fix package:base

fix f is the least fixed point of the function f, i.e. the least defined x such that f x = x. For example, we can write the factorial function using direct recursion as

>>> let fac n = if n <= 1 then 1 else n * fac (n-1) in fac 5
120

This uses the fact that Haskell’s let introduces recursive bindings. We can rewrite this definition using fix,

>>> fix (\rec n -> if n <= 1 then 1 else n * rec (n-1)) 5
120

Instead of making a recursive call, we introduce a dummy parameter rec; when used within fix, this parameter then refers to fix’s argument, hence the recursion is reintroduced.

Monadic fixpoints. For a detailed discussion, see Levent Erkok's thesis, Value Recursion in Monadic Computations, Oregon Graduate Institute, 2002.

Allow the result of an ST computation to be used (lazily) inside the computation. Note that if f is strict, fixST f = _|_.

Allow the result of an ST computation to be used (lazily) inside the computation. Note that if f is strict, fixST f = _|_.

The implementation of mfix for IO. If the function passed to fixIO inspects its argument, the resulting action will throw FixIOException.

The exception thrown when an infinite cycle is detected in fixIO.

Fixity of constructors

This module defines a "Fixed" type for fixed-precision arithmetic. The parameter to Fixed is any type that's an instance of HasResolution. HasResolution has a single method that gives the resolution of the Fixed type. This module also contains generalisations of div, mod, and divMod to work with any Real instance.

The type parameter should be an instance of HasResolution.

Datatype to represent the fixity of a constructor. An infix | declaration directly corresponds to an application of Infix.

This variant of Fixity appears at the type level.

The isInfixOf function takes two lists and returns True iff the first list is contained, wholly and intact, anywhere within the second.

>>> isInfixOf "Haskell" "I really like Haskell."
True

>>> isInfixOf "Ial" "I really like Haskell."
False

For the result to be True, the first list must be finite; for the result to be False, the second list must be finite:

>>> [20..50] `isInfixOf` [0..]
True

>>> [0..] `isInfixOf` [20..50]
False

>>> [0..] `isInfixOf` [0..]
* Hangs forever *

The isPrefixOf function takes two lists and returns True iff the first list is a prefix of the second.

>>> "Hello" `isPrefixOf` "Hello World!"
True

>>> "Hello" `isPrefixOf` "Wello Horld!"
False

For the result to be True, the first list must be finite; False, however, results from any mismatch:

>>> [0..] `isPrefixOf` [1..]
False

>>> [0..] `isPrefixOf` [0..99]
False

>>> [0..99] `isPrefixOf` [0..]
True

>>> [0..] `isPrefixOf` [0..]
* Hangs forever *

The isSuffixOf function takes two lists and returns True iff the first list is a suffix of the second.

>>> "ld!" `isSuffixOf` "Hello World!"
True

>>> "World" `isSuffixOf` "Hello World!"
False

The second list must be finite; however the first list may be infinite:

>>> [0..] `isSuffixOf` [0..99]
False

>>> [0..99] `isSuffixOf` [0..]
* Hangs forever *

The stripPrefix function drops the given prefix from a list. It returns Nothing if the list did not start with the prefix given, or Just the list after the prefix, if it does.

>>> stripPrefix "foo" "foobar"
Just "bar"

>>> stripPrefix "foo" "foo"
Just ""

>>> stripPrefix "foo" "barfoo"
Nothing

>>> stripPrefix "foo" "barfoobaz"
Nothing

Monads having fixed points with a 'knot-tying' semantics. Instances of MonadFix should satisfy the following laws:

• Purity mfix (return . h) = return (fix h)
• Left shrinking (or Tightening) mfix (\x -> a >>= \y -> f x y) = a >>= \y -> mfix (\x -> f x y)
• Sliding mfix (liftM h . f) = liftM h (mfix (f . h)), for strict h.
• Nesting mfix (\x -> mfix (\y -> f x y)) = mfix (\x -> f x x)

This class is used in the translation of the recursive do notation supported by GHC and Hugs.

The fixed point of a monadic computation. mfix f executes the action f only once, with the eventual output fed back as the input. Hence f should not be strict, for then mfix f would diverge.

Gets the fixity of a constructor

First arg is whether to chop off trailing zeros

The isPrefixOf function returns True if the first argument is a prefix of the second.

A slightly faster version of fixIO that may not be safe to use with multiple threads. The unsafety arises when used like this:

unsafeFixIO $ \r -> do
forkIO (print r)
return (...)

In this case, the child thread will receive a NonTermination exception instead of waiting for the value of r to be computed.