Cactus Language • Preliminaries 6

Posted on April 16, 2025 by Jon Awbrey

The definitions of the syntactic connectives can be made a little more succinct by defining the following pair of generic operators on strings.

Concatenation

The concatenation \mathrm{Conc}_{k=1}^n of the sequence of n strings (s_k)_{k=1}^n is defined recursively as follows.

\text{For}~ n = 1, ~\mathrm{Conc}_{k=1}^n s_k = s_1.

\text{For}~ n > 1, ~\mathrm{Conc}_{k=1}^n s_k = \mathrm{Conc}_{k=1}^{n-1} s_k \cdot s_n.

Surcatenation

The surcatenation \mathrm{Surc}_{k=1}^n of the sequence of n strings (s_k)_{k=1}^n is defined recursively as follows.

\text{For}~ n = 1, ~\mathrm{Surc}_{k=1}^n s_k = ``\text{(}" \cdot s_1 \cdot ``\text{)}".

\text{For}~ n > 1, ~\mathrm{Surc}_{k=1}^n s_k = \mathrm{Surc}_{k=1}^{n-1} s_k \cdot (``\text{)}")^{-1} \cdot ``\text{,}" \cdot s_n \cdot ``\text{)}".

Resources

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

This entry was posted in Automata, Boolean Algebra, Boolean Functions, C.S. Peirce, Cactus Graphs, Differential Logic, Equational Inference, Formal Grammars, Formal Languages, Graph Theory, Logic, Logical Graphs, Mathematics, Minimal Negation Operators, Painted Cacti, Propositional Calculus, Visualization and tagged , , , , , , , , , , , , , , , , . Bookmark the permalink.

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