Parallel Iteration

Sometimes you want to iterate across two lists in parallel, or perhaps you want to traverse a list while incrementing a variable.

The general syntax of a repeat loop is

iterator1, iterator2, ..., iteratorN repeat loopbody

where each iterator is either a for or a while clause. The loop terminates immediately when the end test of any iterator succeeds or when a leave or return expression is evaluated in loopbody. The value returned by the loop is the unique value of Void.

l := [1,3,5,7]
 [1,3,5,7]
                    Type: List PositiveInteger

m := [100,200]
 [100,200]
                    Type: List PositiveInteger

sum := 0
 0
                    Type: NonNegativeInteger

Here we write a loop to iterate across two lists, computing the sum of the pairwise product of the elements:

for x in l for y in m repeat
  sum := sum + x*y
                    Type: Void

The last two elements of l are not used in the calculation because m has two fewer elements than l.

sum
 700
                    Type: NonNegativeInteger

This is the “dot product”.

Next we write a loop to compute the sum of the products of the loop elements with their positions in the loop.

l := [2,3,5,7,11,13,17,19,23,29,31,37]
 [2,3,5,7,11,13,17,19,23,29,31,37]
                    Type: List PositiveInteger

sum := 0
 0
                    Type: NonNegativeInteger

for i in 0.. for x in l repeat sum := i * x
                    Type: Void

Here looping stops when the list l is exhaused, even though the for i in 0.. specifies no terminating condition.

sum
 407
                    Type: NonNegativeInteger

When “|” is used to qualify any of the for clauses in a parallel iteration, the variables in the predicates can be from an outer scope or from a for clause in or to the left of the modified clause.

This is correct:

for i in 1..10 repeat
  for j in 200..300 | ood? (i+j) repeat
    output [i,j]

But this is not correct. The variable j has not been defined outside the inner loop:

for i in 1..01 | odd? (i+j) repeat -- wrong, j not defined
  for j in 200..300 repeat
    output [i,j]

It is possible to mix several of repeat modifying clauses on a loop:

for i in 1..10
  for j in 151..160 | odd? j
    while i + j < 160 repeat
      output [i,j]
 [1,151]
 [3,153]
                    Type: Void

Here are useful rules for composing loop expressions:

1. while predicates can only refer to variables that are global (or in an outer scope) or that are defined in for clauses to the left of the predicate.
2. A “such that” predicate (somthing following “|”) must directly follow a for clause and can only refer to variables that are global (or in an outer scope) or defined in the modified for clause or any for clause to the left.