Under the Curry Howard correspondence, the above conversion process for the deduction meta-theorem is analogous to the conversion process from lambda calculus terms to terms of combinatory logic, where axiom 1 corresponds to the K combinator, and axiom 2 corresponds to the S combinator.
42.
Smullyan's exposition takes the form of an imaginary account of two men going into a forest and discussing the unusual " birds " ( combinators ) they find there ( bird watching was a hobby of one of the founders of combinatory logic, Haskell Curry ).
43.
At the level of proof systems and models of computations, the correspondence mainly shows the identity of structure, first, between some particular formulations of systems known as Hilbert-style deduction system and combinatory logic, and, secondly, between some particular formulations of systems known as natural deduction and lambda calculus.
44.
"' Corrado B�hm "'( born 17 January 1923 ), Professor Emeritus at the University of Rome " La Sapienza ", is a computer scientist known especially for his contributions to the theory of structured programming, constructive mathematics, combinatory logic, lambda-calculus, and the semantics and implementation of functional programming languages.
