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| | || and <math>\operatorname{Surc}_{j=1}^k s_j</math> is a sentence. | | | || and <math>\operatorname{Surc}_{j=1}^k s_j</math> is a sentence. |
| |} | | |} |
| + | |
| + | As usual, saying that <math>s\!</math> is a sentence is just a conventional way of stating that the string <math>s\!</math> belongs to the relevant formal language <math>\mathfrak{L}.</math> An individual sentence of <math>\mathfrak{C} (\mathfrak{P}),</math> for any palette <math>\mathfrak{P},</math> is referred to as a ''painted and rooted cactus expression'' (PARCE) on the palette <math>\mathfrak{P},</math> or a ''cactus expression'', for short. Anticipating the forms that the parse graphs of these PARCE's will take, to be described in the next Subsection, the language <math>\mathfrak{L} = \mathfrak{C} (\mathfrak{P})</math> is also described as the set <math>\operatorname{PARCE} (\mathfrak{P})</math> of PARCE's on the palette <math>\mathfrak{P},</math> more generically, as the PARCE's that constitute the language <math>\operatorname{PARCE}.</math> |
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| <pre> | | <pre> |
− | As usual, saying that z is a sentence is just a conventional way of
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− | stating that the string z belongs to the relevant formal language !L!.
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− | An individual sentence of !C!(!P!), for any palette !P!, is referred to
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− | as a "painted and rooted cactus expression" (PARCE) on the palette !P!,
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− | or a "cactus expression", for short. Anticipating the forms that the
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− | parse graphs of these PARCE's will take, to be described in the next
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− | Subsection, the language !L! = !C!(!P!) is also described as the
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− | set PARCE(!P!) of PARCE's on the palette !P!, more generically,
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− | as the PARCE's that constitute the language PARCE.
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− |
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| A "bare" PARCE, a bit loosely referred to as a "bare cactus expression", | | A "bare" PARCE, a bit loosely referred to as a "bare cactus expression", |
| is a PARCE on the empty palette !P! = {}. A bare PARCE is a sentence | | is a PARCE on the empty palette !P! = {}. A bare PARCE is a sentence |