Module Prelude

(.) :: (a -> b) -> (c -> a) -> c -> b   

Function composition.

Further infos:

• defined as right-associative infix operator with precedence 9

id :: a -> a   

Identity function.

Further infos:

• solution complete, i.e., able to compute all solutions

const :: a -> b -> a   

Constant function.

Further infos:

• solution complete, i.e., able to compute all solutions

curry :: ((a,b) -> c) -> a -> b -> c   

Converts an uncurried function to a curried function.

uncurry :: (a -> b -> c) -> (a,b) -> c   

Converts an curried function to a function on pairs.

flip :: (a -> b -> c) -> b -> a -> c   

(flip f) is identical to f but with the order of arguments reversed.

until :: (a -> Bool) -> (a -> a) -> a -> a   

Repeats application of a function until a predicate holds.

seq :: a -> b -> b   

Evaluates the first argument to head normal form (which could also be a free variable) and returns the second argument.

Further infos:

• defined as right-associative infix operator with precedence 0

ensureNotFree :: a -> a   

Evaluates the argument to head normal form and returns it. Suspends until the result is bound to a non-variable term.

Further infos:

• externally defined

ensureSpine :: [a] -> [a]   

Evaluates the argument to spine form and returns it. Suspends until the result is bound to a non-variable spine.

($) :: (a -> b) -> a -> b   

Right-associative application.

Further infos:

• defined as right-associative infix operator with precedence 0

($!) :: (a -> b) -> a -> b   

Right-associative application with strict evaluation of its argument to head normal form.

Further infos:

• defined as right-associative infix operator with precedence 0
• externally defined

($!!) :: (a -> b) -> a -> b   

Right-associative application with strict evaluation of its argument to normal form.

Further infos:

• defined as right-associative infix operator with precedence 0
• externally defined

($#) :: (a -> b) -> a -> b   

Right-associative application with strict evaluation of its argument to a non-variable term.

Further infos:

• defined as right-associative infix operator with precedence 0

($##) :: (a -> b) -> a -> b   

Right-associative application with strict evaluation of its argument to ground normal form.

Further infos:

• defined as right-associative infix operator with precedence 0
• externally defined

error :: String -> a   

Aborts the execution with an error message.

failed :: a   

A non-reducible polymorphic function. It is useful to express a failure in a search branch of the execution. It could be defined by: failed = head []

Further infos:

• externally defined

(&&) :: Bool -> Bool -> Bool   

Sequential conjunction on Booleans.

Further infos:

• defined as right-associative infix operator with precedence 3
• solution complete, i.e., able to compute all solutions

(||) :: Bool -> Bool -> Bool   

Sequential disjunction on Booleans.

Further infos:

• defined as right-associative infix operator with precedence 2
• solution complete, i.e., able to compute all solutions

not :: Bool -> Bool   

Negation on Booleans.

Further infos:

• solution complete, i.e., able to compute all solutions

otherwise :: Bool   

Useful name for the last condition in a sequence of conditional equations.

Further infos:

• solution complete, i.e., able to compute all solutions

if_then_else :: Bool -> a -> a -> a   

The standard conditional. It suspends if the condition is a free variable.

solve :: Bool -> Bool   

Enforce a Boolean condition to be true. The computation fails if the argument evaluates to False.

Further infos:

• partially defined
• solution complete, i.e., able to compute all solutions

(&>) :: Bool -> a -> a   

Conditional expression. An expression like (c &> e) is evaluated by evaluating the first argument to True and then evaluating e. The expression has no value if the condition does not evaluate to True.

Further infos:

• defined as right-associative infix operator with precedence 0
• partially defined
• solution complete, i.e., able to compute all solutions

(=:=) :: a -> a -> Bool   

The equational constraint. (e1 =:= e2) is satisfiable if both sides e1 and e2 can be reduced to a unifiable data term (i.e., a term without defined function symbols).

Further infos:

• defined as non-associative infix operator with precedence 4
• solution complete, i.e., able to compute all solutions
• externally defined

(&) :: Bool -> Bool -> Bool   

Concurrent conjunction. An expression like (c1 & c2) is evaluated by evaluating the c1 and c2 in a concurrent manner.

Further infos:

• defined as right-associative infix operator with precedence 0
• solution complete, i.e., able to compute all solutions
• externally defined

fst :: (a,b) -> a   

Selects the first component of a pair.

Further infos:

• solution complete, i.e., able to compute all solutions

snd :: (a,b) -> b   

Selects the second component of a pair.

Further infos:

• solution complete, i.e., able to compute all solutions

head :: [a] -> a   

Computes the first element of a list.

