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Such reduction is often called rewriting (or (equational) simplification ). To avoid confusion with non-equational rewriting in rewriting logic, I use reduction when equations are applied, and rewriting for the application of (“non-equational”) rewrite rules in rewriting logic. Similarly, I use the symbol instead of the more common arrow \(\,\longrightarrow \,\) for equational reduction/simplification.
Some authors write that u matches t in this case.
This is called the inverse relation.
This is called the symmetric closure of .
This is called the reflexive-transitive closure of \(\rightsquigarrow _E\).
This is the reflexive-symmetric-transitive closure of .
This is the transitive closure of \(\rightsquigarrow _E\).
- Operational Semantics of Equational Specifications
Peter Csaba Ölveczky
- Springer London
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- Chapter 3