Logic¶

Booleans¶

The type of booleans, written B or Bool, represents logical truth and falsehood. The two values of this type are written true and false. (For convenience True and False also work.)

Logical AND can be written and, &&, or ∧.
Logical OR is written or, ||, or ∨.
Logical negation (NOT) is written not or ¬.

Disco> true and false
false
Disco> true || false
true
Disco> not (true ∧ true)
false
Disco> ¬ (false or false or false or true)
false

Equality testing¶

If you have two disco values of the type, in almost all cases you can compare them to see whether they are equal using =, resulting in a Bool value.

Disco> 2 = 5
false
Disco> 3 * 7 = 2*10 + 1
true
Disco> (3/5)^2 + (4/5)^2 = 1
true
Disco> false = false
true

The /= operator tests whether two values are not equal; it is just the logical negation of =.

Comparison¶

Again, in almost all cases values can be compared to see which is less or greater, using operators <, <=, >, or >=.

Disco> 2 < 5
true
Disco> false < true
true
Disco> (5 : Z7) < (9 : Z7)
false

(The last example is false because (9 : Z7) is equivalent to (2 : Z7).)

Comparisons can also be chained; the result is obtained by comparing each pair of values according to the comparison between them, and taking the logical AND of all the results. For example:

Disco> 1 < 3 < 8 < 99
true
Disco> 2.2 < 5.9 > 3.7 < 8.8 > 1.0 < 9
true