On Mints' reduction for ccc-calculus
In this paper, we present a divide- and-conquer lemma to infer the SN+CR (Strongly Normalization and Church-Rosser) property of a reduction system from that property of its subsystems. Then we apply the lemma to show the property of Mints' reduction for ccc-calculus with restricted η-expansion and restricted π-expansion. In the course of the proof, we obtain some relations of the two restricted expansions against traditional reductions. Among others, we get a simple characterization of the restricted η-expansion in terms of traditional β- and η-reductions, and a similar characterization for the restricted π-expansion.
KeywordsNormal Form Induction Hypothesis Atomic Type Reduction System Proof Theory
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