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++                             agsyHOL                             ++
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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 parallelization
(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.


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Prerequisites
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To build agsyHOL you need
 ghc [http://www.haskell.org/ghc/]

If you want to manipulate the soundness proof or check automatically
generated proofs you need
 agda [http://wiki.portal.chalmers.se/agda/pmwiki.php]

If you want to recompile the THF syntax parser you need
 happy [http://www.haskell.org/happy/]


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Building agsyHOL
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Run
 ghc -O -o agsyHOL --make -rtsopts Main
or
 make

This creates an executable named 'agsyHOL'.


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Using agsyHOL
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Type
 agsyHOL --help
to get a list of possible arguments.

example:
 agsyHOL --include-dir /<path>/TPTP-vN.N.N/ /<path>/TPTP-vN.N.N/Problems/XXX/XXXNNN^N.p


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Soundness Proof
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Soundness is proved with respect to Church's simple type theory, STT.
The deductive system of the proof language is called FSC, and is a
variant of focused sequent calculus. The proof is found in the sub
directory called 'soundness'. The formalisation uses de Bruijn
indeces. The main result is 'sound-top', located in the file
'Soundness.agda'. When checking Agda proofs constructed by agsyHOL,
the 'soundness' directory must be in scope.


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Contact
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For questions, comments, bug reports, please contact

 Fredrik Lindblad <[email protected]>

If you use agsyHOL or the code, I'd be very happy if you let me know.