Safe Haskell | None |
---|

The standard set of functions and variables available to all programs.

You may use any of these functions and variables without defining them.

- data Number
- (+) :: Number -> Number -> Number
- (-) :: Number -> Number -> Number
- (*) :: Number -> Number -> Number
- (/) :: Number -> Number -> Number
- (^) :: Number -> Number -> Number
- (>) :: Number -> Number -> Bool
- (>=) :: Number -> Number -> Bool
- (<) :: Number -> Number -> Bool
- (<=) :: Number -> Number -> Bool
- max :: (Number, Number) -> Number
- min :: (Number, Number) -> Number
- negate :: Number -> Number
- abs :: Number -> Number
- signum :: Number -> Number
- truncate :: Number -> Number
- round :: Number -> Number
- ceiling :: Number -> Number
- floor :: Number -> Number
- quotient :: (Number, Number) -> Number
- remainder :: (Number, Number) -> Number
- reciprocal :: Number -> Number
- pi :: Number
- exp :: Number -> Number
- sqrt :: Number -> Number
- log :: Number -> Number
- logBase :: (Number, Number) -> Number
- sin :: Number -> Number
- tan :: Number -> Number
- cos :: Number -> Number
- asin :: Number -> Number
- atan :: Number -> Number
- atan2 :: (Number, Number) -> Number
- acos :: Number -> Number
- properFraction :: Number -> (Number, Number)
- even :: Number -> Bool
- odd :: Number -> Bool
- gcd :: (Number, Number) -> Number
- lcm :: (Number, Number) -> Number
- sum :: [Number] -> Number
- product :: [Number] -> Number
- maximum :: [Number] -> Number
- minimum :: [Number] -> Number
- isInteger :: Number -> Bool
- fromInteger :: Integer -> Number
- fromRational :: Rational -> Number
- fromInt :: Int -> Number
- toInt :: Number -> Int
- fromDouble :: Double -> Number
- toDouble :: Number -> Double
- data Text :: *
- fromString :: String -> Text
- empty :: Text -> Bool
- append :: (Text, Text) -> Text
- (<>) :: Text -> Text -> Text
- appendAll :: [Text] -> Text
- numberOfCharacters :: Text -> Number
- numberOfWords :: Text -> Number
- numberOfLines :: Text -> Number
- characters :: Text -> [Text]
- lines :: Text -> [Text]
- words :: Text -> [Text]
- unlines :: [Text] -> Text
- unwords :: [Text] -> Text
- show :: Number -> Text
- join :: ([Text], Text) -> Text
- replace :: (Text, Text, Text) -> Text
- toLower :: Text -> Text
- toUpper :: Text -> Text
- strip :: Text -> Text
- stripPrefix :: (Text, Text) -> Text
- stripSuffix :: (Text, Text) -> Text
- search :: (Text, Text) -> [Number]
- substring :: (Text, Number, Number) -> Text
- data Bool :: *
- (&&) :: Bool -> Bool -> Bool
- (||) :: Bool -> Bool -> Bool
- not :: Bool -> Bool
- otherwise :: Bool
- data Maybe a :: * -> *
- withDefault :: (Maybe a, a) -> a
- maybe :: (Maybe a, a -> b, b) -> b
- data Either a b :: * -> * -> *
- either :: (Either a b, a -> c, b -> c) -> c
- (==) :: a -> a -> Bool
- (/=) :: a -> a -> Bool
- fst :: (a, b) -> a
- snd :: (a, b) -> b
- toOperator :: ((a, b) -> c) -> a -> b -> c
- fromOperator :: (a -> b -> c) -> (a, b) -> c
- id :: a -> a
- const :: a -> b -> a
- (.) :: (b -> c) -> (a -> b) -> a -> c
- flip :: ((a, b) -> c) -> (b, a) -> c
