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1. class Semigroup a => Monoid a

   numhask	NumHask.Prelude

   The class of monoids (types with an associative binary operation that has an identity). Instances should satisfy the following:

   • Right identity x <> mempty = x
   • Left identity mempty <> x = x
   • Associativity x <> (y <> z) = (x <> y) <> z (Semigroup law)
   • Concatenation mconcat = foldr (<>) mempty
   You can alternatively define mconcat instead of mempty, in which case the laws are:
   • Unit mconcat (pure x) = x
   • Multiplication mconcat (join xss) = mconcat (fmap mconcat xss)
   • Subclass mconcat (toList xs) = sconcat xs
   The method names refer to the monoid of lists under concatenation, but there are many other instances. Some types can be viewed as a monoid in more than one way, e.g. both addition and multiplication on numbers. In such cases we often define newtypes and make those instances of Monoid, e.g. Sum and Product. NOTE: Semigroup is a superclass of Monoid since base-4.11.0.0.

2. WrapMonoid :: m -> WrappedMonoid m

   numhask	NumHask.Prelude

   No documentation available.

3. newtype WrappedMonoid m

   numhask	NumHask.Prelude

   Provide a Semigroup for an arbitrary Monoid. NOTE: This is not needed anymore since Semigroup became a superclass of Monoid in base-4.11 and this newtype be deprecated at some point in the future.

4. stimesIdempotent :: Integral b => b -> a -> a

   numhask	NumHask.Prelude

   This is a valid definition of stimes for an idempotent Semigroup. When x <> x = x, this definition should be preferred, because it works in <math> rather than <math>.

5. stimesIdempotentMonoid :: (Integral b, Monoid a) => b -> a -> a

   numhask	NumHask.Prelude

   This is a valid definition of stimes for an idempotent Monoid. When x <> x = x, this definition should be preferred, because it works in <math> rather than <math>

6. stimesMonoid :: (Integral b, Monoid a) => b -> a -> a

   numhask	NumHask.Prelude

   This is a valid definition of stimes for a Monoid. Unlike the default definition of stimes, it is defined for 0 and so it should be preferred where possible.

7. unwrapMonoid :: WrappedMonoid m -> m

   numhask	NumHask.Prelude

   No documentation available.

8. 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.

9. 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.

10. module Data.Parameterized.DecidableEq

    This defines a class DecidableEq, which represents decidable equality on a type family. This is different from GHC's TestEquality in that it provides evidence of non-equality. In fact, it is a superclass of TestEquality.

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