on package:foundation

on b u x y runs the binary function b on the results of applying unary function u to two arguments x and y. From the opposite perspective, it transforms two inputs and combines the outputs.

((+) `on` f) x y = f x + f y

Typical usage: sortBy (compare `on` fst). Algebraic properties:

• (*) `on` id = (*) -- (if (*) ∉ {⊥, const
  ⊥})

• ((*) `on` f) `on` g = (*) `on` (f . g)

• flip on f . flip on g = flip on (g .
  f)

Alternative prelude with batteries and no dependencies A custom prelude with no dependencies apart from base. This package has the following goals:

• provide a base like sets of modules that provide a consistent set of features and bugfixes across multiple versions of GHC (unlike base).
• provide a better and more efficient prelude than base's prelude.
• be self-sufficient: no external dependencies apart from base.
• provide better data-types: packed unicode string by default, arrays.
• Better numerical classes that better represent mathematical thing (No more all-in-one Num).
• Better I/O system with less Lazy IO
• Usual partial functions distinguished through type system

I tried to picture clusters of information As they moved through the computer What do they look like? Alternative Prelude

A set of methods for ordered colection

Any type that you wish to throw or catch as an exception must be an instance of the Exception class. The simplest case is a new exception type directly below the root:

data MyException = ThisException | ThatException
deriving Show

instance Exception MyException

The default method definitions in the Exception class do what we need in this case. You can now throw and catch ThisException and ThatException as exceptions:

*Main> throw ThisException `catch` \e -> putStrLn ("Caught " ++ show (e :: MyException))
Caught ThisException

In more complicated examples, you may wish to define a whole hierarchy of exceptions:

---------------------------------------------------------------------
-- Make the root exception type for all the exceptions in a compiler

data SomeCompilerException = forall e . Exception e => SomeCompilerException e

instance Show SomeCompilerException where
show (SomeCompilerException e) = show e

instance Exception SomeCompilerException

compilerExceptionToException :: Exception e => e -> SomeException
compilerExceptionToException = toException . SomeCompilerException

compilerExceptionFromException :: Exception e => SomeException -> Maybe e
compilerExceptionFromException x = do
SomeCompilerException a <- fromException x
cast a

---------------------------------------------------------------------
-- Make a subhierarchy for exceptions in the frontend of the compiler

data SomeFrontendException = forall e . Exception e => SomeFrontendException e

instance Show SomeFrontendException where
show (SomeFrontendException e) = show e

instance Exception SomeFrontendException where
toException = compilerExceptionToException
fromException = compilerExceptionFromException

frontendExceptionToException :: Exception e => e -> SomeException
frontendExceptionToException = toException . SomeFrontendException

frontendExceptionFromException :: Exception e => SomeException -> Maybe e
frontendExceptionFromException x = do
SomeFrontendException a <- fromException x
cast a

---------------------------------------------------------------------
-- Make an exception type for a particular frontend compiler exception

data MismatchedParentheses = MismatchedParentheses
deriving Show

instance Exception MismatchedParentheses where
toException   = frontendExceptionToException
fromException = frontendExceptionFromException

We can now catch a MismatchedParentheses exception as MismatchedParentheses, SomeFrontendException or SomeCompilerException, but not other types, e.g. IOException:

*Main> throw MismatchedParentheses `catch` \e -> putStrLn ("Caught " ++ show (e :: MismatchedParentheses))
Caught MismatchedParentheses
*Main> throw MismatchedParentheses `catch` \e -> putStrLn ("Caught " ++ show (e :: SomeFrontendException))
Caught MismatchedParentheses
*Main> throw MismatchedParentheses `catch` \e -> putStrLn ("Caught " ++ show (e :: SomeCompilerException))
Caught MismatchedParentheses
*Main> throw MismatchedParentheses `catch` \e -> putStrLn ("Caught " ++ show (e :: IOException))
*** Exception: MismatchedParentheses

Fractional Literal support e.g. 1.2 :: Double 0.03 :: Float

Negation support e.g. -(f x)

Exceptions that occur in the IO monad. An IOException records a more specific error type, a descriptive string and maybe the handle that was used when the error was flagged.

The Monad class defines the basic operations over a monad, a concept from a branch of mathematics known as category theory. From the perspective of a Haskell programmer, however, it is best to think of a monad as an abstract datatype of actions. Haskell's do expressions provide a convenient syntax for writing monadic expressions. Instances of Monad should satisfy the following:

• Left identity return a >>= k = k a
• Right identity m >>= return = m
• Associativity m >>= (\x -> k x >>= h) = (m >>= k) >>= h

Furthermore, the Monad and Applicative operations should relate as follows:

• pure = return

• m1 <*> m2 = m1 >>= (x1 -> m2
  >>= (x2 -> return (x1 x2)))

The above laws imply:

• fmap f xs = xs >>= return .
  f

• (>>) = (*>)

and that pure and (<*>) satisfy the applicative functor laws. The instances of Monad for lists, Maybe and IO defined in the Prelude satisfy these laws.

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

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.

NonEmpty property for any Collection

Arbitrary-precision rational numbers, represented as a ratio of two Integer values. A rational number may be constructed using the % operator.

The SomeException type is the root of the exception type hierarchy. When an exception of type e is thrown, behind the scenes it is encapsulated in a SomeException.

Append an element to an ordered collection

const x is a unary function which evaluates to x for all inputs.

>>> const 42 "hello"
42

>>> map (const 42) [0..3]
[42,42,42,42]

Render this exception value in a human-friendly manner. Default implementation: show.

Fold a list using the monoid. For most types, the default definition for mconcat will be used, but the function is included in the class definition so that an optimized version can be provided for specific types.

>>> mconcat ["Hello", " ", "Haskell", "!"]
"Hello Haskell!"

Smart constructor to create a NonEmpty collection If the collection is empty, then Nothing is returned Otherwise, the collection is wrapped in the NonEmpty property

Partition the elements that satisfy the predicate and those that don't

Partitions a list of Either into two lists. All the Left elements are extracted, in order, to the first component of the output. Similarly the Right elements are extracted to the second component of the output.

Examples

Basic usage:

>>> let list = [ Left "foo", Right 3, Left "bar", Right 7, Left "baz" ]

>>> partitionEithers list
(["foo","bar","baz"],[3,7])

The pair returned by partitionEithers x should be the same pair as (lefts x, rights x):

>>> let list = [ Left "foo", Right 3, Left "bar", Right 7, Left "baz" ]

>>> partitionEithers list == (lefts list, rights list)
True

Map covariantly over the second argument.

second ≡ bimap id

Examples

>>> second (+1) ('j', 3)
('j',4)

>>> second (+1) (Right 3)
Right 4

Create a collection with a single element