COMMENT ⊗   VALID 00005 PAGES
C REC  PAGE   DESCRIPTION
C00001 00001
C00002 00002	.ASEC(AM's Initial Knowledge)
C00006 00003	.ASSECP(Sets)
C00010 00004	.ASSECP(Unordered-objects)
C00013 00005	.ASSECP(Structures)
C00016 ENDMK
C⊗;
.ASEC(AM's Initial Knowledge)

<<Should there be a separate appendix for some of the concepts discovered? >

<<Should there be a separate appendix for some of the geometry concepts? >

<<Should there be a separate appendix for ALL concepts ever created by AM? >

This huge appendix lists the full set of knowledge AM started with.
It  is not  very
readable,  nor is it central  to any of the ⊗4ideas⊗*  on which AM is
based. The  reader is  therefore warned to  proceed at  his own  risk
through this material. It is arranged alphabetically, since the primary use of
it will probably be as a dictionary. When the reader encounters a poorly-named
or poorly-explained concept, he may wish to glance here for its definition.

.ONCE TURN ON "{}"

Each concpet  is listed, followed by  a desription of  the entries in
each facet$$ Each of these  was supplied by hand,  by the author. $.
For each such entry, an English condensation is provided,
of all the knowledge initially supplied to AM about that facet of that concept. 
If there is any unmentioned facet for a concept, then it started out blank.
The reader desiring to gawk at some real live LISP encodings of concepts
may look at Appendix {[2] CONS}, wherein a few are chained up. In
chapter {[2] EXAM2},  some examples of AM  in action were given, and
the  reader observed what  kinds of concepts  -- and  entries for
⊗4their⊗* facets -- AM was able to derive from this base. Many of the
facets  of  the  original  concepts were  left  blank  intentionally,
knowing that AM would be able to fill ⊗4them⊗* in as well. After all,
if you can fill in examples of any new concept, you  ought to be able
to fill in examples of Sets!

Any  concepts which are  mentioned in  this document, but  not listed
here, were discovered by AM$$ This is not quite true. One  experiment
involved adding a new base of geometric primitives, and watching what
was  derived. 
See {"Page" GEOEX}.
Also,  AM  occasionally  re-derived  an  already-known
concept, like Empty-set. $.

<< Assemble here all the concepts and  all their facets, incl. heurs.
>

.ASSECP(Sets)


.WBOX(4,10)
MBOX	Name(s): Set, Class, Collection $
MBOX	Definitions: $
MBOX		Recursive: λ (S) (S=α{α} or Set.Definition (Remove(Any-member(S),S))) $
MBOX		Recursive quick: λ (S) (S=α{α} or Set.Definition (CDR(S))) $
MBOX		Quick: λ (S) (Match S with α{...α} ) $
MBOX	Intuitions: $
MBOX		Geometric: rectangle of points with integral coordinates $
MBOX		Arrows: a quiver of arrows, the archers, the targets $
MBOX	Specializations: Empty-set, Nonempty-set, Set-of-structures, Singleton $
MBOX	Generalizations: Unordered-Structure, No-multiple-elements-Structure $
MBOX	Worth: 400 $
MBOX	Interest: λ (S)  (∃ interesting predicate P over X) (S={xεX | P(x)}). $
MBOX	Sugg: If P is an interesting predicate over X, consider {xεX | P(x)}. $
MBOX	In-domain-of: Union, Intersection, Set-difference, Set-insert, Set-delete $
MBOX	In-range-of: Union, Intersection, Set-difference, Set-insert, Set-delete $
MBOX	View:  Structure: λ (x) Enclose-in-braces(x) $
.EBOX


