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diff --git a/content/zettel/3b3b.md b/content/zettel/3b3b.md new file mode 100644 index 0000000..63e06ee --- /dev/null +++ b/content/zettel/3b3b.md @@ -0,0 +1,19 @@ ++++ +title = "Reflexive Types" +author = "Yann Herklotz" +tags = [] +categories = [] +backlinks = ["3b3a"] +forwardlinks = ["3b3c"] +zettelid = "3b3b" ++++ + +Reflexive types are of the nature of taking an argument which is a +function and returning the Inductive type. Some of these are not legal +in Coq, even though they would be legal in Haskell/ML, as they might +produce computations that run forever. This would destroy all the +confidence that one could have in the proof system, as that would mean +that one could produce a proof for any theorem using an infinite loop. +This can be done because proofs are combined with functions. For +example, a reflexive type that takes the type it defines as an argument +could recurse indefinitely, which should not be allowed to be defined. |