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Python function

Python function

Database System Concepts
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
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Please help me solve Problem 2 on induction. 

**Problem 2** **Motivation** In computer science, we often use induction to prove the correctness of a function—that is, we prove formally that the function does what it is supposed to do. This is sometimes called "proving a function." For example, consider the Python function below, which reverses an input string using recursion. ```python def reverse_string(s): """ reverse the string s. The first letter becomes the last letter, the second letter becomes the second- args: s, the string to be reversed returns: the reversed string """ if s == "": return "" else: return reverse_string(s[1:]) + s[0] ``` Here it is in action. ```python reverse_string("CSCI 0200") ``` ``` '0020 ICSC' ``` We got the right answer for this input! But…would we get the right answer on *every* possible input? Let's write a proof which will guarantee that we will.
Transcribed Image Text:**Problem 2** **Motivation** In computer science, we often use induction to prove the correctness of a function—that is, we prove formally that the function does what it is supposed to do. This is sometimes called "proving a function." For example, consider the Python function below, which reverses an input string using recursion. ```python def reverse_string(s): """ reverse the string s. The first letter becomes the last letter, the second letter becomes the second- args: s, the string to be reversed returns: the reversed string """ if s == "": return "" else: return reverse_string(s[1:]) + s[0] ``` Here it is in action. ```python reverse_string("CSCI 0200") ``` ``` '0020 ICSC' ``` We got the right answer for this input! But…would we get the right answer on *every* possible input? Let's write a proof which will guarantee that we will.
**Problem Statement** We’ll write a string with \( n \) characters as \( s_1s_2s_3 \cdots s_{n-2}s_{n-1}s_n \). Now we can state the thing we want to prove: **Proposition:** For any \( n \in \mathbb{N} \), the result of calling the function `reverse_string` on the string \( s_1s_2s_3 \cdots s_{n-2}s_{n-1}s_n \) is the reversal of \( s \), that is, the string \( s_ns_{n-1}s_{n-2} \cdots s_3s_2s_1 \). Prove this claim using induction. **Note:** The empty string \( \varepsilon \) is the string with no elements at all; this string is its own reversal.
Transcribed Image Text:**Problem Statement** We’ll write a string with \( n \) characters as \( s_1s_2s_3 \cdots s_{n-2}s_{n-1}s_n \). Now we can state the thing we want to prove: **Proposition:** For any \( n \in \mathbb{N} \), the result of calling the function `reverse_string` on the string \( s_1s_2s_3 \cdots s_{n-2}s_{n-1}s_n \) is the reversal of \( s \), that is, the string \( s_ns_{n-1}s_{n-2} \cdots s_3s_2s_1 \). Prove this claim using induction. **Note:** The empty string \( \varepsilon \) is the string with no elements at all; this string is its own reversal.
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