- until :: (a -> Bool, a -> a, a) -> a
- error :: Text -> a
- undefined :: a
- ifThenElse :: Bool -> a -> a -> a
- map :: (a -> b, [a]) -> [b]
- (++) :: [a] -> [a] -> [a]
- filter :: (a -> Bool, [a]) -> [a]
- reduce :: ((a, a) -> a, [a]) -> a
- first :: [a] -> a
- rest :: [a] -> [a]
- init :: [a] -> [a]
- last :: [a] -> a
- null :: [a] -> Bool
- length :: [a] -> Number
- (!!) :: [a] -> Number -> a
- reverse :: [a] -> [a]
- and :: [Bool] -> Bool
- or :: [Bool] -> Bool
- any :: ([a], a -> Bool) -> Bool
- all :: ([a], a -> Bool) -> Bool
- concat :: [[a]] -> [a]
- concatMap :: ([a], a -> [b]) -> [b]
- repeat :: a -> [a]
- replicate :: (a, Number) -> [a]
- cycle :: [a] -> [a]
- take :: ([a], Number) -> [a]
- drop :: ([a], Number) -> [a]
- splitAt :: ([a], Number) -> ([a], [a])
- takeWhile :: (a -> Bool) -> [a] -> [a]
- dropWhile :: (a -> Bool) -> [a] -> [a]
- span :: (a -> Bool) -> [a] -> ([a], [a])
- break :: (a -> Bool) -> [a] -> ([a], [a])
- isMember :: ([a], a) -> Bool
- lookup :: ([(a, b)], a) -> Maybe b
- transpose :: [[a]] -> [[a]]
- subsequences :: [a] -> [[a]]
- permutations :: [a] -> [[a]]
- nub :: [a] -> [a]
- sort :: [Number] -> [Number]
- shuffle :: ([a], Number) -> [a]
- data IO a :: * -> *
- data Number
- data Text :: *
- shuffle :: ([a], Number) -> [a]
- newtype Color = RGBA (Number, Number, Number, Number)
- black :: Color
- white :: Color
- red :: Color
- green :: Color
- blue :: Color
- cyan :: Color
- magenta :: Color
- yellow :: Color
- aquamarine :: Color
- orange :: Color
- azure :: Color
- violet :: Color
- chartreuse :: Color
- rose :: Color
- brown :: Color
- pink :: Color
- purple :: Color
- gray :: Number -> Color
- grey :: Number -> Color
- light :: Color -> Color
- dark :: Color -> Color
- translucent :: Color -> Color
- type Point = (Number, Number)
- type Vector = (Number, Number)
- addVectors :: (Vector, Vector) -> Vector
- scaleVector :: (Vector, Number) -> Vector
- rotateVector :: (Vector, Number) -> Vector
- data Picture
- blank :: Picture
- line :: [Point] -> Picture
- thickLine :: ([Point], Number) -> Picture
- polygon :: [Point] -> Picture
- thickPolygon :: ([Point], Number) -> Picture
- solidPolygon :: [Point] -> Picture
- rectangle :: (Number, Number) -> Picture
- solidRectangle :: (Number, Number) -> Picture
- thickRectangle :: (Number, Number, Number) -> Picture
- circle :: Number -> Picture
- solidCircle :: Number -> Picture
- thickCircle :: (Number, Number) -> Picture
- arc :: (Number, Number, Number) -> Picture
- sector :: (Number, Number, Number) -> Picture
- thickArc :: (Number, Number, Number, Number) -> Picture
- text :: Text -> Picture
- color :: (Picture, Color) -> Picture
- translate :: (Picture, Number, Number) -> Picture
- scale :: (Picture, Number, Number) -> Picture
- rotate :: (Picture, Number) -> Picture
- pictures :: [Picture] -> Picture
- (&) :: Picture -> Picture -> Picture
- coordinatePlane :: Picture
- codeWorldLogo :: Picture
- data Event
- = KeyPress !Text
- | KeyRelease !Text
- | MousePress !(MouseButton, Point)
- | MouseRelease !(MouseButton, Point)
- | MouseMovement !Point

