[Agda] subset types? refinement types? type synonyms? type abbreviations?

[Andreas Abel]

Hello Ramana,

> Also, I am indexing terms by whether or not they are a variable (as
> well as by their type); I use that information for the Abs
> constructor.

I would not do it like that.  Rather have a separate type of variables,

   data Var : Type -> Set

and then

   data Term : Type -> Set where
     var : {t : Type} -> Var t -> Term t
     ...
     abs : {t u : Type} -> Var t -> Term u -> Term (t => u)

Or even better, use some flavor of nameless term representation.  You 
see a lot of approaches advertized in the later messages of the threat 
"Associativity for free!".

> How can I define Formula?
 >
> Formula : Bool ->  Set
> Formula = Term bool

I am confused, didn't you just define Formula?  It is a Term of type 
bool, that's it.

Cheers,
Andreas

-- 
Andreas Abel  <><      Du bist der geliebte Mensch.

Theoretical Computer Science, University of Munich
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