{-# LANGUAGE BangPatterns #-}
{-# LANGUAGE ScopedTypeVariables #-}
{-# LANGUAGE FlexibleContexts #-}

module GHC.Core.Reduction
  (
     -- * Reductions
     Reduction(..), ReductionN, ReductionR, HetReduction(..),
     Reductions(..),
     mkReduction, mkReductions, mkHetReduction, coercionRedn,
     reductionOriginalType,
     downgradeRedn, mkSubRedn,
     mkTransRedn, mkCoherenceRightRedn, mkCoherenceRightMRedn,
     mkCastRedn1, mkCastRedn2,
     mkReflRedn, mkGReflRightRedn, mkGReflRightMRedn,
     mkGReflLeftRedn, mkGReflLeftMRedn,
     mkAppRedn, mkAppRedns, mkFunRedn,
     mkForAllRedn, mkHomoForAllRedn, mkTyConAppRedn, mkClassPredRedn,
     mkProofIrrelRedn, mkReflCoRedn,
     homogeniseHetRedn,
     unzipRedns,

     -- * Rewriting type arguments
     ArgsReductions(..),
     simplifyArgsWorker

  ) where

import GHC.Prelude

import GHC.Core.Class      ( Class(classTyCon) )
import GHC.Core.Coercion
import GHC.Core.Predicate  ( mkClassPred )
import GHC.Core.TyCon      ( TyCon )
import GHC.Core.Type

import GHC.Data.Pair       ( Pair(Pair) )
import GHC.Data.List.Infinite ( Infinite (..) )
import qualified GHC.Data.List.Infinite as Inf

import GHC.Types.Var       ( VarBndr(..), setTyVarKind )
import GHC.Types.Var.Env   ( mkInScopeSet )
import GHC.Types.Var.Set   ( TyCoVarSet )

import GHC.Utils.Misc      ( HasDebugCallStack, equalLength )
import GHC.Utils.Outputable
import GHC.Utils.Panic     ( assertPpr )

{-
%************************************************************************
%*                                                                      *
      Reductions
%*                                                                      *
%************************************************************************

