A more abstract syntax tree representing images. Comparisons between values of this type are intentionally fuzzy: Concrete number or point values are abstracted into coarser categories. Notably, those values are not lost and can be retrieved if desired.

The constructors of this type are not exposed. Values are built using the CodeWorld API.

Draw an abstract, hollow circle.

Draw an abstract, filled in circle.

Draw an abstract, hollow square.

Draw an abstract, hollow rectangle. This is an alias for someSquare.

Draw an abstract, hollow rectangle that is taller than wide.

Draw an abstract, hollow rectangle that is wider than tall.

Draw an abstract, filled in square.

Draw an abstract, filled in rectangle. This is an alias for someSolidSquare.

Draw an abstract, filled in rectangle that is taller than wide.

Draw an abstract, filled in rectangle that is wider than tall.

Draw an abstract, open curve with this many segments.

Draw an abstract, filled in and closed curve with this many segments.

Provide an abstract shape with a specific color. The color will be treated as equal to any color with *similar* HSL values. (See isSameColor for more information)

Provide an abstract shape with a wildcard color. The color will be treated as equal to any other color.

Rotate an abstract shape by between a quarter and half turn.

Rotate an abstract shape by up to a quarter turn.

Rotate an abstract shape by between a half and three quarters turn.

Rotate an abstract shape by between a three quarters and up to a full turn. The full turn itself is excluded.

Enlarge an abstract shape. Both directions are scaled an equal amount.

Enlarge an abstract shape in X-direction. The Y-direction is unchanged.

Enlarge an abstract shape in Y-direction. The X-direction is unchanged.

Shrink an abstract shape. Both directions are scaled an equal amount.

Shrink an abstract shape in X-direction. The Y-direction is unchanged.

Shrink an abstract shape in Y-direction. The X-direction is unchanged.

Compose two abstract pictures.

True if the first image contains the second image. This uses fuzzy comparison.

Returns how often a subpicture appears in the image.

Returns the AbsColor of the image. Nothing if it is one of logo or coordinate plane. Black if none.

Returns abstract rotation of the image if it has any.

Returns actual rotation of the image if it has any.

Returns the abstract scaling factors of the image. Neutral factors if none.

Returns actual scaling factors of the image. (1,1) if none.

Returns the abstract translation of the image. Neutral translation if none.

Returns the actual translation of the image. (0,0) if none.

Returns abstract reflection of the image if it has any.

Returns actual reflection of the image if it has any.

Returns abstract radius of the image if it actually a circle or circle segment.

Returns actual radius of the image if it actually a circle or circle segment.

Returns abstract side lengths of the image if it actually a rectangle.

Returns actual side lengths of the image if it actually a rectangle.

Returns actual list of points in the image if it is a "free shape", [] otherwise.

Abstract representation of radii and side lengths. All values are considered equal.

Abstract representation of line drawing and filling mode. Differentiates between the three common shapes: standard, thick, filled.

This does not retain the concrete value.

Abstract representation of angles. Rotation is divided into four equal sections on the unit circle.

Abstract representation of scaling factors. Considers values equal if both are scaled larger, smaller or not at all.

Abstract representation of translations. Considers values equal if both are translated by a positive or negative number or not at all.

Abstract representation of points in 2D space. All values are considered equal.

Abstract representation of Color. Equal if each HSLA parameter has an acceptable distance from those of the other color.

A more strict equality test for AbsColor. Contrary to the Eq instance, this only succeeds if both colors are completely identical in their HSLA values.

Abstract representation of spatial positioning between two picture components.

Alias for queries on spatial relationships.

True if the first argument is below the second and aligned on the X-axis.

True if the first argument is above the second and aligned on the X-axis.

True if the first argument is left of the second and aligned on the Y-axis.

True if the first argument is right of the second and aligned on the Y-axis.

True if the first argument is below and to the right of the second.

True if the first argument is below and to the left of the second.

True if the first argument is above and to the right of the second.

True if the first argument is above and to the left of the second.

True if the first argument is below the second, ignoring horizontal positioning.

True if the first argument is above the second, ignoring horizontal positioning.

True if the first argument is left of the second, ignoring vertical positioning.

True if the first argument is right of the second, ignoring vertical positioning.

True if the first argument is at the same position as the second.

