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Directory:Jon Awbrey/Papers/Cactus Language (view source)
Revision as of 19:35, 10 January 2009
, 19:35, 10 January 2009→The Cactus Language : Stylistics: markup
The <math>j^\text{th}\!</math> ''excerpt'' of a stricture of the form <math>^{\backprime\backprime} \, S_1 \times \ldots \times S_k \, ^{\prime\prime},</math> regarded within a frame of discussion where the number of places is limited to <math>k,\!</math> is the stricture of the form <math>^{\backprime\backprime} \, X \times \ldots \times S_j \times \ldots \times X \, ^{\prime\prime}.</math> In the proper context, this can be written more succinctly as the stricture <math>^{\backprime\backprime} \, (S_j)_{[j]} \, ^{\prime\prime},</math> an assertion that places the <math>j^\text{th}\!</math> set in the <math>j^\text{th}\!</math> place of the product.
The <math>j^\text{th}\!</math> ''excerpt'' of a stricture of the form <math>^{\backprime\backprime} \, S_1 \times \ldots \times S_k \, ^{\prime\prime},</math> regarded within a frame of discussion where the number of places is limited to <math>k,\!</math> is the stricture of the form <math>^{\backprime\backprime} \, X \times \ldots \times S_j \times \ldots \times X \, ^{\prime\prime}.</math> In the proper context, this can be written more succinctly as the stricture <math>^{\backprime\backprime} \, (S_j)_{[j]} \, ^{\prime\prime},</math> an assertion that places the <math>j^\text{th}\!</math> set in the <math>j^\text{th}\!</math> place of the product.
The <math>j^\text{th}\!</math> ''extract'' of a strait of the form <math>S_1 \times \ldots \times S_k,\!</math> constrained to a frame of discussion where the number of places is restricted to <math>k,\!</math> is the strait of the form <math>X \times \ldots \times S_j \times \ldots \times X.</math> In the appropriate context, this can be denoted more succinctly by the stricture <math>^{\backprime\backprime} \, (S_j)_{[j]} \, ^{\prime\prime},</math> an assertion that places the <math>j^\text{th}\!</math> set in the <math>j^\text{th}\!</math> place of the product.
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In these terms, a stricture of the form "S_1 x ... x S_k"
In these terms, a stricture of the form "S_1 x ... x S_k"
can be expressed in terms of simpler strictures, to wit,
can be expressed in terms of simpler strictures, to wit,