We introduce graph reduction technology that implements functional languages with control, such as Scheme with call/cc, where continuations can be manipulated explicitly as values, and can be optimally reduced in the sense of Lévy. The technology is founded on proofnets for multiplicative-exponential linear logic, extending the techniques originally proposed by Lamping, where we adapt the continuation-passing style transformation to yield a new understanding of sharable values. Confluence is maintained by returning multiple answers to a (shared) continuation. Proofnets provide a concurrent version of linear logic proofs, eliminating structurally irrelevant sequentialization, and ignoring asymmetric distinctions between inputs and outputs -- dually, expressions and continuations. While Lamping's graphs and their variants encode an embedding of intuitionistic logic into linear logic, our construction implicitly contains an embedding of classical logic into linear logic. We propose...

A uniform framework of port graph grammars, encompassing connection graphs, interaction nets and Lamping's partial sharing graphs, has been presented by the author in the article `Reducibility between classes of port graph grammar'. The aims of this report are to 1. Give a complete proof of reducibility between general PGGs and simple PGGs (only an outline of the proof was given in that article); 2. Give a short summary of the design of an implementation executing rewrite steps for simple port graph grammars, to justify the claim that port graph grammars are a reasonably efficient representation for code in a distributed environment; 3. Dicuss critically the fundamental notion of reducibility between rewrite systems provided in that article.