Ppt Soft Linear Logic Lambda Calculus And Intersection Types These considerations lead to a more natural notion of lambda definability in the presence of types, which requires that a term representing a function must be uniformly typed independently from its possible inputs. This paper presents a novel method to compare computational properties of λ terms typeable with intersection types, with respect to terms typeable with curry types.
Pdf Intersection Types For The Lambda Mu Calculus Intersection types are syntactical objects built inductively by closing a given set cc of type atoms (constants) which contains the universal type w under the function type constructor → and the intersection type constructor ∩. This is a short survey of the use of intersection types for reasoning in a finitary way about terms interpretations in various models of lambda calculus. We study the semantics of an untyped lambda calculus equipped with oper ators representing read and write operations from and to a global store. we adopt the monadic approach to model side effects and treat read and write as algebraic operations over a monad. We then explain the importance of intersection types for the semantics of $\lambda$ calculus, through the construction of filter models and the representation of algebraic lattices.
Pdf Intersection Types For The Computational Lambda Calculus We study the semantics of an untyped lambda calculus equipped with oper ators representing read and write operations from and to a global store. we adopt the monadic approach to model side effects and treat read and write as algebraic operations over a monad. We then explain the importance of intersection types for the semantics of $\lambda$ calculus, through the construction of filter models and the representation of algebraic lattices. This section is devoted to introducing two type systems which go beyond oracle intersection types and towards a more tractable type system. however, the resulting system is bound to be complicated. We start by describingthe well known results showing thedeep connection between intersection type systems and normalization properties, i.e., their power of naturally characterizing solvable, normalizing, and strongly normal izing pure. This simple extension made the proof of many strong semantic and characterisation results achievable for the λ calculus, the most important of which we will discuss here in the context of strict intersection types. We introduce intersection type systems for the lambda! calculus, by extending standard intersection types with a ! u operator. these induce affine combinatory algebras, and, via suitable quotients, models of the lambda! calculus.
Pdf Intersection Types This section is devoted to introducing two type systems which go beyond oracle intersection types and towards a more tractable type system. however, the resulting system is bound to be complicated. We start by describingthe well known results showing thedeep connection between intersection type systems and normalization properties, i.e., their power of naturally characterizing solvable, normalizing, and strongly normal izing pure. This simple extension made the proof of many strong semantic and characterisation results achievable for the λ calculus, the most important of which we will discuss here in the context of strict intersection types. We introduce intersection type systems for the lambda! calculus, by extending standard intersection types with a ! u operator. these induce affine combinatory algebras, and, via suitable quotients, models of the lambda! calculus.
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