Note [The Reduction type]
~~~~~~~~~~~~~~~~~~~~~~~~~
Many functions in the type-checker rewrite a type, using Given type equalitie
or type-family reductions, and return a Reduction, which is just a pair of the
coercion and the RHS type of the coercion:
  data Reduction = Reduction Coercion !Type

The order of the arguments to the constructor serves as a reminder
of what the Type is.  In
    Reduction co ty
`ty` appears to the right of `co`, reminding us that we must have:
    co :: unrewritten_ty ~ ty

Example functions that use this datatype:
   GHC.Core.FamInstEnv.topNormaliseType_maybe
     :: FamInstEnvs -> Type -> Maybe Reduction
   GHC.Tc.Solver.Rewrite.rewrite
     :: CtEvidence -> TcType -> TcS Reduction

Having Reduction as a data type, with a strict Type field, rather than using
a pair (Coercion,Type) gives several advantages (see #20161)
* The strictness in Type improved performance in rewriting of type families
  (around 2.5% improvement in T9872),
* Compared to the situation before, it gives improved consistency around
  orientation of rewritings, as a Reduction is always left-to-right
  (the coercion's RHS type is always the type stored in the 'Reduction').
  No more 'mkSymCo's needed to convert between left-to-right and right-to-left.

One could imagine storing the LHS type of the coercion in the Reduction as well,
but in fact `reductionOriginalType` is very seldom used, so it's not worth it.
-}

-- | A 'Reduction' is the result of an operation that rewrites a type @ty_in@.
-- The 'Reduction' includes the rewritten type @ty_out@ and a 'Coercion' @co@
-- such that @co :: ty_in ~ ty_out@, where the role of the coercion is determined
-- by the context. That is, the LHS type of the coercion is the original type
-- @ty_in@, while its RHS type is the rewritten type @ty_out@.
--
-- A Reduction is always homogeneous, unless it is wrapped inside a 'HetReduction',
-- which separately stores the kind coercion.
--
-- See Note [The Reduction type].
data Reduction =
  Reduction
    { Reduction -> Coercion
reductionCoercion    :: Coercion
    , Reduction -> Type
reductionReducedType :: !Type
    }
-- N.B. the 'Coercion' field must be lazy: see for instance GHC.Tc.Solver.Rewrite.rewrite_tyvar2
-- which returns an error in the 'Coercion' field when dealing with a Derived constraint
-- (which is OK as this Coercion gets ignored later).
-- We might want to revisit the strictness once Deriveds are removed.

-- | Stores a heterogeneous reduction.
--
-- The stored kind coercion must relate the kinds of the
-- stored reduction. That is, in @HetReduction (Reduction co xi) kco@,
-- we must have:
--
-- >  co :: ty ~ xi
-- > kco :: typeKind ty ~ typeKind xi
data HetReduction =
  HetReduction
    Reduction
    MCoercionN
  -- N.B. strictness annotations don't seem to make a difference here

-- | Create a heterogeneous reduction.
--
-- Pre-condition: the provided kind coercion (second argument)
-- relates the kinds of the stored reduction.
-- That is, if the coercion stored in the 'Reduction' is of the form
--
-- > co :: ty ~ xi
--
-- Then the kind coercion supplied must be of the form:
--
-- > kco :: typeKind ty ~ typeKind xi
mkHetReduction :: Reduction  -- ^ heterogeneous reduction
               -> MCoercionN -- ^ kind coercion
               -> HetReduction
mkHetReduction :: Reduction -> MCoercionN -> HetReduction
mkHetReduction Reduction
redn MCoercionN
mco = Reduction -> MCoercionN -> HetReduction
HetReduction Reduction
redn MCoercionN
mco
{-# INLINE mkHetReduction #-}

-- | Homogenise a heterogeneous reduction.
--
-- Given @HetReduction (Reduction co xi) kco@, with
--
-- >  co :: ty ~ xi
-- > kco :: typeKind(ty) ~ typeKind(xi)
--
-- this returns the homogeneous reduction:
--
-- > hco :: ty ~ ( xi |> sym kco )
homogeniseHetRedn :: Role -> HetReduction -> Reduction
homogeniseHetRedn :: Role -> HetReduction -> Reduction
homogeniseHetRedn Role
role (HetReduction Reduction
redn MCoercionN
kco)
  = Role -> Reduction -> MCoercionN -> Reduction
mkCoherenceRightMRedn Role
role Reduction
redn (MCoercionN -> MCoercionN
mkSymMCo MCoercionN
kco)
{-# INLINE homogeniseHetRedn #-}

-- | Create a 'Reduction' from a pair of a 'Coercion' and a 'Type.
--
-- Pre-condition: the RHS type of the coercion matches the provided type
-- (perhaps up to zonking).
--
-- Use 'coercionRedn' when you only have the coercion.
mkReduction :: Coercion -> Type -> Reduction
mkReduction :: Coercion -> Type -> Reduction
mkReduction Coercion
co Type
ty = Coercion -> Type -> Reduction
Reduction Coercion
co Type
ty
{-# INLINE mkReduction #-}

instance Outputable Reduction where
  ppr :: Reduction -> SDoc
ppr Reduction
redn =
    SDoc -> SDoc
forall doc. IsLine doc => doc -> doc
braces (SDoc -> SDoc) -> SDoc -> SDoc
forall a b. (a -> b) -> a -> b
$ [SDoc] -> SDoc
forall doc. IsDoc doc => [doc] -> doc
vcat
      [ String -> SDoc
forall doc. IsLine doc => String -> doc
text String
"reductionOriginalType:" SDoc -> SDoc -> SDoc
forall doc. IsLine doc => doc -> doc -> doc
<+> Type -> SDoc
forall a. Outputable a => a -> SDoc
ppr (Reduction -> Type
reductionOriginalType Reduction
redn)
      , String -> SDoc
forall doc. IsLine doc => String -> doc
text String
" reductionReducedType:" SDoc -> SDoc -> SDoc
forall doc. IsLine doc => doc -> doc -> doc
<+> Type -> SDoc
forall a. Outputable a => a -> SDoc
ppr (Reduction -> Type
reductionReducedType Reduction
redn)
      , String -> SDoc
forall doc. IsLine doc => String -> doc
text String
"    reductionCoercion:" SDoc -> SDoc -> SDoc
forall doc. IsLine doc => doc -> doc -> doc
<+> Coercion -> SDoc
forall a. Outputable a => a -> SDoc
ppr (Reduction -> Coercion
reductionCoercion Reduction
redn)
      ]

-- | A 'Reduction' in which the 'Coercion' has 'Nominal' role.
type ReductionN = Reduction

-- | A 'Reduction' in which the 'Coercion' has 'Representational' role.
type ReductionR = Reduction

-- | Get the original, unreduced type corresponding to a 'Reduction'.
--
-- This is obtained by computing the LHS kind of the stored coercion,
-- which may be slow.
reductionOriginalType :: Reduction -> Type
reductionOriginalType :: Reduction -> Type
reductionOriginalType = Coercion -> Type
coercionLKind (Coercion -> Type) -> (Reduction -> Coercion) -> Reduction -> Type
forall b c a. (b -> c) -> (a -> b) -> a -> c
. Reduction -> Coercion
reductionCoercion
{-# INLINE reductionOriginalType #-}

-- | Turn a 'Coercion' into a 'Reduction'
-- by inspecting the RHS type of the coercion.
--
-- Prefer using 'mkReduction' when you already know
-- the RHS type of the coercion, to avoid computing it anew.
coercionRedn :: Coercion -> Reduction
coercionRedn :: Coercion -> Reduction
coercionRedn Coercion
co = Coercion -> Type -> Reduction
Reduction Coercion
co (Coercion -> Type
coercionRKind Coercion
co)
{-# INLINE coercionRedn #-}

-- | Downgrade the role of the coercion stored in the 'Reduction'.
downgradeRedn :: Role -- ^ desired role
              -> Role -- ^ current role
              -> Reduction
              -> Reduction
downgradeRedn :: Role -> Role -> Reduction -> Reduction
downgradeRedn Role
new_role Role
old_role redn :: Reduction
redn@(Reduction Coercion
co Type
_)
  = Reduction
redn { reductionCoercion = downgradeRole new_role old_role co }
{-# INLINE downgradeRedn #-}

-- | Downgrade the role of the coercion stored in the 'Reduction',
-- from 'Nominal' to 'Representational'.
mkSubRedn :: Reduction -> Reduction
mkSubRedn :: Reduction -> Reduction
mkSubRedn redn :: Reduction
redn@(Reduction Coercion
co Type
_) = Reduction
redn { reductionCoercion = mkSubCo co }
{-# INLINE mkSubRedn #-}

-- | Compose a reduction with a coercion on the left.
--
-- Pre-condition: the provided coercion's RHS type must match the LHS type
-- of the coercion that is stored in the reduction.
