Naproche-SAD is a recent tool by Frerix and Koepke, based on the original System for Automated Deduction (SAD) by Paskevich and others. It processes the Formal Theory Language (ForTheL), which is designed to look like mathematical text, but it is restricted to a small subset of natural language.
The tool is implemented in Haskell as a plain function from input text to output messages. A file is like a chapter of mathematical text, with a nested tree-structure of elements and sub-elements (for signatures, axiomatizations, statements, proofs). Output messages inform about the translation of mathematical text to problems of first-order logic, and indicate success or failure of external proof checking; the latter is delegated to the E Prover by Stephan Schulz and can take several seconds for each proof obligation.
To integrate Naproche-SAD into PIDE, Frerix and Wenzel have reworked the Haskell program over 2 months in 2018, to turn the command-line tool into a service for reactive checking of ForTheL texts. Isabelle integration was done via the new Isabelle/Haskell library and some glue code in Isabelle/Scala to register ForTheL as auxiliary file-format (extension
The resulting Isabelle/Naproche application is available as multi-platform download. A running instance is shown in the screenshot: users can directly open ForTheL files (e.g. from
Examples) and wait briefly to see output messages attached to the text in the usual IDE manner. Further edits produce a new version of the text, which is sent in total to Naproche-SAD again. The back-end is sufficiently smart to avoid redundant checking of unchanged sub-elements: it keeps a global state with results of old versions: this is easy to implement as the program keeps running until shutdown of Isabelle/PIDE.
(Cited from section 1.2 of the paper Interaction with Formal Mathematical Documents in Isabelle/PIDE.)