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and :: Int -> Int -> Int

Bitwise AND.

or :: Int -> Int -> Int

Bitwise OR.

pow :: Int -> Int -> Int

Raise an Int to the power of another Int.

quot :: Int -> Int -> Int

The quot function provides truncating integer division (see the documentation for the EuclideanRing class). It is identical to div in the EuclideanRing Int instance if the dividend is positive, but will be slightly different if the dividend is negative. For example:

div 2 3 == 0
quot 2 3 == 0

div (-2) 3 == (-1)
quot (-2) 3 == 0

div 2 (-3) == 0
quot 2 (-3) == 0

rem :: Int -> Int -> Int

The rem function provides the remainder after truncating integer division (see the documentation for the EuclideanRing class). It is identical to mod in the EuclideanRing Int instance if the dividend is positive, but will be slightly different if the dividend is negative. For example:

mod 2 3 == 2
rem 2 3 == 2

mod (-2) 3 == 1
rem (-2) 3 == (-2)

mod 2 (-3) == 2
rem 2 (-3) == 2

shl :: Int -> Int -> Int

Bitwise shift left.

shr :: Int -> Int -> Int

Bitwise shift right.

xor :: Int -> Int -> Int

Bitwise XOR.

zshr :: Int -> Int -> Int

Bitwise zero-fill shift right.

imul :: Int -> Int -> Int

Returns the result of the C-like 32-bit multiplication of the two arguments.

stirling1 :: Int -> Int -> Int

Returns the number of permutations compound of products of exactly k disjoint cycles over n elements. For instance, stirling1 5 3 = 35 for

• 20 for cardinality of type (abc)(d)(e) and
• 15 for cardinality of type (ab)(cd)(e)

unPrecise :: Int -> Int -> Int

zorder :: Int -> Int -> Int

power :: forall m. Monoid m => m -> Int -> m

Append a value to itself a certain number of times. For the Multiplicative type, and for a non-negative power, this is the same as normal number exponentiation.

If the second argument is negative this function will return mempty (unlike normal number exponentiation). The Monoid constraint alone is not enough to write a power function with the property that power x n cancels with power x (-n), i.e. power x n <> power x (-n) = mempty. For that, we would additionally need the ability to invert elements, i.e. a Group.

power [1,2] 3    == [1,2,1,2,1,2]
power [1,2] 1    == [1,2]
power [1,2] 0    == []
power [1,2] (-3) == []

repeat :: forall a. Monoid a => a -> Int -> a

power :: forall g. Group g => g -> Int -> g

Append a value (or its inverse) to itself a certain number of times.

For the Additive Int type, this is the same as multiplication.

pow :: forall a. Semiring a => a -> Int -> a

Integer power

addLeadingZeros :: forall a. Elastic a => Int -> a -> a

offset :: forall q sql. ToOffset q => Resume q (Offset E) sql => Int -> q -> sql

OFFSET statement

Note: OFFSET must always follow after LIMIT or ORDER BY

setUuid :: forall m. HasUuid m => Int -> m -> m

add :: forall a. Semiring a => a -> a -> a

append :: forall a. Semigroup a => a -> a -> a

conj :: forall a. HeytingAlgebra a => a -> a -> a

const :: forall a b. a -> b -> a

Returns its first argument and ignores its second.

const 1 "hello" = 1

It can also be thought of as creating a function that ignores its argument:

const 1 = \_ -> 1

disj :: forall a. HeytingAlgebra a => a -> a -> a

div :: forall a. EuclideanRing a => a -> a -> a

gcd :: forall a. Eq a => EuclideanRing a => a -> a -> a

The greatest common divisor of two values.

genericAdd :: forall a rep. Generic a rep => GenericSemiring rep => a -> a -> a

A Generic implementation of the add member from the Semiring type class.

genericAdd' :: forall a. GenericSemiring a => a -> a -> a

genericAppend :: forall a rep. Generic a rep => GenericSemigroup rep => a -> a -> a

A Generic implementation of the append member from the Semigroup type class.

