Function

Command: Function


Synopsis

{proc} literal_1 ... literal_n Function -> proc'
string literal_1 ... literal_n Function -> proc'
[literal_1 ... literal_n] {proc} Function -> proc'
[literal_1 ... literal_n] string Function -> proc'


References

[1] The Mathematica Book "Function"
File
lib/sli/mathematica.sli
Parameters

proc - code body using variables
string - code body using variables in infix notation
literal_i - the name of the ith argument
proc' - pure function with named arguments

Author
Diesmann
Description

Pure functions are one of the most powerful features of SLI. They are
first class objects and can be assembled at run time like arrays. Some
times pure functions are constructed for one time execution however more
often they are used as arguments of functional operators like Map and Fold
executing the pure function many times.
If a pure function has several arguments or a particular argument is used many
times in the code managing the location of the arguments on the stack can be
cumbersome. In these situations operator Function is helpful it assigns each
argument of the pure function to a formal name which can be used in the body
of function. If the pure function is specified as a string Compile Math is
called for conversion to rpn. Note that the example combining Function and Map
is efficient. The pure function is constructed from the string only once but
executed 4 times with different arguments. In the alternative syntax the variables
are declared by an array prior to the body of the function. This notation increases
the readability of definitions of named functions because in most programming
languages the declaration of variables preceeds the function body. In combination
with operator def also the type of the arguments can be specified. The definition
of a function without arguments is useful if the body of the function introduces
local variables and therefore profits from the automatic restriction of scope by
operator Function. This is shown in the last example. Without the empty array the
arguments of Function would not be unique.
The availability of the alternative version ExecFunction with immediate execution
highlights the fact that a pure function with named arguments maybe used
for clarity even in situations where it needs to be evaluated only once.

Examples

2 {x 1 x add mul} /x Function exec --> 6
2 3 {x 1 x add mul} /x /y Function exec --> 6
2 3 {x y x add mul} /x /y Function exec --> 10
2 3 ( x*(y+x) ) /x /y Function exec --> 10

( x*(y+x) ) /x /y Function --> {<< >> begin /y Set /x Set x y x add mul end}

[2. 3. 4. 5.] (x + (1+x)^3) /x Function Map --> [29. 67. 129. 221.]

/f ( x*(y+x) ) /x /y Function def
/f [/x /y] ( x*(y+x) ) Function def

/f [/doubletype /doubletype] [/x /y] (y+x^2) Function def
/f [/doubletype /doubletype] [/x /y] {y x dup mul add} Function def


/f [] (x=sin(0.7);x^2-3*x) Function def


Version: 090302