CODEWITHSUNDEEP
haskell
Data
Data

Reputation: 769

Why is [a..b] an empty list when a > b?

If I enter [5..1] into the Haskell console it returns [], whereas I expected [5, 4, 3, 2, 1].

In general, [a..b] = [] if a > b. Why?

Upvotes: 4

Views: 165

Answers (1)

Daniel Wagner
Daniel Wagner

Reputation: 153162

The Report covers the details. In Section 3.10:

Arithmetic sequences satisfy these identities:

[ e1..e3 ]    =   enumFromTo e1 e3

In Section 6.3.4:

For the types Int and Integer, the enumeration functions have the following meaning:

  • The sequence enumFromTo e1 e3 is the list [e1,e1 + 1,e1 + 2,…e3]. The list is empty if e1 > e3.

For Float and Double, the semantics of the enumFrom family is given by the rules for Int above, except that the list terminates when the elements become greater than e3 + i∕2 for positive increment i, or when they become less than e3 + i∕2 for negative i.

Then the next question is, "Why was the Report specified that way?". There I think the answer is that this choice is quite natural for a mathematician, which most of the original committee were to some extent. It also has a number of nice properties:

  • If [x..y] has n values, then [x..y-1] and [x+1..y] have n-1 values (where in n-1, the subtraction saturates at 0, an ahem natural choice).
  • Checking whether a particular element is in the range [x..y] only requires checking that it is bigger than x and smaller than y -- you need not first determine which of x or y is bigger.
  • It prevents a certain class of surprising off-by-one errors: if you want to take the next n>=0 elements after x, you can write [x..x+n-1]. If you choose the other rule, where [x..y] might mean [y,y+1,...,x] if y is smaller, there is no way to create an empty list with [_.._] syntax, so no uniform way to take the next n elements. One would have to write the more cumbersome if n>0 then [x..x+n-1] else []; and it would be very easy to forget to write this check.

If you would like the list [5,4,3,2,1], that may be achieved by specifying an explicit second step, as in [5,4..1].

Upvotes: 15

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