genericAppend' :: forall a. GenericSemigroup a => a -> a -> a

genericConj :: forall a rep. Generic a rep => GenericHeytingAlgebra rep => a -> a -> a

A Generic implementation of the conj member from the HeytingAlgebra type class.

genericConj' :: forall a. GenericHeytingAlgebra a => a -> a -> a

genericDisj :: forall a rep. Generic a rep => GenericHeytingAlgebra rep => a -> a -> a

A Generic implementation of the disj member from the HeytingAlgebra type class.

genericDisj' :: forall a. GenericHeytingAlgebra a => a -> a -> a

genericImplies :: forall a rep. Generic a rep => GenericHeytingAlgebra rep => a -> a -> a

A Generic implementation of the implies member from the HeytingAlgebra type class.

genericImplies' :: forall a. GenericHeytingAlgebra a => a -> a -> a

genericMul :: forall a rep. Generic a rep => GenericSemiring rep => a -> a -> a

A Generic implementation of the mul member from the Semiring type class.

genericMul' :: forall a. GenericSemiring a => a -> a -> a

genericSub :: forall a rep. Generic a rep => GenericRing rep => a -> a -> a

A Generic implementation of the sub member from the Ring type class.

genericSub' :: forall a. GenericRing a => a -> a -> a

implies :: forall a. HeytingAlgebra a => a -> a -> a

lcm :: forall a. Eq a => EuclideanRing a => a -> a -> a

The least common multiple of two values.

leftDiv :: forall a. DivisionRing a => a -> a -> a

Left division, defined as leftDiv a b = recip b * a. Left and right division are distinct in this module because a DivisionRing is not necessarily commutative.

If the type a is also a EuclideanRing, then this function is equivalent to div from the EuclideanRing class. When working abstractly, div should generally be preferred, unless you know that you need your code to work with noncommutative rings.

max :: forall a. Ord a => a -> a -> a

Take the maximum of two values. If they are considered equal, the first argument is chosen.

min :: forall a. Ord a => a -> a -> a

Take the minimum of two values. If they are considered equal, the first argument is chosen.

mod :: forall a. EuclideanRing a => a -> a -> a

mul :: forall a. Semiring a => a -> a -> a

rightDiv :: forall a. DivisionRing a => a -> a -> a

Right division, defined as rightDiv a b = a * recip b. Left and right division are distinct in this module because a DivisionRing is not necessarily commutative.

If the type a is also a EuclideanRing, then this function is equivalent to div from the EuclideanRing class. When working abstractly, div should generally be preferred, unless you know that you need your code to work with noncommutative rings.

sub :: forall a. Ring a => a -> a -> a

create :: forall buf m. MutableBuffer buf m => Int -> m buf

Creates a new buffer of the specified size.

size :: forall buf m. MutableBuffer buf m => buf -> m Int

Returns the size of a buffer.

sans :: forall m a b. At m a b => a -> m -> m

add :: forall x y z. Add x y z => x -> y -> z

and :: forall b1 b2 b3. And b1 b2 b3 => b1 -> b2 -> b3

div :: forall x y z. Div x y z => x -> y -> z

eq :: forall b1 b2 b3. Eq b1 b2 b3 => b1 -> b2 -> b3

gcd :: forall x y z. GCD x y z => x -> y -> z

imp :: forall b1 b2 b3. Imp b1 b2 b3 => b1 -> b2 -> b3

max :: forall x y z. Max x y z => x -> y -> z

min :: forall x y z. Min x y z => x -> y -> z

mod :: forall x y r. Mod x y r => x -> y -> r

mul :: forall x y z. Mul x y z => x -> y -> z

or :: forall b1 b2 b3. Or b1 b2 b3 => b1 -> b2 -> b3

sub :: forall x y z. Sub x y z => x -> y -> z

trich :: forall x y r. Trich x y r => x -> y -> r

xor :: forall b1 b2 b3. Xor b1 b2 b3 => b1 -> b2 -> b3

hmap :: forall f a b. HMap f a b => f -> a -> b

hmapWithIndex :: forall f a b. HMapWithIndex f a b => f -> a -> b

mapping :: forall f a b. Mapping f a b => f -> a -> b

call :: forall s. IsString s => Monoid s => s -> s -> s

Syntax for CSS function call.

