Reduce

(NOTE: WORK IN PROGRESS!)

To reduce a sequence using a binary infix function is to combine the elements of the sequence by place the operator "between" each element. For example, the reduction of [2 3 4] using + is 2+3+4.

The symbol @ is used for reduction. This use of @ is related to its use for making tuples. See Tuples.

A recursive definition:

[] @OP R == R
(x,L) @OP R == x OP (L @OP R)

[] @OP == left_identity OP # If defined
[x] @OP == x
(x,L) @OP == x OP (L @OP)

L OP@ [] == L
L OP@ (x,R) == (L OP x) OP@ R

Note that right(?)-reduction OP@ uses the same syntax as tupling: X@. However, the former requires OP to be a binary function, while the latter requires X to be a sequence.

Note that @, is append, while @@, appends all the elements.

The operator | is syntax, not a function. However, it is convenient to define @| and |@ using the same definitions as before (NOT IMPLEMENTED). The left_identity and right_identity of | are assumed to be (;) (i.e. the empty sequence).

It is also convenient to define ~|@ EXPR to collect each result from evaluating EXPR, and make a sequence of them all.