ob.txt 0.1.6 smoothing and elaboration

Resolve issue #16 typo and issue #20 enclosure explanation, thanks to review by @band.  Further smoothing of the text at the same time.

oMiser/ob.txt

@@ -1,19 +1,19 @@
-ob.txt 0.1.5 UTF-8 dh:2019-04-30
+ob.txt 0.1.6 UTF-8 dh:2019-05-10
 
  The Miser Project Code
  ======================
 
  <https://github.com/orcmid/miser/blob/master/oMiser/ob.txt>
 
  ‹ob› MATHEMATICAL STRUCTURE, DATA REPRESENTATION, AND EXPRESSIONS
- ----------------------------------------------------------------
+ -----------------------------------------------------------------
 
  Formulation of the mathematical structure, ‹ob›, illustrates the bridge
  between mathematical logic and theoretical limitations of all present-
  day computation systems. The ‹ob›-based computation model, although
  low-level, is as powerful, with respect to those limits, as any other
  model. A central purpose of the Miser Project is demonstration of how
- that and then to draw the connection with an operational realization.
+ that is the case, drawing the connection with an operational realization.
 
  Under the Miser ‹ob› computational model, obs serve interchangeably as
  data and as scripts of procedures -- computational methods -- operating on
@@ -31,18 +31,18 @@ ob.txt 0.1.5 UTF-8 dh:2019-04-30
  <https://github.com/orcmid/miser/blob/master/oMiser/obtheory.txt>.
 
  * There are two selector functions, ob.a(z) and ob.b(z) that given
- any ob and determine an ob as their result.
+ any ob determine an ob as their result.
 
  * There is an arbitrary supply of distinct individuals, including
  ob.NIL. For any individual, z, ob.a(z) = ob.b(z) = z.
 
  * For z any ob, the function ob.e(z) determines the ob such that
  ob.a(ob.e(z)) = z and ob.b(ob.e(z)) = ob.e(z). We speak of ob.e(z)
- as encapsulation of z.
+ as the enclosure of z.
 
- * The individuals and encapsulations together are identified as
- singletons because they have in common that ob.b(z) = z. There
- are oMiser idioms that exploit this.
+ * The individuals and enclosure together are identified as singletons
+ because they have in common that ob.b(z) = z. There are oMiser idioms
+ that exploit this.
 
  * For any obs x and y, the function ob.c(x, y) determines the pair
  such that ob.a(ob.c(x,y)) = x and ob.b(ob.c(x,y)) = y and neither
@@ -52,11 +52,12 @@ ob.txt 0.1.5 UTF-8 dh:2019-04-30
  determine when obs are the same or different based on structure alone,
  - ob.is-individual(z) true whenever ob.a(z) = z
  - ob.is-singleton(z) true whenever ob.b(z) = z
- - ob.is-pair(z) whenever ob.is-singleton(z) is false
- - ob.is-enclosure(z) whenever ob.is-singleton(z) is true
+ - ob.is-pair(z) true whenever ob.is-singleton(z) is false
+ - ob.is-enclosure(z) true whenever ob.is-singleton(z) is true
  and ob.is-individual(z) is false.
 
  * The enrichment of obs for particular applications is solely by
+ exploitation of these structural characteristics of obs along with
  introduction of distinct individuals.
 
  2. DATA REPRESENTATION TEXT NOTATION
@@ -78,7 +79,7 @@ ob.txt 0.1.5 UTF-8 dh:2019-04-30
  Having a finite canonical form for every ob provides a basis for
  computational manipulation of obs, a kind of ob arithmetic. We can
  always answer the question, "which ob is this?" if its canonical
- form can be obtained.
+ form can be determined.
 
  There is similarity with ordinary arithmetic. Consider that each decimal
  numeral written out without any leading zeroes (except for "0" alone)
@@ -102,7 +103,7 @@ ob.txt 0.1.5 UTF-8 dh:2019-04-30
  significed at keyboards by using the grave accent, U+0060 `, although
  the preferred substitute is the apostrophe, U+0027. Keep in mind
  that this is an expression operator and not the same as syntactical
- "quotation."
+ "quotation" (although there is a similarity of function in scripts).
 
  * ob.c(x, y) is expressed x :: y
 
@@ -134,14 +135,14 @@ ob.txt 0.1.5 UTF-8 dh:2019-04-30
 
  All of the individual terms in that expression are lindies.
 
