Functions and procedures Rules of Processing Announcements In - PowerPoint PPT Presentation

Functions and procedures Rules of Processing

Announcements • In Gradescope, change your name to be your Banner ID • Without this, we cannot grade your homework anonymously, so we will not grade it at all.

Ways to describe sets: Restriction • Restriction: You say “set consists of all elements of set that have such-and-such a property.” • Digression: We often use the name to denote the set of natural numbers , i.e., • Example of restriction: • Fancy-pants math way of writing that: The vertical bar is read “such that.”

Restriction: why we care •

Lecture recorded; see course website.

Functions • Key idea: it’s machine-like! • Put in the same input twice in a row, you’ll get the same output! From teacherspayteachers.com, mathinsight.org,

T ypical high-school math description of a function •

More sophisticated function- descriptions (math, then Racket) •

Naming of parts •

Good habits •

Ways to describe functions • Algebra • “By cases” • “tabular”

Algebraic description examples •

“by cases” example • A classic example: • A silly example • Notes • Both of these have multi-letter names, unusual in math, common in programming • The ”cases” should be mutually exclusive (nothing should fall into more than one) • In the rare cases where something fjts in two cases, the answers produced must be the same

T abular example • T abular just means “expressed using a table” • It’s really an example of a by-cases function In tabular form: z q(z) 1 11 2 0 5 4

Activity •

Lecture recorded; see course website.

“Functions” in Racket • I’ll call these “procedures” --- the computational analog of functions • Created (for now) with a new kind of defjnition (define (f x) (* x x)) • You can tell it’s difgerent from the defjnitions we’ve seen before • the second item isn’t a name • The overall ”shape” is <fdef> := ( define (<name> <name>) <expr>) • The fjrst <name> (f, in our example) becomes the name of a new function. • The “argument” of that function is given by the second name (x, in our example) • The “body” of the function is the <expr> part

Revised: “Functions” in Racket • The overall ”shape” is <fdef> := ( define (<name> <name>*) <expr>) • The fjrst <name> becomes the name of a new function. • The “arguments” of that function are given by the second, third, fourth… names • A function is allowed to have no arguments at all • we’ll never need such a thing in Racket; useful in ReasonML • The “body” of the function is the <expr> part

What to do with a function when you’ve defjned it (define (f x) (* x x)) (f 12) => 144 • Roughly speaking, you say “make x be 12; then evaluate the body, (* x x) , to get 144” • More formally, you apply the “rules of processing” – later today or Friday. • Quick sanity check: In (define (add x y) (+ x y)) , what is the name of the function we’ve defjned? What are the names of its arguments? • Function-name: add; argument names: x, y.

How we defjne functions in CS17 • A very specifjc procedure, in a particular order • T akes about 2 minutes per function, total • Helps you get started when you haven’t got a clue what to do! • This “Design Recipe” is due to Felleisen et al (including my colleague Shriram Krishnamurthi), and has been tested on thousands of students learning Racket • I use it every time I write a program • T oday: simple version; will evolve slightly during semester

• Missing picture of rectangular fjeld surrounded by fenceposts

Problem statement (short form) The total number of posts is . Write a procedure, count-posts that takes in two positive integers and , and produces the integer number of fenceposts required to surround a property that's posts wide and posts deep.

Design recipe, step 1: Data defjnition • What kind of data does this procedure work on? • Pieces of property? • integers? • positive integers? • For this part, for CS17, for now, the answer will always be one of a very few data types: • num • string • bool • This part of recipe will change somewhat, soon.

;; Data Definition ;; num:

Design recipe, step 2: Example data • For the data type chosen, give some examples. • If your actual data is limited in some way, it’s wise to stick to examples in that limited set, but you don't have to if that’s inconvenient • Example: social security numbers: maybe you don’t know a particular sequence of nine digits that IS an SSN! • Example: you’re planning working with positive integers, but the data type is ”num". You might pick 2, 11, 42 as examples.

;; Data Definition ;; Example data: ;; num: 0, 6, 41, 7.2

Design recipe, step 3: T ype- signature • Just as in math we write things like , we do the red part in our procedures. • In this case, we take in two numbers, and produce an number.

;; Data Definition ;; Example data: ;; num: 0, -6, 41, 7.2 ;; ;; count-posts: num * num -> num

• In num * num -> num , the "*" means there are two arguments, both nums. • If we had num * string * bool, there would be three arguments: a num, a string, and a bool. • The only things allowed in this section right now are num, string, bool, although this list will grow • These are the “data types” used in Racket

Design recipe, step 4: Call structure • The "call structure" is the part of a procedure defjnition before the body. • In (define (f x) (* x x) ) , the red part is the "call structure" • When we say to write out the call-structure, we actually mean to write (define (f x) ...) • That's not legal Racket, but we'll soon replace the "…" part.

;; Data Definition ;; Example data: ;; num: 0, -6, 41, 7.2 ;; ;; count-posts: num * num -> num (define (count-posts width-count depth-count) . . .)

Call structure • The procedure name (count-posts) was given in the problem description. • The argument-names were given in the problem description. • This step is almost mechanical!

Design recipe, step 5: Input-output specifjcation • Write a comment describing the inputs and outputs of the procedure. • One line for each argument, using the name of the argument, and describing its role • An opportunity to restrict the inputs to a smaller set than the stated domain • Example: input: count, a positive integer indicating how many cars there are • Example: input: state-name, a string containing the two-letter abbreviation of some US state, written in capital letters, such as "MA" or "RI" or "AK". • One line for the result that's computed

;; Data Definition ;; Example data: ;; num: 0, -6, 41, 7.2 ;; ;; count-posts: num * num -> num ;; inputs: ;; width-count, an integer, the number of posts along one ;; side of the property, at least 2. ;; depth-count, an integer, the number of posts along the perpendicular ;; side of the property, also at least 2. ;; output: the total number of posts needed to fence in the ;; property, an integer. (define (count-posts width-count depth-count) . . .)

Design recipe, step 6: test-cases/examples • Label a section for test-cases • Write several tests cases • Explore "edge cases" of the domain • Explore "generic cases" of the domain • For "positive integers", an edge-case is "1", because if you move one step further left, you're at 0, which is no longer positive. • For "integers between 1 and 100, inclusive", both 1 and 100 are edge cases. • For small fjnite sets, like "four amino acids in DNA, A, C, T, G", test all of them. • For this problem: width and depth 2 are edge cases.

;; Data Definition ;; Example data: ;; num: 0, -6, 41, 7.2 ;; ;; count-posts: num * num -> num ;; inputs: ;; width, an integer, the number of posts along one ;; side of the property, at least 2. ;; depth, an integer, the number of posts along the perpendicular ;; side of the property, also at least 2. ;; output: the total number of posts needed to fence in the ;; property, an integer. (define (count-posts width depth) . . .) ;; test cases for count-posts (check-expect (count-posts 2 2) 4) (check-expect (count-posts 2 5) 10) (check-expect (count-posts 7 2) 14) (check-expect (count-posts 5 8) 22)

(check-expect (count-posts 2 2) 4) • Special feature of CS17 Racket/DrRacket • Says “If I process with (count-posts 2 2) DrRacket, I expect the result to be 4 • If that turns out to be the case, then check-expect does nothing – it produces no output • If the two things don’t match, then check-expect produces a warning message saying so! • That gives you a failure case that you can use to debug (i.e., fjx) your program.

Design recipe, step 7: write the program •