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The Lazy Lambda Calculus
 Research Topics in Functional Programming
, 1990
"... Introduction The commonly accepted basis for functional programming is the calculus; and it is folklore that the calculus is the prototypical functional language in puri ed form. But what is the calculus? The syntax is simple and classical; variables, abstraction and application in the pure cal ..."
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Cited by 254 (3 self)
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Introduction The commonly accepted basis for functional programming is the calculus; and it is folklore that the calculus is the prototypical functional language in puri ed form. But what is the calculus? The syntax is simple and classical; variables, abstraction and application in the pure calculus, with applied calculi obtained by adding constants. The further elaboration of the theory, covering conversion, reduction, theories and models, is laid out in Barendregt's already classical treatise [Bar84]. It is instructive to recall the following crux, which occurs rather early in that work (p. 39): Meaning of terms: rst attempt The meaning of a term is its normal form (if it exists). All terms without normal forms are identi ed. This proposal incorporates such a simple and natural interpretation of the calculus as
Filter Models and Easy Terms
, 2001
"... We illustrate the use of intersection types as a tool for synthesizing models which exhibit special purpose features. We focus on semantical proofs of easiness. This allows us to prove that the class of theories induced by graph models is strictly included in the class of theories induced by n ..."
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Cited by 14 (3 self)
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We illustrate the use of intersection types as a tool for synthesizing models which exhibit special purpose features. We focus on semantical proofs of easiness. This allows us to prove that the class of theories induced by graph models is strictly included in the class of theories induced by nonextensional lter models.
A Complete Characterization of Complete IntersectionType Theories (Extended Abstract)
 ACM TOCL
, 2000
"... M. DEZANICIANCAGLINI Universita di Torino, Italy F. HONSELL Universita di Udine, Italy F. ALESSI Universita di Udine, Italy Abstract We characterize those intersectiontype theories which yield complete intersectiontype assignment systems for lcalculi, with respect to the three canonical ..."
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Cited by 12 (5 self)
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M. DEZANICIANCAGLINI Universita di Torino, Italy F. HONSELL Universita di Udine, Italy F. ALESSI Universita di Udine, Italy Abstract We characterize those intersectiontype theories which yield complete intersectiontype assignment systems for lcalculi, with respect to the three canonical settheoretical semantics for intersectiontypes: the inference semantics, the simple semantics and the Fsemantics. Keywords Lambda Calculus, Intersection Types, Semantic Completeness, Filter Structures. 1 Introduction Intersectiontypes disciplines originated in [6] to overcome the limitations of Curry 's type assignment system and to provide a characterization of strongly normalizing terms of the lcalculus. But very early on, the issue of completeness became crucial. Intersectiontype theories and filter lmodels have been introduced, in [5], precisely to achieve the completeness for the type assignment system l" BCD W , with respect to Scott's simple semantics. And this result, ...
A kappadenotational semantics for Map Theory in ZFC + SI
 in ZFC+SI, Theoretical Computer Science 179
, 1997
"... Map theory, or MT for short, has been designed as an \integrated" foundation for mathematics, logic and computer science. By this we mean that most primitives and tools are designed from the beginning to bear the three intended meanings: logical, computational, and settheoretic. MT was ori ..."
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Map theory, or MT for short, has been designed as an \integrated" foundation for mathematics, logic and computer science. By this we mean that most primitives and tools are designed from the beginning to bear the three intended meanings: logical, computational, and settheoretic. MT was originally introduced in [17]. It is based on calculus instead of logic and sets, and it fullls Church's original aim of introducing calculus. In particular, it embodies all of ZFC set theory, including classical propositional and classical rst order predicate calculus. MT also embodies the unrestricted, untyped lambda calculus including unrestricted abstraction and unrestricted use of the xed point operator. MT is an equational theory. We present here a semantic proof of the consistency of map theory within ZFC + SI, where SI asserts the existence of an inaccessible cardinal. The proof is in the spirit of denotational semantics and relies on mathematical tools which reect faithful...