Ordinal Arithmetic in ACL2
نویسندگان
چکیده
Ordinals form the basis for termination proofs in ACL2. Currently, ACL2 uses a rather inefficient representation for the ordinals up to 0 and provides limited support for reasoning about them. We present algorithms for ordinal arithmetic on an exponentially more compact representation than the one used by ACL2. The algorithms have been implemented and numerous properties of the arithmetic operators have been mechanically verified, thereby greatly extending ACL2’s ability to reason about the ordinals. We describe how to use the libraries containing these results, which are currently distributed with ACL2 version 2.7.
منابع مشابه
Algorithms for Ordinal Arithmetic
Proofs of termination are essential for establishing the correct behavior of computing systems. There are various ways of establishing termination, but the most general involves the use of ordinals. An example of a theorem proving system in which ordinals are used to prove termination is ACL2. In ACL2, every function defined must be shown to terminate using the ordinals up to 0. We use a compac...
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