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30 lines
1.5 KiB
Text
30 lines
1.5 KiB
Text
Abella is an interactive theorem prover based on lambda-tree syntax.
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This means that Abella is well-suited for reasoning about the meta-theory
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of programming languages and other logical systems which manipulate
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objects with binding. For example, the following applications are included
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in the distribution of Abella.
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* Various results on the lambda calculus involving big-step evaluation, small-step evaluation, and typing judgments
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* Cut-admissibility for a sequent calculus
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* Part 1a and Part 2a of the POPLmark challenge
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* Takahashi's proof of the Church-Rosser theorem
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* Tait's logical relations argument for weak normalization of the simply-typed lambda calculus
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* Girard's proof of strong normalization of the simply-typed lambda calculus
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* Some ?-calculus meta-theory
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* Relation between ?-reduction and paths in A-calculus
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For Full List:
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http://abella-prover.org/examples/index.html
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Abella uses a two-level logic approach to reasoning. Specifications
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are made in the logic of second-order hereditary Harrop formulas using
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lambda-tree syntax. This logic is executable and is a subset of the
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AProlog language (see the Teyjus system for an implementation of this
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language).
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The reasoning logic of Abella is the culmination of a series of extensions
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to proof theory for the treatment of definitions, lambda-tree syntax,
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and generic judgments. The reasoning logic of Abella is able to encode
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the semantics of our specification logic as a definition and thereby
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reason over specifications in that logic.
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