Term Graph Rewriting

ion operator, 38 acyclic, 48 algebraic specification, 3 alpha conversion of cyclic terms, 44 annotated path, 47 ARS with finite information content, 105 with information content, 105 ARSI, 105 bisimilarity of terms, 92 context, 43 context restricted rewrite system, 39 continuity substitutive -, 134 syntactic -, 134 CRS rewrite rule, 38 cyclic term, 43 dag, 6 directed acyclic graph, 6 directed set, 31 disjoint union, 31 downward closed, 32 edge expansion, 58 equational logic, 73, 74 equivalent modulo garbage collection, 88 equivalent modulo scopes, 94 finite element of a CPO, 32 finite information content ARS with -, 105 first order terms, 3 flat cyclic term, 43 garbage free, 48, 88 generalized μ-calculus, 121 homeomorphic embedding, 57–59 horizontal sharing, 60 ideal, 32 completion, 32 indirection node, 49 infinitarily sound, 123 infinite normal form, 105 infinity, 31 information content ARS with -, 105 labeled translation, 48 lambda calculus with positions, 35 left-linear CRS rule, 39 letrec, 7 lower bound, 32 greatest -, 32 metaterms, 38 metavariables, 38 natural numbers, 31 plus infinity, 31 partial order, 31 complete -, 32 path 155 156 INDEX in a graph, 47 annotated -, 47 positions in a term, 35 power set, 31 pre-term, 41 recursion variables, 43 regular cyclic extension, 130 regular information content, 129 rooted subgraph, 59 scopable, 48 set of words, 31 sharing, 5 signature, 3, 34 simplification, 50 skeleton graph, 58 skeleton of a term graph, 58, 59 skew confluence, 102 skew CR, 102 standard reduction, 143 substitution of cyclic terms, 44 syntactic replacement, 44 term, 35 term graph first order, 46 term rewriting system, 4 tree, 47 trivial unwinding calculus, 121 twisted sharing, 60 unique infinite normal forms, 105 unwinding of a cyclic term, 121 labeled -, 55 scoped -, 55 unwinding calculus, 120, 121 value -, 148 upper bound, 32 least -, 32 variables -,recursion, 43 vertical sharing, 60 weak homeomorphic embedding, 69