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The class Ix
- To: firstname.lastname@example.org
- Subject: The class Ix
- From: Simon L Peyton Jones <email@example.com>
- Date: Thu, 6 Feb 1992 13:23:00 +0000
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I have realised that the class Ix is under-documented in the Haskell Report.
I propose to add the following:
New section 6.9.1 "The Class Ix". (Renumber subsections in 6.9).
Arrays may be subscripted by any type in the class @Ix@, which
is defined as follows (definition repeated from Section 4.3.2)
class (Ord a) => Ix a where
range :: (a,a) -> a
index :: (a,a) -> a -> Int
inRange :: (a,a) -> a -> Bool
The @index@ operation maps the upper and lower bounds of the array, and a
subscript, to an integer. Typically, this integer is used to index a linear
representation of the array. The @range@ operation enumerates all
subscripts, and the @inRange@ operation tells whether a particular subscript
lies in the domain of the array.
An implementation is entitled to assume the following laws about these
and [ index (l,u) l <= index (l,u) s &&
index (l,u) s <= index (l,u) u
| s <- range (l,u)
inRange (l,u) i == i `elem` range (l,u)
The first law states that the index of any in-range subscript falls
between the index of the first subscript and that of the last.
The law is required so that the implementation can allocate a
suitably-sized array representation given only the array bounds.
The second law is an obvious consistency condition on @inRange@.
End of proposed text.
It would be possible to be a bit more draconian on the first law. For
example the following is simpler but more restrictive:
range (l,u) !! index (l,u) i == i