# AgsyHOL

AgsyHOL source code and Agda formalization. agsyHol is a theorem prover for higher-order logic. It reads problems in the TPTP THF format. It is based on a generic lazy narrowing search algorithm applied to a proof checker for a HOL proof term language. The term language is designed with proof search in mind. The proof checker is annotated with search control information, such as priorities controlling the order of sub proof term instantiation. The search is based on back-tracking and is characterised by a typically small search state, making it suitable for arallelization (not realized yet). On success the proof term constituting the solution can be displayed. Proof terms are a kind of sequent calculus derivations and are so far only printed in internal format. Showing derivations in TPTP format has not been implemented yet. Hence the reported SZS dataform category is not Proof or Derivation, although a proof is reported. Soundness of the proof language has been established in Agda, a dependently typed programming language. The theorem prover can output solutions in Agda format, enabling checking the validity independently and against the formalised soundness proof. Before proof search begins the problem is transformed in order to reduce the need for reasoning by RAA. Double negations are removed and de Morgan laws applied to reduce the number of negations. Reasoning by RAA is costly for agsyHOL. Constructed Agda proofs for problems do currently not include this transformation step.

## References in zbMATH (referenced in 1 article )

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