Answered: Recall the encodings in lambda calculus…

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Recall the encodings in lambda calculus of Church numerals and the operation of multiplication of two numbers. For example:
the numeral 2 stands for the corresponding encoding λf.λx.f(f(x));
the term mul ≜ λx.λy.λz.x(yz), a function on two arguments, encodes multiplication of two numbers.
a) Using the definitions, verify that mul 1 2 computes 2 . Show your working.
b) The term sqr encodes the function of one argument, which squares a number. Define the term sqr and then verify your definition by checking that sqr 1 and mul 1 1
compute the same numeral.

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