Since the time of Noam Chomsky's introduction of phrase structure grammars in 1956-1957, it has been known that formal methods can be applied to the parsing of an infinite variety of input. In practice, however, grammars of sufficient formal power to generate context-sensitive languages in their various forms have lacked efficient generalizable algorithms, or have been of such cumbersome notation and implementation that practitioners in various fields that could otherwise greatly benefit from applied language theory have been shackled to much less powerful underlying parsing engines. The §-Calculus (pronounced: meta-ess calculus), an adaptive grammar formalism, and the corresponding adaptive(k) parsing algorithm are shown to have theoretical and practical utility in the fields of classical formal language, combinatorics, computational linguistics, bioinformatics, data mining, and programming language semantics, making tractable many previously difficult to parse languages. This is demonstrated by first building a formal foundation around the septuple of the §-Calculus, and then introducing the predicated pushdown automaton augmented with name-indexed tries (PDA-Ts), a new computational machine built upon the classical single stack PDA. After the formal model is established, implementation issues and their time complexity are examined in terms of optimizations used in practice to reduce time complexity. After this framework is established, each of the areas benefited by the §-Calculus and its corresponding automata and algorithms is examined in turn using empirical methods.