Dynamic typing: syntax and proof theory

Dynamic Typing: Syntax and Proof Theory

We present the dynamically typed λ-calculus, an extension of the statically typed λcalculus with a special type Dyn and explicit dynamic type coercions corresponding to runtime type tagging and type check-and-untag operations. Programs in run-time typed languages can be interpreted in the dynamically typed λ-calculus via a nondeterministic completion process that inserts explicit coercions and ...

Proof-nets : the Parallel Syntax for Proof-theory

The paper is mainly concerned with the extension of proof-nets to additives, for which the best known solution is presented. It proposes two cut-elimination procedures, the lazy one being in linear time. The solution is shown to be compatible with quantifiers, and the structural rules of exponentials are also accommodated. Traditional proof-theory deals with cut-elimination ; these results are ...

Crash-Proof Syntax

The Minimalist Program is guided by the idea that the syntactic system of the language faculty is designed to optimally meet design specifications imposed by the interface systems. In this paper we argue that an optimal derivational system, at least from a computational point of view, is a system that generates only objects that are well-formed and satisfy conditions imposed by the interface sy...

typing dynamic typing

Dynamic Typing

We present an extension of a statically typed language with a special type Dynamic and explicit type tagging and checking operations (coercions). Programs in run-time typed languages are viewed as incomplete programs that are to be completed to well-typed programs by explicitly inserting coercions into them. Such completions are generally not unique. If the meaning of an incomplete program is t...