Idris2Doc : Data.Vect

Data.Vect

(++) : Vectmelem -> Vectnelem -> Vect (m+n) elem
  Append two vectors

```idris example
[1,2,3,4] ++ [5,6]
```

Totality: total
Fixity Declaration: infixr operator, level 7
dataVect : Nat -> Type -> Type
Totality: total
Constructors:
Nil : Vect0elem
  Empty vector
(::) : elem -> Vectlenelem -> Vect (Slen) elem
  A non-empty vector of length `S len`, consisting of a head element and
the rest of the list, of length `len`.
catMaybes : Vectn (Maybeelem) -> DPairNat (\p => Vectpelem)
  Filter out Nothings from Vect and unwrap the Justs

```idris example
catMaybes [Just 1, Just 2, Nothing, Nothing, Just 5]
```

Totality: total
concat : Vectm (Vectnelem) -> Vect (m*n) elem
  Flatten a vector of equal-length vectors

```idris example
concat [[1,2,3], [4,5,6]]
```

Totality: total
delete : Eqelem => elem -> Vectlenelem -> DPairNat (\p => Vectpelem)
  Delete first element from list equal to the given one

```idris example
delete 2 (fromList [1,2,2,3,4,4])
```

Totality: total
deleteAt : Fin (Slen) -> Vect (Slen) elem -> Vectlenelem
  Construct a new vector consisting of all but the indicated element

```idris example
deleteAt 1 [1,2,3,4]
```

Totality: total
deleteBy : (elem -> elem -> Bool) -> elem -> Vectlenelem -> DPairNat (\p => Vectpelem)
  Delete first element from list according to some test

```idris example
deleteBy (<) 3 (fromList [1,2,2,3,4,4])
```

Totality: total
diag : Vectlen (Vectlenelem) -> Vectlenelem
  Get diagonal elements

```idris example
diag [[1,2,3], [4,5,6], [7,8,9]]
```

Totality: total
drop : (n : Nat) -> Vect (n+m) elem -> Vectmelem
  Drop the first `n` elements of a Vect.

Totality: total
drop' : (n : Nat) -> Vectlelem -> Vect (minusln) elem
  Drop up to the first `n` elements of a Vect.

Totality: total
elem : Eqelem => elem -> Vectlenelem -> Bool
  Use the default Boolean equality on elements to search for an item
@ x what to search for
@ xs where to search

```idris example
elem 3 [1,2,3,4]
```

Totality: total
elemBy : (elem -> elem -> Bool) -> elem -> Vectlenelem -> Bool
  Search for an item using a user-provided test
@ p the equality test
@ e the item to search for
@ xs the vector to search in

```idris example
elemBy (==) 2 [1,2,3,4]
```

Totality: total
elemIndex : Eqelem => elem -> Vectmelem -> Maybe (Finm)
  Find the index of the first element of the vector equal to the given one.

```idris example
elemIndex 3 [1,2,3,4]
```

Totality: total
elemIndexBy : (elem -> elem -> Bool) -> elem -> Vectmelem -> Maybe (Finm)
  Find the index of the first element of the vector that satisfies some test

```idris example
elemIndexBy (==) 3 [1,2,3,4]
```

Totality: total
elemIndices : Eqelem => elem -> Vectmelem -> List (Finm)
  Find the indices of all elements uquals to the given one

```idris example
elemIndices 3 [1,2,3,4,3]
```

Totality: total
elemIndicesBy : (elem -> elem -> Bool) -> elem -> Vectmelem -> List (Finm)
  Find the indices of all elements that satisfy some test

```idris example
elemIndicesBy (<=) 3 [1,2,3,4]
```

Totality: total
exactLength : (len : Nat) -> Vectma -> Maybe (Vectlena)
Totality: total
filter : (elem -> Bool) -> Vectlenelem -> DPairNat (\p => Vectpelem)
  Find all elements of a vector that satisfy some test

```idris example
filter (< 3) (fromList [1,2,3,4])
```

