What I had in mind is proof search.

Given a type, which represents a theorem, synthesizing an argument
of the type is like searching a proof for the theorem. Sometimes, a theorem
has only one (natural) proof. In such a case, there is no ambiguity as to 
which
proof should be used: There is only one.

On Friday, March 9, 2018 at 5:00:46 AM UTC-5, Brandon Barker wrote:
>
> My (likely incorrect) understanding from theory is that type families are 
> required for dependent types, or are even synonymous with dependent types. 
> When you said " the ability to synthesize an argument according to the type
> of the argument", it sounds like a type family. And ATS has support for 
> dependent types, but maybe it is too restricted for this?

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