DsArrows.hs

{-
(c) The University of Glasgow 2006
(c) The GRASP/AQUA Project, Glasgow University, 1992-1998


Desugaring arrow commands
-}

{-# LANGUAGE CPP #-}
{-# LANGUAGE TypeFamilies #-}
{-# LANGUAGE ViewPatterns #-}

module DsArrows ( dsProcExpr ) where

#include "HsVersions.h"

import GhcPrelude

import Match
import DsUtils
import DsMonad

import HsSyn    hiding (collectPatBinders, collectPatsBinders,
                        collectLStmtsBinders, collectLStmtBinders,
                        collectStmtBinders )
import TcHsSyn
import qualified HsUtils

-- NB: The desugarer, which straddles the source and Core worlds, sometimes
--     needs to see source types (newtypes etc), and sometimes not
--     So WATCH OUT; check each use of split*Ty functions.
-- Sigh.  This is a pain.

import {-# SOURCE #-} DsExpr ( dsExpr, dsLExpr, dsLExprNoLP, dsLocalBinds,
                               dsSyntaxExpr )

import TcType
import Type ( splitPiTy )
import TcEvidence
import CoreSyn
import CoreFVs
import CoreUtils
import MkCore
import DsBinds (dsHsWrapper)

import Name
import Id
import ConLike
import TysWiredIn
import BasicTypes
import PrelNames
import Outputable
import VarSet
import SrcLoc
import ListSetOps( assocMaybe )
import Data.List
import Util
import UniqDSet

data DsCmdEnv = DsCmdEnv {
        arr_id, compose_id, first_id, app_id, choice_id, loop_id :: CoreExpr
    }

mkCmdEnv :: CmdSyntaxTable GhcTc -> DsM ([CoreBind], DsCmdEnv)
-- See Note [CmdSyntaxTable] in HsExpr
mkCmdEnv tc_meths
  = do { (meth_binds, prs) <- mapAndUnzipM mk_bind tc_meths

       -- NB: Some of these lookups might fail, but that's OK if the
       -- symbol is never used. That's why we use Maybe first and then
       -- panic. An eager panic caused trouble in typecheck/should_compile/tc192
       ; let the_arr_id     = assocMaybe prs arrAName
             the_compose_id = assocMaybe prs composeAName
             the_first_id   = assocMaybe prs firstAName
             the_app_id     = assocMaybe prs appAName
             the_choice_id  = assocMaybe prs choiceAName
             the_loop_id    = assocMaybe prs loopAName

           -- used as an argument in, e.g., do_premap
       ; check_lev_poly 3 the_arr_id

           -- used as an argument in, e.g., dsCmdStmt/BodyStmt
       ; check_lev_poly 5 the_compose_id

           -- used as an argument in, e.g., dsCmdStmt/BodyStmt
       ; check_lev_poly 4 the_first_id

           -- the result of the_app_id is used as an argument in, e.g.,
           -- dsCmd/HsCmdArrApp/HsHigherOrderApp
       ; check_lev_poly 2 the_app_id

           -- used as an argument in, e.g., HsCmdIf
       ; check_lev_poly 5 the_choice_id

           -- used as an argument in, e.g., RecStmt
       ; check_lev_poly 4 the_loop_id

       ; return (meth_binds, DsCmdEnv {
               arr_id     = Var (unmaybe the_arr_id arrAName),
               compose_id = Var (unmaybe the_compose_id composeAName),
               first_id   = Var (unmaybe the_first_id firstAName),
               app_id     = Var (unmaybe the_app_id appAName),
               choice_id  = Var (unmaybe the_choice_id choiceAName),
               loop_id    = Var (unmaybe the_loop_id loopAName)
             }) }
  where
    mk_bind (std_name, expr)
      = do { rhs <- dsExpr expr
           ; id <- newSysLocalDs (exprType rhs)
           -- no check needed; these are functions
           ; return (NonRec id rhs, (std_name, id)) }

    unmaybe Nothing name = pprPanic "mkCmdEnv" (text "Not found:" <+> ppr name)
    unmaybe (Just id) _  = id

