A type which behaves similarly to Record, except all elements must fit in the same UArray. A consequence of this is that RecordU has the following properties:

• it is strict in the element types
• it cannot do type-changing updates of RecordU, except if the function applies to all elements
• it probably is slower to update the very first elements of the RecordU

The benefit is that lookups should be faster and records should take up less space. However benchmarks done with a slow HNat2Integral do not suggest that RecordU is faster than Record.

RecordUS is stored as a HList of RecordU to allow the RecordUS to contain elements of different types, so long all of the types can be put into an unboxed array (UArray).

It is advantageous (at least space-wise) to sort the record to keep elements with the same types elements adjacent. See SortForRecordUS for more details.

Reorders a Record such that the RecordUS made from it takes up less space

Bad has alternating Double and Int fields

>>> bad
Record{x=1.0,i=2,y=3.0,j=4}

4 arrays containing one element each are needed when this Record is stored as a RecordUS

>>> recordToRecordUS bad
RecordUS H[RecordU (array (0,0) [(0,1.0)]),RecordU (array (0,0) [(0,2)]),RecordU (array (0,0) [(0,3.0)]),RecordU (array (0,0) [(0,4)])]

It is possible to sort the record

>>> sortForRecordUS bad
Record{x=1.0,y=3.0,i=2,j=4}

This allows the same content to be stored in two unboxed arrays

>>> recordToRecordUS (sortForRecordUS bad)
RecordUS H[RecordU (array (0,1) [(0,1.0),(1,3.0)]),RecordU (array (0,1) [(0,2),(1,4)])]

analogous flip //. Similar to .<++., except it is restricted to cases where the left argument holds a subset of elements.

hMap specialized to RecordU

behaves like map HFind

connect the unpacked x representation with the corresponding list of RecordU u representation.

HSubtract a b is Left (a-b), Right (b-a) or Right HZero

proof that hMap UnboxF :: r xs -> r us can determine xs from us and us from xs

all elements of the list have the same type

HSpanEq x y fst snd is analogous to (fst,snd) = span (== x) y

HGroupBy f x y is analogous to y = groupBy f x

given that f is used by HEqBy

HPartitionEq f x1 xs xi xo is analogous to

(xi,xo) = partition (f x1) xs

where f is a "function" passed in using it's instance of HEqBy

evidence to satisfy the fundeps in HInits

evidence to satisfy the fundeps in HInits

similar to FHCons

behaves like tail . inits

inits

tails

analog of stripPrefix

HAppendList1 xs ys xsys is the type-level way of saying xs ++ ys == xsys

used by HSplitAt

HLengthGe xs n says that HLength xs >= n.

unlike the expression with a type family HLength, ghc assumes xs ~ (aFresh ': bFresh) when given a constraint HLengthGe xs (HSucc HZero)

a better way to write HLength xs ~ n because:

1. it works properly with ghc-7.10 (probably another example of ghc bug #10009)
2. it works backwards a bit in that if n is known, then xs can be refined:

>>> undefined :: HLengthEq xs HZero => HList xs
H[]

helper for HSplitAt

splitAt

setup

>>> let two = hSucc (hSucc hZero)
>>> let xsys = hEnd $ hBuild 1 2 3 4

If a length is explicitly provided, the resulting lists are inferred

>>> hSplitAt two xsys
(H[1,2],H[3,4])

>>> let sameLength_ :: SameLength a b => r a -> r b -> r a; sameLength_ = const
>>> let len2 x = x `sameLength_` HCons () (HCons () HNil)

If the first chunk of the list (a) has to be a certain length, the type of the Proxy argument can be inferred.

