Well-formed formula

A well-formed formula is an expression built according to the formation rules of a formal language. Its structure makes it a valid expression in that language, though it need not be true or meaningful.

Formal language: A set of finite strings defined over an alphabet, often by explicit formation rules. A well-formed formula is a valid string in a particular formal language.
Inductive definition: A definition that specifies base cases and rules for constructing further members. Formula grammars commonly define well-formedness through base cases and recursive construction rules.
Ill-formed formula: An expression that violates the formation rules of a formal language. It is the direct syntactic opposite of a well-formed formula.
Type system: A set of rules assigning types to program expressions and restricting how they may be used. Type checking extends syntactic acceptance with constraints on expression use.
Alphabet: A finite or specified set of symbols from which strings in a formal language are built. Formula formation starts with the language’s permitted symbols.
Propositional formula: An expression formed from propositional variables and logical connectives according to formal syntax. Its formation rules provide a clear example of building formulas recursively.
Logical validity: A property of a sentence that is true under every interpretation in a specified logic. Validity concerns truth across interpretations, not whether the sentence is syntactically formed.
Compiler: A program that translates source code into another representation, often checking its syntax along the way. Compilers reject source expressions that fail the language’s grammar.
Syntax: Rules governing how symbols combine into valid expressions in a language. Formation rules are the syntactic rules that determine which expressions count as formulas.
First-order formula: A syntactically valid expression built from predicates, terms, quantifiers, variables, and logical connectives. Quantifier scope and variable binding add further formation constraints beyond propositional syntax.

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