 | NumericPrelude-0.0: An experimental alternative hierarchy of numeric type classes | Contents | Index |
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| Synopsis |
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| Class
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| class C a where |
Additive a encapsulates the notion of a commutative group, specified
by the following laws:
a + b === b + a
(a + b) + c === a + (b + c)
zero + a === a
a + negate a === 0
Typical examples include integers, dollars, and vectors.
Minimal definition: +, zero, and (negate or '(-)')
| | | Methods | | zero :: a | | zero element of the vector space
| | | (+) :: a -> a -> a | | add and subtract elements
| | | (-) :: a -> a -> a | | | negate :: a -> a | | inverse with respect to +
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| |  Instances | | C Double | | C Float | | C Int | | C Integer | | C T | | C T | | (C v0, C v1) => C (v0, v1) | | (C v0, C v1, C v2) => C (v0, v1, v2) | | C v => C (b -> v) | | Integral a => C (Ratio a) | | C a => C (T a) | | C a => C (T a) | | (C a, C a, C a) => C (T a) | | C a => C (T a) | | C a => C (T a) | | C a => C (T a) | | C a => C (T a) | | C a => C (T a) | | (C a, C a) => C (T a) | | C a => C (T a) | | C a => C (T a) | | C a => C (T a) | | (Eq a, C a) => C (T a) | | C a => C (T a) | | (Eq a, C a) => C (T a) | | C v => C [v] | | (Ord i, Eq v, C v) => C (Map i v) | | (Ord a, C b) => C (T a b) | | C v => C (T a v) | | C v => C (T a v) | | (Ord i, C a) => C (T i a) |
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| zero :: C a => a |
| zero element of the vector space
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| (+) :: C a => a -> a -> a |
| add and subtract elements
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| (-) :: C a => a -> a -> a |
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| negate :: C a => a -> a |
| inverse with respect to +
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| subtract :: C a => a -> a -> a |
| subtract is (-) with swapped operand order.
This is the operand order which will be needed in most cases
of partial application.
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| Complex functions
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| sum :: C a => [a] -> a |
| Sum up all elements of a list.
An empty list yields zero.
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| sum1 :: C a => [a] -> a |
| Sum up all elements of a non-empty list.
This avoids including a zero which is useful for types
where no universal zero is available.
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| Instances for atomic types
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| propAssociative :: (Eq a, C a) => a -> a -> a -> Bool |
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| propCommutative :: (Eq a, C a) => a -> a -> Bool |
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| propIdentity :: (Eq a, C a) => a -> Bool |
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| propInverse :: (Eq a, C a) => a -> Bool |
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| Produced by Haddock version 0.7 |