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Notes Folio n011101
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0.00 2014-04-02 16:16

Status Date Description
     
     
     
     
     
     
  2014-04-02 I was leafing through Church Calculi of Lambda-Conversion and noticing that he was proposing the simply-typed lambda calculus but hadn't narrowed in on it completely.  In proving the representation of combinators, I establish that, given a particular representation, it preserved the combinator interpretation of those arguments it is applied to that represent combinators.   This continues indefinitely by demonstrating a representation for cK and cS, the substitution combinator.  We use Rosenbloom for this part.  Note that we don't have to get into lambda-definability at this stage.  The next thing to show is that when a combinator is given procedures on simple types (namely, procedures over Ob), those interpretations are also preserved.  That is the rules of type work out.  So every combinator, including S and K, is an interpretation-preserving operation on Ob procedures, where the interpretation is f:Ob->Ob.  This is a step toward the universality of ob.ap for <ob>.   Not all the dots are connected, but this is part of the program to be followed.
  2014-03-28 I am musing about computational manifestation and also how the primitives on ob structure are not combinators, especially ob.a, ob.b that operate at the Ob structural level not in any sensible combinator level.  The ob.c, ob.d, and ob.self and ob.arg special forms are not amenable to interpretation as combinators. The nature of ob.e as quotation does provide a direct interpretation, but there are still interpretation issues concerning the operand.  There is some sort of breach of type here, and that needs to be dealt with.  Not every ob.ap(proc, x) has interpretation as a combinator given by the interpretation of proc.
  2014-03-28 Manifestation and the appearance of platonic existence needs to be added.
done 2014-03-28 Share 2001/11/ to the hosted-site mirror
done 2014-03-28 Have the synopsis.htm tied to n011101b.
done 2014-03-28 n011101d: Customize as version 0.02 and the questions from band
done 2014-03-28 n011101: Customize as a folio title page, version 0.02
done 2014-03-28 n011101c: Create a revision history block that will lead to n021000e when it is different enough.
done 2014-03-28 n011101c: Customize as a folio page, version 0.02
done 2014-03-28 Customize n011101a and n011101b for the new location, styles, and formatting
done 2014-03-28


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$$Author: Orcmid $
$$Date: 14-04-02 17:17 $
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