mkTransRedn :: Coercion -> Reduction -> Reduction
mkTransRedn :: Coercion -> Reduction -> Reduction
mkTransRedn Coercion
co1 redn :: Reduction
redn@(Reduction Coercion
co2 Type
_)
  = Reduction
redn { reductionCoercion = co1 `mkTransCo` co2 }
{-# INLINE mkTransRedn #-}

-- | The reflexive reduction.
mkReflRedn :: Role -> Type -> Reduction
mkReflRedn :: Role -> Type -> Reduction
mkReflRedn Role
r Type
ty = Coercion -> Type -> Reduction
mkReduction (Role -> Type -> Coercion
mkReflCo Role
r Type
ty) Type
ty

-- | Create a 'Reduction' from a kind cast, in which
-- the casted type is the rewritten type.
--
-- Given @ty :: k1@, @mco :: k1 ~ k2@,
-- produces the 'Reduction' @ty ~res_co~> (ty |> mco)@
-- at the given 'Role'.
mkGReflRightRedn :: Role -> Type -> CoercionN -> Reduction
mkGReflRightRedn :: Role -> Type -> Coercion -> Reduction
mkGReflRightRedn Role
role Type
ty Coercion
co
  = Coercion -> Type -> Reduction
mkReduction
      (Role -> Type -> Coercion -> Coercion
mkGReflRightCo Role
role Type
ty Coercion
co)
      (Type -> Coercion -> Type
mkCastTy Type
ty Coercion
co)
{-# INLINE mkGReflRightRedn #-}

-- | Create a 'Reduction' from a kind cast, in which
-- the casted type is the rewritten type.
--
-- Given @ty :: k1@, @mco :: k1 ~ k2@,
-- produces the 'Reduction' @ty ~res_co~> (ty |> mco)@
-- at the given 'Role'.
mkGReflRightMRedn :: Role -> Type -> MCoercionN -> Reduction
mkGReflRightMRedn :: Role -> Type -> MCoercionN -> Reduction
mkGReflRightMRedn Role
role Type
ty MCoercionN
mco
  = Coercion -> Type -> Reduction
mkReduction
      (Role -> Type -> MCoercionN -> Coercion
mkGReflRightMCo Role
role Type
ty MCoercionN
mco)
      (Type -> MCoercionN -> Type
mkCastTyMCo Type
ty MCoercionN
mco)
{-# INLINE mkGReflRightMRedn #-}

-- | Create a 'Reduction' from a kind cast, in which
-- the casted type is the original (non-rewritten) type.
--
-- Given @ty :: k1@, @mco :: k1 ~ k2@,
-- produces the 'Reduction' @(ty |> mco) ~res_co~> ty@
-- at the given 'Role'.
mkGReflLeftRedn :: Role -> Type -> CoercionN -> Reduction
mkGReflLeftRedn :: Role -> Type -> Coercion -> Reduction
mkGReflLeftRedn Role
role Type
ty Coercion
co
  = Coercion -> Type -> Reduction
mkReduction
      (Role -> Type -> Coercion -> Coercion
mkGReflLeftCo Role
role Type
ty Coercion
co)
      Type
ty
{-# INLINE mkGReflLeftRedn #-}

-- | Create a 'Reduction' from a kind cast, in which
-- the casted type is the original (non-rewritten) type.
--
-- Given @ty :: k1@, @mco :: k1 ~ k2@,
-- produces the 'Reduction' @(ty |> mco) ~res_co~> ty@
-- at the given 'Role'.
mkGReflLeftMRedn :: Role -> Type -> MCoercionN -> Reduction
mkGReflLeftMRedn :: Role -> Type -> MCoercionN -> Reduction
mkGReflLeftMRedn Role
role Type
ty MCoercionN
mco
  = Coercion -> Type -> Reduction
mkReduction
      (Role -> Type -> MCoercionN -> Coercion
mkGReflLeftMCo Role
role Type
ty MCoercionN
mco)
      Type
ty
{-# INLINE mkGReflLeftMRedn #-}

-- | Apply a cast to the result of a 'Reduction'.
--
-- Given a 'Reduction' @ty1 ~co1~> (ty2 :: k2)@ and a kind coercion @kco@
-- with LHS kind @k2@, produce a new 'Reduction' @ty1 ~co2~> ( ty2 |> kco )@
-- of the given 'Role' (which must match the role of the coercion stored
-- in the 'Reduction' argument).
mkCoherenceRightRedn :: Role -> Reduction -> CoercionN -> Reduction
mkCoherenceRightRedn :: Role -> Reduction -> Coercion -> Reduction
mkCoherenceRightRedn Role
r (Reduction Coercion
co1 Type
ty2) Coercion
kco
  = Coercion -> Type -> Reduction
mkReduction
      (Role -> Type -> Coercion -> Coercion -> Coercion
mkCoherenceRightCo Role
r Type
ty2 Coercion
kco Coercion
co1)
      (Type -> Coercion -> Type
mkCastTy Type
ty2 Coercion
kco)
{-# INLINE mkCoherenceRightRedn #-}

-- | Apply a cast to the result of a 'Reduction', using an 'MCoercionN'.
--
-- Given a 'Reduction' @ty1 ~co1~> (ty2 :: k2)@ and a kind coercion @mco@
-- with LHS kind @k2@, produce a new 'Reduction' @ty1 ~co2~> ( ty2 |> mco )@
-- of the given 'Role' (which must match the role of the coercion stored
-- in the 'Reduction' argument).
mkCoherenceRightMRedn :: Role -> Reduction -> MCoercionN -> Reduction
mkCoherenceRightMRedn :: Role -> Reduction -> MCoercionN -> Reduction
mkCoherenceRightMRedn Role
r (Reduction Coercion
co1 Type
ty2) MCoercionN
kco
  = Coercion -> Type -> Reduction
mkReduction
      (Role -> Type -> MCoercionN -> Coercion -> Coercion
mkCoherenceRightMCo Role
r Type
ty2 MCoercionN
kco Coercion
co1)
      (Type -> MCoercionN -> Type
mkCastTyMCo Type
ty2 MCoercionN
kco)
{-# INLINE mkCoherenceRightMRedn #-}

-- | Apply a cast to a 'Reduction', casting both the original and the reduced type.
--
-- Given @cast_co@ and 'Reduction' @ty ~co~> xi@, this function returns
-- the 'Reduction' @(ty |> cast_co) ~return_co~> (xi |> cast_co)@
-- of the given 'Role' (which must match the role of the coercion stored
-- in the 'Reduction' argument).
--
-- Pre-condition: the 'Type' passed in is the same as the LHS type
-- of the coercion stored in the 'Reduction'.
mkCastRedn1 :: Role
            -> Type      -- ^ original type
            -> CoercionN -- ^ coercion to cast with
            -> Reduction -- ^ rewritten type, with rewriting coercion
            -> Reduction
mkCastRedn1 :: Role -> Type -> Coercion -> Reduction -> Reduction
mkCastRedn1 Role
r Type
ty Coercion
cast_co (Reduction Coercion
co Type
xi)
  -- co :: ty ~r ty'
  -- return_co :: (ty |> cast_co) ~r (ty' |> cast_co)
  = Coercion -> Type -> Reduction
mkReduction
      (Coercion -> Role -> Type -> Type -> Coercion -> Coercion
castCoercionKind1 Coercion
co Role
r Type
ty Type
xi Coercion
cast_co)
      (Type -> Coercion -> Type
mkCastTy Type
xi Coercion
cast_co)
{-# INLINE mkCastRedn1 #-}

-- | Apply casts on both sides of a 'Reduction' (of the given 'Role').
--
-- Use 'mkCastRedn1' when you want to cast both the original and reduced types
-- in a 'Reduction' using the same coercion.
--
-- Pre-condition: the 'Type' passed in is the same as the LHS type
-- of the coercion stored in the 'Reduction'.
mkCastRedn2 :: Role
            -> Type      -- ^ original type
            -> CoercionN -- ^ coercion to cast with on the left
            -> Reduction -- ^ rewritten type, with rewriting coercion
            -> CoercionN -- ^ coercion to cast with on the right
            -> Reduction
mkCastRedn2 :: Role -> Type -> Coercion -> Reduction -> Coercion -> Reduction
mkCastRedn2 Role
r Type
ty Coercion
cast_co (Reduction Coercion
nco Type
nty) Coercion
cast_co'
  = Coercion -> Type -> Reduction
mkReduction
      (Coercion
-> Role -> Type -> Type -> Coercion -> Coercion -> Coercion
castCoercionKind2 Coercion
nco Role
r Type
ty Type
nty Coercion
cast_co Coercion
cast_co')
      (Type -> Coercion -> Type
mkCastTy Type
nty Coercion
cast_co')
{-# INLINE mkCastRedn2 #-}

-- | Apply one 'Reduction' to another.
--
-- Combines 'mkAppCo' and 'mkAppTy`.
mkAppRedn :: Reduction -> Reduction -> Reduction
mkAppRedn :: Reduction -> Reduction -> Reduction
mkAppRedn (Reduction Coercion
co1 Type
ty1) (Reduction Coercion
co2 Type
ty2)
  = Coercion -> Type -> Reduction
mkReduction (Coercion -> Coercion -> Coercion
mkAppCo Coercion
co1 Coercion
co2) (Type -> Type -> Type
mkAppTy Type
ty1 Type
ty2)
{-# INLINE mkAppRedn #-}

-- | Create a function 'Reduction'.
--
-- Combines 'mkFunCo' and 'mkFunTy'.
mkFunRedn :: Role
          -> FunTyFlag
          -> ReductionN -- ^ multiplicity reduction
          -> Reduction  -- ^ argument reduction
          -> Reduction  -- ^ result reduction
          -> Reduction
mkFunRedn :: Role
-> FunTyFlag -> Reduction -> Reduction -> Reduction -> Reduction
mkFunRedn Role
r FunTyFlag
af
  (Reduction Coercion
w_co Type
w_ty)
  (Reduction Coercion
arg_co Type
arg_ty)
  (Reduction Coercion
res_co Type
res_ty)
