CS 135 (Module 2: Functions)

Imperative Language and Examples?

Based on frequent changes to data. (Ex: Machine language, Java, C++, Turing, Visual Basic, Python)

Functional Language and Examples?

Based on the computation of new values rather than the transformation of old ones. (Ex: Racket, Excel formulas, LISP, ML, Haskell)

What are a subset of Racket?

Graduate set of teaching languages

What is the background of racket?

A dialect of Scheme and a descendant of Lisp

What are the two windows of Racket?

Interactions (now) and Definitions (later)

What is the Interactions window of Racket?

A read-evaluate-print loop (REPL)

Are integers in Racket bounded or unbounded?

Unbounded

How are rational numbers represented?

Exact

Expressions whose values are not rational numbers are flagged as being:

Inexact (Ex: [sqrt 2] -> #i1.4142135623709)

Given: f(x) = x^2, g(x, y) = x + y
1. What is the name of the function?
2. What is its parameters?

1. g 2. (x, y)

An ____ of a function supplies ___ for the ____, which are substituted into the algebraic expression.

1. application 2. arguments 3. parameters

Define Canonical form

A natural unique representation of an object, or a preferred notation for some object

What are the two rules for canonical substitutions?

1. Functions are applied to values
2. When there is a choice of possible substitutions, always take the leftmost choice

What are the two uses of parentheses?

1. Function application
2. To specify ordering

+, - are examples of:

Infix/Arithmetic operators

When should parentheses be used in Racket?

To signal a function application or some other Racket syntax

A syntax error is:

An error discovered when reading an expression. Ex: (* (5) 3)

A run-time error is:

An error discovered when evaluating an expression. Ex: (/ 25 0)

e and pi are examples of:

Constant

(abs x), (max x y ..), (ceiling x) are examples of:

Functions

A function definition consists of:

1. A name for the function
2. A list of parameters
3. A single body expression

Give (define (g x y) (+ x y):
1. What does define do?
2. What is the name of the function?
3. What are the parameters?
4. What is the body (expression)?

1. "binds" name to body
2. g
3. (x y)
4. (+ x y)

What is define and what does it do?

define is a special form that binds a name to an expression (which uses the parameters that follow the name).

What does an application of a user-defined function do?

It substitutes arguments for the corresponding parameters throughout the definition's expression.

What are identifiers?

Functions and parameters are named by identifiers, like, f, x-ray, WhaTeVer.

What can identifiers not contain?

Space, brackets of any kind, or quotation marks

Does changing names of parameters change what the function does?

No

Can functions use the same parameter name?

Yes

Does parameter order matter?

Yes

What does (define k 3) do?

Binds the name k to the value 3.

What does (define p (sqr k)) do?

The expression (sqr k) is first evaluated to give 9, and then p is bound to that value.

What are the advantages of Constants?

1. can give meaningful names to useful values
2. reduce typing and errors when such values need to be changed
3. make programs easier to understand

pi and e are:

built-in constants

Where can constants be used?

In any expression, including the body of function definitions

What is a helper function?

A function that helps implement another function.

What 3 purposes are helper functions used for?

1. Reduce repeated code by generalizing similar expressions
2. Factor out complex calculations
3. Give meaningful names to operations

1. Where are helper functions placed?
2. What are the exceptions?

1. After the function that uses them.
2. i) Helpers used to define constants must be defined before being used. For (define c (distance 1 1 3 9)), distance must be already defined
ii) Helpers used in several functions in the same file are often placed first
iii) The order of functions specified in an assignment takes precedence over the rules above

What is a scope and what are the two kinds of scope?

The scope of an identifier is where it has effect within the program. The two kinds are global and function. The smallest enclosing scope has priority where duplicate identifiers within the same scope will cause an error.

What is a Racket program?

A Racket program is a sequence of definitions and expressions.

What do the expressions do?

The expressions are evaluated, using substitution, to produce values.

Expressions make use of what?

Expressions may also make use of special forms (e.g. define), which look like functions, but don't necessarily evaluate all their arguments.

When substituting, we must:

Substitute each one by one