Safe Haskell | None |
---|---|

Language | Haskell98 |

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 -> Truth
- (>=) :: Number -> Number -> Truth
- (<) :: Number -> Number -> Truth
- (<=) :: Number -> Number -> Truth
- max :: (Number, Number) -> Number
- min :: (Number, Number) -> Number
- opposite :: Number -> Number
- negate :: Number -> Number
- abs :: Number -> Number
- absoluteValue :: Number -> Number
- signum :: Number -> Number
- truncation :: Number -> Number
- rounded :: 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
- squareRoot :: 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 -> Truth
- odd :: Number -> Truth
- gcd :: (Number, Number) -> Number
- lcm :: (Number, Number) -> Number
- sum :: [Number] -> Number
- product :: [Number] -> Number
- maximum :: [Number] -> Number
- minimum :: [Number] -> Number
- isInteger :: Number -> Truth
- fromInteger :: Integer -> Number
- fromRational :: Rational -> Number
- fromInt :: Int -> Number
- toInt :: Number -> Int
- fromDouble :: Double -> Number
- toDouble :: Number -> Double
- data Text
- fromString :: String -> Text
- toString :: Text -> String
- fromCWText :: Text -> Text
- toCWText :: Text -> Text
- (<>) :: Text -> Text -> Text
- numberOfCharacters :: Text -> Number
- numberOfWords :: Text -> Number
- numberOfLines :: Text -> Number
- lines :: Text -> [Text]
- unlines :: [Text] -> Text
- words :: Text -> [Text]
- unwords :: [Text] -> Text
- characters :: Text -> [Text]
- printed :: Number -> Text
- joined :: [Text] -> Text
- joinedWith :: ([Text], Text) -> Text
- lowercase :: Text -> Text
- uppercase :: Text -> Text
- startsWith :: (Text, Text) -> Truth
- endsWith :: (Text, Text) -> Truth
- substitution :: (Text, Text, Text) -> Text
- substitutions :: (Text, [(Text, Text)]) -> Text
- ifThenElse :: Truth -> a -> a -> a
- (==) :: a -> a -> Truth
- (/=) :: a -> a -> Truth
- type Truth = Bool
- data Bool :: *
- (&&) :: Truth -> Truth -> Truth
- (||) :: Truth -> Truth -> Truth
- not :: Truth -> Truth
- otherwise :: Truth
- toOperator :: ((a, b) -> c) -> a -> b -> c
- fromOperator :: (a -> b -> c) -> (a, b) -> c
- id :: a -> a
- (.) :: (b -> c) -> (a -> b) -> a -> c
- firstOfPair :: (a, b) -> a
- secondOfPair :: (a, b) -> b
- error :: Text -> a
- undefined :: a
- (++) :: [a] -> [a] -> [a]
- empty :: [a] -> Truth
- contains :: ([a], a) -> Truth
- length :: [a] -> Number
- at :: ([a], Number) -> a
- (#) :: [a] -> Number -> a
- any :: [Truth] -> Truth
- all :: [Truth] -> Truth
- none :: [Truth] -> Truth
- repeated :: ([a], Number) -> [a]
- repeating :: [a] -> [a]
- first :: ([a], Number) -> [a]
- last :: ([a], Number) -> [a]
- rest :: ([a], Number) -> [a]
- while :: ([a], a -> Truth) -> [a]
- until :: ([a], a -> Truth) -> [a]
- after :: ([a], a -> Truth) -> [a]
- concatenation :: [[a]] -> [a]
- subsequences :: [a] -> [[a]]
- permutations :: [a] -> [[a]]
- sorted :: [Number] -> [Number]
- reversed :: [a] -> [a]
- unique :: [a] -> [a]
- transposed :: [[a]] -> [[a]]
- combined :: ((a, a) -> a, [a]) -> a
- data Maybe a :: * -> *
- withDefault :: (Maybe a, a) -> a
- hasValue :: Maybe a -> Truth
- definitely :: Maybe a -> a
- fromRandomSeed :: Number -> [Number]
- shuffled :: ([a], Number) -> [a]
- randomsFrom :: StdGen -> [Number]
- data IO a :: * -> *
- data Number
- data Text
- newtype Color = RGBA (Number, Number, Number, Number)
- type Colour = Color
- 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
- mixed :: (Color, Color) -> Color
- lighter :: (Color, Number) -> Color
- light :: Color -> Color
- darker :: (Color, Number) -> Color
- dark :: Color -> Color
- brighter :: (Color, Number) -> Color
- bright :: Color -> Color
- duller :: (Color, Number) -> Color
- dull :: Color -> Color
- translucent :: Color -> Color
- hue :: Color -> Number
- saturation :: Color -> Number
- luminosity :: Color -> Number
- fromHSL :: (Number, Number, Number) -> Color
- type Point = (Number, Number)
- type Vector = (Number, Number)
- vectorSum :: (Vector, Vector) -> Vector
- vectorDifference :: (Vector, Vector) -> Vector
- scaledVector :: (Vector, Number) -> Vector
- rotatedVector :: (Vector, Number) -> Vector
- dotProduct :: (Vector, Vector) -> Number
- data Picture
- data Font
- data TextStyle
- blank :: Picture
- path :: [Point] -> Picture
- thickPath :: ([Point], Number) -> Picture
- polygon :: [Point] -> Picture
- thickPolygon :: ([Point], Number) -> Picture
- solidPolygon :: [Point] -> Picture
- curve :: [Point] -> Picture
- thickCurve :: ([Point], Number) -> Picture
- loop :: [Point] -> Picture
- thickLoop :: ([Point], Number) -> Picture
- solidLoop :: [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
- styledText :: (Text, Font, TextStyle) -> Picture
- colored :: (Picture, Color) -> Picture
- coloured :: (Picture, Color) -> Picture
- translated :: (Picture, Number, Number) -> Picture
- scaled :: (Picture, Number, Number) -> Picture
- dilated :: (Picture, Number, Number) -> Picture
- rotated :: (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 :: *
- traced :: (a, Text) -> a
- type Program = IO ()
- drawingOf :: Picture -> Program
- animationOf :: (Number -> Picture) -> Program
- simulationOf :: ([Number] -> world, (world, Number) -> world, world -> Picture) -> Program
- interactionOf :: ([Number] -> world, (world, Number) -> world, (world, Event) -> world, world -> Picture) -> Program
- gameOf :: (Number, [Number] -> state, (state, Number) -> state, (state, Event, Number) -> state, (state, Number) -> 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 -> Truth infix 4

