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Martin-Löf's type theory contains a logic, a specification language and a programming language, so it is a tool with different uses. Although it is traditionally used as anintegrated programming logic, it may well be used as anexternal logic, which is necessary if one wants to use the formalism of type theory to verify the correctness of an external program. Different tools, such as well founded recursion, measure functions, or the separation of correctness into termination and partial correctness, may be used to obtain a correct type theory program. Type theory is viewed as anopen system with respect toinductively defined types and predicates, which makes it easy to represent an external program as agraph. Formal proofs have been edited using Larry Paulson's ISABELLE.

Normalising the associative law: An experiment with Martin-L�f's type theory