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The Y-combinator in Scott's lambda-calculus models

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Park, David (1976) The Y-combinator in Scott's lambda-calculus models. University of Warwick. Department of Computer Science. (Theory of Computation Report). (Unpublished)

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Abstract

Assume the notation and terminology of Dana Scott's paper
"Models for the Lambda-Calculus". In this note I want to exhibit the
relationship between the lambda-calculus "paradoxical operator"
Y = λx((λy.x(yy))λy.x(yy))
and the minimal fixpoint operator
Y* = λx.∞Un=0 xnΩ
obtained by regarding the lambda-calculus model as a lattice.

Item Type: Report
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science, Engineering and Medicine > Science > Computer Science
Library of Congress Subject Headings (LCSH): Lambda calculus
Series Name: Theory of Computation Report
Publisher: University of Warwick. Department of Computer Science
Official Date: June 1976
Dates:
DateEvent
June 1976["eprint_fieldopt_dates_date_type_available" not defined]
Number: Number 13
Number of Pages: 8
DOI: CS-RR-013
Institution: University of Warwick
Theses Department: Department of Computer Science
Status: Not Peer Reviewed
Publication Status: Unpublished
Access rights to Published version: Open Access (Creative Commons)
Date of first compliant deposit: 1 August 2016
Date of first compliant Open Access: 1 August 2016

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