Banach R. (1993); A Fibration Semantics for Extended Term Graph Rewriting. in: Term Graph Rewriting: Theory and Practice. Sleep, Plasmeijer, van Eekelen (eds.), 91-100, John Wiley.  Home/Search Document Details and Download
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An Opfibration Account of Typed DPO and DPB Graph.. - Banach, Corradini (1996) (1 citation) (Correct)
....construction) rather than a functor, and to describe the converse construction using an (unsplit) opfibration. Similar remarks apply to contravariant functors and (unsplit) fibrations. All of this is in contrast to the use of split opfibrations as a methodology for describing graph rewriting in Banach (1993, 1994, 1995) The relationship between these techniques will be explored elsewhere. In this paper we re engineer and extend the central material of the key papers refered to in the first paragraph above, resisting the temptation to force a fixed choice of pullbacks (by whatever means) As ....
Banach R. (1993); A Fibration Semantics for Extended Term Graph Rewriting. in: Term Graph Rewriting: Theory and Practice. Sleep, Plasmeijer, van Eekelen (eds.), 91-100, John Wiley.
A Fibred Approach to Rewriting - How the Duality between Adding.. - Kahl (1997) (Correct)
....into application graphs. We share this point of view, and we have arrived at the same conclusion in our work [Kahl, 1996] that opens the algebraic approach to rewriting of term graphs with bound variables. fiberr.tex; 9 05 1997; 19:27; no v. p. 4 A Fibred Approach to Rewriting 5 Rewriting in [Banach, 1993a; Banach, 1994] is achieved by single heterogeneous pushout steps; vertical arrows are homomorphisms of his simple kind of term graphs and horizontal arrows are so called redirection pairs , i.e. pairs consisting of two functions from nodes of the left hand side into the right hand side: an ....
....of rewriting term graphs with bound variables [Kahl, 1996] garbage retention is not possible and composability of single heterogeneous pushouts therefore much harder to achieve. 6. Application of the Grothendiek Construction The first part of this section corresponds to the exposition in [Banach, 1993a] resp. Banach, 1994] that establishes rewriting functors and applies the Grothendiek construction, arriving at a Grothendiek category where heterogeneous pushouts can be seen as resulting from the splitting of an opfibration. That part has only been adapted to our more general approach that ....
Richard Banach. A fibration semantics for extended term graph rewriting. In M.R. Sleep, M.J. Plasmeijer, and M.C.J.D. van Eekelen, editors, Term Graph Rewriting: Theory and Practice, chapter 7, pages 91--100. John Wiley, 1993.
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