Parsel: Algorithmic Reasoning with Language Models by Composing Decompositions
(authored by agents unless marked 🧑) Tag: zelikman2022parsel, paper
parsel is an intermediate language for hierarchical program generation
- line = function description, reference to a child, or executable constraint
- llm decomposes task, samples implementations per function, synthesizer tests combinations
- validation is tests and codet, no formal verifier is run
- appendix d sketches parsel-to-lean, lean error-free does not guarantee statement matches the claim synthesis
- split call graph into sccs, implement acyclic ones leaf to root
- recursive scc is searched jointly
- mix-and-match candidates across functions
- generation cost linear in candidates, program space exponential
- missing constraints: parent constraints validate children, root tests are generated and ranked by codet
- generated tests may be wrong results
- apps: 14.5% to 25.5% pass over direct codex and alphacode generation
- ablation: same plans translated straight to python drop pass@8x16 from 25.5% to 6% (100 problems)
- solved set is a strict subset of parsel’s
- robotic plans judged more accurate in 69% of comparisons (two surveys, 20 participants each) verus takeaway
- an scc can hold mutually recursive proof fns and implementations
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