Abstract representation of a picture in terms of its components and the pairwise spatial positioning between them.

The environment for tests on still images.

The environment for tests on animations.

True if image contains at least this subpicture and optionally something else.

True if image contains at least these subpictures and optionally something else.

True if image contains exactly these subpictures and nothing else.

True if image contains this subpicture exactly this many times.

True if image contains this subpicture at least this many times.

True if image contains this subpicture at most many times.

True if amount of times this subpicture is contained in the image lies in the specified range.

True if image contains the specified spatial relations. Used with corresponding functions like isNorthOf, isLeftOf, etc.

At least one of two predicates evaluates to True.

Both predicates evaluate to True.

Only one of two predicates evaluate to True (XOR).

Alias for (<||>)

At least one of many predicates evaluates to True.

Runs the first predicate p, then the second q if p evaluated to True. Does not run q if p evaluates to False.

The predicate is satisfied by at least one of the given options. Use when there's multiple shape primitives a student could use to solve the task.

Returns the unmodified Picture.

Returns the normalized Picture.

Returns all subpictures satisfying the predicate. (translation is removed)

Finds all subpictures satisfying a predicate, then applies a function. (translation is removed)

Returns all subpictures satisfying the predicate. (includes translation)

Finds all subpictures satisfying a predicate, then applies a function. (includes translation)

Returns the first subpictures satisfying the predicate if it exists. (translation is removed)

Finds the first subpictures satisfying a predicate, then applies a function if it exists. (translation is removed)

Returns the first subpicture satisfying the predicate if it exists. (includes translation)

Finds the first subpicture satisfying a predicate, then applies a function if it exists. (includes translation)

Returns the animation environment with its output mapped over by the argument.

Samples the animation at the given time point and applies a predicate or query to it.

Samples the animation at multiple time points and returns a list of unmodified results.

Samples the animation at multiple time points and returns a list of normalized results.

Samples the animation at multiple time points and applies a predicate to each image. Returns True if any sample satisfied the predicate.

Samples the animation at multiple time points and applies a predicate to each image. Returns True if all samples satisfied the predicate.

Samples the animation at multiple time points and applies a predicate dependent on the current time point to each image. Returns True if all samples satisfied the predicate.

Samples the animation at multiple time points and applies a predicate to each image. Returns True if none of the samples satisfied the predicate.

Samples the animation at multiple time points and applies a predicate or query to each image, then returns a list of results.

Builds a fallible test given an error message and a predicate.

Executes the given test suite on a static image and returns the error message of the first failed test or the empty String if all tests passed.

Executes the given test suite on an animation and returns the error message of the first failed test or the empty String if all tests passed.

Student facing, basic picture type. A value of this type can be build using the CodeWorld API.

CodeWorld.Test also exports pattern synonyms for all contained constructors. This allows for easier pattern matching in generic traversals.

Returns True if the argument is not a basic shape.

Warning: This is intended to be used on non-composite pictures only. Pictures and And will be treated as a basic picture (i.e. returning False) if used as an argument.

Returns the contained Picture if the argument is not a basic shape and the argument itself if it is.

Warning: This is intended to be used on non-composite pictures only. Pictures and And will be treated as a basic picture (i.e. the function will behave like id) if used as an argument.

Checks if the argument is contained completely inside a box. The coordinates of the box are given as two points with the following format:

1. (minimum x-value, maximum x-value)
2. (minimum y-value, maximum y-value)

Apply a set of rewriting rules to the Picture's syntax tree. The result is a normalized and simplified tree in canonical form, which draws the same image.

Same as normalize, but also erases information on which subpictures are drawn in front or behind others.

Apply a set of rewriting rules to the Picture's syntax tree, then abstract concrete parameters of the nodes, resulting in an AbstractPicture.

The new tree is normalized, simplified and allows for more fuzzy comparisons and queries.

Transform an AbstractPicture into a Picture. Used to compare normalized sample solution to student submission in plain form. This only makes sense if there's exactly one way to solve the given task.

Returns which translation needs to be applied to argument 1 to get argument 2. Nothing if the polygons are different.

This can be used to detect translation in point list based shapes.

Returns which scaling factors need to be applied to argument 1 to get argument 2.

