Functions

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Functions
The University of the West Indies
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Functions

• In Mathematics, a function f associates each
  member of a set A ( the domain of f ) with the
  single member of a set B ( the co-domain of f )
  which we write as
• f A ? B
• If a ? A then f(a) is the associated member of B.

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Functions

• Example
• f(x) x2 for f R ? R
• Haskell uses the same concept and similar
  notation to represent functions.

Set of Real Numbers
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Functions
f(x) x2 for f R ? R
becomes
Domain Type
Co-Domain Type
f Float ? Float f x x2
Output
Input value
Function name
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Functions

• A notational difference in Haskell to be aware of
  is that we write
• f x instead of f (x)
• The brackets are not required and can make for
  clearer notation.

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Functions

• Be careful
• square x1
• is interpreted by Haskell as
• (square x) 1

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Functions

• Remember
• Function application has the highest precedence (
  priority ) than any other operator and is
  left-associative.

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Functions

• Another Example

add Float ? Float ? Float -- add two inputs x
and y add x y x y
Comments begin with -- and the line is ignored by
Haskell
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Functions

• Firstly we give the type of the function
• Read as add takes two inputs of type Float and
  returns a value of type Float

add Float ? Float ? Float
Function name
Output Argument Type
Input Argument Types
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Functions

• Secondly we give the specification ( or
  post-condition ) of the function
• The specification describes what the function
  does in English for the benefit other people.

-- add two inputs x and y
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Functions

• Finally we give the equation for the function
• The equation describes how to calculate a result
  for the function.

add x y x y
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Functions

• The separates the left-hand side from the
  right-hand side ( the body )
• The left-hand side gives the name of the function
  and the name(s) of its argument(s)
• The right-hand side of the equation gives the
  expression that describes how the result of the
  function is calculated from the values of the
  argument(s)

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Functions

• Note
• Choose meaningful names for your functions
• Function names must begin with a lowercase letter
• Do not use a function name that has already been
  used.

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Functions

• Once a function has been defined, we can apply it
  to given argument(s), provided the argument(s)
  have the right type.

Preludegt add 5.6 7.4 13.0
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Functions

• Example

distFromOrigin ( Float, Float) ?
Float distFromOrigin (x,y) sqrt ( x2 y2)
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Functions

• Exercises Write and test the following function
  definitions
• A function to calculate the absolute difference
  of two integers ( use the if conditional )
• A function to test if an input integer is even
• ( hint use the Haskell function mod )