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Using standard domain-theoretic fixed-points, we present an approach fordefining recursive functions that are formulated in monadic style. The methodworks both in the simple option monad and the state-exception monad ofIsabelle/HOL's imperative programming extension, which results in a convenientdefinition principle for imperative programs, which were previously hard todefine.  For such monadic functions, the recursion equation can always be derivedwithout preconditions, even if the function is partial. The construction iseasy to automate, and convenient induction principles can be derivedautomatically.

Recursive Definitions of Monadic Functions