Well-formed syntax

• Preface
• Parsing input (SLR parser)
• Parser F# code
• Well-formed syntax
• Semantics of propositional logic
• Constructing tables
• The application

A well formed formula is closely related to the CFG (Context Free Grammar) used in the former chapter. To check whether a formula is well formed, we recursively apply these rules

• ¬: If φ is well-formed, so is ¬φ
• ∧: If φ and ψ are well-formed, so is (φ ∧ ψ).
• ∨: If φ and ψ are well-formed, so is (φ ∨ ψ).
• ⇒: If φ and ψ are well-formed, so is (φ ⇒ ψ).
• ⇔: If φ and ψ are well-formed, so is (φ ⇔ ψ).

Nothing else is a well-formed formula.

To put this into context: if our parser does not return an error, we can brag about how well-formed our input formula is :-).