      -- returns the result type of a pi-type (that is, a forall or a function)
      -- Note that this result type may be ill-scoped.
    res_type :: Type -> Type
    res_type ty = res_ty
      where
        (_, res_ty) = splitPiTy ty

    check_lev_poly :: Int -- arity
                   -> Maybe Id -> DsM ()
    check_lev_poly _     Nothing = return ()
    check_lev_poly arity (Just id)
      = dsNoLevPoly (nTimes arity res_type (idType id))
          (text "In the result of the function" <+> quotes (ppr id))


-- arr :: forall b c. (b -> c) -> a b c
do_arr :: DsCmdEnv -> Type -> Type -> CoreExpr -> CoreExpr
do_arr ids b_ty c_ty f = mkApps (arr_id ids) [Type b_ty, Type c_ty, f]

-- (>>>) :: forall b c d. a b c -> a c d -> a b d
do_compose :: DsCmdEnv -> Type -> Type -> Type ->
                CoreExpr -> CoreExpr -> CoreExpr
do_compose ids b_ty c_ty d_ty f g
  = mkApps (compose_id ids) [Type b_ty, Type c_ty, Type d_ty, f, g]

-- first :: forall b c d. a b c -> a (b,d) (c,d)
do_first :: DsCmdEnv -> Type -> Type -> Type -> CoreExpr -> CoreExpr
do_first ids b_ty c_ty d_ty f
  = mkApps (first_id ids) [Type b_ty, Type c_ty, Type d_ty, f]

-- app :: forall b c. a (a b c, b) c
do_app :: DsCmdEnv -> Type -> Type -> CoreExpr
do_app ids b_ty c_ty = mkApps (app_id ids) [Type b_ty, Type c_ty]

-- (|||) :: forall b d c. a b d -> a c d -> a (Either b c) d
-- note the swapping of d and c
do_choice :: DsCmdEnv -> Type -> Type -> Type ->
                CoreExpr -> CoreExpr -> CoreExpr
do_choice ids b_ty c_ty d_ty f g
  = mkApps (choice_id ids) [Type b_ty, Type d_ty, Type c_ty, f, g]

-- loop :: forall b d c. a (b,d) (c,d) -> a b c
-- note the swapping of d and c
do_loop :: DsCmdEnv -> Type -> Type -> Type -> CoreExpr -> CoreExpr
do_loop ids b_ty c_ty d_ty f
  = mkApps (loop_id ids) [Type b_ty, Type d_ty, Type c_ty, f]

-- premap :: forall b c d. (b -> c) -> a c d -> a b d
-- premap f g = arr f >>> g
do_premap :: DsCmdEnv -> Type -> Type -> Type ->
                CoreExpr -> CoreExpr -> CoreExpr
do_premap ids b_ty c_ty d_ty f g
   = do_compose ids b_ty c_ty d_ty (do_arr ids b_ty c_ty f) g

mkFailExpr :: HsMatchContext Id -> Type -> DsM CoreExpr
mkFailExpr ctxt ty
  = mkErrorAppDs pAT_ERROR_ID ty (matchContextErrString ctxt)

-- construct CoreExpr for \ (a :: a_ty, b :: b_ty) -> a
mkFstExpr :: Type -> Type -> DsM CoreExpr
mkFstExpr a_ty b_ty = do
    a_var <- newSysLocalDs a_ty
    b_var <- newSysLocalDs b_ty
    pair_var <- newSysLocalDs (mkCorePairTy a_ty b_ty)
    return (Lam pair_var
               (coreCasePair pair_var a_var b_var (Var a_var)))

-- construct CoreExpr for \ (a :: a_ty, b :: b_ty) -> b
mkSndExpr :: Type -> Type -> DsM CoreExpr
mkSndExpr a_ty b_ty = do
    a_var <- newSysLocalDs a_ty
    b_var <- newSysLocalDs b_ty
    pair_var <- newSysLocalDs (mkCorePairTy a_ty b_ty)
    return (Lam pair_var
               (coreCasePair pair_var a_var b_var (Var b_var)))

