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An honest question - what is the problem with inconsistency in using lambda calculus as a programming language and not as foundation of mathematics? """The lam
by zbyforgotpass 5y ago
An honest question - what is the problem with inconsistency in using lambda calculus as a programming language and not as foundation of mathematics?
"""The lambda calculus was introduced by mathematician Alonzo Church in the 1930s as part of an investigation into the foundations of mathematics.[7][a] The original system was shown to be logically inconsistent in 1935 when Stephen Kleene and J. B. Rosser developed the Kleene–Rosser paradox.[8][9]"""
https://en.wikipedia.org/wiki/Lambda_calculus#History https://en.wikipedia.org/wiki/Lambda_calculus#History
- ukj 5y agoPractically nothing. By virtue of all programming being resource-bounded computations can be interpreted in Linear logic [1]. Linear logic is paraconsistent [2] not consistent. Untyped Lambda calculus is essentially an assembly language and Assembly languages treat their own code as data [3]. Contradictions arrise when a system can mutate its own state. That is the power and pitfall of reflection [4] [1] https://en.wikipedia.org/wiki/Linear_logic https://en.wikipedia.org/wiki/Linear_logic [2] http://nlab-pages.s3.us-east-2.amazonaws.com/nlab/show/paraconsistent+logic#linear_logic http://nlab-pages.s3.us-east-2.amazonaws.com/nlab/show/parac... [3] https://en.wikipedia.org/wiki/Metaprogramming https://en.wikipedia.org/wiki/Metaprogramming [4] https://en.wikipedia.org/wiki/Reflective_programming https://en.wikipedia.org/wiki/Reflective_programming