Historical linguists have long written “programs” that convert reconstructed words in an ancestor language into their attested descendants via ordered string rewrite functions (called sound laws) However, writing these programs is time-consuming, motivating the development of automated Sound Law Induction (SLI) which we formulate as Programming by Examples (PBE) with Large Language Models (LLMs) in this paper. While LLMs have been effective for code generation, recent work has shown that PBE is challenging but improvable by fine-tuning, especially with training data drawn from the same distribution as evaluation data. In this paper, we create a conceptual framework of what constitutes a “similar distribution” for SLI and propose four kinds of synthetic data generation methods with varying amounts of inductive bias to investigate what leads to the best performance. Based on the results, we create a SOTA open-source model for SLI as PBE (+6% pass rate with a third of the parameters of the second-best LLM) and also highlight exciting future directions for PBE research.

Traditionally, historical phonologists have relied on tedious manual derivations to calibrate the sequences of sound changes that shaped the phonological evolution of languages. However, humans are prone to errors, and cannot track thousands of parallel word derivations in any efficient manner. We propose to instead automatically derive each lexical item in parallel, and we demonstrate forward reconstruction as both a computational task with metrics to optimize, and as an empirical tool for inquiry. For this end we present DiaSim, a user-facing application that simulates “cascades” of diachronic developments over a language’s lexicon and provides diagnostics for “debugging” those cascades. We test our methodology on a Latin-to-French reflex prediction task, using a newly compiled dataset FLLex with 1368 paired Latin/French forms. We also present, FLLAPS, which maps 310 Latin reflexes through five stages until Modern French, derived from Pope (1934)’s sound tables. Our publicly available rule cascades include the baselines BaseCLEF and BaseCLEF*, representing the received view of Latin to French development, and DiaCLEF, build by incremental corrections to BaseCLEF aided by DiaSim’s diagnostics. DiaCLEF vastly outperforms the baselines, improving final accuracy on FLLex from 3.2%to 84.9%, and similar improvements across FLLAPS’ stages.