Ranges and enumeration

Ranges

Two dots between two values of an enumerable type produce the list of everything in between. The upper bound is included:

[1..5] -- [1,2,3,4,5] ['a'..'e'] -- "abcde" [1.0,1.5..3.0] -- [1.0,1.5,2.0,2.5,3.0]

A range needs an Enum instance, which numbers, characters, and booleans have. It works because the type knows how to walk from one value to the next.

Step sizes

Give two starting values and the range continues with the same difference. The third value is the upper bound, not the step:

[0,2..10] -- [0,2,4,6,8,10] [10,8..0] -- [10,8,6,4,2,0] [1,4..20] -- [1,4,7,10,13,16,19]

A step that never reaches the bound produces a short list rather than an error: [1,3..10] ends at 9. A descending range with a positive step is empty, which is the usual cause of a function that silently returns nothing.

Infinite ranges

Leave the upper bound out and the list never ends. Because Haskell is lazy, nothing is computed until a consumer asks:

take 5 [1..] -- [1,2,3,4,5] take 4 [0,5..] -- [0,5,10,15] takeWhile (< 100) (map (^2) [1..]) -- [1,4,9,16,25,36,49,64,81]

take and takeWhile are the two standard ways to cut an infinite list down to size. A bare infinite range printed at the prompt runs until you press Ctrl+C.

repeat, cycle, replicate

Three generators cover the cases that a range cannot express. repeat never stops, cycle loops a finite list, and replicate counts:

take 3 (repeat 7) -- [7,7,7] take 5 (cycle [1,2]) -- [1,2,1,2,1] replicate 3 "ha" -- ["ha","ha","ha"]

concat (replicate 3 "ha") builds a string from repeated pieces, which is the usual reason to reach for replicate.

Next: List comprehensions

Article author: Arthur Isaev