Semantics with applications: a formal introduction
Semantics with applications: a formal introduction
Transfinite reductions in orthogonal term rewriting systems
Information and Computation
Non-Standard Semantics for Program Slicing
Higher-Order and Symbolic Computation
Nordic Journal of Computing
Trace-Based Coinductive Operational Semantics for While
TPHOLs '09 Proceedings of the 22nd International Conference on Theorem Proving in Higher Order Logics
A hoare logic for the coinductive trace-based big-step semantics of while
ESOP'10 Proceedings of the 19th European conference on Programming Languages and Systems
| Hi-index | 0.00 |
Transfinite semantics have been argued to be a proper framework for reasoning about correctness of certain program transformation techniques, e.g. program slicing. But transfinite semantics work fine only for non-recursive programs because of infinity being “one-way”. This paper presents transfinite trace semantics in a different form which we call fractional semantics. The components of traces are indexed with rational numbers rather than ordinals. Rational numbers form both infinite ascending and infinite descending chains, so the principal obstacle of handling recursion disappears. Although we have not yet found a fractional semantics appropriate for all cases of recursion, the approach seems to be promising. Another contribution achieved with help of fractional semantics is presenting both standard and transfinite trace semantics uniformly using fixpoints.