Lambda-Calculus and Combinators in the 20th Century

P.726, lines 3–4. Replace “However, none of these authors gave formal definitions of substitution and conversion, which are characteristic of CL and λ proper. These did not appear ...” by “However, none of these authors showed the interplay between reduction, substitution and conversion explicitly by means of a formal theory, as is done in CL and λ. The latter theories did not appear ...”. P.727, footnote 3 (about the date of Schönfinkel’s birth). Add “The date 4-91889 comes from his entry in the records of the registration-office of the city of Göttingen for 1914.” P.733, footnote 19. The 2008 edition of [Hindley and Seldin, 1986] does not treat Curry’s paradox. P.737, footnote 25. Add “But note that Henkin’s definition of general model needs modifying, otherwise his completeness theorem does not work; see Andrews General models and extensionality, J. Symbolic Logic 37 (1972), pp. 395–397.” P.738, footnote 27. To “[Hindley and Seldin 1986, Def. A1.3]”, add “(Def. A2.5 in the 2008 edition)”. P.757, lines 1–2. “A× (·)” should be “(·) ×A” in two places. P.763, last line but one. “proposition” should be “propositions”. P.764. Below the four displayed equations, add “(Here X is not free in A, B.)”. P.766, last line. “..” should be “.”. P.768, §8.3. In line 8, after “gave no procedure” should be added “(i.e. no explicit procedure of normalisation in the style of reduction in λ and CL)”. In line 11, “The first proof to contain a procedure” should be “The first proof (at least, for a Natural Deduction analogue of GLC) to contain such a procedure”. In line 15, “solved Takeuti’s problem” should be “proved a Natural Deduction analogue of Takeuti’s conjecture”. P.769. Below the displayed equations for σ × τ , σ + τ , add “(Here t is not free in σ, τ .)”. P.772. Replace the last sentence of §8.3 by “Proofs of SN for deductions and WN for terms were included in [Seldin, 1987 §§4.3, 4.4] and [Seldin, 1997, §3]; a proof of SN for terms was given by Pottinger in Strong normalization for terms of the theory of constructions (Technical Report TR 11-7, 1987, Odyssey Research Associates, Ithaca, N.Y., U.S.A.), but not published.”