Totality: total
find : (elem -> Bool) -> Vectlenelem -> Maybeelem
  Find the first element of the vector that satisfies some test
@ p the test to satisfy

```idris example
find (== 3) [1,2,3,4]
```

Totality: total
findIndex : (elem -> Bool) -> Vectlenelem -> Maybe (Finlen)
  Find the index of the first element of the vector that satisfies some test

```idris example
findIndex (== 3) [1,2,3,4]
```

Totality: total
findIndices : (elem -> Bool) -> Vectmelem -> List (Finm)
  Find the indices of all elements that satisfy some test

```idris example
findIndices (< 3) [1,2,3,4]
```

Totality: total
foldl1 : (t -> t -> t) -> Vect (Sn) t -> t
  Foldl without seeding the accumulator

```idris example
foldl1 (-) (fromList [1,2,3])
```

Totality: total
foldr1 : (t -> t -> t) -> Vect (Sn) t -> t
  Foldr without seeding the accumulator

```idris example
foldr1 (-) (fromList [1,2,3])
```

Totality: total
foldrImpl : (t -> acc -> acc) -> acc -> (acc -> acc) -> Vectnt -> acc
Totality: total
fromList : (xs : Listelem) -> Vect (lengthxs) elem
  Convert a list to a vector.

The length of the list should be statically known.

```idris example
fromList [1,2,3,4]
```

Totality: total
fromList' : Vectlenelem -> (l : Listelem) -> Vect (lengthl+len) elem
Totality: total
hasAny : Eqelem => Vectmelem -> Vectlenelem -> Bool
  Check if any element of xs is found in elems using the default Boolean equality test

```idris example
hasAny [2,5] [1,2,3,4]
```

Totality: total
hasAnyBy : (elem -> elem -> Bool) -> Vectmelem -> Vectlenelem -> Bool
  Check if any element of xs is found in elems by a user-provided comparison
@ p the comparison operator
@ elems the vector to search
@ xs what to search for

```idris example
hasAnyBy (==) [2,5] [1,2,3,4]
```

Totality: total
head : Vect (Slen) elem -> elem
  Only the first element of the vector

```idris example
head [1,2,3,4]
```

Totality: total
index : Finlen -> Vectlenelem -> elem
  Extract a particular element from a vector

```idris example
index 1 [1,2,3,4]
```

Totality: total
init : Vect (Slen) elem -> Vectlenelem
  All but the last element of the vector

```idris example
init [1,2,3,4]
```

Totality: total
insertAt : Fin (Slen) -> elem -> Vectlenelem -> Vect (Slen) elem
  Insert an element at a particular index

```idris example
insertAt 1 8 [1,2,3,4]
```

Totality: total
intersperse : elem -> Vectlenelem -> Vect (len+predlen) elem
  Alternate an element between the other elements of a vector
@ sep the element to intersperse
@ xs the vector to separate with `sep`

```idris example
intersperse 0 [1,2,3,4]
```

Totality: total
isPrefixOf : Eqelem => Vectmelem -> Vectlenelem -> Bool
  Verify vector prefix

```idris example
isPrefixOf (fromList [1,2]) (fromList [1,2,3,4])
```

Totality: total
isPrefixOfBy : (elem -> elem -> Bool) -> Vectmelem -> Vectlenelem -> Bool
  Verify vector prefix

```idris example
isPrefixOfBy (==) (fromList [1,2]) (fromList [1,2,3,4])
```

Totality: total
isSuffixOf : Eqelem => Vectmelem -> Vectlenelem -> Bool
  Verify vector suffix

```idris example
isSuffixOf (fromList [3,4]) (fromList [1,2,3,4])
```