- data MouseButton
- trace :: (a, Text) -> a
- type Program = IO ()
- pictureOf :: Picture -> Program
- animationOf :: (Number -> Picture) -> Program
- simulationOf :: ([Number] -> a, (a, Number) -> a, a -> Picture) -> Program
- interactionOf :: ([Number] -> a, (a, Number) -> a, (a, Event) -> a, a -> Picture) -> Program

# Documentation

Welome to CodeWorld! You can define your own pictures, animations, and games by defining variables and functions. There are four kinds of CodeWorld programs:

- Pictures. To create a picture, you'll define the variable called
`main`

using`pictureOf`

. The parameter to`pictureOf`

should be a`Picture`

. Example:

main = pictureOf(tree)

- Animations. To create an animation, you'll define the variable called
`main`

using`animationOf`

. The parameter to`animationOf`

should be a function, mapping each time in seconds (a`Number`

) to a`Picture`

that is shown at that time. Example:

main = animationOf(spinningWheel)

- Simulations. A simulation is like an animation, in that it changes over
time. But while an animation changes in a simple regular way over time, a
simulation can change in different ways depending on the state of things
at any moment. To create a simulation, you should first decide on the
type to describe the state of things (called the "world" type), and
describe the simulation in terms of the starting state, the step that
says how things change over time, and and a draw function that can build
a picture from a state. Then you'll use
`simulationOf`

to define main. Example:

main = simulationOf(start, step, draw)

- Interactions. Finally, you can build an interactive simulation, such as
a game. This is very like a simulation, except that it also has an event
function, which says how the state of things changes when events (like
keys being pressed or the mouse moving) happen. You'll use
`interactionOf`

to define these. Example:

main = interactionOf(start, step, event, draw)

# Numbers

data Number

The type for numbers.

Numbers can be positive or negative, whole or fractional. For example, 5, 3.2, and -10 are all values of the type Number.

(/) :: Number -> Number -> Number infixl 7

Divides two numbers. The second number should not be zero.

(>=) :: Number -> Number -> Bool infix 4

Tells whether one number is greater than or equal to the other.

(<=) :: Number -> Number -> Bool infix 4

Tells whether one number is less than or equal to the other.

Gives the absolute value of a number.

If the number if positive or zero, the absolute value is the same as the number. If the number is negative, the absolute value is the opposite of the number.

Gives the number without its fractional part.

For example, truncate(4.2) is 4, while truncate(-4.7) is -4.

Gives the number rounded to the nearest integer.

For example, round(4.2) is 4, while round(4.7) is 5.

Gives the smallest integer that is greater than or equal to a number.

For example, ceiling(4) is 4, while ceiling(4.1) is 5. With negative numbers, ceiling(-3.5) is -3, since -3 is greater than -3.5.

Gives the largest integer that is less than or equal to a number.

For example, floor(4) is 4, while floor(3.9) is 3. With negative numbers, floor(-3.5) is -4, since -4 is less than -3.5.

quotient :: (Number, Number) -> Number

Gives the integer part of the result when dividing two numbers.

For example, 3/2 is 1.5, but quotient(3, 2) is 1, which is the integer part.

remainder :: (Number, Number) -> Number

Gives the remainder when dividing two numbers.

For example, remainder(3,2) is 1, which is the remainder when dividing 3 by 2.

reciprocal :: Number -> Number

Gives the repicrocal of a number.

For example, reciprocal(5) is 1/5 (also written as 0.2).

The constant pi, which is equal to the ration between the circumference and diameter of a circle.

pi is approximately 3.14159.

Gives the exponential of a number. This is equal to the constant e, raised to the power of the number.

The exp function increases faster and faster very quickly. For example, if t is the current time in seconds, exp(t) will reach a million in about 14 seconds. It will reach a billion in around 21 seconds.

Gives the square root of a number. This is the positive number that, when multiplied by itself, gives the original number back.

The sqrt always increases, but slows down. For example, if t is the current time, sqrt(t) will reach 5 in 25 seconds. But it will take 100 seconds to reach 10, and 225 seconds (almost 4 minutes) to reach 15.

Gives the natural log of a number. This is the opposite of the exp function.

Like sqrt, the log function always increases, but slows down. However, it slows down much sooner than the sqrt function. If t is the current time in seconds, it takes more than 2 minutes for log(t) to reach 5, and more than 6 hours to reach 10!

logBase :: (Number, Number) -> Number

Gives the logarithm of the first number, using the base of the second number.

Gives the tangent of an angle, where the angle is measured in degrees.

This is the slope of a line at that angle from horizontal.

Gives the inverse sine of a value, in degrees.

This is the unique angle between -90 and 90 that has the input as its sine.

Gives the inverse tangent of a value, in degrees.

This is the unique angle between -90 and 90 that has the input as its tangent.

atan2 :: (Number, Number) -> Number

Gives the angle between the positive x axis and a given point, in degrees.

