Binding and pattern matching

A binding binds a name or even several names with a function definition.

In Haskell, a binding is defined by symbol “=” whereas

1. on the left hand side
   1. the function name and its parameters
   2. or a pattern is given,
2. and on the right had side the definition of the function.

• examples
  • compile, error and warning free, with compiler: GHC 8.10.4, using compiler option -Wall

• function name an parameter (half x), on the left hand side of the equal sign (=)
  • half is the function that can take parameter x
  • half can be evaluated by name with a parameter just right behind the function name (e.g. half 5)
• function definition (x / 2), on the right hand side
  • if half is demanded to be evaluated then the result is delegated to function (/) with parameter x and 2
• example
  • code line:

    half x = x / 2

  • works in:

    main :: IO ()
    main = 
        do
                print (half 5)
     
    half x = x / 2

  • with compiler warning, which we ignore for pedagogical reasons
  • executes, with output:

    2.5

  • NOTE: The term half 5 is in round brackets, which means half 5 has to be evaluated and its result is the first parameter of print. The expression print half 5 would lead to a compiler error, beause this would be interpreted as print has two parameters.

• pattern matching needs the knowledge of tuples, arrays, and algebraic data types
• unfortunately tuples, arrays, and algebraic data types can only be fully understood with pattern matching
• this is attempt to explain both at the same time, while keeping the focus on bindings

• list construction
  • lists can be written in the form [ <elem 1>, <elem 2>, … <elem n>]
    • whereas [] is an empty list
    • the elements between brackets are comma seperated
  • all elements of a lists have to have the same type
  • list can be defined infinite
  • an empty list is of type [a], whereas a is a type parameter
  • lists can also be written in the form <elem 1> : <elem 2> : … <elem n> : [ ]
    • : is an operator that appends an element on the left hand side to a list on the right hand side
    • : is associated to the right
    • e.g. 3 : 2 : [] equals (3 : (2 : []))
  • lists can be written in a mixed form <elem 1> : <elem 2> : … <elem n> : [ <elem n+1>, <elem n+2>, … <elem m>]
    • e.g. (3 : (2 : [])) equals 3 : [2] equals [3, 2]
• pattern maching with lists
  • in the same form as thay are constructed above
  • but with binding names
• example
  • code line:

    [first, b, zet] = [13, 17, 19]

  • works in:

    main :: IO ()
    main = 
        do
            print first
            print b
            print zet
     
    [first, b, zet] = [13, 17, 19]

  • with compiler warning, which we ignore for pedagogical reasons
  • executes, with output:

    13
    17
    19

• tuple construction
  • tuples are written in the form ( <elem 1>, <elem 2>, … <elem n>)
    • elements between brackets are comma seperated
  • elements of a tuple can have different types
  • tuples can contain two or more elements
    • cannot be empty
    • cannot have a single element only
  • the type of the tuple is the tuple with the order of types e.g. (Char, Int, Double)
  • elements of tuples are finite
• pattern maching with tuples
  • in the same form as thay are constructed above
  • but with binding names
• example
• • code line:

    [first, b, zet] = [13, 17, 19]

  • works in:

    main :: IO ()
    main = 
        do
            print first
            print b
            print zet
     
    (first, b, zet) = ('a',12,23.4)

  • with compiler warning, which we ignore for pedagogical reasons
  • executes, with output:

    'a'
    12  
    23.4

• type definitions
  • algebraic data types can be defined in the form data <TypeName> = <DataConstructorA> <DataTypeA1> <DataTypeA2> … <DataTypeAN> | <DataConstructorB> <DataTypeB1> <DataTypeB2> … <DataTypeBM> | <DataConstructorO> …
  • whereas | devides variants simmilar to variants in unions in programming the language C and C++
  • each variant has to have a constructor
  • each constructor can contain zero, one or more data types
• construction of data of algebraic data types
  • constructed in the form <DataConstructor> <Value1> <Value2> … <ValueN>
  • whereas the values have to conform with the data type declaration
• pattern maching with tuples
  • in the same form as thay are constructed above
  • but with binding names
• example
  • code lines:

    data MyData = MyVariantA Integer Char Double | MyVariantB Int | MyVariantC
    MyVariantA first b zet = MyVariantA 12 'a' 23.4

  • work in:

    main :: IO ()
    main = 
        do
            print first
            print b
            print zet
     
    data MyData = MyVariantA Integer Char Double | MyVariantB Int | MyVariantC
     
    MyVariantA first b zet = MyVariantA 12 'a' 23.4
     
    MyVariantB n = MyVariantB 123
     
    MyVariantC = MyVariantC -- is not binding anything, but compiles consistently

  • with compiler warning, which we ignore for pedagogical reasons
  • executes, with output:

    12
    'a'
    23.4
    123

• NOTE: I may look like: It does'nt make sense to have a constructor no elements. However, MyVariantC is already a value in itself, and can be used to differentiate between the variants.