    = Coercion -> Type -> Reduction
mkReduction
        (Role -> FunTyFlag -> Coercion -> Coercion -> Coercion -> Coercion
mkFunCo Role
r FunTyFlag
af Coercion
w_co Coercion
arg_co Coercion
res_co)
        (HasDebugCallStack => FunTyFlag -> Type -> Type -> Type -> Type
FunTyFlag -> Type -> Type -> Type -> Type
mkFunTy   FunTyFlag
af Type
w_ty Type
arg_ty Type
res_ty)
{-# INLINE mkFunRedn #-}

-- | Create a 'Reduction' associated to a Π type,
-- from a kind 'Reduction' and a body 'Reduction'.
--
-- Combines 'mkForAllCo' and 'mkForAllTy'.
mkForAllRedn :: ForAllTyFlag
             -> TyVar
             -> ReductionN -- ^ kind reduction
             -> Reduction  -- ^ body reduction
             -> Reduction
mkForAllRedn :: ForAllTyFlag -> TyVar -> Reduction -> Reduction -> Reduction
mkForAllRedn ForAllTyFlag
vis TyVar
tv1 (Reduction Coercion
h Type
ki') (Reduction Coercion
co Type
ty)
  = Coercion -> Type -> Reduction
mkReduction
      (TyVar -> Coercion -> Coercion -> Coercion
mkForAllCo TyVar
tv1 Coercion
h Coercion
co)
      (ForAllTyBinder -> Type -> Type
mkForAllTy (TyVar -> ForAllTyFlag -> ForAllTyBinder
forall var argf. var -> argf -> VarBndr var argf
Bndr TyVar
tv2 ForAllTyFlag
vis) Type
ty)
  where
    tv2 :: TyVar
tv2 = TyVar -> Type -> TyVar
setTyVarKind TyVar
tv1 Type
ki'
{-# INLINE mkForAllRedn #-}

-- | Create a 'Reduction' of a quantified type from a
-- 'Reduction' of the body.
--
-- Combines 'mkHomoForAllCos' and 'mkForAllTys'.
mkHomoForAllRedn :: [TyVarBinder] -> Reduction -> Reduction
mkHomoForAllRedn :: [ForAllTyBinder] -> Reduction -> Reduction
mkHomoForAllRedn [ForAllTyBinder]
bndrs (Reduction Coercion
co Type
ty)
  = Coercion -> Type -> Reduction
mkReduction
      ([TyVar] -> Coercion -> Coercion
mkHomoForAllCos ([ForAllTyBinder] -> [TyVar]
forall tv argf. [VarBndr tv argf] -> [tv]
binderVars [ForAllTyBinder]
bndrs) Coercion
co)
      ([ForAllTyBinder] -> Type -> Type
mkForAllTys [ForAllTyBinder]
bndrs Type
ty)
{-# INLINE mkHomoForAllRedn #-}

-- | Create a 'Reduction' from a coercion between coercions.
--
-- Combines 'mkProofIrrelCo' and 'mkCoercionTy'.
mkProofIrrelRedn :: Role      -- ^ role of the created coercion, "r"
                 -> CoercionN -- ^ co :: phi1 ~N phi2
                 -> Coercion  -- ^ g1 :: phi1
                 -> Coercion  -- ^ g2 :: phi2
                 -> Reduction -- ^ res_co :: g1 ~r g2
mkProofIrrelRedn :: Role -> Coercion -> Coercion -> Coercion -> Reduction
mkProofIrrelRedn Role
role Coercion
co Coercion
g1 Coercion
g2
  = Coercion -> Type -> Reduction
mkReduction
      (Role -> Coercion -> Coercion -> Coercion -> Coercion
mkProofIrrelCo Role
role Coercion
co Coercion
g1 Coercion
g2)
      (Coercion -> Type
mkCoercionTy Coercion
g2)
{-# INLINE mkProofIrrelRedn #-}

-- | Create a reflexive 'Reduction' whose RHS is the given 'Coercion',
-- with the specified 'Role'.
mkReflCoRedn :: Role -> Coercion -> Reduction
mkReflCoRedn :: Role -> Coercion -> Reduction
mkReflCoRedn Role
role Coercion
co
  = Coercion -> Type -> Reduction
mkReduction
      (Role -> Type -> Coercion
mkReflCo Role
role Type
co_ty)
      Type
co_ty
  where
    co_ty :: Type
co_ty = Coercion -> Type
mkCoercionTy Coercion
co
{-# INLINE mkReflCoRedn #-}

-- | A collection of 'Reduction's where the coercions and the types are stored separately.
--
-- Use 'unzipRedns' to obtain 'Reductions' from a list of 'Reduction's.
--
-- This datatype is used in 'mkAppRedns', 'mkClassPredRedns' and 'mkTyConAppRedn',
-- which expect separate types and coercions.
--
-- Invariant: the two stored lists are of the same length,
-- and the RHS type of each coercion is the corresponding type.
data Reductions = Reductions [Coercion] [Type]

-- | Create 'Reductions' from individual lists of coercions and types.
--
-- The lists should be of the same length, and the RHS type of each coercion
-- should match the specified type in the other list.
mkReductions :: [Coercion] -> [Type] -> Reductions
mkReductions :: [Coercion] -> [Type] -> Reductions
mkReductions [Coercion]
cos [Type]
tys = [Coercion] -> [Type] -> Reductions
Reductions [Coercion]
cos [Type]
tys
{-# INLINE mkReductions #-}

-- | Combines 'mkAppCos' and 'mkAppTys'.
mkAppRedns :: Reduction -> Reductions -> Reduction
mkAppRedns :: Reduction -> Reductions -> Reduction
mkAppRedns (Reduction Coercion
co Type
ty) (Reductions [Coercion]
cos [Type]
tys)
  = Coercion -> Type -> Reduction
mkReduction (Coercion -> [Coercion] -> Coercion
mkAppCos Coercion
co [Coercion]
cos) (Type -> [Type] -> Type
mkAppTys Type
ty [Type]
tys)
{-# INLINE mkAppRedns #-}

-- | 'TyConAppCo' for 'Reduction's: combines 'mkTyConAppCo' and `mkTyConApp`.
mkTyConAppRedn :: Role -> TyCon -> Reductions -> Reduction
mkTyConAppRedn :: Role -> TyCon -> Reductions -> Reduction
mkTyConAppRedn Role
role TyCon
tc (Reductions [Coercion]
cos [Type]
tys)
  = Coercion -> Type -> Reduction
mkReduction (HasDebugCallStack => Role -> TyCon -> [Coercion] -> Coercion
Role -> TyCon -> [Coercion] -> Coercion
mkTyConAppCo Role
role TyCon
tc [Coercion]
cos) (TyCon -> [Type] -> Type
mkTyConApp TyCon
tc [Type]
tys)
{-# INLINE mkTyConAppRedn #-}

-- | Reduce the arguments of a 'Class' 'TyCon'.
mkClassPredRedn :: Class -> Reductions -> Reduction
mkClassPredRedn :: Class -> Reductions -> Reduction
mkClassPredRedn Class
cls (Reductions [Coercion]
cos [Type]
tys)
  = Coercion -> Type -> Reduction
mkReduction
      (HasDebugCallStack => Role -> TyCon -> [Coercion] -> Coercion
Role -> TyCon -> [Coercion] -> Coercion
mkTyConAppCo Role
Nominal (Class -> TyCon
classTyCon Class
cls) [Coercion]
cos)
      (Class -> [Type] -> Type
mkClassPred Class
cls [Type]
tys)
{-# INLINE mkClassPredRedn #-}

-- | Obtain 'Reductions' from a list of 'Reduction's by unzipping.
unzipRedns :: [Reduction] -> Reductions
unzipRedns :: [Reduction] -> Reductions
unzipRedns = (Reduction -> Reductions -> Reductions)
-> Reductions -> [Reduction] -> Reductions
forall a b. (a -> b -> b) -> b -> [a] -> b
forall (t :: * -> *) a b.
Foldable t =>
(a -> b -> b) -> b -> t a -> b
foldr Reduction -> Reductions -> Reductions
accRedn ([Coercion] -> [Type] -> Reductions
Reductions [] [])
  where
    accRedn :: Reduction -> Reductions -> Reductions
    accRedn :: Reduction -> Reductions -> Reductions
accRedn (Reduction Coercion
co Type
xi) (Reductions [Coercion]
cos [Type]
xis)
      = [Coercion] -> [Type] -> Reductions
Reductions (Coercion
coCoercion -> [Coercion] -> [Coercion]
forall a. a -> [a] -> [a]
:[Coercion]
cos) (Type
xiType -> [Type] -> [Type]
forall a. a -> [a] -> [a]
:[Type]
xis)
{-# INLINE unzipRedns #-}
-- NB: this function is currently used in two locations:
--
-- - GHC.Tc.Gen.Foreign.normaliseFfiType', with one call of the form:
--
--   unzipRedns <$> zipWithM f tys roles
--
-- - GHC.Tc.Solver.Monad.breakTyEqCycle_maybe, with two calls of the form:
--
--   unzipRedns <$> mapM f tys
--
-- It is possible to write 'mapAndUnzipM' functions to handle these cases,
-- but the above locations aren't performance critical, so it was deemed
-- to not be worth it.

{-
%************************************************************************
%*                                                                      *
       Simplifying types
%*                                                                      *
%************************************************************************

The function below morally belongs in GHC.Tc.Solver.Rewrite, but it is used also in
FamInstEnv, and so lives here.

Note [simplifyArgsWorker]
~~~~~~~~~~~~~~~~~~~~~~~~~
Invariant (F2) of Note [Rewriting] in GHC.Tc.Solver.Rewrite says that
rewriting is homogeneous.
This causes some trouble when rewriting a function applied to a telescope
of arguments, perhaps with dependency. For example, suppose