Totality: total
isSuffixOfBy : (elem -> elem -> Bool) -> Vectmelem -> Vectlenelem -> Bool
  Verify vector suffix

```idris example
isSuffixOfBy (==) (fromList [3,4]) (fromList [1,2,3,4])
```

Totality: total
last : Vect (Slen) elem -> elem
  The last element of the vector

```idris example
last [1,2,3,4]
```

Totality: total
length : Vectlenelem -> Nat
Totality: total
lengthCorrect : (xs : Vectlenelem) -> lengthxs = len
  Show that the length function on vectors in fact calculates the length

Totality: total
lookup : Eqkey => key -> Vectn (key, val) -> Maybeval
  Find the assocation of some key using the default Boolean equality test

```idris example
lookup 3 [(1, 'a'), (2, 'b'), (3, 'c')]
```

Totality: total
lookupBy : (key -> key -> Bool) -> key -> Vectn (key, val) -> Maybeval
  Find the association of some key with a user-provided comparison
@ p the comparison operator for keys (True if they match)
@ e the key to look for

```idris example
lookupBy (==) 2 [(1, 'a'), (2, 'b'), (3, 'c')]
```

Totality: total
mapMaybe : (a -> Maybeb) -> Vectlena -> DPairNat (\m => Vectmb)
  Map a partial function across a vector, returning those elements for which
the function had a value.

The first projection of the resulting pair (ie the length) will always be
at most the length of the input vector. This is not, however, guaranteed
by the type.

@ f the partial function (expressed by returning `Maybe`)
@ xs the vector to check for results

```idris example
mapMaybe ((find (=='a')) . unpack) (fromList ["abc","ade","bgh","xyz"])
```

Totality: total
maybeToVect : Maybeelem -> DPairNat (\p => Vectpelem)
  Convert Maybe type into Vect

```idris example
maybeToVect (Just 2)
```

Totality: total
merge : Ordelem => Vectnelem -> Vectmelem -> Vect (n+m) elem
Totality: total
mergeBy : (elem -> elem -> Ordering) -> Vectnelem -> Vectmelem -> Vect (n+m) elem
  Merge two ordered vectors

```idris example
mergeBy compare (fromList [1,3,5]) (fromList [2,3,4,5,6])
```

Totality: total
nub : Eqelem => Vectlenelem -> DPairNat (\p => Vectpelem)
  Make the elements of some vector unique by the default Boolean equality

```idris example
nub (fromList [1,2,2,3,4,4])
```

Totality: total
nubBy : (elem -> elem -> Bool) -> Vectlenelem -> DPairNat (\p => Vectpelem)
  Make the elements of some vector unique by some test

```idris example
nubBy (==) (fromList [1,2,2,3,4,4])
```

Totality: total
overLength : (len : Nat) -> Vectma -> Maybe (DPairNat (\p => Vect (plusplen) a))
  If the given Vect is at least the required length, return a Vect with
at least that length in its type, otherwise return Nothing
@len the required length
@xs the vector with the desired length

Totality: total
partition : (elem -> Bool) -> Vectlenelem -> (DPairNat (\p => Vectpelem), DPairNat (\q => Vectqelem))
  A tuple where the first element is a `Vect` of the `n` elements passing given test
and the second element is a `Vect` of the remaining elements of the original.

```idris example
partition (== 2) (fromList [1,2,3,2,4])
```

Totality: total
replaceAt : Finlen -> elem -> Vectlenelem -> Vectlenelem
  Replace an element at a particlar index with another

```idris example
replaceAt 1 8 [1,2,3,4]
```

Totality: total
replaceAtDiffIndexPreserves : (xs : Vectna) -> (i : Finn) -> (j : Finn) -> Not (i = j) -> (0 y : a) -> indexi (replaceAtjyxs) = indexixs
Totality: total
replaceAtSameIndex : (xs : Vectna) -> (i : Finn) -> (0 y : a) -> indexi (replaceAtiyxs) = y
Totality: total
replicate : (len : Nat) -> elem -> Vectlenelem
  Repeate some value some number of times.

