COMP 3007微积分模块理解

本目的是让您复习-完成两个微积分简单的练习。作为-微积分模块是发展理解的基础
关于Haskell编程语言的派生系统，您必须展示您的所有工作以获得全额信贷。执行这些缩减时，不允许“跳过”任何操作。对于第一个练习，你必须对下面对应于你的*唯一的学生身份号码。
COMP 3007 A/B (Winter 2023) − "Programming Paradigms" Specification for Assignment 2

1.Specification

Your submission for this assignment must be commented and must include both your name and yourstudent number as a comment at the top of every source file you submit. Each of your submitted files mustuse a file name beginning 'comp3007_w23_#########_assignment_02' (replacing the number signs withyour own student number) and any submissions that crash (i.e., terminate with an error) on execution willautomatically receive a mark of 0.Officially, the Due Date for this Assignment is:Friday, February 3rd, 2023, at 11:59pm EST.Late Submissions are Accepted Without Penalty Until Sunday, February 5th, by 11:59pm EST.Submissions received after that will not be accepted and will receive a mark of 0.The objective of this assignment is to have you review some of the basics of -calculus by completingtwosimple exercises. As the purpose of the -calculus module was todevelop a foundation of understandingabout the system from which the Haskell programming language was derived, you must show all your workto receive full credit. You are not permitted to "skip" any operations when performing these reductions.For the first exercise, you must perform a β-reduction on the expression below that corresponds to yourunique student identification number.If the LAST TWO DIGITS of your student number is in the range from 00 to 24 inclusive, then you must reduce:

(𝜆𝑔. (𝜆𝑗. 𝑔)) (𝜆ℎ. (𝜆𝑘. 𝑘)) (𝜆𝑖. (𝜆𝑚. 𝑖))

If the LAST TWO DIGITS of your student number is in the range from 25 to 49 inclusive, then you must reduce:

(𝜆𝑛. (𝜆𝑞. 𝑞)) (𝜆𝑜. (𝜆𝑟. 𝑜)) (𝜆𝑝. (𝜆𝑠. 𝑠))

If the LAST TWO DIGITS of your student number is in the range from 50 to 74 inclusive, then you must reduce:

(𝜆𝑡. (𝜆𝑤. 𝑤)) (𝜆𝑢. (𝜆𝑦. 𝑦)) (𝜆𝑣. (𝜆𝑧. 𝑣))

If the LAST TWO DIGITS of your student number is in the range from 75 to 99 inclusive, then you must reduce:

(𝜆𝑎. (𝜆𝑑. 𝑎)) (𝜆𝑏. (𝜆𝑒. 𝑏)) (𝜆𝑐. (𝜆𝑓. 𝑓))

For the second exercise, you must first write the -calculusexpression corresponding to the Church encoding
of the LARGEST digit in your student number. You must then perform aβ-reduction on the expression below,eventually replacing both zero and yourdigit with their corresponding Church encodings.

𝜆𝑎. (𝜆𝑏. (𝜆𝑐. (𝜆𝑑. ((𝑎 𝑐)((𝑏 𝑐) 𝑑))))) 𝑦𝑜𝑢𝑟𝑑𝑖𝑔𝑖𝑡 𝑧𝑒𝑟𝑜

For this assignment:• your submission must be a single pdf document that you created electronically (using a wordprocessor like Microsoft Word or Google Docs), and please note that scans or digitalphotographs ofhandwritten submissions will not be accepted and will receive a mark of zero• you must include your full name and student number at the top of your submission• you must show all your work and perform no more than one operation per line when reducing
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