- 2.2 Publication Notation
+ 2.3 Publication Notation
 
  In formats having greater typographical flexibility than plaintest, there
  can be useful embellishments. Primitives can be presented in boldface
  and even lower-case, with the leading "." omitted, since the special
  typography reflects their "reserved" and distinct status as primitives.
 
- 2.3 Additional Forms
+ 2.4 Additional Forms
 
  The notation can be "pretty-printed", using indentation, to facilitate
  comprehension. The addition of comments, blank lines, indentations, and
@@ -209,20 +210,24 @@ ob.txt 0.1.5 UTF-8 dh:2019-04-30
 
  Without getting into the details, here is a case where a procedure is used
  to combine obs x and y, also as scripts, into a procedure that involves
- even further applications to achieve the intended result.
+ even further applications to achieve the intended result. Powerful
+ systematic treatment of these applicative operations is expanded on at
+ <https://github.com/orcmid/miser/blob/master/oMiser/combinators.txt>.
 
  Many obs are useful in composing scripts by combining others in this
- manner. Using procedures to compute other scripts from given ones and
- data demonstrates a critical characteristic of stored-program computation.
+ manner. Using procedures to compute other scripts from given ones
+ demonstrates a critical characteristic of stored-program computation.
  This capability is at the heart of how software is used to build higher-
  level tools and their programming languages, although the mechanisms of
  general-purpose procedures do not "rewrite" scripts to make other scripts,
- having alternative mechanisms at hand.
+ there being alternative mechanisms at hand in well-designed general-
+ purpose computers.
 
 4.1 Applicative-Expression Style
 
- In oFrugalese, the evaluation (4) can be expressed using applicative-
- expression style,
+ In oFrugalese, the evaluation (4) can be expressed using a defined
+ applicative-expression style, similar to mathematical and programming-
+ language functional notation.
 
  cS(x,y) z = x(z) y(z) (5)
 
@@ -237,7 +242,7 @@ ob.txt 0.1.5 UTF-8 dh:2019-04-30
  of the result of one ob-yielding application, here x(z), to the result of
  another ob-yielding expression, such as y(z), as in (5). All of the
  examples in (5-6) are formulas for the same applicative operations, namely
- those that deliver (4).
+ those that deliver the same result as (4) with cS eliminated.
 
 4.2 Applicative Expressions in oFrugal
 
@@ -253,7 +258,7 @@ ob.txt 0.1.5 UTF-8 dh:2019-04-30
 
  There is no applicative operation required in the evaluation of (2) to
  arrive at the ob (1). But the leading terms in (7), by their spacing,
- constitute applicative-operation expression, leading to interpretation as
+ signify applicative operation, leading to interpretation as
 
  obap.ap(.A, obap.ap(.B, obap.ap(.B, x)))
  = ob.a(ob.b(ob.b(x))),
@@ -293,8 +298,8 @@ ob.txt 0.1.5 UTF-8 dh:2019-04-30
  all involves just obs.
 
  Given some means to express manipulation of strings of character codes
- and of input-output streams, we could define the oFrugal REPL itself
- in Frugalese.
+ and of input-output streams, we could define oFrugal processing itself in
+ Frugalese.
 
  - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 
@@ -314,16 +319,28 @@ ob.txt 0.1.5 UTF-8 dh:2019-04-30
 
  - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 
+ ATTRIBUTION
+
+ Hamilton, Dennis E. ‹ob› Mathematical Structure, Data Representation, and Expressions. Miser Theory Conception text file ob.txt version 0.1.6 dated
+ 2019-05-10, available on the Internet as a version of
+ <https://github.com/orcmid/miser/blob/master/oMiser/ob.txt>
+
  TODO
 
- * Add an attribution statement
+ * Continue review.
+
+ * Add Notes and Reference section.
+
+ * Also add Content table.
+
+ * Explain more about traces and the ^cS application in the final example.
 
- * Get straight on the elimination of acute accent in 0.0.6 and however this
- works, in ob-exp. It is the case that we will use apostrophe over back-
- tick if it is necessary to make a plaintext substitution for reverse-prime
 
  - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
 
+ 0.1.6 2019-05-10-07:49 Correct issue #16 typo spotted by William L. Anderson.
+ Be more careful about enclosure per issue #20 by William L. Anderson.
+ Provide further editorial improvements throughout the text.
  0.1.5 2019-04-30-13:06 Smooth a few places and make adjustments in early
  passages thanks to comments from colleague William L. Anderson.
  0.1.4 2019-04-29-12:07 Smooth the text flow and touch up in places. Add TODO