Examples

Lambda Calculus Examples

Constants and their operators such as ints 0, 1,2, ..., +, -, ..., Booleans true, false, and, or, not, ..., Lists, nil, cons, hd, tl, null, etc., can all be defined in λ calculus,: [Integers]; [Booleans]; [Lists],; [arithmetic], more of it
so it is (convenient but) not necessary to "build them in."
Recursion (equivalently iteration) can be effected in the pure λ calculus by using the fixed-point operator, Y,: [Y (lazy)].
The lazy version will not work in a strict language; in that case...: [Y (strict)].
Standard operations can be defined on: [Lists] &; [Trees]; [Primes] sieve of Eratosthenese; [Fibonacci] numbers (1)
Circular programs give recursive definitions of data-structures: [Unique], nub; [Hamming numbers]; [Fibonacci] numbers (2), circular program; [Thue] "good" sequences; [Composite & prime] numbers
The Edit distance problem admits an interesting functional programming dynamic programming solution:: [edit distance] × 3.
The examples can be run interactively using the FORM below: let Y = lambda G. (lambda g. G(g g)) (lambda g. G(g g)) in let F = lambda f. lambda n. if n<=0 then 1 else n*f(n-1) in Y F 10 {Factorial by the fixed-point Y combinator}

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