# Abstract Binding Trees

Hakaru makes use of many program transformations in its codebase. Because of this, a special mechanism is included for handing variable bindings and substitutions. We abstract this into its own typeclass called ABT. This can be found in Language.Hakaru.Syntax.ABT.

Below is an excerpt of this typeclass

class ABT (syn :: ([k] -> k -> *) -> k -> *) (abt :: [k] -> k -> *) | abt -> syn where
-- Smart constructors for building a 'View' and then injecting it into the @abt@.
syn  :: syn abt  a -> abt '[] a
var  :: Variable a -> abt '[] a
bind :: Variable a -> abt xs b -> abt (a ': xs) b
caseBind :: abt (x ': xs) a -> (Variable x -> abt xs a -> r) -> r
...


The advantage of having this typeclass is that we think about variable binding independently of the AST for our language. For example, we can define variable substitution once and for all.