Results 1 
2 of
2
A New Paradox in Type Theory
 Logic, Methodology and Philosophy of Science IX : Proceedings of the Ninth International Congress of Logic, Methodology, and Philosophy of Science
, 1994
"... this paper is to present a new paradox for Type Theory, which is a typetheoretic refinement of Reynolds' result [24] that there is no settheoretic model of polymorphism. We discuss then one application of this paradox, which shows unexpected connections between the principle of excluded middle and ..."
Abstract

Cited by 7 (0 self)
 Add to MetaCart
this paper is to present a new paradox for Type Theory, which is a typetheoretic refinement of Reynolds' result [24] that there is no settheoretic model of polymorphism. We discuss then one application of this paradox, which shows unexpected connections between the principle of excluded middle and the axiom of description in impredicative Type Theories. 1 Minimal and Polymorphic HigherOrder Logic
unknown title
"... duality, and computationally still interesting, since dual of polymorphic functions with universal type can be regarded as abstract data types with exis tential type [MP85]. Instead of classical systems like [Pari92], even intuitionistic systems can enjoy that polymorphic types can be interpreted by ..."
Abstract
 Add to MetaCart
duality, and computationally still interesting, since dual of polymorphic functions with universal type can be regarded as abstract data types with exis tential type [MP85]. Instead of classical systems like [Pari92], even intuitionistic systems can enjoy that polymorphic types can be interpreted by existential types and vice versa. This interpretation also contains proof duality, such that the universal introduction rule is interpreted by the use of the existential elimination rule, and the universal elimination by the existential introduction. Moreover, we established not only a Galois connection but also a Galois embedding from polymorphic Acalculus (GirardReynolds) into a calculus with existential types. 2 Polymorphic Acalculus A2 We give the definition of polymorphic Acalculus \‘a la Church as second order intuitionistic logic, denoted by A2. This calculus is also known as the system F. The syntax of types is defined from type variables denoted by $X $ , $\mathrm{u}\mathrm{s}\mathrm{i}\mathrm{n}\mathrm{g}\Rightarrow \mathrm{o}\mathrm{r}$ over type variables. The syntax of A2terms is defined from individual variables denoted by $x $ , using termapplications, typeapplications or Aabstractions over individual variables or type variables.