Results 1 
2 of
2
Notes on Sconing and Relators
, 1993
"... This paper describes a semantics of typed lambda calculi based on relations. The main mathematical tool is a categorytheoretic method of sconing, also called glueing or Freyd covers. Its correspondence to logical relations is also examined. 1 Introduction Many modern programming languages feature ..."
Abstract

Cited by 24 (0 self)
 Add to MetaCart
This paper describes a semantics of typed lambda calculi based on relations. The main mathematical tool is a categorytheoretic method of sconing, also called glueing or Freyd covers. Its correspondence to logical relations is also examined. 1 Introduction Many modern programming languages feature rather sophisticated typing mechanisms. In particular, languages such as ML include polymorphic data types, which allow considerable programming flexibility. Several notions of polymorphism were introduced into computer science by Strachey [Str67], among them the important notion of parametric polymorphism. Strachey's intuitive definition is that a polymorphic function is parametric if it has a uniformly given algorithm in all types, that is, if the function's behavior is independent of the type at which the function is instantiated. Reynolds [Rey83] proposed a mathematical definition of parametric polymorphic functions by means of invariance with respect to certain relations induced by typ...
Parametric and TypeDependent Polymorphism
, 1995
"... Data Types, though, as Reynolds stresses, is not perfectly suited for higher type or higher order systems and, thus, he proposes a "relational" treatment of invariance: computations do not depend on types in the sense that they are "invariant" w.r.t. arbitrary relations on types and between types. R ..."
Abstract

Cited by 10 (5 self)
 Add to MetaCart
Data Types, though, as Reynolds stresses, is not perfectly suited for higher type or higher order systems and, thus, he proposes a "relational" treatment of invariance: computations do not depend on types in the sense that they are "invariant" w.r.t. arbitrary relations on types and between types. Reynolds's approach set the basis for most of the current work on parametricity, as we will review below (.3). Some twelve years earlier, Girard had given just a simple hint towards another understanding of the properties of "computing with types". In [Gir71], it is shown, as a side remark, that, given a type A, if one defines a term J A such that, for any type B, J A B reduces to 1, if A = B, and reduces to 0, if A ยน B, then F + J A does not normalize. In particular, then, J A is not definable in F. This remark on how terms may depend on types is inspired by a view of types which is quite different from Reynolds's. System F was born as the theory of proofs of second order intuitionis...