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PCF, as considered in this paper, is a lazy typed lambda calculus with functions, pairing, fixed-point operators and arbitrary algebraic data types. The natural equational axioms for PCF include η-equivalence and the so-called "surjective pairing" axiom for pairs. However, the reduction system pcf η,sp defined by directing each equational axiom is not confluent, for virtually any choice of algebraic data types. Moreover, neither η-reduction nor surjective pairing seems to have a counterpart indoi:10.1145/91556.91677 dblp:conf/lfp/HowardM90 fatcat:vfqoypttzzhynj2uapkngnsr3i