Prelude.Week1

Basic Types

type Char = Char

type String = [Char]

type Int = Int

type Double = Double

data Bool

Instances

Eq Bool

Ord Bool

Show Bool

NFData Bool

Arithmetic arithmetic and comparison

Integer arithmetic and comparison

(+) :: Int -> Int -> Int

(-) :: Int -> Int -> Int

(*) :: Int -> Int -> Int

mod :: Int -> Int -> Int

(>) :: Int -> Int -> Bool

(<) :: Int -> Int -> Bool

(>=) :: Int -> Int -> Bool

(<=) :: Int -> Int -> Bool

(==) :: Int -> Int -> Bool

(/=) :: Int -> Int -> Bool

Double arithmetic and comparison

(+.) :: Double -> Double -> Double

(-.) :: Double -> Double -> Double

(*.) :: Double -> Double -> Double

(>.) :: Double -> Double -> Bool

(<.) :: Double -> Double -> Bool

(>=.) :: Double -> Double -> Bool

(<=.) :: Double -> Double -> Bool

(==.) :: Double -> Double -> Bool

(/=.) :: Double -> Double -> Bool

Type conversion functions

doubleToString :: Double -> String

intToString :: Int -> String

charToString :: Char -> String

intToDouble :: Int -> Double

intToChar :: Int -> Char

charToInt :: Char -> Int

IO Requests and responses

data IORequest

Constructors

PrintString String

Exit

ReadString

ReadFile String

data IOResponse

Constructors

Success

FileContents String

NextLine String

Instances

NFData IOResponse

run :: ([IOResponse] -> [IORequest]) -> IO ()

String operations

(<>) :: String -> String -> String

Other convenient operators

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

Function composition.

trace :: String -> a -> a

The trace function outputs the trace message given as its first argument, before returning the second argument as its result.

For example, this returns the value of f x but first outputs the message.

 trace ("calling f with x = " ++ show x) (f x)

The trace function should only be used for debugging, or for monitoring execution. The function is not referentially transparent: its type indicates that it is a pure function but it has the side effect of outputting the trace message.

List operators

These should cover everything you implemented in the first assignment.

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

Append two lists, i.e.,

 [x1, ..., xm] ++ [y1, ..., yn] == [x1, ..., xm, y1, ..., yn]
 [x1, ..., xm] ++ [y1, ...] == [x1, ..., xm, y1, ...]

If the first list is not finite, the result is the first list.

head :: [a] -> a

Extract the first element of a list, which must be non-empty.

last :: [a] -> a

Extract the last element of a list, which must be finite and non-empty.

tail :: [a] -> [a]

Extract the elements after the head of a list, which must be non-empty.

init :: [a] -> [a]

Return all the elements of a list except the last one. The list must be non-empty.

null :: [a] -> Bool

Test whether a list is empty.

length :: [a] -> Int

O(n). length returns the length of a finite list as an Int. It is an instance of the more general genericLength, the result type of which may be any kind of number.

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

map f xs is the list obtained by applying f to each element of xs, i.e.,

 map f [x1, x2, ..., xn] == [f x1, f x2, ..., f xn]
 map f [x1, x2, ...] == [f x1, f x2, ...]

reverse :: [a] -> [a]

reverse xs returns the elements of xs in reverse order. xs must be finite.

intersperse :: a -> [a] -> [a]

The intersperse function takes an element and a list and `intersperses' that element between the elements of the list. For example,

 intersperse ',' "abcde" == "a,b,c,d,e"

intercalate :: [a] -> [[a]] -> [a]

intercalate xs xss is equivalent to (concat (intersperse xs xss)). It inserts the list xs in between the lists in xss and concatenates the result.

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

foldl, applied to a binary operator, a starting value (typically the left-identity of the operator), and a list, reduces the list using the binary operator, from left to right:

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

The list must be finite.

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

foldl1 is a variant of foldl that has no starting value argument, and thus must be applied to non-empty lists.

