From Proofs to Programs in the Minlog SystemThe Warshall Algorithm and Higman ' s

The Warshall algorithm computing the transitive closure of a relation is extracted from a constructive proof that repetitions in a path can always be avoided. Secondly a nonconstructive proof of a special case of Higman's lemma is transformed into a constructive proof. From the latter an eecient program is extracted. Both examples are implemented in the interactive theorem prover Minlog developed at the University of Munich.