Gives the inverse cosine of a value, in degrees.

This is the unique angle between 0 and 180 that has the input as its cosine.

properFraction :: Number -> (Number, Number)

Separates a number into its whole and fractional parts.

For example, properFraction(1.2) is (1, 0.2).

gcd :: (Number, Number) -> Number

Gives the greatest common divisor of two numbers.

This is the largest number that divides each of the two parameters. Both parameters must be integers.

lcm :: (Number, Number) -> Number

Gives the least common multiple of two numbers.

This is the smallest number that is divisible by both of the two parameters. Both parameters must be integers.

Tells whether a Number is an integer or not.

An integer is a whole number, such as 5, 0, or -10. Numbers with non-zero decimals, like 5.3, are not integers.

fromInteger :: Integer -> Number

fromRational :: Rational -> Number

fromDouble :: Double -> Number

# Text

data Text :: *

fromString :: String -> Text

numberOfCharacters :: Text -> Number

numberOfWords :: Text -> Number

numberOfLines :: Text -> Number

characters :: Text -> [Text]

replace :: (Text, Text, Text) -> Text

Replaces one piece of text with another.

For example, `replace("How do you do?", "do", "be")` is equal to `"How be you be?"`.

stripPrefix :: (Text, Text) -> Text

Removes a prefix from some text.

For example, `stripPrefix("Dr. Jones", "Dr. ")` is equal to `Jones`. If the prefix isn't there, the result is the same string, unchanged.

stripSuffix :: (Text, Text) -> Text

Removes a suffix from some text.

For example, `stripSuffix("smallest", "est")` is equal to `"small"`. If the suffix isn't there, the result is the same string, unchanged.

search :: (Text, Text) -> [Number]

Finds all indices where some text appears in a larger piece of text.

For example, `search("How do you do?", "do")` is equal to the list `[4, 11]`. Indices start at zero.

substring :: (Text, Number, Number) -> Text

Takes part of a string at a starting index and length.

For example, `substring("funny", 2, 2)` is equal to `"nn"`. Indices start at zero.

# General purpose functions

data Bool :: *

data Maybe a :: * -> *

Alternative Maybe | |

Monad Maybe | |

Functor Maybe | |

MonadFix Maybe | |

MonadPlus Maybe | |

Applicative Maybe | |

Foldable Maybe | |

Traversable Maybe | |

Generic1 Maybe | |

Eq a => Eq (Maybe a) | |

Data a => Data (Maybe a) | |

Ord a => Ord (Maybe a) | |

Read a => Read (Maybe a) | |

Show a => Show (Maybe a) | |

Generic (Maybe a) | |

Monoid a => Monoid (Maybe a) | |

Typeable (* -> *) Maybe | |

type Rep1 Maybe = D1 D1Maybe ((:+:) (C1 C1_0Maybe U1) (C1 C1_1Maybe (S1 NoSelector Par1))) | |

type Rep (Maybe a) = D1 D1Maybe ((:+:) (C1 C1_0Maybe U1) (C1 C1_1Maybe (S1 NoSelector (Rec0 a)))) | |

type (==) (Maybe k) a b = EqMaybe k a b |

withDefault :: (Maybe a, a) -> a

Converts a Maybe value to a plain value, by using a default.

For example, `withDefault(Nothing, 5)` is equal to 5, while `withDefault(Just(3), 5)` is equal to 3.

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

Gets a value from a Maybe value by applying either a default value or another function.

For example, `maybe(Nothing, blank, circle)` is a picture, while `maybe(Just(10), blank, circle)` is a picture of a circle with radius 10.

data Either a b :: * -> * -> *

Error e => Alternative (Either e) | |

Monad (Either e) | |

Functor (Either a) | |

MonadFix (Either e) | |

Error e => MonadPlus (Either e) | |

Applicative (Either e) | |

Foldable (Either a) | |

Traversable (Either a) | |

Generic1 (Either a) | |

(Eq a, Eq b) => Eq (Either a b) | |

(Data a, Data b) => Data (Either a b) | |

(Ord a, Ord b) => Ord (Either a b) | |

(Read a, Read b) => Read (Either a b) | |

(Show a, Show b) => Show (Either a b) | |

Generic (Either a b) | |

Typeable (* -> * -> *) Either | |

type Rep1 (Either a) = D1 D1Either ((:+:) (C1 C1_0Either (S1 NoSelector (Rec0 a))) (C1 C1_1Either (S1 NoSelector Par1))) | |

type Rep (Either a b) = D1 D1Either ((:+:) (C1 C1_0Either (S1 NoSelector (Rec0 a))) (C1 C1_1Either (S1 NoSelector (Rec0 b)))) | |

type (==) (Either k k1) a b = EqEither k k1 a b |

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

Gets a value from an `Either`

value by applying either of two functions,
depending on if the value is the left or right possibility.

