Motor imagery in typing: effects of typing style and action familiarity

On the relation between Church - style typing and Curry - style typing : Extended Abstract ∗

There are two versions of type assignment in λ-calculus: Church-style, in which the type of each variable is fixed, and Curry-style (also called “domain free”), in which it is not. As an example, in Church-style typing, λx : A . x is the identity function on type A, and it has type A → A but not B → B for a type B different from A. In Curry-style typing, λx.x is a general identity function with...

Bridging Curry and Church's typing style

There are two versions of type assignment in the λ-calculus: Church-style, in which the type of each variable is fixed, and Currystyle (also called “domain free”), in which it is not. As an example, in Church-style typing, λx:A.x is the identity function on type A, and it has type A → A but not B → B for a type B different from A. In Currystyle typing, λx.x is a general identity function with t...

Uniqueness Typing in Natural Deduction Style

We present two type systems for graph rewriting: conventional typing and (polymorphic) uniqueness typing. The latter is introduced as a natural extension of simple algebraic and higher-order uniqueness typing. The systems are given in natural deduction style using an inductive syntax of graph denotations with familiar constructs such as let and case. The conventional system resembles traditiona...

typing dynamic typing

Ml-style Typing, Lambda Lifting, and Partial Evaluation

Lambda lifting transforms local function deenitions in functional programming languages into global ones to facilitate their eecient implementation. When considered as a source-to-source transformation for an ML-style typed language, all published algorithms for lambda lifting break typability. We break down two representative lambda lifting algorithms into four elementary transformation steps,...