@ len the number of times to repeat it
@ x the value to repeat

```idris example
replicate 4 1
```

Totality: total
reverse : Vectlenelem -> Vectlenelem
  Reverse the order of the elements of a vector

```idris example
reverse [1,2,3,4]
```

Totality: total
scanl : (res -> elem -> res) -> res -> Vectlenelem -> Vect (Slen) res
  The scanl function is similar to foldl, but returns all the intermediate
accumulator states in the form of a vector.

```idris example
scanl (-) 0 (fromList [1,2,3])
```

Totality: total
scanl1 : (elem -> elem -> elem) -> Vectlenelem -> Vectlenelem
  The scanl1 function is a variant of scanl that doesn't require an explicit
starting value.
It assumes the first element of the vector to be the starting value and then
starts the fold with the element following it.

```idris example
scanl1 (-) (fromList [1,2,3])
```

Totality: total
snoc : Vectna -> a -> Vect (Sn) a
  Add an element at the end of the vector.
The main use case for it is to get the expected type signature
`Vect n a -> a -> Vect (S n) a` instead of
`Vect n a -> a -> Vect (n + 1) a` which you get by using `++ [x]`

Snoc gets its name by reversing `cons`, indicating we are
tacking on the element at the end rather than the begining.
`append` would also be a suitable name.

@ xs The vector to be appended
@ v The value to append

Totality: total
splitAt : (n : Nat) -> Vect (n+m) elem -> (Vectnelem, Vectmelem)
  A tuple where the first element is a `Vect` of the `n` first elements and
the second element is a `Vect` of the remaining elements of the original.
It is equivalent to `(take n xs, drop n xs)` (`splitAtTakeDrop`),
but is more efficient.

@ n the index to split at
@ xs the `Vect` to split in two

```idris example
splitAt 2 (fromList [1,2,3,4])
```

Totality: total
tail : Vect (Slen) elem -> Vectlenelem
  All but the first element of the vector

```idris example
tail [1,2,3,4]
```

Totality: total
take : (n : Nat) -> Vect (n+m) type -> Vectntype
  Extract the first `n` elements of a Vect.

Totality: total
toVect : (n : Nat) -> Lista -> Maybe (Vectna)
Totality: total
transpose : Vectm (Vectnelem) -> Vectn (Vectmelem)
  Transpose a `Vect` of `Vect`s, turning rows into columns and vice versa.

This is like zipping all the inner `Vect`s together and is equivalent to `traverse id` (`transposeTraverse`).

As the types ensure rectangularity, this is an involution, unlike `Prelude.List.transpose`.

```idris example
transpose [[1,2], [3,4], [5,6], [7,8]]
```

Totality: total
updateAt : Finlen -> (elem -> elem) -> Vectlenelem -> Vectlenelem
  Replace the element at a particular index with the result of applying a function to it
@ i the index to replace at
@ f the update function
@ xs the vector to replace in

```idris example
updateAt 1 (+10) [1,2,3,4]
```

Totality: total
vectInjective : x::xs = y::ys -> (x = y, xs = ys)
  If two vectors are equal, their heads and tails are equal

Totality: total
vectToMaybe : Vectlenelem -> Maybeelem
  Convert first element of Vect (if exists) into Maybe.

```idris example
vectToMaybe [2]
```

Totality: total
zipWith3IndexLinear : (0 f : (a -> a -> a -> a)) -> (xs : Vectna) -> (ys : Vectna) -> (zs : Vectna) -> (i : Finn) -> indexi (zipWith3fxsyszs) = f (indexixs) (indexiys) (indexizs)
Totality: total
zipWithIndexLinear : (0 f : (a -> a -> a)) -> (xs : Vectna) -> (ys : Vectna) -> (i : Finn) -> indexi (zipWithfxsys) = f (indexixs) (indexiys)
Totality: total