ΛProlog: Logic programming in higher-order logic
λProlog is a pioneering logic programming language built on higher-order intuitionistic logic, notable for being the first to directly support higher-order abstract syntax (HOAS). Though conceived in the 1980s, it remains actively developed and applied, particularly in meta-programming and formal verification. Its enduring relevance on HN stems from its deep technical foundations and continuous evolution in specialized computing domains.
The Lowdown
λProlog is a sophisticated logic programming language founded on higher-order intuitionistic logic, drawing inspiration from Church's Simple Theory of Types. This robust logical bedrock provides the language with inherently strong support for advanced programming paradigms such as modular programming, abstract datatypes, and higher-order programming. Crucially, it introduced the lambda-tree syntax for handling bound variables, making it the first programming language to directly implement Higher-Order Abstract Syntax (HOAS).
- Historical Roots: First designed and implemented in the late 1980s, with its initial distributed version dating back to 1988.
- Modern Implementations: Interest persists with several active projects, including ELPI (an embeddable interpreter in OCaml by Enrico Tassi, often used with Coq), Teyjus (a compiler by Gopalan Nadathur, also in OCaml, supporting advanced features like separate computation), and Makam (a refinement by Antonis Stampoulis).
- Extensive Documentation: A wealth of resources exists, including the book "Programming with Higher-Order Logic" by Dale Miller and Gopalan Nadathur, video tutorials, and academic course materials.
- Abella Theorem Prover: A key companion tool, Abella is an interactive theorem prover specifically designed for λProlog programs. It excels at inductive and coinductive reasoning, especially for specifications involving binding, leveraging λ-tree syntax and a unique two-level logic approach where a subset of λProlog serves as the specification logic.
- Practical Examples: Code examples are available through the Teyjus distribution, book extractions, and online collections, including web-based execution via the ELPI implementation (e.g., MLTS).
Despite its origins decades ago, λProlog continues to be a vital tool for researchers and developers in areas requiring rigorous logical foundations, particularly meta-programming and theorem proving, showcasing its lasting impact on computational theory and practice.