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Principia Mathematica anticipated lambda-calculus, referential transparency, and type theory
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An essay argues that Whitehead and Russell's 1910 Principia Mathematica contains the first mentions of referential transparency, alpha renaming, domain, and type in the modern sense, and that its propositional functions anticipate lambda-calculus.
Several concepts that working programmers treat as modern, referential transparency, bound variables, type systems, alpha renaming, appear in Principia in recognizably modern form, which reframes their origin from computer science back to mathematical logic and linguistics.
Written by elseif from the cluster below · every claim links back to a sourceThe three things worth knowing
Page 8 of Principia contains what the author calls perhaps the first mention of referential transparency in mathematical literature, including a non-referentially-transparent example ('A believes p') drawn from Frege's work in linguistics.
Propositional functions on page 15 anticipate lambda-calculus, and the book's 'incomplete symbols' anticipate continuations and control operators.
Principia insists on separate notations for 'any' versus 'all', which the author reads as an anticipation of intuitionism, though the authors admitted the equivalence of the two in their theory.
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