Data.Monoid

class (Semigroup m) <= Monoid m  where

A Monoid is a Semigroup with a value mempty, which is both a left and right unit for the associative operation <>:

• Left unit: (mempty <> x) = x
• Right unit: (x <> mempty) = x

Monoids are commonly used as the result of fold operations, where <> is used to combine individual results, and mempty gives the result of folding an empty collection of elements.

Newtypes for Monoid

Some types (e.g. Int, Boolean) can implement multiple law-abiding instances for Monoid. Let's use Int as an example

1. <> could be + and mempty could be 0
2. <> could be * and mempty could be 1.

To clarify these ambiguous situations, one should use the newtypes defined in Data.Monoid.<NewtypeName> modules.

In the above ambiguous situation, we could use Additive for the first situation or Multiplicative for the second one.

Members

• mempty :: m

Instances

• Monoid Unit
• Monoid Ordering
• (Monoid b) => Monoid (a -> b)
• Monoid String
• Monoid (Array a)
• (RowToList row list, MonoidRecord list row row) => Monoid (Record row)

power :: forall m. Monoid m => m -> Int -> m

Append a value to itself a certain number of times. For the Multiplicative type, and for a non-negative power, this is the same as normal number exponentiation.

If the second argument is negative this function will return mempty (unlike normal number exponentiation). The Monoid constraint alone is not enough to write a power function with the property that power x n cancels with power x (-n), i.e. power x n <> power x (-n) = mempty. For that, we would additionally need the ability to invert elements, i.e. a Group.

power [1,2] 3    == [1,2,1,2,1,2]
power [1,2] 1    == [1,2]
power [1,2] 0    == []
power [1,2] (-3) == []

guard :: forall m. Monoid m => Boolean -> m -> m

Allow or "truncate" a Monoid to its mempty value based on a condition.

class (SemigroupRecord rowlist row subrow) <= MonoidRecord rowlist row subrow | rowlist -> row subrow where

Members

• memptyRecord :: forall rlproxy. rlproxy rowlist -> Record subrow

Instances

• MonoidRecord Nil row ()
• (IsSymbol key, Monoid focus, Cons key focus subrowTail subrow, MonoidRecord rowlistTail row subrowTail) => MonoidRecord (Cons key focus rowlistTail) row subrow

class Semigroup a 

The Semigroup type class identifies an associative operation on a type.

Instances are required to satisfy the following law:

• Associativity: (x <> y) <> z = x <> (y <> z)

One example of a Semigroup is String, with (<>) defined as string concatenation. Another example is List a, with (<>) defined as list concatenation.

Newtypes for Semigroup

There are two other ways to implement an instance for this type class regardless of which type is used. These instances can be used by wrapping the values in one of the two newtypes below:

1. First - Use the first argument every time: append first _ = first.
2. Last - Use the last argument every time: append _ last = last.

Instances

• Semigroup String
• Semigroup Unit
• Semigroup Void
• (Semigroup s') => Semigroup (s -> s')
• Semigroup (Array a)
• Semigroup (Proxy a)
• Semigroup (Proxy2 a)
• Semigroup (Proxy3 a)
• (RowToList row list, SemigroupRecord list row row) => Semigroup (Record row)

class SemigroupRecord rowlist row subrow | rowlist -> subrow

Instances

• SemigroupRecord Nil row ()
• (IsSymbol key, Cons key focus subrowTail subrow, SemigroupRecord rowlistTail row subrowTail, Semigroup focus) => SemigroupRecord (Cons key focus rowlistTail) row subrow

Operator alias for Data.Semigroup.append (right-associative / precedence 5)