Programming in Martin-Lo¨f's type theory: an introduction

Part 1 Polymorphic sets: the semantics of the judgement forms general rules enumeration sets Cartesian product of a family of sets equality sets natural numbers lists cartesian product of two sets disjoint union of two sets disjoint union of a family of sets the set of small sets (the first universe) well-orderings general trees. Part 2 Subsets: subsets in the basic set theory the subset theory. Part 3 Monomorphic sets: types defining sets in terms of types. Part 4 Examples: some small examples program derivation specification of abstract data types.

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