On Thu, Apr 2, 2015 at 9:50 AM, Keean Schupke <[email protected]> wrote:
> On 2 April 2015 at 14:25, Matt Oliveri <[email protected]> wrote:
>> You seem to be under the hilarious misimpression that everything in
>> MLTT is a type. It ain't so! Ask any proof assistant: "fun (x : 4) =>
>> x" is nonsense.
>
> There is nothing fundamentally wrong with that statement, I could write;
>
> fun (x : succ (succ (succ (succ zero)))) => x
>
> So I could allow "4" so be a shorthand for succ (succ (succ (succ zero)))
> and then hide the succ/zero types inside a module.

No no no. 4 _is_ a shorthand for that. (Modulo constructor names.)
(succ (succ (succ (succ zero)))) isn't a type.
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