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Directory:Jon Awbrey/Papers/Cactus Language (view source)
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, 17:50, 2 January 2009→The Cactus Language : Syntax: markup
| || 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.
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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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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