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0.3.6 lambda/index.md trapped in a twisty maze of symbolic forms all …
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orcmid committed Dec 21, 2024
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<!-- index.md 0.3.5 UTF-8 2024-12-21
<!-- index.md 0.3.6 UTF-8 2024-12-21
----1----|----2----|----3----|----4----|----5----|----6----|----7----|--*
source <https://github.com/orcmid/miser/blob/master/docs/lambda/index.md>
publication <https://orcmid.github.io/miser/lambda/>
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<a href="index.html" target="_top">index</a>&gt;</code></b>
<br />
<small><small>
0.3.5 2024-12-21T17:51Z<!-- MAINTAIN THIS MANUALLY -->
0.3.6 2024-12-21T22:25Z<!-- MAINTAIN THIS MANUALLY -->
</small></small>
</td>
</tr>
Expand Down Expand Up @@ -68,7 +68,7 @@ structure and not on any applicative interpretation of `M`.
Although `σ.s M` determines an ob, that ob has no occurrences of `s`. In this
sense, `σ.s M` has `s` abstracted away; `(σ.s M) s` determines `M` as-is.

There are handy companion functions, `δ(s, N` and `subst(N, s)`, for use in
There are handy companion functions, `δ(s, N)` and `subst(N, s)`, for use in
particular circumstances, often when one or more particular operands are known
in advance.

Expand All @@ -89,15 +89,16 @@ self-evident, however suggestive the form might be. Purpose for a symbolic
form is revealed only in the context of its usage.

The harmony of symbolic form and applicative-expression, when that
interpretation is the case, is anchored on the fact that the computational
interpretation of `f :: g :: x` is tantamount to the Frugalese applicative
expression `f g x`, both being right-associative and equivalent to `f(g x)`.
interpretation is the case, is encouraged by the computational interpretation
of `f :: g :: x` being tantamount to the Frugalese applicative expression
`f g x`, both being right-associative and equivalent to `f(g x)` were the
lindies `f`, `g`, and `x` taken to be variables for appropriate obs.

The oFrugal definitions of applicative-procedure abstraction rely on that
structural nicety, facilitating abstraction of applicative-function scripts
and confirmation of their operation.
structural nicety, transforming symbolic forms into applicative-function
scripts in a manner that supports confirmation of correct operation.

#### 2.2.1 Examples of symbolic-form preservation
#### 2.2.1 Symbolic-form preservation

When a symbolic form is evaluated or applied directly, the symbolic
form is preserved.
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The oMiser computational model's application function treats lindies as
individuals having no definable/separate applicative interpretations.

Lindies are individual symbolic forms.
Lindies are taken as individual symbolic forms.

When application operator `p` and operand `x` are both symbolic forms, the
result of application is the composed symbolic form `(p) :: x`.
Expand All @@ -138,8 +139,8 @@ When `p` is a symbolic form, `(p)::.NIL` is a symbolic form. Otherwise
when only `p` is a symbolic form, the result of application is `(p) :: ‵ x`,
itself a symbolic form even though `x` may be an ob of any form.

As is done in the examples (2.2.1), symbolic forms are usually written in
canonical form, omitting unnecessary parentheses.
As is done in the examples (2.2.1, above), symbolic forms are usually written
in canonical form, omitting unnecessary parentheses.

## 3. Functional Abstraction Heuristics

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</table>
<!--
0.3.5 2024-12-12T17:51Z Enough fussing with Symbolic Form for now
0.3.6 2024-12-21T22:25Z You are trapped in a twisty symbolic form with
intrpretations all the same
0.3.5 2024-12-21T17:51Z Enough fussing with Symbolic Form for now
0.3.4 2024-12-18T22:53Z Still struggling with Symbolic Form motivation
0.3.3 2024-12-15T23:29Z Smooth 2.2 more
0.3.2 2024-11-28T17:39Z Touch up 2.1 a bit more
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