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  1. sum1 :: Ptr CInt -> Ptr (Complex Float) -> Ptr CInt -> IO Float

    lapack-ffi Numeric.LAPACK.FFI.ComplexFloat

    http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/scsum1.f

  2. sumE :: forall a s e (m :: Type -> Type) . Num a => Wire s e m (Event a) (Event a)

    netwire Control.Wire.Event

    Sum of all events.

    • Depends: now.

  3. sumVec :: Num a => [[a]] -> [a]

    numeric-quest Orthogonals

    Add some lists.

  4. sum_product :: Num a => [a] -> [a] -> a

    numeric-quest Orthogonals

    No documentation available.

  5. sum0 :: Bits a => SHA w -> a -> a

    sbv Documentation.SBV.Examples.Crypto.SHA

    The sum-0 function. We parameterize over the rotation amounts as different variants of SHA use different rotation amounts.

  6. sum0Coefficients :: SHA w -> (Int, Int, Int)

    sbv Documentation.SBV.Examples.Crypto.SHA

    Section 4.1.2-3 : Coefficients of the Sum0 function

  7. sum1 :: Bits a => SHA w -> a -> a

    sbv Documentation.SBV.Examples.Crypto.SHA

    The sum-1 function. Again, parameterized.

  8. sum1Coefficients :: SHA w -> (Int, Int, Int)

    sbv Documentation.SBV.Examples.Crypto.SHA

    Section 4.1.2-3 : Coefficients of the Sum1 function

  9. sumHalves :: IO Proof

    sbv Documentation.SBV.Examples.KnuckleDragger.Lists

    We prove that summing a list can be done by halving the list, summing parts, and adding the results. The proof uses strong induction. We have: 

    >>> sumHalves
Inductive lemma: sumAppend
Step: Base                            Q.E.D.
Step: 1                               Q.E.D.
Step: 2                               Q.E.D.
Step: 3                               Q.E.D.
Result:                               Q.E.D.
Inductive lemma (strong): sumHalves
Step: Measure is non-negative         Q.E.D.
Step: 1 (2 way full case split)
Step: 1.1                           Q.E.D.
Step: 1.2 (2 way full case split)
Step: 1.2.1                       Q.E.D.
Step: 1.2.2.1                     Q.E.D.
Step: 1.2.2.2                     Q.E.D.
Step: 1.2.2.3                     Q.E.D.
Step: 1.2.2.4                     Q.E.D.
Step: 1.2.2.5                     Q.E.D.
Step: 1.2.2.6 (simplify)          Q.E.D.
Result:                               Q.E.D.
[Proven] sumHalves

  10. sumConstProof :: IO Proof

    sbv Documentation.SBV.Examples.KnuckleDragger.Numeric

    Prove that sum of constants c from 0 to n is n*c. We have: 

    >>> sumConstProof
Inductive lemma: sumConst_correct
Step: Base                            Q.E.D.
Step: 1                               Q.E.D.
Step: 2                               Q.E.D.
Step: 3                               Q.E.D.
Step: 4                               Q.E.D.
Step: 5                               Q.E.D.
Result:                               Q.E.D.
[Proven] sumConst_correct

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