1.3.1. Syntax of general predicates A) NOTION :: ALPHA ; NOTION ALPHA.
B) ALPHA :: a ; b ; c ; d ; e ; f ; g ; h ; i ; j ; k ; l ; m ; n ; o ; p ; q ; r ; s ; t ; u ; v ; w ; x ; y ; z.
D) THING :: NOTION ; (NOTETY1) NOTETY2 ; THING (NOTETY1) NOTETY2.
c) where THING1 and THING2 : where THING1, where THING2.
d) where THING1 or THING2 : where THING1 ; where THING2.
e) unless THING1 and THING2 : unless THING1 ; unless THING2.
f) unless THING1 or THING2 : unless THING1, unless THING2.
g) WHETHER (NOTETY1) is (NOTETY2) : WHETHER (NOTETY1) begins with (NOTETY2){h,i,j} and (NOTETY2) begins with (NOTETY1){h,i,j}.
h) WHETHER (EMPTY) begins with (NOTION){g,j} : WHETHER false{b,-}.
i) WHETHER (NOTETY) begins with (EMPTY){g,j} : WHETHER true{a,-}.
j) WHETHER (ALPHA1 NOTETY1) begins with (ALPHA2 NOTETY2){g,j,m} : WHETHER (ALPHA1) coincides with (ALPHA2) in (abcdefghijklmnopqrstuvwxyz){k,l,-} and (NOTETY1) begins with (NOTETY2){h,i,j}.
k) where (ALPHA) coincides with (ALPHA) in (NOTION){j} : where true{a}.
l) unless (ALPHA1) coincides with (ALPHA2) in (NOTION){j} : where (NOTION) contains (ALPHA1 NOTETY ALPHA2){m} or (NOTION) contains (ALPHA2 NOTETY ALPHA1){m}.
m) WHETHER (ALPHA NOTETY) contains (NOTION){l,m} : WHETHER (ALPHA NOTETY) begins with (NOTION){j} or (NOTETY) contains (NOTION){m,n}.
n) WHETHER (EMPTY) contains (NOTION){m} : WHETHER false{b,-}. {The small syntactic marks "(" and ")" are used to ensure, in a simple way, the unambiguous application of these predicates.}
1.3.2. The holding of predicates A "predicate" is a protonotion which begins with 'where' or 'unless' {unified into 'WHETHER'} . For a predicate P, either one or more production trees may be produced {1.1.3.2.f } {all of which are then invisible}, in which case P "holds", or no production tree may be produced {since each attempt to produce one runs into blind alleys}, and then P "does not hold".
{For example, the predicate 'where (ab) is (ab)' holds. Its production tree may be depicted thus:
If a predicate holds, then its production tree always terminates via 'where true' or 'unless false'. If it does not hold, then, in general, the blind alleys are 'where false' and 'unless true'. Although almost all the hyper-rules concerned are for hypernotions beginning with "WHETHER" and so provide, each time, production rules for pairs of predicates such as 'where THING1' and 'unless THING1', this does not mean that in each such case one of the pair must hold. For example, 'where digit four counts iii' {4.3.1.c } does not hold, but no care has been taken to make 'unless digit four counts iii' hold either, since there is no application for it in this Report.
In the semantics, no meaning is ascribed to constructs whose originals are predicates. They serve purely syntactical purposes.}
1.3.3. Syntax of general constructions A) STYLE :: brief ; bold ; style TALLY.
a) NOTION option : NOTION ; EMPTY.
b) NOTION sequence{b} : NOTION ; NOTION, NOTION sequence{b}.
c) NOTION list{c} : NOTION ; NOTION, and also{94f } token, NOTION list{c}.
d) NOTETY STYLE pack : STYLE begin{94f ,-} token, NOTETY, STYLE end{94f ,-} token.
e) NOTION STYLE bracket : STYLE sub{94f ,-} token, NOTION, STYLE bus{94f ,-} token.
f) THING1 or alternatively THING2 : THING1 ; THING2. {It follows from this syntax that production rules such as
digit cypher sequence : digit cypher ; digit cypher, digit cypher sequence.(which was used in the production of the example in 1.1.3.2.f , but for which no more explicit hyper-rule is given) are immediately available. Thus the number of hyper-rules actually written in this Report has been reduced and those that remain have, hopefully, been made more readable, since these general constructions are so worded as to suggest what their productions should be.
For this reason, cross-references {1.1.3.4.f
} to
these rules have been replaced by more helpful references; e.g., in 8.1.1.1.b
,
instead of "digit cypher sequence{133b
} ", the
more helpful "digit cypher{c} sequence" is given. Likewise,
references within the general constructions themselves have been restricted
to a bare minimum.}
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