Context-sensitive Conditional Expression Reduction Systems

Zurab Khasidashvili, Vincent van Oostrom
1995 Electronical Notes in Theoretical Computer Science  
We i n troduce Context-sensitive Conditional Expression Reduction Systems (CERS) by extending and generalizing the notion of conditional TRS to the higher order case. We justify our framework in two w ays. First, we de ne orthogonality for CERSs and show that the usual results for orthogonal systems ( niteness of developments, con uence, permutation equivalence) carry over immediately. This can be used e.g. to infer con uence from the subject reduction property in several typed -calculi
more » ... ed -calculi possibly enriched with pattern-matching de nitions. Second, we express several proof and transition systems as CERSs. In particular, we g i v e encodings of Hilbert-style proof systems, Gentzen-style sequent-calculi, rewrite systems with rule priorities, and the -calculus into CERSs. This last encoding is an (important) example of real context-sensitive rewriting.
doi:10.1016/s1571-0661(05)80193-8 fatcat:5bt2jnz4frdjfbiuqfzb6gz2ea