Reduce this term into normal from, if it exists (show your working):(λx.((λz.zwz)(((λxyx.y)(λx.y)(λy.x))((λx.xx)(λy.yyy)))))t Exercise 1: A combinator is any lambda term which does not contain any free variables,usually denoted with upper case letters. The combinators S, K and I are defined to be thefollowing X-terms:SKI=b)=Xxyz.xz(yz)Xxy.xXx.xReduce the following terms to normal form:a) We underline the redex to be reduced at each step:SKK = (λxyz.xz(yz))KK →ßSSS = (Axyz.xz(yz)) SS8→B(Xyz.Kz(yz))K→B λz.Kz(Kz)Az.(λxy.x)z(Kz)SIK = (Xxyz.xz(yz))IK →ß (\yz.Iz(yz))K→BXz.Iz(K2)===→ Az.(Ay.z) (Kz)→BXz.z=Xz.(λx.x)z(Kz)→BXz.z(Kz)=Az.z((λxy.x)z)→BXz.z(Ay.z)Az.(λxyz.xz(yz))z(Sz)→ Az.(Ayw.zw(yw))(Sz)→ Az.Aw.zw(Szw)(Xyz.Sz(yz))SAz.Sz(Sz)Azw.zw((Axyz.xz(yz))zw)→ Azw.zw((Xyt.zt(yt))w)→ Azw.zw(At.zt(wt)).

To reduce the given lambda calculus expression to its normal form, it will follow the usual steps of…

Answered: Reduce this term into normal from, if…

Reduce this term into normal from, if it exists (show your working): (λx.((λz.zwz)(((λxyx.y)(λx.y)(λy.x))((λx.xx)(λy.yyy)))))t

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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Question

Reduce this term into normal from, if it exists (show your working):
(λx.((λz.zwz)(((λxyx.y)(λx.y)(λy.x))((λx.xx)(λy.yyy)))))t

Exercise 1: A combinator is any lambda term which does not contain any free variables,
usually denoted with upper case letters. The combinators S, K and I are defined to be the
following X-terms:
S
K
I
=
b)
=
Xxyz.xz(yz)
Xxy.x
Xx.x
Reduce the following terms to normal form:
a) We underline the redex to be reduced at each step:
SKK = (λxyz.xz(yz))KK →ß
SSS = (Axyz.xz(yz)) SS8
→B
(Xyz.Kz(yz))K
→B λz.Kz(Kz)
Az.(λxy.x)z(Kz)
SIK = (Xxyz.xz(yz))IK →ß (\yz.Iz(yz))K
→BXz.Iz(K2)
=
=
=
→ Az.(Ay.z) (Kz)
→B
Xz.z
=
Xz.(λx.x)z(Kz)
→BXz.z(Kz)
=
Az.z((λxy.x)z)
→BXz.z(Ay.z)
Az.(λxyz.xz(yz))z(Sz)
→ Az.(Ayw.zw(yw))(Sz)
→ Az.Aw.zw(Szw)
(Xyz.Sz(yz))S
Az.Sz(Sz)
Azw.zw((Axyz.xz(yz))zw)
→ Azw.zw((Xyt.zt(yt))w)
→ Azw.zw(At.zt(wt)).

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