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Rank 2 Type Systems and Recursive Definitions
, 1995
"... We demonstrate an equivalence between the rank 2 fragments of the polymorphic lambda calculus (System F) and the intersection type discipline: exactly the same terms are typable in each system. An immediate consequence is that typability in the rank 2 intersection system is DEXPTIMEcomplete. We int ..."
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Cited by 26 (1 self)
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We demonstrate an equivalence between the rank 2 fragments of the polymorphic lambda calculus (System F) and the intersection type discipline: exactly the same terms are typable in each system. An immediate consequence is that typability in the rank 2 intersection system is DEXPTIMEcomplete. We introduce a rank 2 system combining intersections and polymorphism, and prove that it types exactly the same terms as the other rank 2 systems. The combined system suggests a new rule for typing recursive definitions. The result is a rank 2 type system with decidable type inference that can type some interesting examples of polymorphic recursion. Finally,we discuss some applications of the type system in data representation optimizations such as unboxing and overloading.
Definability and full abstraction
 GDP FESTSCHRIFT
"... Game semantics has renewed denotational semantics. It offers among other things an attractive classification of programming features, and has brought a bunch of new definability results. In parallel, in the denotational semantics of proof theory, several full completeness results have been shown sin ..."
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Cited by 17 (2 self)
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Game semantics has renewed denotational semantics. It offers among other things an attractive classification of programming features, and has brought a bunch of new definability results. In parallel, in the denotational semantics of proof theory, several full completeness results have been shown since the early nineties. In this note, we review the relation between definability and full abstraction, and we put a few old and recent results of this kind in perspective.
Intersection Type Systems and Logics Related to the Meyer–Routley System B +
, 2003
"... Abstract: Some, but not all, closed terms of the lambda calculus have types; these types are exactly the theorems of intuitionistic implicational logic. An extension of these simple (→) types to intersection (or →∧) types allows all closed lambda terms to have types. The corresponding → ∧ logic, rel ..."
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Cited by 1 (1 self)
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Abstract: Some, but not all, closed terms of the lambda calculus have types; these types are exactly the theorems of intuitionistic implicational logic. An extension of these simple (→) types to intersection (or →∧) types allows all closed lambda terms to have types. The corresponding → ∧ logic, related to the Meyer–Routley minimal logic B + (without ∨), is weaker than the → ∧ fragment of intuitionistic logic. In this paper we provide an introduction to the above work and also determine the →∧ logics that correspond to certain interesting subsystems of the full →∧ type theory. 1 Simple Typed Lambda Calculus In standard mathematical notation “f: α → β ” stands for “f is a function from α into β. ” If we interpret “: ” as “∈ ” we have the rule: f: α → β t: α f(t) : β This is one of the formation rules of typed lambda calculus, except that there we write ft instead of f(t). In λcalculus, λx.M represents the function f such that fx = M. This makes the following rule a natural one: [x: α] M: β λx.M: α → β We now set up the λterms and their types more formally.