Typed propositional formulas

typed propositional formula To define typed propositional formulas, we need the notion of a type expression, a term, and a type context because formulas are built in a type context. Then we define propositional variables and propositional-function variables which are used along with terms to make atomic propositions in a context. From these we build compound formulas using the binary connectives $\&, \vee, \Rightarrow$, and the typed quantifiers $\forall x\!:\!A, \exists x\!:\!A$. We let op denote any binary connective and $Qx\!:\!A$ denote either of the quantifiers.