Intuitionistic type theory (also constructive type theory or Martin-Löf type theory) is a formal logical system and philosophical foundation for constructive mathematics. It is a full-scale system which aims to play a similar role for constructive mathematics as Zermelo-Fraenkel Set Theory does for classical mathematics. It is based on the propositions-as-types principle and clarifies the Brouwer-Heyting-Kolmogorov interpretation of intuitionistic logic. It extends this interpretation to the more general setting of intuitionistic type theory and thus provides a general conception not only of what a constructive proof is, but also of what a constructive mathematical object is. The main idea is that mathematical concepts such as elements, sets and functions are explained in terms of concepts from programming such as data structures, data types and programs. This article describes the formal system of intuitionistic type theory and its semantic foundations.

Per Erik Rutger Martin-Löf (born 8 May 1942) is a Swedish logician, philosopher, and mathematical statistician. He is internationally renowned for his work on the foundations of probability, statistics, mathematical logic, and computer science. Since the late 1970s, Martin-Löf's publications have been mainly in logic. In philosophical logic, Martin-Löf has wrestled with the philosophy of logical consequence and judgment, partly inspired by the work of Brentano, Frege, and Husserl. In mathematical logic, Martin-Löf has been active in developing intuitionistic type theory as a constructive foundation of mathematics; Martin-Löf's work on type theory has influenced computer science.

Until his retirement in 2009,[4] Per Martin-Löf held a joint chair for Mathematics and Philosophy at Stockholm University.

His brother Anders Martin-Löf is now emeritus professor of mathematical statistics at Stockholm University; the two brothers have collaborated in research in probability and statistics. The research of Anders and Per Martin-Löf has influenced statistical theory, especially concerning exponential families, the expectation-maximization method for missing data, and model selection.

Per Martin-Löf is an enthusiastic bird-watcher; his first scientific publication was on the mortality rates of ringed birds.