Programming Language
A topic for programming languages, a term for computational languages that are at least as expressive as the lambda calculus.Actually, a proper definition would require Turing machine equivalence, but lambda calculus suffices for non-interacting machines and computations that should halt (but what good are those?). However, not all languages listed here, like C, are sufficiently expressive, but a good enough approximation in practice, once supplemented with proper libraries.
Lambda calculus is turing complete. Here is an example of a program that will run forever in lamba calculus:
(λx. x x) (λx. x x)
When the term on the right is substituted into the term on the left it yields the original program.
A turing machine is a non-interacting machine. A Turing machine program can either halt or run forever - it cannot interact with the outside world.
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