reduce :: forall f i o. Reducible f i o => f -> i -> o

lact :: forall g s. LeftAction g s => g -> s -> s

ract :: forall g s. RightAction g s => s -> g -> s

convertOptions :: forall t i o. ConvertOptions t i o => t -> i -> o

defaults :: forall defaults provided all. Defaults defaults provided all => defaults -> provided -> all

fromInt :: forall a. IntLiftable a => Int -> a

maddL :: forall x r. LeftModule x r => x -> x -> x

maddR :: forall x r. RightModule x r => x -> x -> x

mmulL :: forall x r. LeftModule x r => r -> x -> x

mmulR :: forall x r. RightModule x r => x -> r -> x

msubL :: forall x r. LeftModule x r => x -> x -> x

msubR :: forall x r. RightModule x r => x -> x -> x

bindTo :: forall f o. f -> o -> f

defaultUndef :: forall a. a -> a -> a

new :: forall f a o. f -> a -> o

Call new on the function with an array or pseudoarray of arguments

dot :: forall p n. ToPos n p => Semiring n => p -> p -> n

Get the dot product of two vectors

mapProduct :: forall mp a b. MapProduct mp a b => mp -> a -> b

putInsideMod :: forall r p n. ToRegion n r => AsPosEndo n p => EuclideanRing n => r -> p -> p

Put a position inside a region by using the modulus operator

act :: forall m s. Action m s => m -> s -> s

Convert a value of type @m@ to an action on @s@ values.

at :: forall c k r. Monoid r => Lookup c k r => c -> k -> r

This simple helper works on any Lookup instance where the return type is a Monoid, and is the same as lookup except that it returns a t instead of a Maybe t. If lookup would return Nothing, then at returns mempty.

at :: forall c k r. Monoid r => Lookup c k r => c -> k -> r

This simple helper works on any Lookup instance where the return type is a Monoid, and is the same as lookup except that it returns a t instead of a Maybe t. If lookup would return Nothing, then at returns mempty.

join :: forall a. JoinSemilattice a => a -> a -> a

meet :: forall a. MeetSemilattice a => a -> a -> a

pathAppend :: forall m. XPathLike m => m -> m -> m

Put a path seperator between two XPaths and return the resulting XPath.

pathAppendNSx :: forall m. XPathLike m => m -> m -> m

Useful variant of pathAppend needed for some XPath implementations; insert a separator with a dummy namespace ("x") for the second XPath fragment. For example: root /? "record" /? "identifier" == "/x:record/x:identifier".

setCtx :: forall props' props ctx. WithContextProps props' props ctx => ctx -> props' -> props

adjacentSibling :: forall a b c. IsExtensibleSelector a => ToVal a => Combine b c => a -> b -> c

and :: forall a. Binary a => a -> a -> a

arbitraryEJsonOfSize :: forall t m. MonadGen m => MonadRec m => Corecursive t EJsonF => Int -> m t

child :: forall a b c. IsExtensibleSelector a => ToVal a => Combine b c => a -> b -> c

dbg :: forall s a. Show s => s -> a -> a

descendant :: forall a b c. IsExtensibleSelector a => ToVal a => Combine b c => a -> b -> c

diff :: forall a d. Diff a d => a -> a -> d

fromInt :: forall a. Ring a => Int -> a

generalSibling :: forall a b c. IsExtensibleSelector a => ToVal a => Combine b c => a -> b -> c

join :: forall a. JoinSemilattice a => a -> a -> a

maddL :: forall x r. LeftModule x r => x -> x -> x

maddR :: forall x r. RightModule x r => x -> x -> x

meet :: forall a. MeetSemilattice a => a -> a -> a

mmulL :: forall x r. LeftModule x r => r -> x -> x

mmulR :: forall x r. RightModule x r => x -> r -> x

msubL :: forall x r. LeftModule x r => x -> x -> x

msubR :: forall x r. RightModule x r => x -> x -> x

nand :: forall α. HeytingAlgebra α => α -> α -> α

nor :: forall α. HeytingAlgebra α => α -> α -> α

or :: forall a. Binary a => a -> a -> a

patch :: forall a d. Patch a d => a -> d -> a

pursxStringAnonymous :: forall accumulator next res. PursxStringAnonymous accumulator next res => accumulator -> next -> res

