module Quox.Typing

import public Quox.Typing.Context as Typing
import public Quox.Typing.EqMode as Typing
import public Quox.Typing.Error as Typing

import public Quox.Syntax
import public Quox.Definition
import public Quox.Reduce

%default total


namespace TContext
  export %inline
  pushD : TContext q d n -> TContext q (S d) n
  pushD tel = map (// shift 1) tel

  export %inline
  zeroFor : IsQty q => Context tm n -> QOutput q n
  zeroFor ctx = zero <$ ctx

namespace TyContext
  public export %inline
  empty : {d : Nat} -> TyContext q d 0
  empty = MkTyContext {dctx = new, tctx = [<]}

  export %inline
  extendTyN : Telescope (Term q d) from to ->
              TyContext q d from -> TyContext q d to
  extendTyN ss = {tctx $= (. ss)}

  export %inline
  extendTy : Term q d n -> TyContext q d n -> TyContext q d (S n)
  extendTy s = extendTyN [< s]

  export %inline
  extendDim : TyContext q d n -> TyContext q (S d) n
  extendDim = {dctx $= (:<? Nothing), tctx $= pushD}

  export %inline
  eqDim : Dim d -> Dim d -> TyContext q d n -> TyContext q d n
  eqDim p q = {dctx $= set p q}


namespace QOutput
  parameters {auto _ : IsQty q}
    export %inline
    (+) : QOutput q n -> QOutput q n -> QOutput q n
    (+) = zipWith (+)

    export %inline
    (*) : q -> QOutput q n -> QOutput q n
    (*) pi = map (pi *)

    export %inline
    zeroFor : TyContext q _ n -> QOutput q n
    zeroFor ctx = zeroFor ctx.tctx


public export
CheckResult' : Type -> Nat -> Type
CheckResult' = QOutput

public export
CheckResult : DimEq d -> Type -> Nat -> Type
CheckResult eqs q n = IfConsistent eqs $ CheckResult' q n

public export
record InferResult' q d n where
  constructor InfRes
  type : Term q d n
  qout : QOutput q n

public export
InferResult : DimEq d -> TermLike
InferResult eqs q d n = IfConsistent eqs $ InferResult' q d n


export
lookupFree' : HasErr q m => Definitions' q g -> Name -> m (Definition' q g)
lookupFree' defs x =
  case lookup x defs of
    Just d  => pure d
    Nothing => throwError $ NotInScope x


public export
substCasePairRet : Term q d n -> ScopeTerm q d n -> Term q d (2 + n)
substCasePairRet dty retty =
  let arg = Pair (BVT 0) (BVT 1) :# (dty // fromNat 2) in
  retty.term // (arg ::: shift 2)


parameters {auto _ : HasErr q m} (defs : Definitions' q _)
  export covering %inline
  whnfT : {0 isRedex : RedexTest tm} -> Whnf tm isRedex WhnfError =>
          tm q d n -> m (NonRedex tm q d n defs)
  whnfT = either (throwError . WhnfError) pure . whnf defs

  export covering %inline
  expectTYPE : Term q d n -> m Universe
  expectTYPE s =
    case fst !(whnfT s) of
      TYPE l => pure l
      _      => throwError $ ExpectedTYPE s

  export covering %inline
  expectPi : Term q d n -> m (q, Term q d n, ScopeTerm q d n)
  expectPi s =
    case fst !(whnfT s) of
      Pi {qty, arg, res, _} => pure (qty, arg, res)
      _                     => throwError $ ExpectedPi s

  export covering %inline
  expectSig : Term q d n -> m (Term q d n, ScopeTerm q d n)
  expectSig s =
    case fst !(whnfT s) of
      Sig {fst, snd, _} => pure (fst, snd)
      _                 => throwError $ ExpectedSig s

  export covering %inline
  expectEnum : Term q d n -> m (SortedSet TagVal)
  expectEnum s =
    case fst !(whnfT s) of
      Enum tags => pure tags
      _         => throwError $ ExpectedEnum s

  export covering %inline
  expectEq : Term q d n -> m (DScopeTerm q d n, Term q d n, Term q d n)
  expectEq s =
    case fst !(whnfT s) of
      Eq {ty, l, r, _} => pure (ty, l, r)
      _                => throwError $ ExpectedEq s