Restructure and begin displaying lambdas

src/Props/Lambda.hs

@@ -1,23 +0,0 @@
-{-# LANGUAGE OverloadedStrings #-}
-
-module Props.Lambda
-  ( Term(..)
-  , displayTerm
-  ) where
-
-import qualified Data.Set  as Set
-import qualified Data.Text as T
-
-type Name = T.Text
-type PreferredName = Maybe Name
-
--- | Lambda calculus term using De Bruijn indexing
-data Term a
-  = Var PreferredName Int
-  | Lambda PreferredName (Term a)
-  | App (Term a) (Term a)
-  | Native a
-  deriving (Show)
-
-displayTerm :: (Set.Set Name -> a -> T.Text) -> Term a -> T.Text
-displayTerm = undefined

src/Props/Lambda/Display.hs

@@ -0,0 +1,31 @@
+module Props.Lambda.Display
+  ( displayTerm
+  ) where
+
+import qualified Data.Text         as T
+
+import           Props.Lambda.Term
+
+type Name = T.Text
+
+varNames :: [Name]
+varNames = chars ++ (mappend <$> constNames <*> chars)
+  where
+    chars = map T.singleton ['a'..'z']
+
+constNames :: [Name]
+constNames = chars ++ (mappend <$> constNames <*> chars)
+  where
+    chars = map T.singleton ['A'..'Z']
+
+findConstNames :: Term e (Maybe Name) v -> Term e Name v
+findConstNames = undefined
+
+makeVarNamesUnique :: Term e c (Maybe Name) -> Term e c (Maybe Name)
+makeVarNamesUnique = undefined
+
+findVarNames :: Term e c (Maybe Name) -> Term e c Name
+findVarNames = undefined
+
+displayTerm :: (e -> T.Text) -> Term e (Maybe Name) (Maybe Name) -> T.Text
+displayTerm = undefined

src/Props/Lambda/Term.hs

@@ -0,0 +1,33 @@
+module Props.Lambda.Term
+  ( Term(..)
+  , vars
+  , consts
+  ) where
+
+import           Numeric.Natural
+
+-- | Lambda calculus term using De Bruijn indexing and expanded to deal with
+-- naming complexity and extensions.
+data Term e c v
+  = Var Natural
+  -- ^ Variable using a De Bruijn index
+  | Const c
+  -- ^ Constant living outside the variable namespace
+  | Lambda v (Term e c v)
+  -- ^ Lambda definition
+  | App (Term e c v) (Term e c v)
+  -- ^ Lambda application
+  | Ext e
+  -- ^ Term extension (set @e@ to 'Void' if you don't need this)
+  deriving (Show)
+
+vars :: Term e c v -> [v]
+vars (Lambda v t) = v : vars t
+vars (App l r)    = vars l <> vars r
+vars _            = []
+
+consts :: Term e c v -> [c]
+consts (Const c)    = [c]
+consts (Lambda _ t) = consts t
+consts (App l r)    = consts l <> consts r
+consts _            = []