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¶A simpler definition of sap

2023-11-07

There was a simpler definition of cons. Is there a simpler definition of sap too?

The natural linear concatenative basis

Defining cons with only empty quotations

sap ≜ swap cat i

        ┃ [B] [A] sap
        ┃ [B] [A] swap cat i
    [B] ┃ [A] swap cat i
[B] [A] ┃ swap cat i
[A] [B] ┃ cat i
  [A B] ┃ i
    A B ┃ i

¶Original definition

For reference, here is the original definition:

sap ≜ swap unit cat i i

          ┃ [B] [A] sap
          ┃ [B] [A] swap unit cat i i
      [B] ┃ [A] swap unit cat i i
  [B] [A] ┃ swap unit cat i i
  [A] [B] ┃ unit cat i i
[A] [[B]] ┃ compose i i
  [A [B]] ┃ i i
          ┃ A [B] i
        A ┃ [B] i
    A [B] ┃ i
      A B ┃