Streams and strings in formal proofs

Streams are acyclic directed subgraphs of the logical $ow graph of a proof representing bundles of paths with the same origin and the same end. The notion of stream is used to describe the evolution of proofs during cut-elimination in purely algebraic terms. The algebraic and combinatorial properties of $ow graphs emerging from our analysis serve to elucidate logical phenomena. However, the full logical signi)cance of the combinatorics, e.g. the absence of certain patterns within $ow graphs, remains unclear. c © 2002 Elsevier Science B.V. All rights reserved.