FOR _ _ _ _ _ _ _ _ _ _ _ _ command

The for command is used for iterative loops. There are many possible forms it can take.

                   /                   
   /               |STEP <number> UNTIL|        
   |<var>:=<number>|                   |<number>|
FOR|               |         :         |        |<action> <exprn>
   |                                  /        |
   |EACH <var> IN <list>                        |
                                               /

 where <action> ::= DO|PRODUCT|SUM|COLLECT|JOIN.

<var> can be any valid REDUCE identifier except t o r nil, <inc>, <start> and <stop> can be any expression that evaluates to a positive or negative integer. <list> must be a valid list structure. The action taken must be one of the actions shown above, each of which is followed by a single REDUCE expression, statement or a group (<<...>>) or block ( begin... end) statement.

examples:

for i := 1:10 sum i;                                    
 


  55 


for a := -2 step 3 until 6 product a;
							


  -8 


a := 3; 

  A := 3 


for iter := 4:a do write iter; 

m := 0; 

  M := 0 


for s := 10 step -1 until 3 do <<d := 10*s;m := m + d>>; 

m; 

  520 


for each x in {q,r,s} sum x**2; 

   2    2    2
  Q  + R  + S  


for i := 1:4 collect 1/i;                              
 


     1 1 1
  {1,-,-,-} 
     2 3 4


for i := 1:3 join list solve(x**2 + i*x + 1,x);         
 


        SQRT(3)*I + 1
  {{X= --------------,
              2
        SQRT(3)*I - 1
    X= --------------}
              2
   {X=-1},
         SQRT(5) + 3   SQRT(5) - 3
   {X= - -----------,X=-----------}}
              2             2

The behavior of each of the five action words follows:

                           Action Word Behavior
Keyword   Argument Type                    Action
   do    statement, command, group   Evaluates its argument once
         or block                    for each iteration of the loop,
                                     not saving results
collect expression, statement,       Evaluates its argument once for
        command, group, block, list  each iteration of the loop,
                                     storing the results in a list
                                     which is returned by the for
                                     statement when done
 join   list or an operator which    Evaluates its argument once for
        produces a list              each iteration of the loop,
                                     appending the elements in each
                                     individual result list onto the
                                     overall result list
product expression, statement,       Evaluates its argument once for
        command, group or block      each iteration of the loop,
                                     multiplying the results together
                                     and returning the overall product
  sum   expression, statement,       Evaluates its argument once for
        command, group or block      each iteration of the loop,
                                     adding the results together and
                                     returning the overall sum

For number-driven for statements, if the ending limit is smaller than the beginning limit (larger in the case of negative steps) the action statement is not executed at all. The iterative variable is local to the for statement, and does not affect the value of an identifier with the same name. For list-driven for statements, if the list is empty, the action statement is not executed, but no error occurs.

You can use nested for statements, with the inner for statement after the action keyword. You must make sure that your inner statement returns an expression that the outer statement can handle.