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define --
define a function
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Define F(X_1, .., X_n) C EndDefine
Define F(X_1, .., opt X_n) C EndDefine
Define F(...) C EndDefine
return FUNCTION |
These commands introduce a user-defined function.
F is the name
comprising letters, digits or underscore, but must start with a letter.
X_1 and so on are the parameters (much like local variables).
C is the function body.
(1) INTRODUCTION.
These commands assign a user-defined function to the variable
F;
any previous value
F held will be lost! The function
F can be
called in the following obvious way:
F(E_1,...,E_n)
where the arguments
E_i's are expressions.
The result of the evaluation of each expression
E_i is assigned
to the respective formal parameter
X_i, and the command sequence
C is executed.
If, during the execution of
C, a statement
Return E is executed,
then the result of the evaluation of
E is the return-value of the
function
F. If no
Return command is executed, or
Return is
executed without argument, then the return-value is
Null.
/**/ define square(X) --> simple fn with 1 parameter
/**/ return X^2;
/**/ enddefine;
/**/ square(5);
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(2) SCOPE OF VARIABLES.
Every parameter and every variable used in the function body
C is
local to the function
unless the variable is a
ref
parameter, or
the variable was declared global by
TopLevel
.
See
ref
to learn about passing function arguments
by reference,
i.e. so that the function can change the value of an existing variable.
See
TopLevel
for the use of global variables.
/**/ Define Add5(N) // use helpful name for fn
/**/ N := N + 5;
/**/ Return N;
/**/ EndDefine;
/**/ N := 0;
/**/ Add5(N);
5
/**/ N; --> N is unchanged despite the function call.
0
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(3) VARIABLE NUMBER OF PARAMETERS.
It is also possible to have some optional parameters or a variable
number of parameters. For optional parameters see also
IsDefined
.
-- (3a) OPTIONAL ARGUMENTS
-- These must be in the last position(s).
/**/ define deg0(f, opt x)
/**/ if f=0 then return 0; endif;
/**/ if IsDefined(x) then return deg(f,x); endif;
/**/ return deg(f);
/**/ enddefine;
/**/ use P ::= QQ[x,y,z];
/**/ deg0(zero(P));
0
/**/ deg0(x^2+y);
2
/**/ deg0(x^2+y, y);
1
--------------------------------------
-- (3b) VARIABLE NUMBER OF PARAMETERS
/**/ Define MySum(...) --> arguments are in the LIST "ARGV"
/**/ If len(ARGV) = 0 Then Return 12345; EndIf;
/**/ ans := 0;
/**/ Foreach N In ARGV Do ans := ans+N; EndForeach;
/**/ Return ans;
/**/ EndDefine;
/**/ MySum(1,2,3,4,5);
15
/**/ MySum();
12345
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The CoCoA-4 statement,
Help S; is now OBSOLETE!