  type family F :: forall (j :: Type) (k :: Type). Maybe j -> Either j k -> Bool -> [k]

and we wish to rewrite the args of (with kind applications explicit)

  F @a @b (Just @a c) (Right @a @b d) False

where all variables are skolems and

  a :: Type
  b :: Type
  c :: a
  d :: b

  [G] aco :: a ~ fa
  [G] bco :: b ~ fb
  [G] cco :: c ~ fc
  [G] dco :: d ~ fd

The first step is to rewrite all the arguments. This is done before calling
simplifyArgsWorker. We start from

  a
  b
  Just @a c
  Right @a @b d
  False

and get left-to-right reductions whose coercions are as follows:

  co1 :: a ~ fa
  co2 :: b ~ fb
  co3 :: (Just @a c) ~ (Just @fa (fc |> aco) |> co6)
  co4 :: (Right @a @b d) ~ (Right @fa @fb (fd |> bco) |> co7)
  co5 :: False ~ False

where
  co6 = Maybe (sym aco) :: Maybe fa ~ Maybe a
  co7 = Either (sym aco) (sym bco) :: Either fa fb ~ Either a b

We now process the rewritten args in left-to-right order. The first two args
need no further processing. But now consider the third argument. Let f3 = the rewritten
result, Just fa (fc |> aco) |> co6.
This f3 rewritten argument has kind (Maybe a), due to homogeneity of rewriting (F2).
And yet, when we build the application (F @fa @fb ...), we need this
argument to have kind (Maybe fa), not (Maybe a). We must cast this argument.
The coercion to use is determined by the kind of F:
we see in F's kind that the third argument has kind Maybe j.
Critically, we also know that the argument corresponding to j
(in our example, a) rewrote with a coercion co1. We can thus know the
coercion needed for the 3rd argument is (Maybe co1), thus building
(f3 |> Maybe co1)

More generally, we must use the Lifting Lemma, as implemented in
Coercion.liftCoSubst. As we work left-to-right, any variable that is a
dependent parameter (j and k, in our example) gets mapped in a lifting context
to the coercion that is output from rewriting the corresponding argument (co1
and co2, in our example). Then, after rewriting later arguments, we lift the
kind of these arguments in the lifting context that we've be building up.
This coercion is then used to keep the result of rewriting well-kinded.

