module Quox.Syntax.Term.Split

import Quox.Syntax.Term.Base
import Quox.Syntax.Term.Subst

import Data.So
import Data.Vect

%default total


public export
data IsLam : Term {} -> Type where
  ItIsLam : IsLam $ Lam x body

public export %inline
isLam : (s : Term {}) -> Dec (IsLam s)
isLam (TYPE _)   = No $ \case _ impossible
isLam (Pi {})    = No $ \case _ impossible
isLam (Lam {})   = Yes ItIsLam
isLam (E _)      = No $ \case _ impossible
isLam (CloT {})  = No $ \case _ impossible
isLam (DCloT {}) = No $ \case _ impossible

public export %inline
NotLam : Term {} -> Type
NotLam = Not . IsLam


public export
data IsApp : Elim {} -> Type where
  ItIsApp : IsApp $ f :@ s

public export %inline
isApp : (e : Elim {}) -> Dec (IsApp e)
isApp (F _)      = No $ \case _ impossible
isApp (B _)      = No $ \case _ impossible
isApp (_ :@ _)   = Yes ItIsApp
isApp (_ :# _)   = No $ \case _ impossible
isApp (CloE {})  = No $ \case _ impossible
isApp (DCloE {}) = No $ \case _ impossible

public export
NotApp : Elim {} -> Type
NotApp = Not . IsApp


infixl 9 :@@
||| apply multiple arguments at once
public export %inline
(:@@) : Elim q d n -> List (Term q d n) -> Elim q d n
f :@@ ss = foldl (:@) f ss

public export
record GetArgs q d n where
  constructor GotArgs
  fun      : Elim q d n
  args     : List (Term q d n)
  0 notApp : NotApp fun

export
getArgs' : Elim q d n -> List (Term q d n) -> GetArgs q d n
getArgs' fun args with (isApp fun)
  getArgs' (f :@ a) args | Yes yes = getArgs' f (a :: args)
  getArgs' fun args      | No  no  = GotArgs {fun, args, notApp = no}

||| splits an application into its head and arguments. if it's not an
||| application then the list is just empty
export %inline
getArgs : Elim q d n -> GetArgs q d n
getArgs e = getArgs' e []


infixr 1 :\\
public export
absN : Vect m Name -> Term q d (m + n) -> Term q d n
absN {m = 0}   []        s = s
absN {m = S m} (x :: xs) s = Lam x $ TUsed $ absN xs $
                             rewrite sym $ plusSuccRightSucc m n in s

public export %inline
(:\\) : Vect m Name -> Term q d (m + n) -> Term q d n
(:\\) = absN


public export
record GetLams q d n where
  constructor GotLams
  names    : Vect lams Name
  body     : Term q d rest
  0 eq     : lams + n = rest
  0 notLam : NotLam body

export
getLams' : forall lams, rest.
           Vect lams Name -> Term q d rest -> lams + n = rest -> GetLams q d n
getLams' xs s eq with (isLam s)
  getLams' xs (Lam x sbody) Refl | Yes ItIsLam =
    let 0 s  = Lam x sbody
        body = assert_smaller s $ fromScopeTerm sbody
    in
    getLams' (x :: xs) body Refl
  getLams' xs s eq | No no =
    GotLams xs s eq no

export
getLams : Term q d n -> GetLams q d n
getLams s = getLams' [] s Refl