Towards an Intersection Typed System (original) (raw)
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INTERSECTION TYPE SYSTEM AND LAMBDA CALCULUS WITH DIRECTOR STRINGS
Computer Science & Information Technology (CS & IT), 2019
The operation of substitution in í µí¼-calculus is treated as an atomic operation. It makes that substitution operation is complex to be analyzed. To overcome this drawback, explicit substitution systems are proposed. They bridge the gap between the theory of the í µí¼-calculus and its implementation in programming languages and proof assistants. í µí¼ í µí±-calculus is a name-free explicit substitution. Intersection type systems for various explicit substitution calculi, not including λo-calculus, have been studied by researchers. In this paper, we put our attention to í µí¼ í µí±-calculus. We present an intersection type system for í µí¼ í µí±-calculus and show it satisfies the subject reduction property.
Intersection Types for the Computational lambda-Calculus
ArXiv, 2019
We study polymorphic type assignment systems for untyped lambda-calculi with effects, based on Moggi's monadic approach. Moving from the abstract definition of monads, we introduce a version of the call-by-value computational lambda-calculus based on Wadler's variant with unit and bind combinators, and without let. We define a notion of reduction for the calculus and prove it confluent, and also we relate our calculus to the original work by Moggi showing that his untyped metalanguage can be interpreted and simulated in our calculus. We then introduce an intersection type system inspired to Barendregt, Coppo and Dezani system for ordinary untyped lambda-calculus, establishing type invariance under conversion, and provide models of the calculus via inverse limit and filter model constructions and relate them. We prove soundness and completeness of the type system, together with subject reduction and expansion properties. Finally, we introduce a notion of convergence, which is...