Hoogle Search

Within LTS Haskell 24.58 (ghc-9.10.3)

Note that Stackage only displays results for the latest LTS and Nightly snapshot. Learn more.

Exact lookup

1. toComplexMatrix :: C a => T a -> Array (Int, Int) (T a)

   numeric-prelude	Number.Quaternion

   Map a quaternion to complex valued 2x2 matrix, such that quaternion addition and multiplication is mapped to matrix addition and multiplication. The determinant of the matrix equals the squared quaternion norm (normSqr). Since complex numbers can be turned into real (orthogonal) matrices, a quaternion could also be converted into a real matrix.

2. toRotationMatrix :: C a => T a -> Array (Int, Int) a

   numeric-prelude	Number.Quaternion

   Let c be a unit quaternion, then it holds similarity c (0+::x) == toRotationMatrix c * x

3. fix :: (a -> a) -> a

   numhask	NumHask.Prelude

   fix f is the least fixed point of the function f, i.e. the least defined x such that f x = x. When f is strict, this means that because, by the definition of strictness, f ⊥ = ⊥ and such the least defined fixed point of any strict function is ⊥.

   Examples

   We can write the factorial function using direct recursion as

   >>> let fac n = if n <= 1 then 1 else n * fac (n-1) in fac 5
   120
   

   This uses the fact that Haskell’s let introduces recursive bindings. We can rewrite this definition using fix, Instead of making a recursive call, we introduce a dummy parameter rec; when used within fix, this parameter then refers to fix’s argument, hence the recursion is reintroduced.

   >>> fix (\rec n -> if n <= 1 then 1 else n * rec (n-1)) 5
   120
   

   Using fix, we can implement versions of repeat as fix . (:) and cycle as fix . (++)

   >>> take 10 $ fix (0:)
   [0,0,0,0,0,0,0,0,0,0]
   

   >>> map (fix (\rec n -> if n < 2 then n else rec (n - 1) + rec (n - 2))) [1..10]
   [1,1,2,3,5,8,13,21,34,55]
   

   Implementation Details

   The current implementation of fix uses structural sharing

   fix f = let x = f x in x
   

   A more straightforward but non-sharing version would look like

   fix f = f (fix f)
   

4. floatRadix :: RealFloat a => a -> Integer

   numhask	NumHask.Prelude

   a constant function, returning the radix of the representation (often 2)

5. type family CheckIx (ctx :: Ctx k) (n :: Nat) (b :: Bool)

   parameterized-utils	Data.Parameterized.Context

   Helper type family used to generate descriptive error messages when an index is larger than the length of the Ctx being indexed.

6. type ValidIx (n :: Nat) (ctx :: Ctx k) = CheckIx ctx n n + 1 <=? CtxSize ctx

   parameterized-utils	Data.Parameterized.Context

   A constraint that checks that the nat n is a valid index into the context ctx, and raises a type error if not.

7. type family CheckIx (ctx :: Ctx k) (n :: Nat) (b :: Bool)

   parameterized-utils	Data.Parameterized.Ctx

   Helper type family used to generate descriptive error messages when an index is larger than the length of the Ctx being indexed.

8. type ValidIx (n :: Nat) (ctx :: Ctx k) = CheckIx ctx n n + 1 <=? CtxSize ctx

   parameterized-utils	Data.Parameterized.Ctx

   A constraint that checks that the nat n is a valid index into the context ctx, and raises a type error if not.

9. addPrefixIsLeq :: forall f (m :: Natural) g (n :: Nat) . f m -> g n -> LeqProof n (m + n)

   parameterized-utils	Data.Parameterized.NatRepr

   No documentation available.

10. _reversedPrefix :: PointedList a -> [a]

    pointedlist	Data.List.PointedList

    No documentation available.

Page 283 of many | Previous | Next