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

(<=) :: Number -> Number -> Truth 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.

absoluteValue :: Number -> Number

truncation :: Number -> 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.

squareRoot :: Number -> Number

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

fromString :: String -> Text

fromCWText :: Text -> Text

numberOfCharacters :: Text -> Number

numberOfWords :: Text -> Number

numberOfLines :: Text -> Number

characters :: Text -> [Text]

joinedWith :: ([Text], Text) -> Text

startsWith :: (Text, Text) -> Truth

substitution :: (Text, Text, Text) -> Text

Gives the result of replacing one piece of text with another.

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

substitutions :: (Text, [(Text, Text)]) -> Text

Gives the result of performing many substitutions in a piece of text. This is commonly used to build text to show in a program, as in this example:

substitutions("Lives: [lives] of 3 Score: [score]", [("[lives]", printed(lives)), ("[score]", printed(score))])

# General purpose functions

ifThenElse :: Truth -> a -> a -> a

(/=) :: a -> a -> Truth infix 4

Compares values to see if they are not equal. Note that `a /= b` is the same as `not (a == b)`.

data Bool :: *

Bounded Bool | |

Enum Bool | |

Eq Bool | |

Ord Bool | |

Show Bool | |

Ix Bool | |

Generic Bool | |

Bits Bool | |

FiniteBits Bool | |

Random Bool | |

Unbox Bool | |

MVector MVector Bool | |

Vector Vector Bool | |

type Rep Bool = D1 D1Bool ((:+:) (C1 C1_0Bool U1) (C1 C1_1Bool U1)) | |

data Vector Bool = V_Bool (Vector Word8) | |

data MVector s Bool = MV_Bool (MVector s Word8) | |

type (==) Bool a b = EqBool a 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

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

firstOfPair :: (a, b) -> a

Returns the first element of an ordered pair.

secondOfPair :: (a, b) -> b

Returns the second element of an ordered pair.

undefined :: a

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

Determines if any proposition in a list is true.

For example, `any([even(n) | n <- [1,2,3]])` is `True`

, because 2 is even.

Determines if all propositions in a list are true.

For example, `all([even(n) | n <- [2,3,4]])` is `False`

, because 3 is not even.

Determines if all propositions in a list are false.

For example, `none([odd(n) | n <- [2,3,4]])` is `False`

, because 3 is odd.

repeating :: [a] -> [a]

Forms a list by repeating a source list forever.

