Brief Notes on the Category Theoretic Semantics of Simply Typed Lambda Calculus

When presenting logical systems and type theories, it is common to write finite lists of things using a comma to indicate the cons-operation and with the head of the list at the right. With this convention there is no common notation for the empty list; we will use the symbol “ ”. Thus ML-style list notation nil a :: nil b :: a :: nil etc becomes , a , a, b etc For non-empty lists, it is very common to leave the initial part “ ,” of the above notation implicit, for example just writing a, b instead of , a, b. Write X∗ for the set of such finite lists with elements from the set X.