Theorems and algorithms: an interface between Isabelle and Maple
ISSAC '95 Proceedings of the 1995 international symposium on Symbolic and algebraic computation
Introduction to Mathematical Logic and Type Theory: To Truth through Proof
Introduction to Mathematical Logic and Type Theory: To Truth through Proof
A Skeptic’s Approach to Combining HOL and Maple
Journal of Automated Reasoning
Unification with Sequence Variables and Flexible Arity Symbols and Its Extension with Pattern-Terms
AISC '02/Calculemus '02 Proceedings of the Joint International Conferences on Artificial Intelligence, Automated Reasoning, and Symbolic Computation
COLOG '88 Proceedings of the International Conference on Computer Logic
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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.