A formal language is a set of strings of symbols that are constrained by specific grammatical rules, often used in fields like computer science, linguistics, and mathematics to precisely define computational or logical processes. It serves as the foundation for programming languages, automata theory, and formal verification, enabling the rigorous specification and analysis of algorithms and systems.
A derivation tree, also known as a parse tree, is a graphical representation that illustrates the syntactic structure of a string according to a formal grammar. It is used in computer science to visualize how a string can be generated by applying the production rules of a context-free grammar, showing the hierarchy and order of rule applications.
A nonterminal symbol is a fundamental component of a formal grammar used in computational linguistics and programming languages, representing a set of possible strings that can be generated. It acts as an intermediary step in the production rules, allowing for the recursive generation of complex structures from simpler components.
In formal grammar, a non-terminal is a symbol used to represent a set of strings and can be replaced by other symbols according to production rules. They are essential for defining the structure of a language, as they help in generating strings of a language by recursively applying these rules until only terminal symbols remain.
A programming language grammar is like a set of rules that tells computers how to understand the instructions we give them. It's similar to how we learn grammar rules in school to make sentences that others can read and understand.