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  "body": "\n## Summary\n\nIntuitionistic type theory is the dependent [[type theory|Q48KGV33AH]] introduced by Per Martin-Löf from the 1970s on, also called Martin-Löf type theory.\nIt is a foundation of constructive mathematics based on [[intuitionistic logic|Q11N8X99FK]].\nThrough the [[Curry–Howard correspondence|A77FER1Q5H]], its types are also propositions, and its terms are both proofs and programs.\nIt is the basis of proof assistants such as Agda, and it is close to the systems behind Coq and Lean.\n\n## Explanations\n\n### L1 human\n\nIn this theory, a statement is a type, and a proof of the statement is an element of that type.\nTypes can depend on numbers or other data, as in \"lists of length $n$\".\nA proof of \"for every $n$ there is $m$ with $P(n, m)$\" is a function that sends each $n$ to a pair: a number $m$ and a proof of $P(n, m)$.\nSo every proof of existence is also a program that computes the witness.\nChecking a proof is the same as checking that a program has the right type.\n",
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