iparc/README.md

# IPARC

ILP-flavoured ARC (Abstraction and Reasoning Corpus) tasks, encoded as ILP problems. Each task requires learning a program that transforms a 2D grid of coloured cells. Tasks are grouped into six categories by difficulty and transformation type. 600 tasks total (100 per category).

**Tasks:** 6 categories × 100 tasks = 600 tasks (in `<Category>/Task<NNN>/train/`)

| Category | Description |
|----------|-------------|
| `CatA_Simple` | Category A transformations, simple difficulty |
| `CatA_Hard` | Category A transformations, hard difficulty |
| `CatB_Selection` | Category B: select a subset of input cells for the output |
| `CatB_Iteration` | Category B: iterate over rows or columns to compute output |
| `CatB_Sequence` | Category B: sequential (multi-step) transformations |
| `CatB_Hard` | Category B transformations, hard difficulty |

**Head relation:** `out(Ex, Row, Col, Value)` — cell `(Row, Col)` in the output grid of example `Ex` has colour `Value`.

**Background relations:**

| Relation | Arity | Description |
|----------|-------|-------------|
| `in(Ex, Row, Col, Value)` | 4 | Input grid: cell `(Row, Col)` in example `Ex` has colour `Value` |
| `empty(Ex, Row, Col)` | 3 | Cell `(Row, Col)` is empty (colour 0) in the input of example `Ex` |
| `width(Ex, W)` | 2 | Input grid of example `Ex` has width `W` |
| `height(Ex, H)` | 2 | Input grid of example `Ex` has height `H` |
| `add(V1, V2, V3)` | 3 | `V3 = V1 + V2` (integer arithmetic) |
| `lt(V1, V2)` | 2 | `V1 < V2` |
| `my_succ(V1, V2)` | 2 | `V2 = V1 + 1` |
| `position_N/1` | 1 | Type-constant: value is position N (1–15) |
| `value_N/1` | 1 | Type-constant: value is colour/value N |

**Source:** Challa, A., Srinivasan, A., Bain, M., & Shroff, G. "A Program-Synthesis Challenge for ARC-Like Tasks." In Muggleton, S. & Tamaddoni-Nezhad, A. (eds.), *ILP 2022*, LNCS vol. 13779, pp. 25–39. Springer, 2022.