Intuitionistic type theory (also known as constructive type theory, or Martin-Löf type theory) is a type theory and an alternative foundation of mathematics based on the principles of mathematical constructivism. Intuitionistic type theory was introduced by Per Martin-Löf, a Swedish mathematician and philosopher, in 1972. Martin-Löf has modified his proposal a few times; his 1971 impredicative formulation was inconsistent as demonstrated by Girard's paradox. Later formulations were predicative. He proposed both intensional and extensional variants of the theory. For more detail see the section on Martin-Löf type theories below.