Mathematical Logic and Its Applications by Curt C. Christian (auth.), Dimiter G. Skordev (eds.)

By Curt C. Christian (auth.), Dimiter G. Skordev (eds.)

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The full application/lambda language corresponds to derivations in full constructive conditional logic. But, the Lambek calculus employs only a fragment of this, in which each symbol A binds exactly one free variable occurrence - while, moreover, no subterm is closed. The proof of this result is in van Benthem (1983), which provides the relevant, effective conversions between Lambek derivations and lambda terms. Incidentally, the conversion from derivations to terms is a paradigmatic case of what has been advocated as 'type-driven translation' in the linguistic literature.

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