1.3

## The University of Glasgow The gate to enlightenment

# Introduction to Expressions and Equations

## Expressions

### Haskell has no statements, only expressions!

• In an imperative language like C or Java,
• there are expressions that denote small scale computations (2*x), and
• statements that handle sequencing, looping, conditionals, and all the large scale operation of the program.
• Pure functional programming languages don’t have any statements — no assignments, no jumps.
• Instead, all computation is performed by evaluating expressions
• (We’ll still be working on expressions at the end of the course, since that’s all there is.)

### Examples of integer expressions

An expression evaluates to a result (usually written $e \rightsquigarrow r$ but we’ll use e -- > r). Haskell uses a similar notation for numbers and operators as most languages:

    2 -- > 2
3+4 -- > 7
3+4*5    {equivalent to 3+(4*5)} -- > 23
(3+4)*5   {equivalent to 7*5} -- > 35


### Syntax of expressions

• Parentheses are used for grouping, just as in mathematics.
• If you don’t need parentheses for grouping, they are optional.
• Operators have precedence, e.g. $*$ has “tighter” precedence than $+$, so $2 + 3 * 4$ means $2 + (3 * 4)$.
• Use the reference documentation for complete list of operators and their precedences, if you need them.

### Function applications

• Expressions can contain function calls.
• A function takes argument(s), performs some computation, and produces result(s).
• The function abs gives the absolute value of a number.
• To use a function, you apply it to an argument. Write the function followed by the argument, separated by a space.
  abs 5 -- > 5
abs (-6) -- > 6


### Parentheses are for grouping

Good style

  2+3*5
2+(3*5) -- might be clearer to some readers
abs 7


You don’t need parentheses. The following are legal, but they look silly:

    (2) + ((3+(((((5)))))))
abs (5)
abs (((5)))


### Functions with several arguments

• min and max are functions that take two arguments.
• The arguments are given after the function, separated by whitespace.
• Write min 3 8, don’t write min(3, 8);
    min 3 8 -- > 3

max 3  8 -- > 8


### Precedence of function application

• Function application binds tighter than anything else.
• So f x + 3 means (f x) + 3 and not f (x+3)
• If an argument to a function is an expression, you’ll need to put it in parentheses.

## Equations

### Equations give names to values

• Equations are used to give names to values.
answer = 42

• An equation in Haskell is a mathematical equation: it says that the left hand side and the right hand side denote the same value.
• The left hand side should be a name that you’re giving a value to.
• Correct: x = 5*y
• Incorrect: 2 * x = (3*x)**2 – Reassignment is not allowed in a pure FPL

### Equations are not assignments

• A name can be given only one value.
• Names are often called “variables”, but they do not vary.
• In Haskell variables are constant!
    n = 1    -- just fine!
x = 3*n  -- fine
n = x    -- Wrong: can have only one definition of n

• Once you give a value to a name, you can never change it!
• This is part of the meaning of “pure” and “no side effects”

### What about n = n+1?

• In imperative languages, we frequently say n := n + 1
• This is an assignment, not an equation!
• It means (1) compute the right hand side, using the old value of n; then (2) discard the old value of n and overwrite it with the new value.
• There are no equations in imperative languages like C and Java.

• In Haskell, it is valid to write n = n + 1.
• This is an equation, not an assignment!
• It means: compute the value of n that has the property that n = n + 1.
• Haskell will try, and it will fail.

### How can you compute without assignments?

• Think of an assignment statement as doing three things:
1. It evaluates the right hand side: computing a useful value.
2. It discards the value of the variable on the left hand side: destroying a value that might or might not be useful.
3. It saves the useful value of the RHS into the variable.
• In a pure functional language
• We never destroy old values.
• We just compute new useful ones.
• If the old value was truly useless, the garbage collector will reclaim its storage.

• You can install the Haskell compiler/interpreter on your own computer. Go to https://www.haskell.org/platform to get the Haskell Platform for your system, it is very easy to install. For more details see Installing Haskell for Yourself in Week 2.
• All software used in this course is free software.
• Try experimenting with the expressions shown in this lecture.
• And try some experiments of your own.

To launch the interactive Haskell interpreter ghci, just type ghci in your terminal:

[wim@fp4 ~]\$ghci
GHCi, version 7.8.3: http://www.haskell.org/ghc/  :? for help

To exit the Haskell interpreter, type :quit at the interactive prompt.