Cactus Language • Mechanics 4

To develop a parser for cactus languages in a functional programming style takes a way to express the description of a PARC in terms of its nodes, by recursion from the root up. That requires each node to be specified by a functional expression, having a call of the generic function name $``\mathrm{Node}"$ be followed by a list of arguments naming the attachments of the node in question and having a call of the generic function name $``\mathrm{Lobe}"$ be followed by a list of arguments naming the appendants of the lobe in question. Thus one writes expressions of the following forms.

Working from a structural description of the cactus language, or any suitable formal grammar for $\mathfrak{C} (\mathfrak{P}),$ it is possible to give a recursive definition of a function called $``\mathrm{Parse}"$ which maps each expression in $\textsc{parce} (\mathfrak{P})$ to the corresponding graph in $\textsc{parc} (\mathfrak{P}).$ One way to do that proceeds as follows.

The Concatenation $\mathrm{Conc}_{j=1}^k$ of the $k$ sentences $(s_j)_{j=1}^k$ has a Parse defined as follows.

$\mathrm{Parse} (\mathrm{Conc}^0) ~=~ \mathrm{Node}^0.$
For $k > 0,$
$\mathrm{Parse} (\mathrm{Conc}_{j=1}^k s_j) ~=~ \mathrm{Node}_{j=1}^k \mathrm{Parse} (s_j).$

The Surcatenation $\mathrm{Surc}_{j=1}^k$ of the $k$ sentences $(s_j)_{j=1}^k$ has a Parse defined as follows.

$\mathrm{Parse} (\mathrm{Surc}^0) ~=~ \mathrm{Lobe}^0.$
For $k > 0,$
$\mathrm{Parse} (\mathrm{Surc}_{j=1}^k s_j) ~=~ \mathrm{Lobe}_{j=1}^k \mathrm{Parse} (s_j).$

Resources

cc: Academia.edu • BlueSky • Laws of Form • Ma^thstodon • Research Gate
cc: Conceptual Graphs • Cybernetics • Structural Modeling • Systems Science

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