Further infos:

• partially defined
• solution complete, i.e., able to compute all solutions

tail :: [a] -> [a]   

Computes the remaining elements of a list.

Further infos:

• partially defined
• solution complete, i.e., able to compute all solutions

null :: [a] -> Bool   

Is a list empty?

Further infos:

• solution complete, i.e., able to compute all solutions

(++) :: [a] -> [a] -> [a]   

Concatenates two lists. Since it is flexible, it could be also used to split a list into two sublists etc.

Further infos:

• defined as right-associative infix operator with precedence 5
• solution complete, i.e., able to compute all solutions

length :: [a] -> Int   

Computes the length of a list.

(!!) :: [a] -> Int -> a   

List index (subscript) operator, head has index 0.

Further infos:

• defined as left-associative infix operator with precedence 9
• partially defined

map :: (a -> b) -> [a] -> [b]   

Map a function on all elements of a list.

foldl :: (a -> b -> a) -> a -> [b] -> a   

Accumulates all list elements by applying a binary operator from left to right. Thus,

foldl f z [x1,x2,...,xn] = (...((z `f` x1) `f` x2) ...) `f` xn

foldl1 :: (a -> a -> a) -> [a] -> a   

Accumulates a non-empty list from left to right.

Further infos:

• partially defined

foldr :: (a -> b -> b) -> b -> [a] -> b   

Accumulates all list elements by applying a binary operator from right to left. Thus,

foldr f z [x1,x2,...,xn] = (x1 `f` (x2 `f` ... (xn `f` z)...))

foldr1 :: (a -> a -> a) -> [a] -> a   

Accumulates a non-empty list from right to left:

Further infos:

• partially defined

filter :: (a -> Bool) -> [a] -> [a]   

Filters all elements satisfying a given predicate in a list.

zip :: [a] -> [b] -> [(a,b)]   

Joins two lists into one list of pairs. If one input list is shorter than the other, the additional elements of the longer list are discarded.

Further infos:

• solution complete, i.e., able to compute all solutions

zip3 :: [a] -> [b] -> [c] -> [(a,b,c)]   

Joins three lists into one list of triples. If one input list is shorter than the other, the additional elements of the longer lists are discarded.

Further infos:

• solution complete, i.e., able to compute all solutions

zipWith :: (a -> b -> c) -> [a] -> [b] -> [c]   

Joins two lists into one list by applying a combination function to corresponding pairs of elements. Thus zip = zipWith (,)

zipWith3 :: (a -> b -> c -> d) -> [a] -> [b] -> [c] -> [d]   

Joins three lists into one list by applying a combination function to corresponding triples of elements. Thus zip3 = zipWith3 (,,)

unzip :: [(a,b)] -> ([a],[b])   

Transforms a list of pairs into a pair of lists.

Further infos:

• solution complete, i.e., able to compute all solutions

unzip3 :: [(a,b,c)] -> ([a],[b],[c])   

Transforms a list of triples into a triple of lists.

Further infos:

• solution complete, i.e., able to compute all solutions

concat :: [[a]] -> [a]   

Concatenates a list of lists into one list.

concatMap :: (a -> [b]) -> [a] -> [b]   

Maps a function from elements to lists and merges the result into one list.

iterate :: (a -> a) -> a -> [a]   

Infinite list of repeated applications of a function f to an element x. Thus, iterate f x = [x, f x, f (f x),...]

repeat :: a -> [a]   

Infinite list where all elements have the same value. Thus, repeat x = [x, x, x,...]

Further infos:

• solution complete, i.e., able to compute all solutions

replicate :: Int -> a -> [a]   

List of length n where all elements have the same value.

take :: Int -> [a] -> [a]   

Returns prefix of length n.

drop :: Int -> [a] -> [a]   

Returns suffix without first n elements.

splitAt :: Int -> [a] -> ([a],[a])   

(splitAt n xs) is equivalent to (take n xs, drop n xs)

takeWhile :: (a -> Bool) -> [a] -> [a]   

Returns longest prefix with elements satisfying a predicate.

dropWhile :: (a -> Bool) -> [a] -> [a]   

Returns suffix without takeWhile prefix.

span :: (a -> Bool) -> [a] -> ([a],[a])   

(span p xs) is equivalent to (takeWhile p xs, dropWhile p xs)

break :: (a -> Bool) -> [a] -> ([a],[a])   

(break p xs) is equivalent to (takeWhile (not.p) xs, dropWhile (not.p) xs). Thus, it breaks a list at the first occurrence of an element satisfying p.

lines :: String -> [String]   

Breaks a string into a list of lines where a line is terminated at a newline character. The resulting lines do not contain newline characters.

