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Introduction to Gofer            5. STANDARD AND USER-DEFINED FUNCTIONS


5. STANDARD AND USER-DEFINED FUNCTIONS

The function "sum" used in the examples above, and indeed the  addition
and multiplication functions (+) and (*), are  all  standard  functions
which are included as part of a large collection  of  functions  called
the `standard prelude' which are loaded into the Gofer system each time
that you start the interpreter.  Quite a number of useful  calculations
can be carried out using these functions alone, but  for  more  general
use you can also define your own functions and store the definitions in
a file so that these functions can be loaded and used by by  the  Gofer
system.  For example, suppose that you create a file "fact"  containing
the following definition:

     fact n = product [1..n]

The "product" function is another standard function which can  be  used
to calculate the product of a list of integers, and so the  line  above
defines a  function  "fact"  which  calculates  the  factorial  of  its
argument.  In standard  mathematical notation,  fact n = n!   which  is
usually defined informally by an equation of the form:

                 n! = 1 * 2 * ... * (n-1) * n

Once you become familiar with the notation used by Gofer, you will  see
that the Gofer definition of the  factorial  function  is  really  very
similar to this informal mathematical definition.

In order to use this definition from the  Gofer  interpreter,  we  must
first load the definitions of  the  file  into  the  interpreter.   The
simplest way to do this uses the ":l" command:

    ? :l fact
    Reading script file "fact":
    Parsing......................................................
    Dependency analysis..........................................
    Type checking................................................
    Compiling....................................................

    Gofer session for:
    /gofer/prelude
    fact
    ?

Notice the list of filenames displayed after "Gofer session for:"; this
tells you which files of definitions are currently being used by Gofer,
the first of which is the  file  containing  the  definitions  for  the
standard prelude.  Since the file  containing  the  definition  of  the
factorial function has now  been  loaded,  we  can  make  use  of  this
function in expressions entered to the interpreter:

    ? fact 6
    720
    (57 reductions, 85 cells)

For another example, recall the  standard  mathematical  formula  which
tells us that  the  number  of  ways  of  choosing  r  objects  from  a


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Introduction to Gofer            5. STANDARD AND USER-DEFINED FUNCTIONS


collection of n objects is given by n! / (r! * (n-r)!).  In Gofer, this
function can be defined by:

    comb n r = fact n /(fact r * fact (n-r))

In order to use this function, we can either edit the file "fact" which
contains  the  definition  of  the  factorial  function,   adding   the
definition of "comb" on a new line, or we can include the definition as
part of an expression entered whilst using Gofer:

    ? comb 5 2 where comb n r = fact n /(fact r * fact (n-r))
    10
    (110 reductions, 161 cells)
    ?

The ability to define a function as part of an expression like this  is
often quite useful.  However, if the function "comb" were likely to  be
wanted on a number of occasions, it would be more sensible to  add  its
definition to the contents of the file "fact",  instead  of  having  to
repeat the definition each time it is used.

You will learn more about the functions defined in the standard prelude
and find out  how  to  define  your  own  functions  in  the  following
sections.


































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