Working through our example, this is what happens:

  1. Extend the (empty) LC with [j |-> co1]. No new casting must be done,
     because the binder associated with the first argument has a closed type (no
     variables).

  2. Extend the LC with [k |-> co2]. No casting to do.

  3. Lifting the kind (Maybe j) with our LC
     yields co8 :: Maybe a ~ Maybe fa. Use (f3 |> co8) as the argument to F.

  4. Lifting the kind (Either j k) with our LC
     yields co9 :: Either a b ~ Either fa fb. Use (f4 |> co9) as the 4th
     argument to F, where f4 is the rewritten form of argument 4, written above.

  5. We lift Bool with our LC, getting <Bool>; casting has no effect.

We're now almost done, but the new application

  F @fa @fb (f3 |> co8) (f4 |> co9) False

has the wrong kind. Its kind is [fb], instead of the original [b].
So we must use our LC one last time to lift the result kind [k],
getting res_co :: [fb] ~ [b], and we cast our result.

Accordingly, the final result is

  F
    @fa
    @fb
    (Just @fa (fc |> aco) |> Maybe (sym aco) |> sym (Maybe (sym aco)))
    (Right @fa @fb (fd |> bco) |> Either (sym aco) (sym bco) |> sym (Either (sym aco) (sym bco)))
    False
  |> [sym bco]

The res_co (in this case, [sym bco]) is the third component of the
tuple returned by simplifyArgsWorker.

Note [Last case in simplifyArgsWorker]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
In writing simplifyArgsWorker's `go`, we know here that args cannot be empty,
because that case is first. We've run out of
binders. But perhaps inner_ki is a tyvar that has been instantiated with a
Π-type.

Here is an example.

  a :: forall (k :: Type). k -> k
  Proxy :: forall j. j -> Type
  type family Star
  axStar :: Star ~ Type
  type family NoWay :: Bool
  axNoWay :: NoWay ~ False
  bo :: Type
  [G] bc :: bo ~ Bool   (in inert set)

  co :: (forall j. j -> Type) ~ (forall (j :: Star). (j |> axStar) -> Star)
  co = forall (j :: sym axStar). (<j> -> sym axStar)

  We are rewriting:
  a (forall (j :: Star). (j |> axStar) -> Star)   -- 1
    (Proxy |> co)                                 -- 2
    (bo |> sym axStar)                            -- 3
    (NoWay |> sym bc)                             -- 4
      :: Star

First, we rewrite all the arguments (before simplifyArgsWorker), like so:

    co1 :: (forall (j :: Star). (j |> axStar) -> Star) ~ (forall j. j -> Type) -- 1
    co2 :: (Proxy |> co) ~ (Proxy |> co)                                       -- 2
    co3 :: (bo |> sym axStar) ~ (Bool |> sym axStar)                           -- 3
    co4 :: (NoWay |> sym bc) ~ (False |> sym bc)                               -- 4

Then we do the process described in Note [simplifyArgsWorker].

1. Lifting Type (the kind of the first arg) gives us a reflexive coercion, so we
   don't use it. But we do build a lifting context [k -> co1] (where co1 is a
   result of rewriting an argument, written above).

2. Lifting k gives us co1, so the second argument becomes (Proxy |> co |> co1).
   This is not a dependent argument, so we don't extend the lifting context.

Now we need to deal with argument (3).
The way we normally proceed is to lift the kind of the binder, to see whether
it's dependent.
But here, the remainder of the kind of `a` that we're left with
after processing two arguments is just `k`.

The way forward is look up k in the lifting context, getting co1. If we're at
all well-typed, co1 will be a coercion between Π-types, with at least one binder.
So, let's decompose co1 with decomposePiCos. This decomposition needs arguments to use
to instantiate any kind parameters. Look at the type of co1. If we just
decomposed it, we would end up with coercions whose types include j, which is
out of scope here. Accordingly, decomposePiCos takes a list of types whose
kinds are the *unrewritten* types in the decomposed coercion. (See comments on
decomposePiCos.) Because the rewritten types have unrewritten kinds (because
rewriting is homogeneous), passing the list of rewritten types to decomposePiCos
just won't do: later arguments' kinds won't be as expected. So we need to get
the *unrewritten* types to pass to decomposePiCos. We can do this easily enough
by taking the kind of the argument coercions, passed in originally.

(Alternative 1: We could re-engineer decomposePiCos to deal with this situation.
But that function is already gnarly, and other call sites of decomposePiCos
would suffer from the change, even though they are much more common than this one.)

(Alternative 2: We could avoid calling decomposePiCos entirely, integrating its
behavior into simplifyArgsWorker. This would work, I think, but then all of the
complication of decomposePiCos would end up layered on top of all the complication
here. Please, no.)

(Alternative 3: We could pass the unrewritten arguments into simplifyArgsWorker
so that we don't have to recreate them. But that would complicate the interface
of this function to handle a very dark, dark corner case. Better to keep our
demons to ourselves here instead of exposing them to callers. This decision is
easily reversed if there is ever any performance trouble due to the call of
coercionKind.)

So we now call

  decomposePiCos co1
                 (Pair (forall (j :: Star). (j |> axStar) -> Star) (forall j. j -> Type))
                 [bo |> sym axStar, NoWay |> sym bc]

to get

  co5 :: Star ~ Type
  co6 :: (j |> axStar) ~ (j |> co5), substituted to
                              (bo |> sym axStar |> axStar) ~ (bo |> sym axStar |> co5)
                           == bo ~ bo
  res_co :: Type ~ Star

We then use these casts on (the rewritten) (3) and (4) to get

  (Bool |> sym axStar |> co5 :: Type)   -- (C3)
  (False |> sym bc |> co6    :: bo)     -- (C4)

We can simplify to

  Bool                        -- (C3)
  (False |> sym bc :: bo)     -- (C4)

Of course, we still must do the processing in Note [simplifyArgsWorker] to finish
the job. We thus want to recur. Our new function kind is the left-hand type of
co1 (gotten, recall, by lifting the variable k that was the return kind of the
original function). Why the left-hand type (as opposed to the right-hand type)?
Because we have casted all the arguments according to decomposePiCos, which gets
us from the right-hand type to the left-hand one. We thus recur with that new
function kind, zapping our lifting context, because we have essentially applied
it.