unlines :: [String] -> String   

Concatenates a list of strings with terminating newlines.

words :: String -> [String]   

Breaks a string into a list of words where the words are delimited by white spaces.

unwords :: [String] -> String   

Concatenates a list of strings with a blank between two strings.

reverse :: [a] -> [a]   

Reverses the order of all elements in a list.

and :: [Bool] -> Bool   

Computes the conjunction of a Boolean list.

or :: [Bool] -> Bool   

Computes the disjunction of a Boolean list.

any :: (a -> Bool) -> [a] -> Bool   

Is there an element in a list satisfying a given predicate?

all :: (a -> Bool) -> [a] -> Bool   

Is a given predicate satisfied by all elements in a list?

elem :: Eq a => a -> [a] -> Bool   

Element of a list?

Further infos:

• defined as non-associative infix operator with precedence 4

notElem :: Eq a => a -> [a] -> Bool   

Not element of a list?

Further infos:

• defined as non-associative infix operator with precedence 4

lookup :: Eq a => a -> [(a,b)] -> Maybe b   

Looks up a key in an association list.

enumFrom_ :: Int -> [Int]   

Generates an infinite sequence of ascending integers.

enumFromThen_ :: Int -> Int -> [Int]   

Generates an infinite sequence of integers with a particular in/decrement.

enumFromTo_ :: Int -> Int -> [Int]   

Generates a sequence of ascending integers.

enumFromThenTo_ :: Int -> Int -> Int -> [Int]   

Generates a sequence of integers with a particular in/decrement.

ord :: Char -> Int   

Converts a character into its ASCII value.

chr :: Int -> Char   

Converts a Unicode value into a character. The conversion is total, i.e., for out-of-bound values, the smallest or largest character is generated.

negate_ :: Int -> Int   

Unary minus. Usually written as "- e".

negateFloat :: Float -> Float   

Unary minus on Floats. Usually written as "-e".

Further infos:

• externally defined

success :: Bool   

The always satisfiable constraint.

Further infos:

• solution complete, i.e., able to compute all solutions

maybe :: a -> (b -> a) -> Maybe b -> a   

either :: (a -> b) -> (c -> b) -> Either a c -> b   

done :: IO ()   

The empty IO action that returns nothing.

putChar :: Char -> IO ()   

An action that puts its character argument on standard output.

getChar :: IO Char   

An action that reads a character from standard output and returns it.

Further infos:

• externally defined

readFile :: String -> IO String   

An action that (lazily) reads a file and returns its contents.

writeFile :: String -> String -> IO ()   

An action that writes a file.

Example call:

(writeFile filename contents)

Parameters:

• filename : The name of the file to be written.
• contents : The contents to be written to the file.

appendFile :: String -> String -> IO ()   

An action that appends a string to a file. It behaves like writeFile if the file does not exist.

Example call:

(appendFile filename contents)

Parameters:

• filename : The name of the file to be written.
• contents : The contents to be appended to the file.

putStr :: String -> IO ()   

Action to print a string on stdout.

putStrLn :: String -> IO ()   

Action to print a string with a newline on stdout.

getLine :: IO String   

Action to read a line from stdin.

userError :: String -> IOError   

A user error value is created by providing a description of the error situation as a string.

Further infos:

• solution complete, i.e., able to compute all solutions

ioError :: IOError -> IO a   

Raises an I/O exception with a given error value.

showError :: IOError -> String   

Shows an error values as a string.

Further infos:

• solution complete, i.e., able to compute all solutions

catch :: IO a -> (IOError -> IO a) -> IO a   

Catches a possible error or failure during the execution of an I/O action. (catch act errfun) executes the I/O action act. If an exception or failure occurs during this I/O action, the function errfun is applied to the error value.

Further infos:

• externally defined

print :: Show a => a -> IO ()   

Converts a term into a string and prints it.

doSolve :: Bool -> IO ()   

Solves a constraint as an I/O action. Note: the constraint should be always solvable in a deterministic way

sequenceIO :: [IO a] -> IO [a]   

Executes a sequence of I/O actions and collects all results in a list.

sequenceIO_ :: [IO a] -> IO ()   

Executes a sequence of I/O actions and ignores the results.

mapIO :: (a -> IO b) -> [a] -> IO [b]   

Maps an I/O action function on a list of elements. The results of all I/O actions are collected in a list.

mapIO_ :: (a -> IO b) -> [a] -> IO ()   

Maps an I/O action function on a list of elements. The results of all I/O actions are ignored.

foldIO :: (a -> b -> IO a) -> a -> [b] -> IO a   

Folds a list of elements using an binary I/O action and a value for the empty list.

liftIO :: (a -> b) -> IO a -> IO b   

Apply a pure function to the result of an I/O action.

forIO :: [a] -> (a -> IO b) -> IO [b]   

Like mapIO, but with flipped arguments.