{-
Build case analysis of a tuple.  This cannot be done in the DsM monad,
because the list of variables is typically not yet defined.
-}

-- coreCaseTuple [u1..] v [x1..xn] body
--      = case v of v { (x1, .., xn) -> body }
-- But the matching may be nested if the tuple is very big

coreCaseTuple :: UniqSupply -> Id -> [Id] -> CoreExpr -> CoreExpr
coreCaseTuple uniqs scrut_var vars body
  = mkTupleCase uniqs vars body scrut_var (Var scrut_var)

coreCasePair :: Id -> Id -> Id -> CoreExpr -> CoreExpr
coreCasePair scrut_var var1 var2 body
  = Case (Var scrut_var) scrut_var (exprType body)
         [(DataAlt (tupleDataCon Boxed 2), [var1, var2], body)]

mkCorePairTy :: Type -> Type -> Type
mkCorePairTy t1 t2 = mkBoxedTupleTy [t1, t2]

mkCorePairExpr :: CoreExpr -> CoreExpr -> CoreExpr
mkCorePairExpr e1 e2 = mkCoreTup [e1, e2]

mkCoreUnitExpr :: CoreExpr
mkCoreUnitExpr = mkCoreTup []

{-
The input is divided into a local environment, which is a flat tuple
(unless it's too big), and a stack, which is a right-nested pair.
In general, the input has the form

        ((x1,...,xn), (s1,...(sk,())...))

where xi are the environment values, and si the ones on the stack,
with s1 being the "top", the first one to be matched with a lambda.
-}

envStackType :: [Id] -> Type -> Type
envStackType ids stack_ty = mkCorePairTy (mkBigCoreVarTupTy ids) stack_ty

-- splitTypeAt n (t1,... (tn,t)...) = ([t1, ..., tn], t)
splitTypeAt :: Int -> Type -> ([Type], Type)
splitTypeAt n ty
  | n == 0 = ([], ty)
  | otherwise = case tcTyConAppArgs ty of
      [t, ty'] -> let (ts, ty_r) = splitTypeAt (n-1) ty' in (t:ts, ty_r)
      _ -> pprPanic "splitTypeAt" (ppr ty)

----------------------------------------------
--              buildEnvStack
--
--      ((x1,...,xn),stk)

buildEnvStack :: [Id] -> Id -> CoreExpr
buildEnvStack env_ids stack_id
  = mkCorePairExpr (mkBigCoreVarTup env_ids) (Var stack_id)

----------------------------------------------
--              matchEnvStack
--
--      \ ((x1,...,xn),stk) -> body
--      =>
--      \ pair ->
--      case pair of (tup,stk) ->
--      case tup of (x1,...,xn) ->
--      body

matchEnvStack   :: [Id]         -- x1..xn
                -> Id           -- stk
                -> CoreExpr     -- e
                -> DsM CoreExpr
matchEnvStack env_ids stack_id body = do
    uniqs <- newUniqueSupply
    tup_var <- newSysLocalDs (mkBigCoreVarTupTy env_ids)
    let match_env = coreCaseTuple uniqs tup_var env_ids body
    pair_id <- newSysLocalDs (mkCorePairTy (idType tup_var) (idType stack_id))
    return (Lam pair_id (coreCasePair pair_id tup_var stack_id match_env))

----------------------------------------------
--              matchEnv
--
--      \ (x1,...,xn) -> body
--      =>
--      \ tup ->
--      case tup of (x1,...,xn) ->
--      body

matchEnv :: [Id]        -- x1..xn
         -> CoreExpr    -- e
         -> DsM CoreExpr
matchEnv env_ids body = do
    uniqs <- newUniqueSupply
    tup_id <- newSysLocalDs (mkBigCoreVarTupTy env_ids)
    return (Lam tup_id (coreCaseTuple uniqs tup_id env_ids body))

