[Inquiry] Re: Propositions As Types -- Series A

[Jon Awbrey]

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PAT.  Note A5

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Composition, or the Composer

Step 1.

Given a specification of the "composition combinator",
or the "composer" P, that has the following effects:

   x(y(zP)))  =  (xy)z

find an explication of P in terms of primitive combinators.

Proceed as follows:

   (xy)z  =  (xy)(x(zK))  =  x(y((zK)S))

   (zK)S  =  (zK)(z(SK))  =  z(K((SK)S)) 

   =>

   x(y(zP))  =  (xy)z  =  x(y(z(K((SK)S))))

   =>

   P  =  (K((SK)S))

Jon Awbrey

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inquiry e-lab: http://stderr.org/pipermail/inquiry/
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