Eq package:base-prelude

The Eq class defines equality (==) and inequality (/=). All the basic datatypes exported by the Prelude are instances of Eq, and Eq may be derived for any datatype whose constituents are also instances of Eq. The Haskell Report defines no laws for Eq. However, instances are encouraged to follow these properties:

• Reflexivity x == x = True
• Symmetry x == y = y == x
• Transitivity if x == y && y == z = True, then x == z = True
• Extensionality if x == y = True and f is a function whose return type is an instance of Eq, then f x == f y = True
• Negation x /= y = not (x == y)

Minimal complete definition: either == or /=.

Lifting of the Eq class to unary type constructors.

Lifting of the Eq class to binary type constructors.

This data type represents an equivalence relation. Equivalence relations are expected to satisfy three laws:

• Reflexivity getEquivalence f a a = True
• Symmetry getEquivalence f a b = getEquivalence f b a
• Transitivity If getEquivalence f a b and getEquivalence f b c are both True then so is getEquivalence f a c.

The types alone do not enforce these laws, so you'll have to check them yourself.

Lift the standard (==) function through the type constructor.

Lift the standard (==) function through the type constructor.

Equality on StableName that does not require that the types of the arguments match.

This type is treated magically within GHC. Any pattern match of the form case unsafeEqualityProof of UnsafeRefl -> body gets transformed just into body. This is ill-typed, but the transformation takes place after type-checking is complete. It is used to implement unsafeCoerce. You probably don't want to use UnsafeRefl in an expression, but you might conceivably want to pattern-match on it. Use unsafeEqualityProof to create one of these.

Check for equivalence with ==. Note: The instances for Double and Float violate reflexivity for NaN.

The isSubsequenceOf function takes two lists and returns True if all the elements of the first list occur, in order, in the second. The elements do not have to occur consecutively. isSubsequenceOf x y is equivalent to elem x (subsequences y).

Examples

>>> isSubsequenceOf "GHC" "The Glorious Haskell Compiler"
True

>>> isSubsequenceOf ['a','d'..'z'] ['a'..'z']
True

>>> isSubsequenceOf [1..10] [10,9..0]
False

Lift an equality test through the type constructor. The function will usually be applied to an equality function, but the more general type ensures that the implementation uses it to compare elements of the first container with elements of the second.

Lift equality tests through the type constructor. The function will usually be applied to equality functions, but the more general type ensures that the implementation uses them to compare elements of the first container with elements of the second.

Evaluate each monadic action in the structure from left to right, and collect the results. For a version that ignores the results see sequence_.

Examples

Basic usage: The first two examples are instances where the input and and output of sequence are isomorphic.

>>> sequence $ Right [1,2,3,4]
[Right 1,Right 2,Right 3,Right 4]

>>> sequence $ [Right 1,Right 2,Right 3,Right 4]
Right [1,2,3,4]

The following examples demonstrate short circuit behavior for sequence.

>>> sequence $ Left [1,2,3,4]
Left [1,2,3,4]

>>> sequence $ [Left 0, Right 1,Right 2,Right 3,Right 4]
Left 0

Evaluate each action in the structure from left to right, and collect the results. For a version that ignores the results see sequenceA_.

Examples

Basic usage: For the first two examples we show sequenceA fully evaluating a a structure and collecting the results.

>>> sequenceA [Just 1, Just 2, Just 3]
Just [1,2,3]

>>> sequenceA [Right 1, Right 2, Right 3]
Right [1,2,3]

The next two example show Nothing and Just will short circuit the resulting structure if present in the input. For more context, check the Traversable instances for Either and Maybe.

>>> sequenceA [Just 1, Just 2, Just 3, Nothing]
Nothing

>>> sequenceA [Right 1, Right 2, Right 3, Left 4]
Left 4

Evaluate each action in the structure from left to right, and ignore the results. For a version that doesn't ignore the results see sequenceA. sequenceA_ is just like sequence_, but generalised to Applicative actions.

Examples

Basic usage:

>>> sequenceA_ [print "Hello", print "world", print "!"]
"Hello"
"world"
"!"

Evaluate each monadic action in the structure from left to right, and ignore the results. For a version that doesn't ignore the results see sequence. sequence_ is just like sequenceA_, but specialised to monadic actions.

The subsequences function returns the list of all subsequences of the argument.

>>> subsequences "abc"
["","a","b","ab","c","ac","bc","abc"]