Completeness and strictness analysis for the evaluation strategy

We propose two analyses of the evaluation strategy (the E-strategy). Firstly, we analyze a completeness of the E-strategy. For a complete E-strategy each evaluated term is guaranteed to be a normal form. In this paper we de ne the notion of the completeness for the context-sensitive rewriting, called -completeness, and show a condition of the E-strategy to satisfy the -completeness. Secondarily, we give a strictness analysis for the E-strategy. A function is called strict in a certain argument if the evaluation of that argument does not change the termination behaviour. From the analyses, we can de ne a method to get a more e ective default strategy for the E-strategy.