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  "body": "\n## Summary\n\nThe Dialectica interpretation translates [[Heyting arithmetic|CK8ZQRN183]] into Gödel's system T.\nThis is a quantifier-free theory of computable functionals of finite type.\nGödel published it in 1958 in the journal Dialectica.\nEach formula becomes a formula of the form $\\exists x\\, \\forall y\\, A_D(x, y)$, and a proof yields a term of system T that gives the witness $x$.\nIt gives a relative consistency proof of arithmetic and is the main tool for extracting bounds from proofs.\n\n## Explanations\n\n### L1 human\n\nThe interpretation reads each statement as a game between two players.\nOne player chooses $x$, the other answers with $y$, and the first wins if the simple condition $A_D(x, y)$ holds.\nA proof of the statement gives a winning strategy, written as a program built from [[primitive recursion|5NVA2JRHPV]] in higher types.\nFor example, a proof of $\\forall n\\, \\exists m\\, (m \u003e n)$ yields the program $n \\mapsto n + 1$.\nIn this way, numbers and bounds can be read off from proofs.\n",
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