{"id":50294636,"url":"https://github.com/digikar99/pl-theorem-prover","last_synced_at":"2026-05-28T08:02:55.105Z","repository":{"id":342578517,"uuid":"1168924825","full_name":"digikar99/pl-theorem-prover","owner":"digikar99","description":"Basic theorem prover for propositional logic that supports `and or not` operators. 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Currently, this has no dependencies.\n\nThis uses the [Method of analytic tableaux](https://en.wikipedia.org/wiki/Method_of_analytic_tableaux), but users can customize the theorem prover.\n\n## Example\n\n```lisp\nCL-USER\u003e (defpackage :pltp-user\n           (:use :cl)\n           (:local-nicknames (:pl :pl-theorem-prover)))\n#\u003cPACKAGE \"PLTP-USER\"\u003e\n\nCL-USER\u003e (in-package :pltp-user)\n#\u003cPACKAGE \"PLTP-USER\"\u003e\n\nPLTP-USER\u003e (set-pprint-dispatch 'pl:node 'pl:pprint-node)\nNIL\n\nPLTP-USER\u003e (pl:well-formed-formula-p '(not))\n; Evaluation aborted on #\u003cSIMPLE-ERROR \"~S is not a well-formed-(sub)formula\" {12063EEF43}\u003e.\n\nPLTP-USER\u003e (pl:well-formed-formula-p '(not a b))\n; Evaluation aborted on #\u003cSIMPLE-ERROR \"~S is not a well-formed-(sub)formula\" {120642E623}\u003e.\n\nPLTP-USER\u003e (pl:well-formed-formula-p '(and a b))\n(AND A B)\n\nPLTP-USER\u003e (pl:well-formed-formula-p '(not a))\n(NOT A)\n\nPLTP-USER\u003e (pl:prove* a (not a))\nUnprovable.\nNIL\n#\u003cPL::TABLEAUX {120BA4A0D3}\u003e\n\nPLTP-USER\u003e (pl:prove* a (or b (not a)))\nProvable.\n\nT: B\n  T: A\n    T: (OR B (NOT A))\n#\u003cPL::TABLEAUX {120BBC20D3}\u003e\n\nPLTP-USER\u003e (pl:prove* (not b) (or b (not a)))\nProvable.\n\nNIL: B\n  T: (NOT A)\n    T: (NOT B)\n      T: (OR B (NOT A))\n#\u003cPL::TABLEAUX {1202D720D3}\u003e\n\nPLTP-USER\u003e (pl:prove* a (not b) (or b (not a)))\nUnprovable.\nNIL\n#\u003cPL::TABLEAUX {1202D72333}\u003e\n\nPLTP-USER\u003e (pl:prove* (and a c)\n                      (or (not a) b))\nProvable.\n\nT: (NOT A)\n  T: A\n    T: C\n      T: (AND A C)\n        T: (OR (NOT A) B)\n#\u003cPL::TABLEAUX {1205E42123}\u003e\n```\n\n## Notes\n\n- `prove*` is a macro. It calls the function `prove`\n- Theorem proving algorithm can be changed using the variable `*prover*`. Its default value is `'semantic-tableau-prover`.\n\n## References\n\n- https://philosophy.stackexchange.com/questions/10785/semantic-vs-syntactic-consequence\n- https://oeis.org/wiki/Propositional_calculus\n- Brute force: https://en.wikipedia.org/wiki/British_Museum_algorithm\n- https://en.wikipedia.org/wiki/Method_of_analytic_tableaux\n","project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fdigikar99%2Fpl-theorem-prover","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Fdigikar99%2Fpl-theorem-prover","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fdigikar99%2Fpl-theorem-prover/lists"}