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Directory:Jon Awbrey/Papers/Cactus Language (view source)
Revision as of 17:12, 7 January 2009
, 17:12, 7 January 2009→Grammar 4: style mods
===Grammar 4===
===Grammar 4===
If one imposes the distinction between empty and significant types on each non-terminal symbol in Grammar 2, then the non-terminal symbols <math>^{\backprime\backprime} S ^{\prime\prime}</math> and <math>^{\backprime\backprime} T ^{\prime\prime}</math> give rise to the expanded set of non-terminal symbols <math>^{\backprime\backprime} S ^{\prime\prime}, \, ^{\backprime\backprime} \, S' \, ^{\prime\prime}, \, ^{\backprime\backprime} T ^{\prime\prime}, \, ^{\backprime\backprime} \, T' \, ^{\prime\prime},</math> leaving the last three of these to form the new intermediate alphabet. Grammar 4 has the intermediate alphabet <math>\mathfrak{Q} \, = \, \{ \, ^{\backprime\backprime} \, S' \, ^{\prime\prime}, \, ^{\backprime\backprime} T ^{\prime\prime}, \, ^{\backprime\backprime} \, T' \, ^{\prime\prime} \, \},</math> with the set <math>\mathfrak{K}</math> of covering rules as listed in the next display.
If one imposes the distinction between empty and significant types on each non-terminal symbol in Grammar 2, then the non-terminal symbols <math>^{\backprime\backprime} S ^{\prime\prime}</math> and <math>^{\backprime\backprime} T ^{\prime\prime}</math> give rise to the expanded set of non-terminal symbols <math>^{\backprime\backprime} S ^{\prime\prime}, \, ^{\backprime\backprime} \, S' \, ^{\prime\prime}, \, ^{\backprime\backprime} T ^{\prime\prime}, \, ^{\backprime\backprime} \, T' \, ^{\prime\prime},</math> leaving the last three of these to form the new intermediate alphabet. Grammar 4 has the intermediate alphabet <math>\mathfrak{Q} \, = \, \{ \, ^{\backprime\backprime} \, S' \, ^{\prime\prime}, \, ^{\backprime\backprime} \, T \, ^{\prime\prime}, \, ^{\backprime\backprime} \, T' \, ^{\prime\prime} \, \},</math> with the set <math>\mathfrak{K}</math> of covering rules as listed in the next display.
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