pursxValAnonymous :: forall accumulator next res. PursxValAnonymous accumulator next res => accumulator -> next -> res

reciprocal :: forall n n1 n2 a r. Add n2 1 n1 => Add n1 1 n => Arity a n => Divisible r => Eq r => EuclideanRing r => Leadable r => Ord r => Pad n2 (Polynomial r) a => Peel r r => Unpad n2 (Polynomial r) a => a -> a -> a

Computes the reciprocal of the first polynomial in the extension whose minimal polynomial is provided by the second polynomial

set :: forall s t a b @sym lenses. IsSymbol sym => ParseSymbol sym lenses => ConstructBarlow lenses Function s t a b => b -> s -> t

xor :: forall a. Binary a => a -> a -> a

xor :: forall a. HeytingAlgebra a => a -> a -> a

xor :: forall α. HeytingAlgebra α => α -> α -> α

_add :: forall a. HasAdd a => a -> a -> a

_and :: forall a. HasAnd a => a -> a -> a

_divide :: forall a. HasDivide a => a -> a -> a

_multiply :: forall a. HasMultiply a => a -> a -> a

_or :: forall a. HasOr a => a -> a -> a

_power :: forall a. HasPower a => a -> a -> a

_remainder :: forall a. HasRemainder a => a -> a -> a

_subtract :: forall a. HasSubtract a => a -> a -> a

add :: forall a. HasAdd a => a -> a -> a

add :: forall a b c r. Arith a b c r => a -> b -> c

always :: forall b a. a -> b -> a

Always returns the first argument.

"anything" :always 1 -- 1

This is the constant function.

and :: forall a. HasAnd a => a -> a -> a

and :: forall a b r. LogicalMatcher a b r => a -> b -> r

asTypeOf :: forall a. a -> a -> a

A type-restricted version of always.

[] :asTypeOf [1] -- [] :: Array Int

bind :: forall a g f. f -> a -> g

cons :: forall a b r. ConsGen a b r => a -> b -> r

decorate :: forall a b. Decorate a b => a -> b -> a

decorateFlipped :: forall b a. Decorate b a => a -> b -> b

diff' :: forall changed model. Diff changed model => changed -> (model -> model)

div :: forall a b c r. Arith a b c r => a -> b -> c

divide :: forall a. HasDivide a => a -> a -> a

dot :: forall p g f. Dottable p g f => p -> g -> f

exec :: forall m q. MonadSession m => AsQuery q => q -> m Int

Executes a query and returns the number of rows affected

fold :: forall stepper a fold. Fold stepper a fold => stepper -> a -> fold

from :: forall f q fields sql. ToFrom f q fields => Resume q (From f fields E) sql => f -> q -> sql

FROM accepts the following sources

• Tables
• Inner and outer joins
• Aliased tables
• Aliased SELECT statements

Due to how SQL binding works, joins and subqueries require brackets to be parsed correctly. For example:

• SELECT column FROM (SELECT column FROM table) AS alias should be select column # from (select column # from table # as alias))
• SELECT column FROM table alias JOIN other_table other_alias should be select column # from ((table # as alias)join(other_table # as other_alias)))

To aid composition, SELECT projections are only validated on FROM

getAllArgs :: forall all given. OptArgs all given => all -> given -> all

groupBy :: forall f s q sql grouped columns. ToGroupBy q s columns => GroupedColumns f columns grouped => ValidGroupByProjection s grouped => Resume q (GroupBy f E) sql => f -> q -> sql

