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):
    x1 = objects(I, T, F, F)
    x2 = colorfilter(x1, ZERO)
    x3 = rbind(bordering, I)
    x4 = compose(flip, x3)
    x5 = mfilter(x2, x4)
    O  = fill(I, FOUR, x5)
    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:

• x1: the set of objects extracted from the input grid I that are single-colored 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
• x2: the subset of the objects x1 which are black; the result of filtering objects by their color, i.e. calling colorfilter with objects=x1 and color=ZERO (black)
• x3: a function with signature $f: object \rightarrow bool$ that returns True iff an 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
• x4: a function that returns the inverse of the previous function, i.e. a function that returns True iff an object does not border the grid border; the result of composing the flip primitive (which simply negates flips a boolean) and x3
• x5: a single object defined as the union of objects x2 for which function x4 returns True, i.e. the black objects which do not border the grid border (corresponding to the "holes" in the green objects); the result of calling mfilter (which combines merge and filter) with container=x2 and condition=x4
• O: the output grid, created by coloring all pixels of the object x5 yellow; the result of calling the fill primitive on I with color=FOUR (yellow) and patch=x5