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

From teacherspayteachers.com, mathinsight.org,

• Key idea: it’s machine-like!
• Put in the same input twice in a row, you’ll get the same output!

T ypical high-school math description

• f 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 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
• day: 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
• f 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

;; 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-count depth-count) (- (+ (* 2 width-count) (* 2 depth-count)) 4) ) ;; 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)

Design recipe, step 8: run the program!

• If all goes well, you'll see "All 4 tests passed!"