----------------------------------------------
--              matchVarStack
--
--      case (x1, ...(xn, s)...) -> e
--      =>
--      case z0 of (x1,z1) ->
--      case zn-1 of (xn,s) ->
--      e
matchVarStack :: [Id] -> Id -> CoreExpr -> DsM (Id, CoreExpr)
matchVarStack [] stack_id body = return (stack_id, body)
matchVarStack (param_id:param_ids) stack_id body = do
    (tail_id, tail_code) <- matchVarStack param_ids stack_id body
    pair_id <- newSysLocalDs (mkCorePairTy (idType param_id) (idType tail_id))
    return (pair_id, coreCasePair pair_id param_id tail_id tail_code)

mkHsEnvStackExpr :: [Id] -> Id -> LHsExpr GhcTc
mkHsEnvStackExpr env_ids stack_id
  = mkLHsTupleExpr [mkLHsVarTuple env_ids, nlHsVar stack_id]

-- Translation of arrow abstraction

-- D; xs |-a c : () --> t'      ---> c'
-- --------------------------
-- D |- proc p -> c :: a t t'   ---> premap (\ p -> ((xs),())) c'
--
--              where (xs) is the tuple of variables bound by p

dsProcExpr
        :: LPat GhcTc
        -> LHsCmdTop GhcTc
        -> DsM CoreExpr
dsProcExpr pat (dL->L _ (HsCmdTop (CmdTopTc _unitTy cmd_ty ids) cmd)) = do
    (meth_binds, meth_ids) <- mkCmdEnv ids
    let locals = mkVarSet (collectPatBinders pat)
    (core_cmd, _free_vars, env_ids)
       <- dsfixCmd meth_ids locals unitTy cmd_ty cmd
    let env_ty = mkBigCoreVarTupTy env_ids
    let env_stk_ty = mkCorePairTy env_ty unitTy
    let env_stk_expr = mkCorePairExpr (mkBigCoreVarTup env_ids) mkCoreUnitExpr
    fail_expr <- mkFailExpr ProcExpr env_stk_ty
    var <- selectSimpleMatchVarL pat
    match_code <- matchSimply (Var var) ProcExpr pat env_stk_expr fail_expr
    let pat_ty = hsLPatType pat
    let proc_code = do_premap meth_ids pat_ty env_stk_ty cmd_ty
                    (Lam var match_code)
                    core_cmd
    return (mkLets meth_binds proc_code)
dsProcExpr _ _ = panic "dsProcExpr"

{-
Translation of a command judgement of the form

        D; xs |-a c : stk --> t

to an expression e such that

        D |- e :: a (xs, stk) t
-}

dsLCmd :: DsCmdEnv -> IdSet -> Type -> Type -> LHsCmd GhcTc -> [Id]
       -> DsM (CoreExpr, DIdSet)
dsLCmd ids local_vars stk_ty res_ty cmd env_ids
  = dsCmd ids local_vars stk_ty res_ty (unLoc cmd) env_ids

dsCmd   :: DsCmdEnv             -- arrow combinators
        -> IdSet                -- set of local vars available to this command
        -> Type                 -- type of the stack (right-nested tuple)
        -> Type                 -- return type of the command
        -> HsCmd GhcTc           -- command to desugar
        -> [Id]           -- list of vars in the input to this command
                                -- This is typically fed back,
                                -- so don't pull on it too early
        -> DsM (CoreExpr,       -- desugared expression
                DIdSet)         -- subset of local vars that occur free

-- D |- fun :: a t1 t2
-- D, xs |- arg :: t1
-- -----------------------------
-- D; xs |-a fun -< arg : stk --> t2
--
--              ---> premap (\ ((xs), _stk) -> arg) fun

dsCmd ids local_vars stack_ty res_ty
        (HsCmdArrApp arrow_ty arrow arg HsFirstOrderApp _)
        env_ids = do
    let
        (a_arg_ty, _res_ty') = tcSplitAppTy arrow_ty
        (_a_ty, arg_ty) = tcSplitAppTy a_arg_ty
    core_arrow <- dsLExprNoLP arrow
    core_arg   <- dsLExpr arg
    stack_id   <- newSysLocalDs stack_ty
    core_make_arg <- matchEnvStack env_ids stack_id core_arg
    return (do_premap ids
              (envStackType env_ids stack_ty)
              arg_ty
              res_ty
              core_make_arg
              core_arrow,
            exprFreeIdsDSet core_arg `uniqDSetIntersectUniqSet` local_vars)

