragment of the “core framework” of CLOS.
Provable Isomorphisms of Types
A constructive characterization is given of the isomorphisms which must hold in all models of the typed lambda calculus with surjective pairing, by the correspondence between these calculi and proofs in intuitionistic positive propositional logic.
Categories, types and structures - an introduction to category theory for the working computer scientist
This book introduces category theory at a level appropriate for computer scientists and provides practical examples in the context of programming language design and pursues the more complex mathematical semantics of data types and programs as objects and morphisms of categories.
The error exponent for the noiseless encoding of finite ergodic Markov sources
A new approach to the classical fixed-length noiseless source coding problem is proposed for the case of finite ergodic Markov sources. This approach is based on simple counting arguments. The…
Source Coding Theory
- G. Longo
In what follows, a communication system as schematized by the block-diagram of Fig. 1.1 is referred to.
Lambda-Calculus Models and Extensionality
Constructive Natural Deduction and its 'Omega-Set' Interpretation
The first part of this paper may be viewed as a short tutorial with a constructive understanding of the deduction theorem and some work on the expressive power of first and second order quantification and the presentation is meant to be elementary.
The Deluge of Spurious Correlations in Big Data
It is proved that very large databases have to contain arbitrary correlations, and can be found in “randomly” generated, large enough databases, whichimplies that most correlations are spurious.