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Making simple proofs simpler
An open partition \pi{} [Cod09a, Cod09b] of a tree T is a partition of the
vertices of T with the property that, for each block B of \pi, the upset of B
is a union of blocks of \pi. This paper deals with the number, NP(n), of open
partitions of the tree, V_n, made of two chains with n points each, that share
the root
Recursive Definitions of Monadic Functions
Using standard domain-theoretic fixed-points, we present an approach for
defining recursive functions that are formulated in monadic style. The method
works both in the simple option monad and the state-exception monad of
Isabelle/HOL's imperative programming extension, which results in a convenient
definition principle for imperative programs, which were previously hard to
define.
For such monadic functions, the recursion equation can always be derived
without preconditions, even if the function is partial. The construction is
easy to automate, and convenient induction principles can be derived
automatically.Comment: In Proceedings PAR 2010, arXiv:1012.455
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