When we examine the reduce function:
my $result = reduce &reduction_procedure, @array;
we conclude with the following simple rules to the inner workings:
Reduction Rules
---------------
1. For the first pair of objects from our input (@array)
we apply the reduction procedure (&reduction_procedure) and we get our first result.
2. We apply the reduction procedure (&reduction_procedure) to the result (object)
of the previous rule and the next input (object) from our input (@array),
and we get an intermediate result (object).
3. We run rule.2 for every of the remaining objects from our input (@array)
This simple rules work also the same for the reduction metaoperator []. For example:
example.1
---------
say [+] [1,2,3,4]; # result : 10
For example.1 the reduction rules apply as is:
Step.1 use Rule.1 : 1 + 2 = 3 1(first value) + 2(second value) = 3
Step.2 use Rule.2 : 3 + 3 = 6 3(previous result) + 3(current value) = 6
Step.3 use Rule.2 : 6 + 4 = 10 6(previous result) + 4(current value) = 10
but NOT for the following example:
example.2
----------
say [<] 1,2,3,4; # result : True
For example.2 we observe an inconsistency:
Step.1 use Rule.1 : 1 < 2 = True 1(first value) < 2(second value) = True
Step.2 use Rule.2 : 2 < 3 = True True(previous result) && True(current result) = True
Step.3 use Rule.2 : 3 < 4 = True True(previous result) && True(current result) = True(result)
The inconsistency is that from Step.2 and onwards we can NOT use the result of the previous step as the first parameter of subsequent reduce operations, but instead we calculate a logical intermediate result, with use of the actual values and finally we add as a final step the use of "logical AND" upon the intermediate logical results of each step:
Reduction Result = True && True && True = True (use of logical AND as "meta-reduction" operator)
Sort of speak we have a "meta-reduction" metaoperator!
Questions:
1. Is that an inconsistency with a purpose?
2. Can we exploit this behavior? For instance instead of use of && (logical AND)
as "meta-reduction" operator can we use || (logical OR) or ?^ (logical XOR) ?
It is not an inconsistency but and example of how operator associativity works in Raku.
Writing :
[<] 1,2,3,4
Is the same as writing :
1 < 2 < 3 < 4
In most languages this wouldn't work but the < operator has chain associativity so it effectively treats this as :
(1 < 2) and (2 < 3) and (3 < 4)
Which is True.