This recursive call returns ([Bool, False], [...], Refl). The Bool and False
are the correct arguments we wish to return. But we must be careful about the
result coercion: our new, rewritten application will have kind Type, but we
want to make sure that the result coercion casts this back to Star. (Why?
Because we started with an application of kind Star, and rewriting is homogeneous.)

So, we have to twiddle the result coercion appropriately.

Let's check whether this is well-typed. We know

  a :: forall (k :: Type). k -> k

  a (forall j. j -> Type) :: (forall j. j -> Type) -> forall j. j -> Type

  a (forall j. j -> Type)
    Proxy
      :: forall j. j -> Type

  a (forall j. j -> Type)
    Proxy
    Bool
      :: Bool -> Type

  a (forall j. j -> Type)
    Proxy
    Bool
    False
      :: Type

  a (forall j. j -> Type)
    Proxy
    Bool
    False
     |> res_co
     :: Star

as desired.

Whew.

Historical note: I (Richard E) once thought that the final part of the kind
had to be a variable k (as in the example above). But it might not be: it could
be an application of a variable. Here is the example:

  let f :: forall (a :: Type) (b :: a -> Type). b (Any @a)
      k :: Type
      x :: k

  rewrite (f @Type @((->) k) x)

After instantiating [a |-> Type, b |-> ((->) k)], we see that `b (Any @a)`
is `k -> Any @a`, and thus the third argument of `x :: k` is well-kinded.

-}

-- | Stores 'Reductions' as well as a kind coercion.
--
-- Used when rewriting arguments to a type function @f@.
--
-- Invariant:
--   when the stored reductions are of the form
--     co_i :: ty_i ~ xi_i,
--   the kind coercion is of the form
--      kco :: typeKind (f ty_1 ... ty_n) ~ typeKind (f xi_1 ... xi_n)
--
-- The type function @f@ depends on context.
data ArgsReductions =
  ArgsReductions
    {-# UNPACK #-} !Reductions
    !MCoercionN
  -- The strictness annotations and UNPACK pragma here are crucial
  -- to getting good performance in simplifyArgsWorker's tight loop.

-- This is shared between the rewriter and the normaliser in GHC.Core.FamInstEnv.
-- See Note [simplifyArgsWorker]
{-# INLINE simplifyArgsWorker #-}
-- NB. INLINE yields a ~1% decrease in allocations in T9872d compared to INLINEABLE
-- This function is only called in two locations, so the amount of code duplication
-- should be rather reasonable despite the size of the function.
simplifyArgsWorker :: HasDebugCallStack
                   => [PiTyBinder] -> Kind
                       -- the binders & result kind (not a Π-type) of the function applied to the args
                       -- list of binders can be shorter or longer than the list of args
                   -> TyCoVarSet   -- free vars of the args
                   -> Infinite Role-- list of roles, r
                   -> [Reduction]  -- rewritten type arguments, arg_i
                                   -- each comes with the coercion used to rewrite it,
                                   -- arg_co_i :: ty_i ~ arg_i
                   -> ArgsReductions
-- Returns ArgsReductions (Reductions cos xis) res_co, where co_i :: ty_i ~ xi_i,
-- and res_co :: kind (f ty_1 ... ty_n) ~ kind (f xi_1 ... xi_n), where f is the function
-- that we are applying.
-- Precondition: if f :: forall bndrs. inner_ki (where bndrs and inner_ki are passed in),
-- then (f ty_1 ... ty_n) is well kinded. Note that (f arg_1 ... arg_n) might *not* be well-kinded.
-- Massaging the arg_i in order to make the function application well-kinded is what this
-- function is all about. That is, (f xi_1 ... xi_n), where xi_i are the returned arguments,
-- *is* well kinded.
simplifyArgsWorker :: HasDebugCallStack =>
[PiTyBinder]
-> Type
-> TyCoVarSet
-> Infinite Role
-> [Reduction]
-> ArgsReductions
simplifyArgsWorker [PiTyBinder]
orig_ki_binders Type
orig_inner_ki TyCoVarSet
orig_fvs
                   Infinite Role
orig_roles [Reduction]
orig_simplified_args
  = LiftingContext
-> [PiTyBinder]
-> Type
-> Infinite Role
-> [Reduction]
-> ArgsReductions
go LiftingContext
orig_lc
       [PiTyBinder]
orig_ki_binders Type
orig_inner_ki
       Infinite Role
orig_roles [Reduction]
orig_simplified_args
  where
    orig_lc :: LiftingContext
orig_lc = InScopeSet -> LiftingContext
emptyLiftingContext (InScopeSet -> LiftingContext) -> InScopeSet -> LiftingContext
forall a b. (a -> b) -> a -> b
$ TyCoVarSet -> InScopeSet
mkInScopeSet TyCoVarSet
orig_fvs

    go :: LiftingContext  -- mapping from tyvars to rewriting coercions
       -> [PiTyBinder]    -- Unsubsted binders of function's kind
       -> Kind            -- Unsubsted result kind of function (not a Pi-type)
       -> Infinite Role   -- Roles at which to rewrite these ...
       -> [Reduction]     -- rewritten arguments, with their rewriting coercions
       -> ArgsReductions
    go :: LiftingContext
-> [PiTyBinder]
-> Type
-> Infinite Role
-> [Reduction]
-> ArgsReductions
go !LiftingContext
lc [PiTyBinder]
binders Type
inner_ki Infinite Role
_ []
        -- The !lc makes the function strict in the lifting context
        -- which means GHC can unbox that pair.  A modest win.
      = Reductions -> MCoercionN -> ArgsReductions
ArgsReductions
          ([Coercion] -> [Type] -> Reductions
mkReductions [] [])
          MCoercionN
kind_co
      where
        final_kind :: Type
final_kind = [PiTyBinder] -> Type -> Type
mkPiTys [PiTyBinder]
binders Type
inner_ki
        kind_co :: MCoercionN
kind_co | Type -> Bool
noFreeVarsOfType Type
final_kind = MCoercionN
MRefl
                | Bool
otherwise                   = Coercion -> MCoercionN
MCo (Coercion -> MCoercionN) -> Coercion -> MCoercionN
forall a b. (a -> b) -> a -> b
$ HasDebugCallStack => Role -> LiftingContext -> Type -> Coercion
Role -> LiftingContext -> Type -> Coercion
liftCoSubst Role
Nominal LiftingContext
lc Type
final_kind