Gives all members of a list after the given number.

In general, `xs = first(xs, n) ++ rest(xs, n)`.

while :: ([a], a -> Truth) -> [a]

Gives the longest prefix of a list for which a condition is true.

For example, `while([2,4,5,6], even) = [2,4]`.

until :: ([a], a -> Truth) -> [a]

Gives the longest prefix of a list for which a condition is false.

For example, `until([2,4,5,6], odd) = [2,4]`.

after :: ([a], a -> Truth) -> [a]

Gives the remaining portion of a list after the longest prefix for which a condition is true.

In general, `xs = while(xs, cond) ++ after(xs, cond)

concatenation :: [[a]] -> [a]

Gives the concatenation of all of the lists in its input.

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

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

reversed :: [a] -> [a]

Gives a list in the opposite order of the original.

unique :: [a] -> [a]

Gives a list with all duplicate members removed.

transposed :: [[a]] -> [[a]]

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

Combines a list of values into a single value, by merging members 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, `combined(fromOperator(+), [1, 3, 5])` is equal to `9`.

data Maybe a :: * -> *

Monad Maybe | |

Functor Maybe | |

Applicative Maybe | |

Foldable Maybe | |

Generic1 Maybe | |

Alternative Maybe | |

MonadPlus Maybe | |

Show1 Maybe | |

Read1 Maybe | |

Ord1 Maybe | |

Eq1 Maybe | |

Eq a => Eq (Maybe a) | |

Ord a => Ord (Maybe a) | |

Show a => Show (Maybe a) | |

Generic (Maybe a) | |

Monoid a => Monoid (Maybe a) | |

(Selector s, ToJSON a) => RecordToPairs (S1 s (K1 i (Maybe a))) | |

(Selector s, FromJSON a) => FromRecord (S1 s (K1 i (Maybe a))) | |

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.

definitely :: Maybe a -> a

Extracts the value from a Maybe, and crashes the program if there is no such value.

fromRandomSeed :: Number -> [Number]

randomsFrom :: StdGen -> [Number]

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.

# Colors

aquamarine :: Color

chartreuse :: Color

translucent :: Color -> Color

saturation :: Color -> Number

luminosity :: Color -> Number

# Pictures

vectorDifference :: (Vector, Vector) -> Vector

scaledVector :: (Vector, Number) -> Vector

rotatedVector :: (Vector, Number) -> Vector

dotProduct :: (Vector, Vector) -> Number

data Picture

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

A thin sequence of line segments, with these endpoints and line width

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

A thin polygon with these points as vertices

solidPolygon :: [Point] -> Picture

A solid polygon with these points as vertices

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

A thick curve passing through these points, with this line width

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

A thick closed loop passing through these points, with this line width.

solidRectangle :: (Number, Number) -> Picture

A solid rectangle, with this width and height

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

A thick rectangle, with this width and height and line width

solidCircle :: Number -> Picture

A solid circle, with this radius

thickCircle :: (Number, Number) -> Picture

A thick circle, with this radius and line width

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

A thin arc, starting and ending at these angles, with this radius

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

A solid sector of a circle (i.e., a pie slice) starting and ending at these angles, with this radius

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

A thick arc, starting and ending at these angles, with this radius and line width

styledText :: (Text, Font, TextStyle) -> Picture

A styled piece of text

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

A picture drawn translated in these directions.

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

An event initiated by the user.

Values of this type represent events that the user triggers when
using an interaction, defined with `interactionOf`

.

Key events describe the key as `Text`

. Most keys are represented
by a single character text string, with the capital letter or other
symbol from the key. Keys that don't correspond to a single
character use longer names from the following list. Keep in mind
that not all of these keys appear on all keyboards.

- Up, Down, Left, and Right for the cursor keys.
- F1, F2, etc. for function keys.
- Backspace
- Tab
- Enter
- Shift
- Ctrl
- Alt
- Esc
- PageUp
- PageDown
- End
- Home
- Insert
- Delete
- CapsLock
- NumLock
- ScrollLock
- PrintScreen
- Break
- Separator
- Cancel
- Help

KeyPress !Text | |

KeyRelease !Text | |

MousePress !(MouseButton, Point) | |

MouseRelease !(MouseButton, Point) | |

MouseMovement !Point |

Eq Event |

data MouseButton :: *

Eq MouseButton | |

Read MouseButton | |

Show MouseButton |

# Debugging

# Entry points

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

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