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NummSquared 2006a0 Explained. Edition No. 1
VDM Publishing House, June 2008, Pages: 300
Set theory is the standard foundation for mathematics, but often lacks rules of reduction for function calls. Thus, for computer science, the untyped lambda calculus or type theory is usually preferred. The untyped lambda calculus and several improvements make functions fundamental, but suffer from non-terminating reductions and have partially non-classical logics. Type theory is a good foundation for logic, math and computer science, yet with both types and functions fundamental, it is more complex than set theory or the untyped lambda calculus. NummSquared, a new foundational language, makes only functions fundamental, yet ensures terminating reductions, has a classical logic, and attempts to follow set theory as much as possible. NummSquared builds on John von Neumann's 1925 work and R. B. Jones's 1998 work. NummSquared is well-founded, has reduction and proof, and supports computation and reflection. Because of coercion, there are no types, and functions are defined and called without proof, yet reduction terminates. An interpreter, NsGo (in progress when Samuel Howse died), is an F#/C# .NET assembly, mostly automatically extracted from a program of the Coq proof assistant.
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