Modular Termination Checking Theorems for Second-Order Computation
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We present new theorems of modular termination checking for second-order computation. They are useful for proving termination of higher-order programs and foundational calculi. Moreover, they offer a decomposition technique for difficult termination problems. Our proof is based on two SN-preserving translations and nontrivial use of Blanqui's General Schema: a syntactic criterion of strong normalisation (SN). The first translation is to attach partial terms to the original system, which is a variation of author's previous work on higher-order semantic labelling. The second is to translation it to an explicit substitution system, which makes it possible to apply our modularity theorem. Experimental results obtained with our implementation SOL demonstrate that this modular SN is effective for application to various problems.
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