Pattern

A pattern is a function that maps a list of words into another list of words, usually performing some mutation on letter on a word-by-word basis.

Patterns can most easily be described as a series of word cases to transfer the input into. Below is a list of common patterns and how they could be defined from word cases.

pattern name	series	example
lower	lower, lower, …	my word list
upper	upper, upper, …	MY WORD LIST
capitalized	capitalized, capitalized, …	My Word List
sentence	capitalized, lower, lower, …	My word list
camel	lower, capitalized, capitalized, …	my Word List

Broadly speaking, a pattern is just a function, and doesn’t need to follow word cases, and could be dependent on the number of words, for instance. However, it is a requirement that the newly mapped space contain the same number of words.

Let $W_n$ be the space of lists of words that are of length $n$. Then a pattern can defined as

$$pattern: W_n \rightarrow W_n$$