GROUP BY statement

heightSegments :: forall nt r. Newtype nt (Variant (heightSegments :: Int | r)) => Int -> nt

hmap :: forall f a b. HMap f a b => f -> a -> b

hmapWithIndex :: forall f a b. HMapWithIndex f a b => f -> a -> b

int :: forall t. Corecursive t (SqlF EJsonF) => Int -> t

investigate :: forall b a. Warn "Debug.Trace usage" => Show a => a -> b -> b

Once in a while, we all need to debug. A lot of programmers from imperative languages find real trouble with debugging, as they can't just bung in a console.log to see values. Well, what if I told you... you can! So, we can cheat a little bit, and use some escape hatches in the Debug package, including traceShow, which will log anything Showable. With this function, we can show a value at any point, and return anything!

kestrel :: forall b a. a -> b -> a

K combinator - kestrel

K

Λ a b . a → b → a

λ x y . x

mapping :: forall f a b. Mapping f a b => f -> a -> b

max :: forall a. HasGreater a => a -> a -> a

Returns the greater value.

max 1 2 -- 2
max 2 1 -- 2

maxByOrder :: forall a. Ord a => a -> a -> a

min :: forall a. HasLess a => a -> a -> a

Returns the lesser value.

min 1 2 -- 1
min 2 1 -- 1

minByOrder :: forall a. Ord a => a -> a -> a

mod_ :: forall a b c r. Arith a b c r => a -> b -> c

mul :: forall a b c r. Arith a b c r => a -> b -> c

multiply :: forall a. HasMultiply a => a -> a -> a

new1 :: forall b a1 o. o -> a1 -> b

oneShotChange :: forall tau p au. OneShotChange tau p au => tau -> p -> au

or :: forall a. HasOr a => a -> a -> a

or :: forall a b r. LogicalMatcher a b r => a -> b -> r

or :: forall a. Bitwise a => a -> a -> a

orderBy :: forall f q sql. ToOrderBy f q => Resume q (OrderBy f E) sql => f -> q -> sql

ORDER BY statement

perform :: forall a o op. SymbioteOperation a o op => op -> a -> o

plus :: forall a b. Summable a b => a -> b -> a

plus :: forall a b. Summable a b => a -> b -> a

pow :: forall a b c r. Arith a b c r => a -> b -> c

power :: forall a. HasPower a => a -> a -> a

property :: forall c b a. a -> b -> c

provide :: forall result a. a -> (Ask a => result) -> result

Provide an implicit parameter to a computation which requires it

queryReturnsImpl :: forall schema query returns. QueryReturns schema query returns => schema -> query -> returns

Do not use this. Use queryReturns instead. Only exported due to compiler restrictions

remainder :: forall a. HasRemainder a => a -> a -> a

resume :: forall a b c. Resume a b c => a -> b -> c

returning :: forall f q sql. ToReturning f q => Resume q (Returning f) sql => f -> q -> sql

rotate :: forall input tail output. ArgsRotater input tail output => input -> tail -> output

scale :: forall a. Space a => a -> (a -> a)

scoped :: forall f output mod. Scoped f output => mod -> f -> output

sub :: forall a b c r. Arith a b c r => a -> b -> c

subtract :: forall a. HasSubtract a => a -> a -> a

transform :: forall function return constructor. EtaConversionTransformer function return constructor => constructor -> function -> return

transformFlipped :: forall function return constructor. EtaConversionTransformer function return constructor => function -> constructor -> return

transformWith :: forall function return constructor. WithInputEtaConversionTransformer function return constructor => constructor -> function -> return

transformWithFlipped :: forall function return constructor. WithInputEtaConversionTransformer function return constructor => function -> constructor -> return

tupleRev :: forall t1 acc t2. TupleRev t1 acc t2 => t1 -> acc -> t2

unionObject :: forall from to. ObjectUnion from to => from -> to -> to

unsafeAdd :: forall a b c. a -> b -> c

unsafeDiv :: forall a b c. a -> b -> c

unsafeMod :: forall a b c. a -> b -> c

unsafeMul :: forall a b c. a -> b -> c

unsafePow :: forall a b c. a -> b -> c

unsafeSub :: forall a b c. a -> b -> c