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Well-formed syntax

18.05.2018

Contents/Index

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 :-).

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