On Functors Expressible in the Polymorphic Typed Lambda Calculus

On Functors Expressible in the Polymorphic Typed Lambda Calculus

Given a model of the polymorphic typed lambda calculus based upon a Cartesian closed category K, there will be functors from K to K whose action on objects can be expressed by type expressions and whose action on morphisms can be expressed by ordinary expressions. We show that if T is such a functor then there is a weak initial T -algebra and if, in addition, K possesses equalizers of all subse...

Recognizability in the Simply Typed Lambda-Calculus

We define a notion of recognizable sets of simply typed λterms that extends the notion of recognizable sets of strings or trees. This definition is based on finite models. Using intersection types, we generalize the notions of automata for strings and trees so as to grasp recognizability for λ-terms. We then expose the closure properties of this notion and present some of its applications.

2 Dynamically typed lambda calculus

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...

Metacircularity in the Polymorphic lambda-Calculus

Constructive Data Reenement in Typed Lambda Calculus

A new treatment of data reenement in typed lambda calculus is proposed, based on pre-logical relations HS99] rather than logical relations as in Ten94], and incorporating a constructive element. Constructive data reenement is shown to have desirable properties, and a substantial example of reenement is presented.