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  • KurohaKafka

    Turing-incomplete

    October 27, 2017 by KurohaKafka

    Restrict Ξ function to S, K, I only or S and I only.

    Ξ[I](x)=1 (const)

    Ξ[K](x)=x

    Ξ[S](x)≧multiplication level

    Generation S(SAB)XY→SABY(XY)
    Conversion S(SA)XY→SAY(XY)
    Consumption SSXY→SY(XY)

    Ξ[S,I](x)=?

    Ξ[S,I,Ω](x)=?

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  • KurohaKafka

    Some large functions appear in the process of defining large numbers. All large numbers belong to N and all functions belong N→N. Large functions are defined from successor.

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  • KurohaKafka

    Iff we have a matrix such as

    \(G\frown B_0\frown B_1\frown\cdots\frown B_n\)

    which β-reduced from \(G\frown B\frown N\) , then it is holds that

    \(B_k\frown N_k

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