Boolean Functions

Boolean functions operate on values of 0 and 1.

∧ And

Dyadic only

Returns 1 when both arguments are 1.

      1∧1
1
      1∧0
0
      0∧0
0
      1 1 0 0∧1 0 1 0
1 0 0 0

∨ Or

Dyadic only

Returns 1 when either argument is 1.

      0∨1
1
      0∨0
0
      1 1 0 0∨1 0 1 0
1 1 1 0

~ Tilde

Monadic: Not

Flips 0 to 1 and 1 to 0.

      ~1
0
      ~0
1
      ~1 0 1 1 0
0 1 0 0 1

Note

⍲ (nand) and ⍱ (nor) are not yet implemented. Dyadic ~ (without / set difference) is not yet implemented.

Boolean idioms

Boolean vectors are commonly used with compress (/) to filter:

      v←3 1 4 1 5 9 2 6
      (v>3)/v
4 5 9 6

∧/ tests if all elements are true, ∨/ if any are true:

      ∧/1 1 1 1
1
      ∧/1 1 0 1
0
      ∨/0 0 1 0
1