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Combining the singleton set <math>\{ S \}\!</math> whose sole member is the initial symbol with the set <math>\mathfrak{Q}</math> that assembles together all of the intermediate symbols results in the set <math>\{ S \} \cup \mathfrak{Q}</math> of ''non-terminal symbols''. Completing the package, the alphabet <math>\mathfrak{A}</math> of the language is also known as the set of ''terminal symbols''. In this discussion, I will adopt the convention that <math>\mathfrak{Q}</math> is the set of ''intermediate symbols'', but I will often use <math>q\!</math> as a typical variable that ranges over all of the non-terminal symbols, <math>q \in \{ S \} \cup \mathfrak{Q}.</math> Finally, it is convenient to refer to all of the symbols in <math>\{ S \} \cup \mathfrak{Q} \cup \mathfrak{A}</math> as the ''augmented alphabet'' of the prospective grammar for the language, and accordingly to describe the strings in <math>( \{ S \} \cup \mathfrak{Q} \cup \mathfrak{A} )^*</math> as the ''augmented strings'', in effect, expressing the forms that are superimposed on a language by one of its conceivable grammars. In certain settings is becomes desirable to separate the augmented strings that contain the symbol <math>S\!</math> from all other sorts of augmented strings. In these situations, the strings in the disjoint union <math>\{ S \} \cup (\mathfrak{Q} \cup \mathfrak{A} )^*</math> are known as the ''sentential forms'' of the associated grammar.
Combining the singleton set <math>\{ S \}\!</math> whose sole member is the initial symbol with the set <math>\mathfrak{Q}</math> that assembles together all of the intermediate symbols results in the set <math>\{ S \} \cup \mathfrak{Q}</math> of ''non-terminal symbols''. Completing the package, the alphabet <math>\mathfrak{A}</math> of the language is also known as the set of ''terminal symbols''. In this discussion, I will adopt the convention that <math>\mathfrak{Q}</math> is the set of ''intermediate symbols'', but I will often use <math>q\!</math> as a typical variable that ranges over all of the non-terminal symbols, <math>q \in \{ S \} \cup \mathfrak{Q}.</math> Finally, it is convenient to refer to all of the symbols in <math>\{ S \} \cup \mathfrak{Q} \cup \mathfrak{A}</math> as the ''augmented alphabet'' of the prospective grammar for the language, and accordingly to describe the strings in <math>( \{ S \} \cup \mathfrak{Q} \cup \mathfrak{A} )^*</math> as the ''augmented strings'', in effect, expressing the forms that are superimposed on a language by one of its conceivable grammars. In certain settings is becomes desirable to separate the augmented strings that contain the symbol <math>S\!</math> from all other sorts of augmented strings. In these situations, the strings in the disjoint union <math>\{ S \} \cup (\mathfrak{Q} \cup \mathfrak{A} )^*</math> are known as the ''sentential forms'' of the associated grammar.
In forming a grammar for a language statements of the form <math>W :> W',\!</math>
where <math>W\!</math> and <math>W'\!</math> are augmented strings or sentential forms of specified types that depend on the style of the grammar that is being sought, are variously known as ''characterizations'', ''covering rules'', ''productions'', ''rewrite rules'', ''subsumptions'', ''transformations'', or ''typing rules''. These are collected together into a set <math>\mathfrak{K}</math> that serves to complete the definition of the formal grammar in question.
<pre>
<pre>
Correlative with the use of this notation, an expression of the
Correlative with the use of this notation, an expression of the
form "T <: S", read as "T is covered by S", can be interpreted
form "T <: S", read as "T is covered by S", can be interpreted
