The paper develops notation for strings of abstracters in typed lambda calculus, and shows how to treat them more or less as single abstracters. 0 1991 Academic Press. Inc. 1.

The purpose of this course is to provide an introduction to λ-calculi, specifically the simply typed lambda calculus (λ →). λ-calculi are formalisms that are useful in computer science. They are languages that express both computational and logical information. Computational information

Two different formulations of the simply typed lambda calculus: the natural deduction and the sequent system, are considered. An analogue of cut elimination is proved for the sequent lambda calculus.

A typed lambda calculus with categorical type constructors is introduced. It has a uniform category theoretic mechanism to declare new types. Its type structure includes categorical objects like products and coproducts as well as recursive types like natural numbers and lists. It also allows duals

We solve the decision problem for simply typed lambda calculus with strong binary sums, equivalently the word problem for free cartesian closed categories with binary coproducts. Our method is based on the semantical technique known as “normalization by evaluation ” and involves inverting

Abstract. This paper concerns retracts in simply typed lambda calculus assuming βη-equality. We provide a simple tableau proof system which characterises when a type is a retract of another type and which leads to an exponential decision procedure. 1

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Abstract. In this paper, we present an explicitly typed version of the Lambda Calculus of Objects of [7], which is a development of the object-calculi defined in [10, 2]. This calculus supports object extension in presence of object subsumption. Extension is the ability of modify the behavior

-style formal system, H . . . . . . . . . . . . . . . . 1-4 1.2.2 Natural Deduction . . . . . . . . . . . . . . . . . . . . . . . . 1-5 1.2.3 Sequent Formulation, ND, of Natural Deduction . . . . . . . 1-7 1.2.4 Normal ND tree-proofs . . . . . . . . . . . . . . . . . . . . . 1-7 1.2.5 Sequent Calculus SC . . . . . . . . . . . .

subsumption allows to use objects with a bigger interface in a context expecting another object with a smaller interface. This calculus has a sound and decidable type system, "width" subtyping, and it allows for first-class method bodies. 1 Introduction l o , the Lambda Calculus of Objects of [7