rdk/arc1

Domain Specific Language for the Abstraction and Reasoning Corpus

Domain Specific Language for the Abstraction and Reasoning Corpus (ARC-DSL)

The DSL was created with the aim of being expressive enough to allow programs solving arbitrary ARC tasks, and generic, i.e. consisting of only few primitives, each useful for many tasks (see dsl.py). As a proof of concept, solver programs for the training tasks were written (see solvers.py). See arc_dsl_writeup.pdf for a more detailed description of the work.

Example solver program for task 00d62c1b written in the DSL

def solve_00d62c1b(I):
    objs = objects(grid=I, univalued=T, diagonal=F, without_bg=F)
    black_objs = colorfilter(objs=objs, value=ZERO)
    borders = rbind(function=bordering, fixed=I)
    does_not_border = compose(outer=flip, inner=borders)
    enclosed = mfilter(container=black_objs, function=does_not_border)
    O = fill(grid=I, value=FOUR, patch=enclosed)
    return O

The function solve_00d62c1b takes an input grid I and returns the correct output grid O. An explanation of what the variables store and how their values were computed:

• objs: the set of objects extracted from the input grid I that are single-color only, where individual objects may only have cells that are connected directly, and cells may be of the background color (black); the result of calling the objects primitive on I with univalued=True, diagonal=False and without_background=True
• black_objs: the subset of the objects objs which are black; the result of filtering objects by their color, i.e. calling colorfilter with objects=objs and color=ZERO (black)
• borders: a function taking an object and returning True iff that object is at the border of the grid; the result of fixing the right argument of the bordering primitive to I by calling the function rbind on function=bordering and fixed=I
• does_not_border: a function that returns the inverse of the previous function, i.e. a function that returns True iff an object does not touch the grid border; the result of composing the flip primitive (which simply negates a boolean) and borders
• enclosed: a single object defined as the union of objects black_objs for which function does_not_border returns True, i.e. the black objects which do not touch the grid border (corresponding to the "holes" in the green objects); the result of calling mfilter (which combines merge and filter) with container=black_objs and condition=does_not_border
• O: the output grid, created by coloring all pixels of the object enclosed yellow; the result of calling the fill primitive on I with color=FOUR (yellow) and patch=enclosed

Another solver example: 5521c0d9

def solve_5521c0d9(I):
    objs = objects(grid=I, univalued=T, diagonal=F, without_bgT)
    foreground = merge(containers=objs)
    empty_grid = cover(grid=I, patch=foreground)
    offset_getter = chain(h=toivec, g=invert, f=height)
    shifter = fork(outer=shift, a=identity, b=offset_getter)
    shifted = mapply(function=shifter, container=objs)
    O = paint(grid=empty_grid, obj=shifted)
    return O

• objs: the set of objects extracted from the input grid I that are single-color only, ignoring the background color; the result of calling the objects primitive on I with univalued=True, diagonal=False and without_background=True
• foreground: all the objects treated as a single object, the result of calling the merge primitive on the objects objs
• empty_grid: a new grid, where foreground is removed (covered), i.e. replaced with the background color (black); the result of calling the cover primitive with grid=I and patch=foreground
• offset_getter: a function that takes an object and returns a vector pointing up by as much as that object is high; the result of composing the three functions toivec, invert and height; the result of calling the chain primitive with h=toivec, g=invert and f=height
• shifter: a function that takes an object and shifts it as much upwards as it is high; the result of calling the fork primitive with outer=shift, a=identity and b=offset_getter
• shifted: all the objects shifted up by their heights, as a single object, obtained by appling the constructed function on the set of objects and merging the results; the result of calling the mapply primitive on function=shifter and container=objs
• O the desired output grid, obtained by painting the resulting object onto the grid empty_grid where the original objects were removed from; the result of calling the paint primitive on grid=empty_grid and obj=shifted