On the λ Definable Higher Order Boolean Operations

Article type: Research Article

Authors: Zaionc, Marek^{; *}

Affiliations: Department of Computer & Information Sciences, University of Alabama at Birmingham, University Station, Birmingham, Alabama 35294, USA

Note: [*] On leave from the Department of Computer Science, Jagiellonian University, Krakov, Poland.

Abstract: The purpose of this work is to show the methods of representing higher order boolean functionals in the simple typed λ calculus. In the paper is presented an algorithm for construction the λ representation of a functional given by generalized truth table. This technique is useful especially in functional programming languages such as ML in which functionals are expressed in the form of typed λ terms. Also λ representability of higher order functionals in many valued logics is discussed.

Keywords: boolean operations, typed λ calculus, representability

DOI: 10.3233/FI-1989-12205

Journal: Fundamenta Informaticae, vol. 12, no. 2, pp. 181-189, 1989