Abstract
Formal methods for program verification, optimization, and synthesis rely on complex mathematical proofs, which often involve reasoning about computations. Because of that there is no single automated proof procedure that can handle all the reasoning problems occurring during a program derivation or verification. Instead, one usually relies on proof assistants like NuPRL (Constable et al., 1986), Coq (Dowek and et. al, 1991), Alf (Altenkirch et al., 1994) etc., which are based on very expressive logical calculi and support interactive and tactic controlled proof and program development. Proof assistants, however, suffer from a very low degree of automation, since all their inferences must eventually be based on sequent or natural deduction rules. Even proof parts that rely entirely on predicate logic can seldomly be found automatically, as there are no complete proof search procedures embedded into these systems. It is therefore desirable to extend the reasoning power of proof assistants by integrating well-understood techniques from automated theorem proving.
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Kreitz, C., Otten, J., Schmitt, S., Pientka, B. (2000). Matrix-Based Constructive Theorem Proving. In: Hölldobler, S. (eds) Intellectics and Computational Logic. Applied Logic Series, vol 19. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-9383-0_12
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