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1.2.4 obaptheory.txt small touch-ups, removing completed TODOs
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orcmid committed Jan 16, 2025
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Showing 1 changed file with 17 additions and 18 deletions.
35 changes: 17 additions & 18 deletions docs/obap/obaptheory.txt
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obaptheory.txt 1.3.3 UTF-8 2024-12-15
obaptheory.txt 1.3.4 UTF-8 2025-01-16
*---|----1----|----2----|----3----|----4----|----5----|----6----|----7----|--*

MISER THEORETICAL CONCEPTION
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a. The right-associative infix pair operator, ::, is introduced, with

x :: y = ob.c(x,y)
t :: u :: v:: ... :: y :: z = t :: (u :: (v :: ... :: (y :: z) ... ) )

n. The prefix form ‵ x is equivalent to ob.e(x). E.g.,
t :: u :: v:: ... :: y :: z
= t :: (u :: (v :: ... :: (y :: z) ... ) )

b. The prefix form ‵ x is equivalent to ob.e(x). E.g.,

‵(ob.NIL :: ‵ ‵ob.NIL :: ‵ob.NIL)
= ob.e(ob.c( ob.NIL,
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intentionally. They need not survive input to oFrugal and may be
treated as erroneous.

Here is an applicative-expression script form in which in which
lindies are preserved, having no definable applicative
interpretation.
There is an applicative-operation script form in which lindies are
preserved, having no definable applicative interpretation
other-wise.

obap.is-lindy(x) => is-symbolic-form(x) (a)

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applicative-expression forms, and other potential purposes.

Note that symbolic forms are still parsed and subject to being
marched through Obap6(d) and Obap6(i) although the form is returned
intact.
marched through Obap6(d) and Obap6(i) in the computational
interpretation, even though the form is returned intact.

The intended practical value is in the ability to transform such
forms into operational scripts by successive abstraction operations
that are more-easily confirmed by experimental demonstration. See
<https://orcmid.github.io/miser/lambda> for practical benefits.
forms into operational scripts by successive abstraction operations.
See <https://orcmid.github.io/miser/lambda> for practical benefits.

It should also be clear from the definition of oFrugalese that
the preserved form could be intended entirely as "data" since
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⇒ obap.ap(p,x) = p :: x
is-symbolic-form(p) ∧ ¬ is-symbolic-form(x)
⇒ obap.ap(p,x) = p :: ob.e(x)

Symbolic forms are resolved in this manner to be more informative
on inspection when an occurrence is unintended. Intensional usage
is also supported by preservation of the symbolic form appearing
applicatively.
is also supported, as in the lambda abstraction of applicative-
operations.

¬ is-symbolic-form(p) (d)
=> ob.is-pair(p) ⇒ obap.ap(p,x) = ev(p,x,p)
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ATTRIBUTION

Hamilton, Dennis E. ‹ob› Universal Applicative Functions. Miser Theory
Conception text file obaptheory.txt version 1.3.3 dated 2024-12-16,
Conception text file obaptheory.txt version 1.3.4 dated 2025-01-16,
available on the Internet as a version of
<https://orcmid.github.io/miser/obap/obaptheory.txt>

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TODO

* Ensure there's a tombstone on the miser/oMiser folder.

* Ensure that attributions have the refactored locations.

* Be very clear about the inspiration of this in McCarthy's LISP approach.

* Items related to the ob-exp concrete syntax should be resolved there, and
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*---|----1----|----2----|----3----|----4----|----5----|----6----|----7----|--*

1.3.4 2025-01-16T21:38Z Smoothing, including on symbolic forms
1.3.3 2024-12-15T21:28Z More Obap3 touch-ups
1.3.2 2024-11-28T19:22Z Cleanup Obap3 explanation
1.3.1 2024-11-27T00:40Z Smooth Symbolic Form a bit
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