Changes

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For brevity in the present case, and to serve as a generic device in any similar array of situations, let <math>S\!</math> be the type of an arbitrary sentence, possibly empty, and let <math>S'\!</math> be the type of a specifically non-empty sentence.  In addition, let <math>\underline\varepsilon</math> be the type of the empty sentence, in effect, the language

For brevity in the present case, and to serve as a generic device

<math>\underline\varepsilon = \{ \varepsilon \}</math> that contains a single empty string, and let a plus sign "+" signify a disjoint union of types.  In the most general type of situation, where the type <math>S\!</math> is permitted to include the empty string, one notes the following relation among types:

in any similar array of situations, let the symbol "S" be used to

signify the type of an arbitrary sentence, possibly empty, whereas

the symbol "S'" is reserved to designate the type of a specifically

non-empty sentence.  In addition, let the symbol "%e%" be employed

to indicate the type of the empty sentence, in effect, the language

%e% = {""} that contains a single empty string, and let a plus sign

"+" signify a disjoint union of types.  In the most general type of

situation, where the type S is permitted to include the empty string,

one notes the following relation among types:

S = %e%  + S'.

| <math>S \ = \ \underline\varepsilon \ + \ S'</math>

Consequences of the distinction between empty expressions and

Consequences of the distinction between empty expressions and significant expressions are taken up for discussion next time.

significant expressions are taken up for discussion next time.

With the distinction between empty and significant expressions in mind,

With the distinction between empty and significant expressions in mind,

I return to the grasp of the cactus language !L! = !C!(!P!) = PARCE(!P!)

I return to the grasp of the cactus language !L! = !C!(!P!) = PARCE(!P!)