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This is just the surcatenation of the sentences <math>S_1, \ldots, S_k.\!</math>  Given the possibility that this sequence of sentences is empty, and thus that the tract <math>T\!</math> is the empty string, the minimum foil <math>F\!</math> is the expression <math>^{\backprime\backprime} \, \operatorname{()} \, ^{\prime\prime}.</math> Explicitly marking each foil <math>F\!</math> that is embodied in a cactus expression is tantamount to recognizing another intermediate symbol, <math>^{\backprime\backprime} F ^{\prime\prime} \in \mathfrak{Q},</math> further articulating the structures of sentences and expanding the grammar for the language

This is just the surcatenation of the sentences S_1, ..., S_k.

<math>\mathfrak{C} (\mathfrak{P}).</math> All of the same remarks about the versatile uses of the intermediate symbols, as string variables and as type names, apply again to the letter <math>^{\backprime\backprime} F ^{\prime\prime}.</math>

Given the possibility that this sequence of sentences is empty,

and thus that the tract T is the empty string, the minimum foil

F is the expression "-()-".  Explicitly marking each foil F that

is embodied in a cactus expression is tantamount to recognizing

another intermediate symbol, "F" in !Q!, further articulating the

structures of sentences and expanding the grammar for the language

!C!(!P!).  All of the same remarks about the versatile uses of the

intermediate symbols, as string variables and as type names, apply

again to the letter "F".

</pre>

===Grammar 3===

===Grammar 3===