# Expressions and Evaluation

## Introduction

In this subsection, you will learn more about Functional Programming. You will also learn about expressions and evaluation.

## Functional Programming

Before we jump into the Racket language itself, we will go over the deceptively simple big idea for this lesson. In short, it states that, when evaluating an expression, we can take the value returned by one function and use it as an argument to another function. By "hooking up" two functions in this way, we invent a new, third function. For example, let's say we have a function that adds the letter s to the end of a word (in pseudo-code):

add-s("run") = "runs"


and another function that puts two words together into a sentence:

sentence("day", "tripper") = "day tripper"


We can combine these to create a new function that represents the third person singular form of a verb:

third-person(verb) = sentence("she", add-s(verb))


That general formula looks like this when applied to a particular verb:

third-person("sing") = "she sings"


The way we say it in Racket is

(define (third-person verb)
(sentence 'she (add-s verb)))


Don't worry if this is confusing or unintuitive to you; you'll get plenty of practice on this concept. Nevertheless, it will turn out that we can express a wide variety of computational algorithms by linking functions together in this way. This linking is what we mean by functional programming.

## Expressions

The Big Idea: You can ask Racket "questions", called expressions. The Racket interpreter will then "think" about your question, or evaluate your expression. You then get back answers, called values. Everything we type into Racket (that does not error) is an expression.

When you want Racket to do something (e.g. add two numbers together), you write an expression in prefix notation. Although all non-error inputs are expressions, the most interesting kind is a call to a procedure. Take a look at the following example:

(+ 3 4)


In this example:

• + is the procedure, or the operator of the expression
• 3 is an argument to +, or an operand of the expression
• 4 is also an argument/operand

This syntax allows us to nest expressions:

(* (max 2 3) (/ 8 4))

• *, max, and / are all procedures
• * is the operator of the large expression, while (max 2 3) and (/ 8 4) are the operands of the large expression
• max is the operator of the first subexpression, while 2 and 3 are the operands of the first subexpression
• / is the operator of the second subexpression, while 8 and 4 are the operands of the second subexpression
Test Your Understanding

Which of the following are valid Racket expressions? Select all that apply.

Now, open up the Racket interpreter on your computer and try out some expressions of your own.

## Evaluation

Racket evaluates expressions using Applicative Order (taught in Lesson 1), which follows these rules:

1. Evaluate the operator and operands
2. Apply the operator to the operands

How Racket actually understands and evaluates an expression is rather complex, and is gone over in Lesson 11. For now, let's move on to the next subsection!