This is a test, with the wbox command fed args: 1,1

.WBOX(1,1)
MBOX	Name(s): Set, Class, Collection $
MBOX	Definitions: $
MBOX		Recursive: λ (S) (S=α{α} or Set.Definition (Remove(Any-member(S),S))) $
MBOX		Recursive quick: λ (S) (S=α{α} or Set.Definition (CDR(S))) $
MBOX		Quick: λ (S) (Match S with α{...α} ) $
MBOX	Intuitions: $
MBOX		Geometric: rectangle of points with integral coordinates $
MBOX		Arrows: a quiver of arrows, the archers, the targets $
MBOX	Specializations: Empty-set, Nonempty-set, Set-of-structures, Singleton $
MBOX	Generalizations: Unordered-Structure, No-multiple-elements-Structure $
MBOX	Worth: 400 $
MBOX	Interest: λ (S)  (∃ interesting predicate P over X) (S={xεX | P(x)}). $
MBOX	Sugg: If P is an interesting predicate over X, consider {xεX | P(x)}. $
MBOX	In-domain-of: Union, Intersection, Set-difference, Set-insert, Set-delete $
MBOX	In-range-of: Union, Intersection, Set-difference, Set-insert, Set-delete $
MBOX	View:  Structure: λ (x) Enclose-in-braces(x) $
.EBOX

.ASSECP(Unordered-objects)


.BEGIN NOFILL PREFACE 0
⊗6Name(s):⊗* Unordered-objects
⊗6Specializations:⊗* Sets, Bags
⊗6Generalizations:⊗* Structures
⊗6Worth:⊗* 200
⊗6View:⊗* Ordered-objects: λ (x) Sort(x)
⊗6Check:⊗* λ (x) Sorted(x)
	
.END

NOTES:

There is no supplied definition. When somebody asks whether x 
satisfies the definition of this concept, AM must ripple downwards to see if
it satisfies the diefinition of any specialziation. So the implicit definition
of the concept is  [λ (x) (Set(x) OR Bag(x))].

Similarly, there is no explicit mention of what this concept is In-Ran-of.
If AM wishes to find operations which will result in instances of Unordered-objects,
it ripples downward, and plucks, e.g., the operation Set-union from the facet
In-ran-of of the concept Sets.

In fact, there only two small reasons for this concept to exist:

.BN

λλ This concept shows in what way the two concepts Sets and Bags are related.

λλ The heuristic for checking Unordered-objects is applicable to checking both
bags and sets; AM would be less "intelligent" if it stored this piece of
information (the little program which says to sort the argument) redundantly.

.E

When examples of Sets are found, AM notices then that ⊗4all⊗* known examples
of Unordered-objects are sets. It formulates that as a conjecture, inspects the
Spec facet of this concept, and then decides that it will postpone
judgment until after AM has tried to fill in examples of Bags. Thus a new
task to that effect gets added to the agenda, and "Fillin Examples of Bags"
will probably be the very next task chosen from the agenda.

All unordered objects are maintained in an alphanumerically-ordered order,
so that two of them can be tested for equality using the LISP function EQUAL.
In fact, any two structures can therefore be tested for equality using this
fast list-structure comparator.

.ASSECP(Structures)

This concept is a specialized kind of Object. It has four specialized
flavors: Sets, bags, ordered-sets, and lists.
Along another dimension, its specialziations include Empty-structures and
Non-empty-structures.
This concept has a mediocre worth rating (200). 

In addition to all the operations that can be applie to Objects, this
concept is a domain component of the predicate Structure-equality, and of
the operations Some-member, Structure-delete,...

One way to view ⊗4anything⊗* as a structure is to insert it into an empty structure.

There are three ways$$
In addition, of course, all the criteria for judging the interestingness of
Objects in general may be applied. Finally (actually, FIRST), AM would 
apply the criteria
tacked onto any and all of the concepts which are ISA's of the given structure. $
that a given structure might be interesting:
if there is one ⊗4very⊗* interesting member of the structure;
if all the members of the structure are examples of some interesting concept C;
or if all n-tuples of members satisfy some interesting predicate P.
For each such criterion, a little formula is provided to estimate how interesting
this really is. For example, the last  formula  will involve the worth(P), the
rarity of P's being satisfied, whether the current cocnept has some easily-explainable
tie to P already, etc.