From LCF to HOL: a short history
Proof, language, and interaction
On the notion of interestingness in automated mathematical discovery
International Journal of Human-Computer Studies - Special issue on Machine Discovery
The Definition of Standard ML
HOL Light: A Tutorial Introduction
FMCAD '96 Proceedings of the First International Conference on Formal Methods in Computer-Aided Design
Monads for Functional Programming
Advanced Functional Programming, First International Spring School on Advanced Functional Programming Techniques-Tutorial Text
MATHsAiD: A Mathematical Theorem Discovery Tool
SYNASC '06 Proceedings of the Eighth International Symposium on Symbolic and Numeric Algorithms for Scientific Computing
Algebras for combinatorial search
Journal of Functional Programming
Composable discovery engines for interactive theorem proving
ITP'11 Proceedings of the Second international conference on Interactive theorem proving
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We define and implement a combinator language for intermediate lemma discovery. We start by generalising an algebraic data-structure for unbounded search and then extend it to support case-analysis. With our language defined, we expect users to be able to write discoverers which collaborate intelligently in specific problem domains. For now, the language integrates rewriting, forward-deduction, and case-analysis and discovers lemmas concurrently based on an interactive proof context. We argue that the language is most suitable for adding domain-specific automation to mechanically formalised proofs written in a forward-style, and we show how the language is used via a case-study in geometry.