For example, `either(Left(5), circle, text)` is a circle with radius 5. But `either(Right("hello"), circle, text)` is a picture with the text `"hello"`.

fst :: (a, b) -> a

snd :: (a, b) -> b

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

Converts a function to an operator.

Example use:

f(x,y) = 2*x + y (%) = toOperator(f)

eight = 3 % 2

This has the same effect as defining % as:

x % y = 2*x + y eight = 3 % 2

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

Converts an operator into a normal function.

Example use:

divide = fromOperator(/) four = divide(16, 4)

id :: a -> a

const :: a -> b -> a

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

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

Converts a function into a version that takes the arguments in the opposite order.

Example:

f(x,y) = 2*x + y g = flip(f) eight = g(2,3)

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

Continues passing a value through a function until it meets a condition.

Example:

seven = until(odd, (/ 2), 56)

undefined :: a

ifThenElse :: Bool -> a -> a -> a

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

Applies a function to each element of a list, and produces a list of results.

For example, `map(circle, [1, 2, 3, 4, 5])` is a list of circles of different sizes.

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

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

Keeps only the elements of a list for which a function evaluates
to `True`

.

For example, `filter(even, [1, 2, 3, 4, 5])` is equal to `[2, 4]`.

reduce :: ((a, a) -> a, [a]) -> a

Reduces a list of values into a single value, by combining elements with a function. The function should take two parameters, and should be associative (so `f(x,f(y,z)) = f(f(x,y),z)`). The list should be non-empty.

For example, `reduce(fromOperator(+), [1, 3, 5])` is equal to `9`.

first :: [a] -> a

rest :: [a] -> [a]

init :: [a] -> [a]

last :: [a] -> a

reverse :: [a] -> [a]

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

Determines if any member of a list matches a condition.

For example, `any([1, 2, 3], even)` is `True`

, because 2 is even.

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

Determines if all members of a list match a condition.

For example, `all([2, 3, 4], even)` is `False`

, because 3 is not even.

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

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

Builds a list from all of the members in the lists produced by applying a function to each element of the given list.

repeat :: a -> [a]

cycle :: [a] -> [a]

transpose :: [[a]] -> [[a]]

subsequences :: [a] -> [[a]]

permutations :: [a] -> [[a]]

nub :: [a] -> [a]

data IO a :: * -> *

data Number

The type for numbers.

Numbers can be positive or negative, whole or fractional. For example, 5, 3.2, and -10 are all values of the type Number.

data Text :: *

# Colors

aquamarine :: Color

chartreuse :: Color

translucent :: Color -> Color

# Pictures

addVectors :: (Vector, Vector) -> Vector

scaleVector :: (Vector, Number) -> Vector

rotateVector :: (Vector, Number) -> Vector

thickPolygon :: ([Point], Number) -> Picture

solidPolygon :: [Point] -> Picture

solidRectangle :: (Number, Number) -> Picture

thickRectangle :: (Number, Number, Number) -> Picture

solidCircle :: Number -> Picture

thickCircle :: (Number, Number) -> Picture

A coordinate plane. Adding this to your pictures can help you measure distances more accurately.

Example:

main = pictureOf(myPicture & coordinatePlane) myPicture = ...

The CodeWorld logo.

# Events

data Event

KeyPress !Text | |

KeyRelease !Text | |

MousePress !(MouseButton, Point) | |

MouseRelease !(MouseButton, Point) | |

MouseMovement !Point |

Show Event |

# Debugging

# Entry points

animationOf :: (Number -> Picture) -> Program

simulationOf :: ([Number] -> a, (a, Number) -> a, a -> Picture) -> Program