Les types de donn\'ees syntaxiques du syst\`eme F

TL;DR

This paper provides a purely syntactical characterization of input and output types in system F, demonstrating that types with positive quantifiers are both input and output types, with specific restrictions ensuring their equivalence.

Contribution

It introduces a syntactical framework for defining input and output types in system F and establishes conditions under which these types coincide.

Findings

Types with positive quantifiers are syntactical data types.

Any input type is also an output type.

Restrictions on the ∀-elimination rule ensure output types are input types.

Abstract

We give in this paper a purely syntactical definition of input and output types of system F. We define the syntactical data types as input and output types. We show that any type with positive quantifiers is a syntactical data type and that an input type is an output type. We give some restrictions on the $\forall$-elimination rule in order to prove that an output type is an input type.