Connecting Logical Representations and Efficient Computations

When combining logic level theorem proving with computational methods it is important to identify both functions that can be efficiently computed and the objects they can be applied to. This is generally achieved by mappings of logic level terms and functions to their computational counterparts. However, these mappings are often quite ad hoc and fragile depending very much on the particular logic representations of terms. We present a method of annotating terms in logic proofs with their computational properties. This enables the compact representation of computational objects in deduction systems as well as their connection to functions that can be easily computed for them. This eases the identification of deduction problems that can be treated efficiently by computational methods and also abstracts from trivial properties that are artefacts of a particular representation. We ensure logical correctness of our concepts by providing the possibility to replace terms by their logical representation and by expanding computational procedures by tactic application that can be rigorously checked.