ence card): -- \Pi-types, -abstraction and applications: fx:AgB, A-?B, [x:A]b, (f a). -- Inductive types: macro Inductive with options such as Theorems, Relation, Inversion, Double, etc. For example (also see examples like the less-than relation in exercises): Inductive [List : Type] Theorems Parameters [A : Type] Constructors [nil : List] [cons : A-?List-?List]; Lecture notes for Types Summer School'99: Theory and Practice of Formal Proofs, Giens, France, 1999. 1 -- Predicative universes (with `typical ambiguity'): Type(i), Type. -- Logical universe (impredicative, giving HOL): Prop. -- Local definitions: [x=a]b. -- Argument synthesis: fx---A