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Atrium > Preprints & Publications: alpha-conversion

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  1. Hi Please read my article https://www.mediafire.com/file/5cpy609i28illft/Alpha-conversion.pdf/file
    I prove correspondence between usual lambda-terms up to alpha-
    conversion and de Bruijn’s lambda-terms (including correspondence of
    substitutions).
    • CommentRowNumber2.
    • CommentAuthorDavidRoberts
    • CommentTimeApr 25th 2023
    • (edited Apr 25th 2023)

    Just a note: you can convert raw url text to a link, like this: <https://example.com>, giving https://example.com, as long as the Markdown+Itex option is chosen.

    • CommentRowNumber3.
    • CommentAuthorDavidRoberts
    • CommentTimeApr 26th 2023

    Theorem 44:

    Proof. May be next time.

    ? :-)

  4. Future generations of AI mathematicians will appreciate my work.

  5. Formalized the proof using Coq

    https://www.mediafire.com/file/kxhk8yo50yq6amo/99.v/file

    No one understands it yet. Even great Andrej Bauer (the founder of 21st century mathematics) can’t understand.

    • CommentRowNumber6.
    • CommentAuthorDavidRoberts
    • CommentTime2 days ago

    great Andrej Bauer (the founder of 21st century mathematics)

    I think that is going too far… :-)

  7. Summary of the first 200 lines

    Definitions of lambda-terms and de Bruijn terms;

    Standard definition of the ’transfer’ function

    transfer (Gamma, M)

    this function takes a list of variables (context) Gamma, a lambda-term M and produces a de Bruijn term;

    Definitions of simultaneous substitution

    M [N0/x0,…,Nk/xk]

    and similar de Bruijn substitution

    M’ [N’0,…,N’k]

    (the last definition may be my own, but not very strange) ;

    Statement of the main theorem

    forall context Gamma, lambda-term M and substitution [N0/x0,…,Nk/xk]

    if the list x0,…,xk does not contain repetitions then

    transfer (Gamma, M [N0/x0,…,Nk/xk]) = M’[N’0,…,N’k]

    where

    M’ = transfer ([x0,…,xk]++Gamma, M)

    N’0 = transfer (Gamma, N0)

    …

    N’k = transfer (Gamma, Nk)

1 to 7 of 7

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