This can be useful if the definition of the function is longer than those of the list, like in

forIO [1..10] $ \n -> do ...

forIO_ :: [a] -> (a -> IO b) -> IO ()   

Like mapIO_, but with flipped arguments.

This can be useful if the definition of the function is longer than those of the list, like in

forIO_ [1..10] $ \n -> do ...

unless :: Bool -> IO () -> IO ()   

Performs an IO action unless the condition is met.

when :: Bool -> IO () -> IO ()   

Performs an IO action when the condition is met.

(?) :: a -> a -> a   

Non-deterministic choice par excellence. The value of x ? y is either x or y.

Example call:

(x ? y)

Parameters:

• x : The right argument.
• y : The left argument.

Returns:

either x or y non-deterministically.

Further infos:

• defined as right-associative infix operator with precedence 0
• solution complete, i.e., able to compute all solutions

anyOf :: [a] -> a   

unknown :: a   

Evaluates to a fresh free variable.

Further infos:

• solution complete, i.e., able to compute all solutions

PEVAL :: a -> a   

Identity function used by the partial evaluator to mark expressions to be partially evaluated.

Further infos:

• solution complete, i.e., able to compute all solutions

normalForm :: a -> a   

Evaluates the argument to normal form and returns it.

groundNormalForm :: a -> a   

Evaluates the argument to ground normal form and returns it. Suspends as long as the normal form of the argument is not ground.

apply :: (a -> b) -> a -> b   

Further infos:

• externally defined

cond :: Bool -> a -> a   

Further infos:

• externally defined

letrec :: a -> a -> Bool   

This operation is internally used by PAKCS to implement recursive lets by using cyclic term structures. Basically, the effect of

letrec ones (1:ones)

(where ones is a logic variable) is the binding of ones to (1:ones).

Further infos:

• solution complete, i.e., able to compute all solutions

(=:<=) :: a -> a -> Bool   

Non-strict equational constraint. Used to implement functional patterns.

Further infos:

• defined as non-associative infix operator with precedence 4
• externally defined

shows :: Show a => a -> String -> String   

showChar :: Char -> String -> String   

Further infos:

• solution complete, i.e., able to compute all solutions

showString :: String -> String -> String   

showParen :: Bool -> (String -> String) -> String -> String   

reads :: Read a => String -> [(a,String)]   

readParen :: Bool -> (String -> [(a,String)]) -> String -> [(a,String)]   

read :: Read a => String -> a   

lex :: String -> [(String,String)]   

boundedEnumFrom :: (Bounded a, Enum a) => a -> [a]   

boundedEnumFromThen :: (Bounded a, Enum a) => a -> a -> [a]   

asTypeOf :: a -> a -> a   

Further infos:

• solution complete, i.e., able to compute all solutions

sequence :: Monad a => [a b] -> a [b]   

Evaluates a sequence of monadic actions and collects all results in a list.

sequence_ :: Monad a => [a b] -> a ()   

Evaluates a sequence of monadic actions and ignores the results.

mapM :: Monad a => (b -> a c) -> [b] -> a [c]   

Maps a monadic action function on a list of elements. The results of all monadic actions are collected in a list.

mapM_ :: Monad a => (b -> a c) -> [b] -> a ()   

Maps a monadic action function on a list of elements. The results of all monadic actions are ignored.

foldM :: Monad a => (b -> c -> a b) -> b -> [c] -> a b   

Folds a list of elements using a binary monadic action and a value for the empty list.

liftM :: Monad a => (b -> c) -> a b -> a c   

Apply a pure function to the result of a monadic action.

liftM2 :: Monad a => (b -> c -> d) -> a b -> a c -> a d   

Apply a pure binary function to the result of two monadic actions.

forM :: Monad a => [b] -> (b -> a c) -> a [c]   

Like mapM, but with flipped arguments.

This can be useful if the definition of the function is longer than those of the list, like in

forM [1..10] $ \n -> do ...

forM_ :: Monad a => [b] -> (b -> a c) -> a ()   

Like mapM_, but with flipped arguments.

This can be useful if the definition of the function is longer than those of the list, like in

forM_ [1..10] $ \n -> do ...

unlessM :: Monad a => Bool -> a () -> a ()   

Performs a monadic action unless the condition is met.

whenM :: Monad a => Bool -> a () -> a ()   

Performs a monadic action when the condition is met.