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

foldr, applied to a binary operator, a starting value (typically the right-identity of the operator), and a list, reduces the list using the binary operator, from right to left:

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

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

foldr1 is a variant of foldr that has no starting value argument, and thus must be applied to non-empty lists.

concat :: [[a]] -> [a]

Concatenate a list of lists.

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

Map a function over a list and concatenate the results.

and :: [Bool] -> Bool

and returns the conjunction of a Boolean list. For the result to be True, the list must be finite; False, however, results from a False value at a finite index of a finite or infinite list.

or :: [Bool] -> Bool

or returns the disjunction of a Boolean list. For the result to be False, the list must be finite; True, however, results from a True value at a finite index of a finite or infinite list.

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

Applied to a predicate and a list, any determines if any element of the list satisfies the predicate. For the result to be False, the list must be finite; True, however, results from a True value for the predicate applied to an element at a finite index of a finite or infinite list.

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

Applied to a predicate and a list, all determines if all elements of the list satisfy the predicate. For the result to be True, the list must be finite; False, however, results from a False value for the predicate applied to an element at a finite index of a finite or infinite list.

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

iterate f x returns an infinite list of repeated applications of f to x:

 iterate f x == [x, f x, f (f x), ...]

repeat :: a -> [a]

repeat x is an infinite list, with x the value of every element.

replicate :: Int -> a -> [a]

replicate n x is a list of length n with x the value of every element. It is an instance of the more general genericReplicate, in which n may be of any integral type.

cycle :: [a] -> [a]

cycle ties a finite list into a circular one, or equivalently, the infinite repetition of the original list. It is the identity on infinite lists.

take :: Int -> [a] -> [a]

take n, applied to a list xs, returns the prefix of xs of length n, or xs itself if n > length xs:

 take 5 "Hello World!" == "Hello"
 take 3 [1,2,3,4,5] == [1,2,3]
 take 3 [1,2] == [1,2]
 take 3 [] == []
 take (-1) [1,2] == []
 take 0 [1,2] == []

It is an instance of the more general genericTake, in which n may be of any integral type.

drop :: Int -> [a] -> [a]

drop n xs returns the suffix of xs after the first n elements, or [] if n > length xs:

 drop 6 "Hello World!" == "World!"
 drop 3 [1,2,3,4,5] == [4,5]
 drop 3 [1,2] == []
 drop 3 [] == []
 drop (-1) [1,2] == [1,2]
 drop 0 [1,2] == [1,2]

It is an instance of the more general genericDrop, in which n may be of any integral type.

splitAt :: Int -> [a] -> ([a], [a])

splitAt n xs returns a tuple where first element is xs prefix of length n and second element is the remainder of the list:

 splitAt 6 "Hello World!" == ("Hello ","World!")
 splitAt 3 [1,2,3,4,5] == ([1,2,3],[4,5])
 splitAt 1 [1,2,3] == ([1],[2,3])
 splitAt 3 [1,2,3] == ([1,2,3],[])
 splitAt 4 [1,2,3] == ([1,2,3],[])
 splitAt 0 [1,2,3] == ([],[1,2,3])
 splitAt (-1) [1,2,3] == ([],[1,2,3])

It is equivalent to (take n xs, drop n xs) when n is not _|_ (splitAt _|_ xs = _|_). splitAt is an instance of the more general genericSplitAt, in which n may be of any integral type.

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

takeWhile, applied to a predicate p and a list xs, returns the longest prefix (possibly empty) of xs of elements that satisfy p:

 takeWhile (< 3) [1,2,3,4,1,2,3,4] == [1,2]
 takeWhile (< 9) [1,2,3] == [1,2,3]
 takeWhile (< 0) [1,2,3] == []

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

dropWhile p xs returns the suffix remaining after takeWhile p xs:

 dropWhile (< 3) [1,2,3,4,5,1,2,3] == [3,4,5,1,2,3]
 dropWhile (< 9) [1,2,3] == []
 dropWhile (< 0) [1,2,3] == [1,2,3]