:: Int -> Integer -package:base

Create an Integer from an Int

Helper function for constructing IDs of any sort.

Convert from an Int.

conversion to Integer

Conversion to Integer.

fibonacci k calculates the k-th Fibonacci number in O(log (abs k)) steps. The index may be negative. This is efficient for calculating single Fibonacci numbers (with large index), but for computing many Fibonacci numbers in close proximity, it is better to use the simple addition formula starting from an appropriate pair of successive Fibonacci numbers.

lucas k computes the k-th Lucas number. Very similar to fibonacci.

Find the number of digits of an Int.

equalFuncList (\k -> round (Bell.bellSeries (fromInteger k) :: Double)) (Bell.bellRec :: [Integer]) 20

Highly, terribly dangerous coercion from one representation type to another. Misuse of this function can invite the garbage collector to trounce upon your data and then laugh in your face. You don't want this function. Really.

Coerce a value from one type to another, bypassing the type-checker. There are several legitimate ways to use unsafeCoerce:

1. To coerce e.g. Int to HValue, put it in a list of HValue, and then later coerce it back to Int before using it.
2. To produce e.g. (a+b) :~: (b+a) from unsafeCoerce Refl. Here the two sides really are the same type -- so nothing unsafe is happening -- but GHC is not clever enough to see it.
3. In Data.Typeable we have

eqTypeRep :: forall k1 k2 (a :: k1) (b :: k2).
TypeRep a -> TypeRep b -> Maybe (a :~~: b)
eqTypeRep a b
| sameTypeRep a b = Just (unsafeCoerce HRefl)
| otherwise       = Nothing

Here again, the unsafeCoerce HRefl is safe, because the two types really are the same -- but the proof of that relies on the complex, trusted implementation of Typeable.

1. The "reflection trick", which takes advantage of the fact that in class C a where { op :: ty }, we can safely coerce between C a and ty (which have different kinds!) because it's really just a newtype. Note: there is no guarantee, at all that this behavior will be supported into perpetuity.