| Safe Haskell | Safe |
|---|---|
| Language | Haskell2010 |
Kleene.Internal.Partition
- newtype Partition a = Partition {
- unPartition :: Set a
- invariant :: (Ord a, Bounded a) => Partition a -> Bool
- fromSeparators :: (Enum a, Bounded a, Ord a) => [a] -> Partition a
- fromRSets :: (Enum a, Bounded a, Ord a) => [RSet a] -> Partition a
- fromRSet :: (Enum a, Bounded a, Ord a) => RSet a -> Partition a
- whole :: Partition a
- size :: Partition a -> Int
- examples :: (Bounded a, Enum a, Ord a) => Partition a -> Set a
- intervals :: (Enum a, Bounded a, Ord a) => Partition a -> NonEmpty (a, a)
- wedge :: Ord a => Partition a -> Partition a -> Partition a
- split :: (Enum a, Bounded a, Eq a) => a -> Partition a
- toSF :: (Enum a, Bounded a, Ord a) => (a -> b) -> Partition a -> SF a b
Documentation
Partition devides type into disjoint connected partitions.
Note: we could have non-connecter partitions too, but that would be more complicated. This variant is correct by construction, but less precise.
It's enought to store last element of each piece.
Partition (fromList [x1, x2, x3]) :: Partition ss, as
\[ \{ x \mid x \le x_1 \} \cup \{ x \mid x_1 < x \le x_2 \} \cup \{ x \mid x_2 < x \le x_3 \} \cup \{ x \mid x_3 < x \} \]
Note: it's enough to check upper bound conditions only if checks are performed in order.
Invariant: maxBound is not in the set.
Constructors
| Partition | |
Fields
| |
Instances
| Eq a => Eq (Partition a) Source # | |
| Ord a => Ord (Partition a) Source # | |
| Show a => Show (Partition a) Source # | |
| (Enum a, Bounded a, Ord a) => Semigroup (Partition a) Source # | See |
| (Enum a, Bounded a, Ord a) => Monoid (Partition a) Source # | |
| (Enum a, Bounded a, Ord a, Arbitrary a) => Arbitrary (Partition a) Source # | invariant (asPartitionChar p) |
size :: Partition a -> Int Source #
Count of sets in a Partition.
>>>size whole1
>>>size $ split (10 :: Word8)2
size (asPartitionChar p) >= 1
examples :: (Bounded a, Enum a, Ord a) => Partition a -> Set a Source #
Extract examples from each subset in a Partition.
>>>examples $ split (10 :: Word8)fromList [10,255]
>>>examples $ split (10 :: Word8) <> split 20fromList [10,20,255]
invariant p ==> size (asPartitionChar p) === length (examples p)
intervals :: (Enum a, Bounded a, Ord a) => Partition a -> NonEmpty (a, a) Source #
all (curry (<=)) $ intervals $ asPartitionChar p
wedge :: Ord a => Partition a -> Partition a -> Partition a Source #
Wedge partitions.
>>>split (10 :: Word8) <> split 20fromSeparators [10,20]
whole `wedge` (p :: Partition Char) === p
(p :: Partition Char) <> whole === p
asPartitionChar p <> q === q <> p
asPartitionChar p <> p === p
invariant $ asPartitionChar p <> q
split :: (Enum a, Bounded a, Eq a) => a -> Partition a Source #
Simplest partition: given x partition space into [min..x) and [x .. max]
>>>split (128 :: Word8)fromSeparators [128]
toSF :: (Enum a, Bounded a, Ord a) => (a -> b) -> Partition a -> SF a b Source #
Make a step function.
>>>import Data.Word>>>import Test.QuickCheck ((===))
>>>let asPartitionChar :: Partition Char -> Partition Char; asPartitionChar = id>>>instance (Ord a, Enum a, Arbitrary a) => Arbitrary (RSet a) where arbitrary = fmap RSet.fromRangeList arbitrary