Answered: Induction Proofs in Ocaml: USING…

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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Induction Proofs in Ocaml:

USING Helper: Lemma

plus (S a) b = S (plus a b)
b = Zero

LHS:

plus (S a) b
= { case }
    plus (S a)Zero
= { def of plus }
    match Zero with
    | Zero -> a
    | S c -> plus (S a) c
= { apply match }
    (S a)

RHS:

S (plus a b)
= { case }
    S (plus a Zero)
= { def of plus }
    match Zero with
    | Zero -> a
    | S c -> plus (S a) c
= { apply match }
    S (a)

Since LHS = RHS, Lemma is proven.

Use helper to prove:
P3) Prove plus a (plus b c) = plus (plus a b) c

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