There are several formats for function definitions:

   Equations
   Conditional Equations
   Patterns

++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
Equations

> flatTax income = 0.25 * income

++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
Conditional Equations

A conditional equation has the form:

   fun params
     | guard1 = exp1
     | guard2 = exp2
     etc
     | otherwise = exp
     
Example:
    
> tax income
>  | (income < 0) = error "negative income?"
>  | (income <= 20000) = 0
>  | (income <= 50000) = 0.3 * income
>  | (income <= 90000) = 0.4 * income
>  | otherwise = 0.5 * income

++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
Patterns

Parameters can be patterns. In this case a function might be defined by multiple equations. Given a call to a function with argument arg, the interpreter selects the first equation with a parameter that matcches arg.

Examples:

> isZero 0 = True
> isZero _ = False -- _ = wildcard

> half 0 = 0
> half n = n `div` 2

> isVowel 'a' = True
> isVowel 'e' = True
> isVowel 'i' = True
> isVowel 'o' = True
> isVowel 'u' = True
> isVowel _ = False

++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
Locals

We can use a where clause to introduce local constants and functions:

> small x
>  = abs(x) <= delta
>   where delta = 1.0e-10

> tax2 income
>  | (income < 0) = error "negative income?"
>  | (income <= income1) = 0
>  | (income <= income2) = rate1 * income
>  | (income <= income3) = rate2 * income
>  | otherwise = rate3 * income
>  where
>   income1 = 20000
>   income2 = 50000
>   income3 = 90000
>   rate1 = 0.3
>   rate2 = 0.4
>   rate3 = 0.5

> myTax = let income = 32345 in tax2 income

> small2 x
>  = dist x 0 <= delta
>   where  
>    delta = 1.0e-10
>    dist x y = sqrt(square x + square y)
>    square x = x * x

++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
Recursion

Selection is achieved by patterns or conditionals. Iteration is achieved by recursion:

> fact:: Int->Int
> fact n
>  | n <= 1    = 1
>  | otherwise = n * fact(n - 1)

> fib:: Int->Int
> fib 0 = 0
> fib 1 = 1
> fib n = fib(n - 1) + fib(n - 2)


++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
Offside Rule

Haskell uses the offsides rule to determine where a definition ends: A defintion is ended by the first text that appears in the same column or to the left of the same column where the defintion began.