Programming with intersection types and bounded polymorphism
Programming with intersection types and bounded polymorphism
Complete restrictions of the intersection type discipline
Theoretical Computer Science
Lambda-calculus, types and models
Lambda-calculus, types and models
Intersection and union types: syntax and semantics
Information and Computation
Intersection type assignment systems
Selected papers of the thirteenth conference on Foundations of software technology and theoretical computer science
Simple imperative polymorphism
Lisp and Symbolic Computation - Special issue on state in programming languages (part I)
A symmetric lambda calculus for classical program extraction
Information and Computation - special issue: symposium on theoretical aspects of computer software TACS '94
Normalization results for typeable rewrite systems
Information and Computation
Basic simple type theory
A calculus for cryptographic protocols: the spi calculus
Proceedings of the 4th ACM conference on Computer and communications security
Communicating and mobile systems: the &pgr;-calculus
Communicating and mobile systems: the &pgr;-calculus
ICFP '00 Proceedings of the fifth ACM SIGPLAN international conference on Functional programming
The Definition of Standard ML
Lambda-My-Calculus: An Algorithmic Interpretation of Classical Natural Deduction
LPAR '92 Proceedings of the International Conference on Logic Programming and Automated Reasoning
An Object Calculus for Asynchronous Communication
ECOOP '91 Proceedings of the European Conference on Object-Oriented Programming
Call-by-value is dual to call-by-name
ICFP '03 Proceedings of the eighth ACM SIGPLAN international conference on Functional programming
A judgmental reconstruction of modal logic
Mathematical Structures in Computer Science
Logical Equivalence for Subtyping Object and Recursive Types
Theory of Computing Systems
Computation with classical sequents
Mathematical Structures in Computer Science
Intersection and Union Types in the λμμ~-calculus
Electronic Notes in Theoretical Computer Science (ENTCS)
Intersection and Union Types for X
Electronic Notes in Theoretical Computer Science (ENTCS)
Type assignment for intersections and unions in call-by-value languages
FOSSACS'03/ETAPS'03 Proceedings of the 6th International conference on Foundations of Software Science and Computation Structures and joint European conference on Theory and practice of software
The language X: circuits, computations and classical logic
ICTCS'05 Proceedings of the 9th Italian conference on Theoretical Computer Science
Strong normalization of the dual classical sequent calculus
LPAR'05 Proceedings of the 12th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
Strong Normalisation of Cut-Elimination in Classical Logic
Fundamenta Informaticae - Typed Lambda Calculi and Applications (TLCA'99)
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With the eye on defining a type-based semantics, this paper defines intersection and union type assignment for the sequent calculus X, a substitution-free language that enjoys the Curry-Howard correspondence with respect to the implicative fragment of Gentzen's sequent calculus for classical logic. We investigate the minimal requirements for such a system to be complete i.e. closed under redex expansion, and show that the non-logical nature of both intersection and union types disturbs the soundness i.e. closed uder reduction properties. This implies that this notion of intersection-union type assignment needs to be restricted to satisfy soundness as well, making it unsuitable to define a semantics. We will look at two confluent notions of reduction, called Call-by-Name and Call-by-Value, and prove soundness results for those.