>>> case hSplitAt Proxy xsys of (a,b) -> (len2 a, b)
(H[1,2],H[3,4])

Analogus to Data.List.partition snd. See also HPartition

>>> let (.=.) :: p x -> y -> Tagged x y; _ .=. y = Tagged y
>>> hSplit $ hTrue .=. 2 .*. hTrue .=. 3 .*. hFalse .=. 1 .*. HNil
(H[2,3],H[1])

it might make more sense to instead have LVPair Bool e instead of (e, Proxy Bool) since the former has the same runtime representation as e

the same as map Just

>>> toHJust (2 .*. 'a' .*. HNil)
H[HJust 2,HJust 'a']

>>> toHJust2 (2 .*. 'a' .*. HNil)
H[HJust 2,HJust 'a']

hMapOut id is similar, except this function is restricted to HLists that actually contain a value (so the list produced will be nonempty). This restriction allows adding a functional dependency, which means that less type annotations can be necessary.

could be an associated type if HEq had one

It is a pure type-level operation

Check to see if an element e occurs in a list l If not, return 'Nothing If the element does occur, return 'Just l1 where l1 is a type-level list without e

The following is a similar type-only membership test It uses the user-supplied curried type equality predicate pred

Check to see if an HList contains an element with a given type This is a type-level only test

We do so constructively, converting the HList whose elements are Proxy HNat to [HNat]. The latter kind is unpopulated and is present only at the type level.

A heterogeneous version of

sequenceA :: (Applicative m) => [m a] -> m [a]

Only now we operate on heterogeneous lists, where different elements may have different types a. In the argument list of monadic values (m a_i), although a_i may differ, the monad m must be the same for all elements. That's why we needed Data.HList.TypeCastGeneric2 (currently (~)). The typechecker will complain if we attempt to use hSequence on a HList of monadic values with different monads.

The hSequence problem was posed by Matthias Fischmann in his message on the Haskell-Cafe list on Oct 8, 2006

http://www.haskell.org/pipermail/haskell-cafe/2006-October/018708.html

http://www.haskell.org/pipermail/haskell-cafe/2006-October/018784.html

Maybe

>>> hSequence $ Just (1 :: Integer) `HCons` (Just 'c') `HCons` HNil
Just H[1,'c']

>>> hSequence $  return 1 `HCons` Just  'c' `HCons` HNil
Just H[1,'c']

List

>>> hSequence $ [1] `HCons` ['c'] `HCons` HNil
[H[1,'c']]

hMap is written such that the length of the result list can be determined from the length of the argument list (and the other way around). Similarly, the type of the elements of the list is propagated in both directions too.

>>> :set -XNoMonomorphismRestriction
>>> let xs = 1 .*. 'c' .*. HNil
>>> :t hMap (HJust ()) xs
hMap (HJust ()) xs :: Num y => HList '[HJust y, HJust Char]

These 4 examples show that the constraint on the length (2 in this case) can be applied before or after the hMap. That inference is independent of the direction that type information is propagated for the individual elements.

>>> let asLen2 xs = xs `asTypeOf` (undefined :: HList '[a,b])

>>> let lr xs = asLen2 (applyAB (HMap HRead) xs)
>>> let ls xs = asLen2 (applyAB (HMap HShow) xs)
>>> let rl xs = applyAB (HMap HRead) (asLen2 xs)
>>> let sl xs = applyAB (HMap HShow) (asLen2 xs)

>>> :t lr
lr
  :: (Read ..., Read ...) => HList '[String, String] -> HList '[..., ...]

>>> :t rl
rl
  :: (Read ..., Read ...) => HList '[String, String] -> HList '[..., ...]

>>> :t ls
ls
  :: (Show ..., Show ...) => HList '[..., ...] -> HList '[String, String]

>>> :t sl
sl
  :: (Show ..., Show ...) => HList '[..., ...] -> HList '[String, String]

Like concat but for HLists of HLists.

Works in ghci... puzzling as what is different in doctest (it isn't -XExtendedDefaultRules)

>>> let a = hEnd $ hBuild 1 2 3
>>> let b = hEnd $ hBuild 'a' "abc"
>>> hConcat $ hBuild a b
H[1,2,3,'a',"abc"]

This function behaves like iterate, with an extra argument to help figure out the result length

>>> let three = hSucc (hSucc (hSucc hZero))
>>> let f = Fun Just :: Fun '() Maybe

>>> :t applyAB f
applyAB f :: a -> Maybe a

f is applied to different types:

>>> hIterate three f ()
H[(),Just (),Just (Just ())]

It is also possible to specify the length later on, as done with Prelude.iterate

>>> let take3 x | _ <- hLength x `asTypeOf` three = x
>>> take3 $ hIterate Proxy f ()
H[(),Just (),Just (Just ())]