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(In continuation-passing style, call/cc becomes a simple function that can be written with lambda.) This is a particularly common strategy in Haskell, where it is easy to construct a "continuation-passing monad" (for example, the Cont monad and ContT monad transformer in the mtl library).
Fixed-point combinators, which are used in lambda calculus for the same purpose as the first recursion theorem.
The use of mathematical logic to represent and execute computer programs is also a feature of the lambda calculus, developed by Alonzo Church in the 1930s.