Thought I'd give this a try using plain lambda calculus. The notation is:
λx.t
λx.(λy.t)
λx y.t
MN
MNO
(MN)O
0 = λf x.x succ = λn f x. f (n f x) add = λm n f x. m f (n f x) mul = λm n f x. m (n f) x alg = λn i s. add n (mul i s)
Example 1:
2 = succ (succ 0) 5 = succ (add 2 2) 10 = add 5 5 alg 2 5 10 --> λf x.f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f(f x)))))))))))))))))))))))))))))))))))))))))))))))))))
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Thought I'd give this a try using plain lambda calculus. The notation is:
λx.t= Function taking x as an argument and producing the expression t. Can simplifyλx.(λy.t)->λx y.tMN= Apply N to MMNO=(MN)OExample 1: