Understanding Expressions

:leaves: This tutorial covers:

  • Expression Identification
  • Expression Examples
  • Operator Types
  • Parenthesis

:seedling: Before starting, you should be familiar with:

:deciduous_tree: At the end, you should be able to:

  • Identify what an expression is
  • Write out math equations using operators
  • How to use the operators in BoGL

An expression is something that must be evaluated in order to determine its value. An expression in BoGL can consist of values, operators, functions, if/else statements, and local value definitions that together evaluate to some value. Not knowing what all of those things are is okay, it is still a good idea to get an early start on understanding the concept of an expression before completely comprehending all that it can be. Let's look at an example to illustrate the idea of an expression.

2 + 3 - 4

The expression above consists of values (2, 3, 4) and operators (+, -). The resulting value is 1 when this expression is evaluated.

Expressions in BoGL are usually found inside of value and function definitions, however, you may still evaluate one by typing it directly into the interpreter. This is useful for experimentation and practice. Try typing the expression 2 + 3 - 4 into the interpreter. It should return 1.

Type 2 + 3 - 4 in the interpreter below and press enter.


Lets look at some more examples!

not(True)

The expression above consists of a built-in function not and a value True. We may not know what this function does yet, but we do know that it will evaluate to some value. Try entering this expression into the interpreter to see the resulting value.

Type not(True) in the interpreter below and press enter.


An expression can be passed as an argument to a function as long as it evaluates to the function's parameter type. We saw in the example above that the function not takes a Bool parameter and returns a Bool. Try and see what happens when you enter the expression not(not(True)) into the interpreter.


Parenthesis

The order in which parts of an expression evaluate first can be very consequential to the resulting value. We can have some control over which parts of an expression are evaluated first by using parenthesis ().

12 / 4 / 2

The expression above currently evaluates to 1. It does this by evaluating operations in the following order:

First operation: 12 / 4, resulting in 3

Second operation: 3 / 2, resulting in 1

If we instead wanted the expression to evaluate 4 / 2 first, we can wrap it in parenthesis.

12 / (4 / 2)

Something that we have been using in these expression examples are operators. The integer operators (+, -, /, *) are fairly intuitve if you know basic arithmetic. There also exist other operators in BoGL that are not necessarily intuitive. Learning these operators and practicing by writing expressions with them will make it easier to work with more complicated expressions, like conditional expressions, which we will cover in further tutorials.


Integer Operators

Expressions will often contain arithmetic logic (addition, multiplication, etc…). The BoGL language provides basic operators that can be used with Int values. The Integer operators in BoGL are binary operators because they have two operands. Operands are the values/expressions on each side of the operator.

Operator Symbol Example Expression Example's Evaluation
Addition + 2 + 2 4
Subtraction - 10 - 3 7
Multiplication * 2 * 5 10
Division / 12 / 4 3

:warning: Note about integer division

Since integers cannot be fractional values, the result of a division in BoGL will always be rounded down.


Relational Operators

Relational operators always evaluate to a Bool. They are commonly used as conditions for conditional expressions. You can think of these operators as evaluating a relationship between two values. For example, the relational operator == will check to see whether the operands are equal to eachother. If the operands are equal, then the expression will evaluate to True, otherwise it will evaluate to False. This operator is evaluating whether a relationship of equivalence exists between the two operands.

Integer Specific Relational Operator Symbol Example Expression Example's Evaluation
Equal to == 5 == 5 True
Not equal to /= 5 != 5 False

:warning: The relational operators in the table below can only be used with Int operands.

Integer Specific Relational Operator Symbol Example Expression Example's Evaluation
Greater than > 10 > 1 True
Less than < 10 < 1 False
Greater than or equal to <= 5 <= 5 True
Less than or equal to >= 4 >= 5 False

:hammer_and_wrench: Example: Parenthesis, Integer Operators, and Relational Operators

Let's do an example using Parenthesis and Integer Operators.

The goal of the Program below is to determine how parenthesis can change integer and relational operators.

Referencing the example above, we've already established adding parenthesis changes the order in which math operations are executed, just as PEMDAS does.

12 / 4 / 2

This evaluates to 1 but,

12 / (4 / 2)

evaluates to 6.

The parenthesis made 4 / 2 be evaluated first and left the 12 / 2 to be the final operation.


:dart: Excercise:
What happens when add parenthesis to Integer and Relational Operators?

Think where you would add parenthesis to make the below mathematical operations equal the desired value

  • Make the first expression equal 4
  • Make the second expression equal 5
  • Make the third expression equal 7
  • Make the fourth expression equal 3
  • Make the fifth expression equal 8
20 / 2 + 3

4 + 16 / 4 - 3

11 + 10 / 5 - 2

6 * 5 / 3 + 7

4 * 6 / 3 + 3 * 4 - 2
:eyes: Click to see a solution (but try yourself first!) 

20 / (2 + 3)

4 + (16 / 4) - 3

(11 + 10) / (5 - 2)

6 * 5 / (3 + 7)

4 * 6 / (3 + 3) * (4 - 2)


Boolean Operators

Boolean operators are similiar to relational operators in that they always evaluate to a Bool. Where Boolean operators differ is that they can only be used on operands that evaluate to Bool. These operators can be used to combine two expressions or invert one. There are three Boolean operators in BoGL, and they are technically implemented as built-in functions. The parameter and return types for these functions are type Bool.

:exclamation: The word expr in the table below is short for expression.

Boolean Operator Function Evaluation
and and(expr, expr) True when both of the expr evaluate to True.
False when one or both of the expr evaluate to False.
or or(expr, expr) True when one or both of the expr evaluate to True.
False when both of the expr evaluate to False.
not not(expr) Negates expr. True when expr evaluates to False.
False when expr evaluates to true.