• Nothing if the polygons are not similar.
• Factors themselves can also be Nothing if the factor is undeterminable.

E.g. a possible result could be Just (Just 3, Nothing). This means the second shape is a scaled version of the first and the factor in X-direction is 3, but the factor in Y-direction cannot be determined.

This can be used to detect size scaling in point list based shapes.

Returns which rotation needs to be applied to argument 1 to get argument 2. Nothing if it does not exist.

This can be used to detect rotation in point list based shapes.

An infinite list of animation sampling points. The basis is made of irrational square roots, exp(1) and π. The provided samples should not overlap with any particular phase a student submitted animation may have.

Generates irregular sample frames starting from 0 with given step size and cutoff point. The step size is only an approximation, since the generated values are based on irrational numbers.

Produce student feedback on common subexpression elimination for a Picture value. This compares the results of the Hashcons and Reify methods to determine unused sharing potential. Returns Nothing if all possible terms are shared.

This runs in an IO context, since Reify uses StableName to track sharing.

Draw a hollow, thin rectangle with this length and height.

Draw a hollow rectangle with this line width, length and height. Specifying a negative line width causes a runtime error (mirrors behaviour in CodeWorld editor).

Draw a filled in rectangle with this length and height.

Draw a hollow, thin circle with this radius.

Draw a hollow circle with this line width and radius. Specifying a negative line width or a line width greater than the circles diameter causes a runtime error (mirrors behaviour in CodeWorld editor).

Draw a filled in circle with this radius.

Draw a thin, hollow circle segment with these start and end angles and radius.

Draw a filled in circle segment with these start and end angles and radius. This would be solidArc following the usual naming scheme.

Draw a hollow circle segment with this line width, these start and end angles and radius. Specifying a negative line width causes a runtime error (mirrors behaviour in CodeWorld editor).

Draw a thin curve passing through the provided points via a number of Bézier splices.

Draw a curve with this line width passing through the provided points via a number of Bézier splices. Specifying a negative line width causes a runtime error (mirrors behaviour in CodeWorld editor).

Same as curve but adds another splice between the start and end points to close the shape.

Same as thickCurve but adds another splice between the start and end points to close the shape.

Draw a curve passing through the provided points via a number of Bézier splices. Adds another splice between the start and end points to close the shape and completely fills the enclosed area.

Draw a sequence of thin line segments passing through the provided points.

Draw a sequence of line segments with this line width passing through the provided points. Specifying a negative line width causes a runtime error (mirrors behaviour in CodeWorld editor).

Same as polyline but adds another segment between the start and end points to close the shape.

Same as thickPolyline but adds another segment between the start and end points to close the shape.

Draw a sequence of line segments with this line width passing through the provided points and completely fill the enclosed area.

Render this text into an image.

Render this text into an image using the provided TextStyle and Font.

Apply this Color to the image.

Alias for colored.

Move the image in x and y-direction.

Scale the image in x and y-directions using these modifiers.

Scale the image in both directions using the same modifier.

Rotate the image around the origin using this angle in radians.

Reflect the image across a line through the origin with this angle to the x-axis.

Clip the image in a rectangle with this length and height.

Compose a list of Pictures. Equivalent to foldr (&) blank.

Compose two Pictures. The left argument will be drawn on top of the right argument if they overlap.

A static image of a coordinate plane extending 5 units in all directions.

A static image of the CodeWorld logo.

An empty Picture. This is the identity element of &.

A point in 2D space. Synonym for a pair of Double values.

A vector in 2D space. Synonym for a pair of Double values.

Moves a point in X and Y-directions.

Rotates a point around the origin by the given angle in radians.

Reflects a point across a line through the origin at this angle from the X-axis.

Scales a point by given X and Y scaling factor. Scaling by a negative factor also reflects across that axis.

Dilates a point by given uniform scaling factor. Dilating by a negative factor also reflects across the origin.

The length of a vector.

The counter-clockwise angle of a vector from the X-axis.

The sum of two vectors.

The difference of two vectors.

Scales a vector by the given scalar multiplier.

Rotates a vector by the given angle in radians.

Text font type used for stylized message rendering.

Font modifier type used for stylized message rendering.

Color type mirroring CodeWorld's equivalent type. The exposed constructors allow for setting colors directly via numerical values.