    go LiftingContext
lc (PiTyBinder
binder:[PiTyBinder]
binders) Type
inner_ki (Inf Role
role Infinite Role
roles) (Reduction
arg_redn:[Reduction]
arg_redns)
      =  -- We rewrite an argument ty with arg_redn = Reduction arg_co arg
         -- By Note [Rewriting] in GHC.Tc.Solver.Rewrite invariant (F2),
         -- typeKind(ty) = typeKind(arg).
         -- However, it is possible that arg will be used as an argument to a function
         -- whose kind is different, if earlier arguments have been rewritten.
         -- We thus need to compose the reduction with a kind coercion to ensure
         -- well-kindedness (see the call to mkCoherenceRightRedn below).
         --
         -- The bangs here have been observed to improve performance
         -- significantly in optimized builds; see #18502
         let !kind_co :: Coercion
kind_co = HasDebugCallStack => Role -> LiftingContext -> Type -> Coercion
Role -> LiftingContext -> Type -> Coercion
liftCoSubst Role
Nominal LiftingContext
lc (PiTyBinder -> Type
piTyBinderType PiTyBinder
binder)
             !(Reduction Coercion
casted_co Type
casted_xi)
                      = Role -> Reduction -> Coercion -> Reduction
mkCoherenceRightRedn Role
role Reduction
arg_redn Coercion
kind_co
         -- now, extend the lifting context with the new binding
             !new_lc :: LiftingContext
new_lc | Just TyVar
tv <- PiTyBinder -> Maybe TyVar
namedPiTyBinder_maybe PiTyBinder
binder
                     = LiftingContext -> TyVar -> Coercion -> LiftingContext
extendLiftingContextAndInScope LiftingContext
lc TyVar
tv Coercion
casted_co
                     | Bool
otherwise
                     = LiftingContext
lc
             !(ArgsReductions (Reductions [Coercion]
cos [Type]
xis) MCoercionN
final_kind_co)
               = LiftingContext
-> [PiTyBinder]
-> Type
-> Infinite Role
-> [Reduction]
-> ArgsReductions
go LiftingContext
new_lc [PiTyBinder]
binders Type
inner_ki Infinite Role
roles [Reduction]
arg_redns
         in Reductions -> MCoercionN -> ArgsReductions
ArgsReductions
              ([Coercion] -> [Type] -> Reductions
Reductions (Coercion
casted_coCoercion -> [Coercion] -> [Coercion]
forall a. a -> [a] -> [a]
:[Coercion]
cos) (Type
casted_xiType -> [Type] -> [Type]
forall a. a -> [a] -> [a]
:[Type]
xis))
              MCoercionN
final_kind_co

    -- See Note [Last case in simplifyArgsWorker]
    go LiftingContext
lc [] Type
inner_ki Infinite Role
roles [Reduction]
arg_redns
      = let co1 :: Coercion
co1 = HasDebugCallStack => Role -> LiftingContext -> Type -> Coercion
Role -> LiftingContext -> Type -> Coercion
liftCoSubst Role
Nominal LiftingContext
lc Type
inner_ki
            co1_kind :: Pair Type
co1_kind              = Coercion -> Pair Type
coercionKind Coercion
co1
            unrewritten_tys :: [Type]
unrewritten_tys       = (Reduction -> Type) -> [Reduction] -> [Type]
forall a b. (a -> b) -> [a] -> [b]
map Reduction -> Type
reductionOriginalType [Reduction]
arg_redns
            ([Coercion]
arg_cos, Coercion
res_co)     = HasDebugCallStack =>
Coercion -> Pair Type -> [Type] -> ([Coercion], Coercion)
Coercion -> Pair Type -> [Type] -> ([Coercion], Coercion)
decomposePiCos Coercion
co1 Pair Type
co1_kind [Type]
unrewritten_tys
            casted_args :: [Reduction]
casted_args           = Bool -> SDoc -> [Reduction] -> [Reduction]
forall a. HasCallStack => Bool -> SDoc -> a -> a
assertPpr ([Reduction] -> [Coercion] -> Bool
forall a b. [a] -> [b] -> Bool
equalLength [Reduction]
arg_redns [Coercion]
arg_cos)
                                              ([Reduction] -> SDoc
forall a. Outputable a => a -> SDoc
ppr [Reduction]
arg_redns SDoc -> SDoc -> SDoc
forall doc. IsDoc doc => doc -> doc -> doc
$$ [Coercion] -> SDoc
forall a. Outputable a => a -> SDoc
ppr [Coercion]
arg_cos)
                                  ([Reduction] -> [Reduction]) -> [Reduction] -> [Reduction]
forall a b. (a -> b) -> a -> b
$ (Role -> Reduction -> Coercion -> Reduction)
-> [Role] -> [Reduction] -> [Coercion] -> [Reduction]
forall a b c d. (a -> b -> c -> d) -> [a] -> [b] -> [c] -> [d]
zipWith3 Role -> Reduction -> Coercion -> Reduction
mkCoherenceRightRedn (Infinite Role -> [Role]
forall a. Infinite a -> [a]
Inf.toList Infinite Role
roles) [Reduction]
arg_redns [Coercion]
arg_cos
               -- In general decomposePiCos can return fewer cos than tys,
               -- but not here; because we're well typed, there will be enough
               -- binders. Note that decomposePiCos does substitutions, so even
               -- if the original substitution results in something ending with
               -- ... -> k, that k will be substituted to perhaps reveal more
               -- binders.
            zapped_lc :: LiftingContext
zapped_lc             = LiftingContext -> LiftingContext
zapLiftingContext LiftingContext
lc
            Pair Type
rewritten_kind Type
_ = Pair Type
co1_kind
            ([PiTyBinder]
bndrs, Type
new_inner)    = Type -> ([PiTyBinder], Type)
splitPiTys Type
rewritten_kind

            ArgsReductions Reductions
redns_out MCoercionN
res_co_out
              = LiftingContext
-> [PiTyBinder]
-> Type
-> Infinite Role
-> [Reduction]
-> ArgsReductions
go LiftingContext
zapped_lc [PiTyBinder]
bndrs Type
new_inner Infinite Role
roles [Reduction]
casted_args
        in
          Reductions -> MCoercionN -> ArgsReductions
ArgsReductions Reductions
redns_out (Coercion
res_co Coercion -> MCoercionN -> MCoercionN
`mkTransMCoR` MCoercionN
res_co_out)