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I've been reading Girard et al's 'Proofs and Types', which in Chapter 6 presents a proof of strong normalisation for the simply typed lambda calculus with products and base types. The proof is based ...

Pure type systems are characterized in an almost combinatorial way: a set of axioms $\star_i : \star_j$, and a set of triples $(\star_i, \star_j, \star_k)$ saying when the dependent product $\prod_{x :...