-- D, xs |- fun :: a t1 t2
-- D, xs |- arg :: t1
-- ------------------------------
-- D; xs |-a fun -<< arg : stk --> t2
--
--              ---> premap (\ ((xs), _stk) -> (fun, arg)) app

dsCmd ids local_vars stack_ty res_ty
        (HsCmdArrApp arrow_ty arrow arg HsHigherOrderApp _)
        env_ids = do
    let
        (a_arg_ty, _res_ty') = tcSplitAppTy arrow_ty
        (_a_ty, arg_ty) = tcSplitAppTy a_arg_ty

    core_arrow <- dsLExpr arrow
    core_arg   <- dsLExpr arg
    stack_id   <- newSysLocalDs stack_ty
    core_make_pair <- matchEnvStack env_ids stack_id
          (mkCorePairExpr core_arrow core_arg)

    return (do_premap ids
              (envStackType env_ids stack_ty)
              (mkCorePairTy arrow_ty arg_ty)
              res_ty
              core_make_pair
              (do_app ids arg_ty res_ty),
            (exprsFreeIdsDSet [core_arrow, core_arg])
              `uniqDSetIntersectUniqSet` local_vars)

-- D; ys |-a cmd : (t,stk) --> t'
-- D, xs |-  exp :: t
-- ------------------------
-- D; xs |-a cmd exp : stk --> t'
--
--              ---> premap (\ ((xs),stk) -> ((ys),(e,stk))) cmd

dsCmd ids local_vars stack_ty res_ty (HsCmdApp _ cmd arg) env_ids = do
    core_arg <- dsLExpr arg
    let
        arg_ty = exprType core_arg
        stack_ty' = mkCorePairTy arg_ty stack_ty
    (core_cmd, free_vars, env_ids')
             <- dsfixCmd ids local_vars stack_ty' res_ty cmd
    stack_id <- newSysLocalDs stack_ty
    arg_id <- newSysLocalDsNoLP arg_ty
    -- push the argument expression onto the stack
    let
        stack' = mkCorePairExpr (Var arg_id) (Var stack_id)
        core_body = bindNonRec arg_id core_arg
                        (mkCorePairExpr (mkBigCoreVarTup env_ids') stack')

    -- match the environment and stack against the input
    core_map <- matchEnvStack env_ids stack_id core_body
    return (do_premap ids
                      (envStackType env_ids stack_ty)
                      (envStackType env_ids' stack_ty')
                      res_ty
                      core_map
                      core_cmd,
            free_vars `unionDVarSet`
              (exprFreeIdsDSet core_arg `uniqDSetIntersectUniqSet` local_vars))

-- D; ys |-a cmd : stk t'
-- -----------------------------------------------
-- D; xs |-a \ p1 ... pk -> cmd : (t1,...(tk,stk)...) t'
--
--              ---> premap (\ ((xs), (p1, ... (pk,stk)...)) -> ((ys),stk)) cmd

dsCmd ids local_vars stack_ty res_ty
        (HsCmdLam _ (MG { mg_alts
          = (dL->L _ [dL->L _ (Match { m_pats  = pats
                       , m_grhss = GRHSs _ [dL->L _ (GRHS _ [] body)] _ })]) }))
        env_ids = do
    let pat_vars = mkVarSet (collectPatsBinders pats)
    let
        local_vars' = pat_vars `unionVarSet` local_vars
        (pat_tys, stack_ty') = splitTypeAt (length pats) stack_ty
    (core_body, free_vars, env_ids')
       <- dsfixCmd ids local_vars' stack_ty' res_ty body
    param_ids <- mapM newSysLocalDsNoLP pat_tys
    stack_id' <- newSysLocalDs stack_ty'

    -- the expression is built from the inside out, so the actions
    -- are presented in reverse order

    let
        -- build a new environment, plus what's left of the stack
        core_expr = buildEnvStack env_ids' stack_id'
        in_ty = envStackType env_ids stack_ty
        in_ty' = envStackType env_ids' stack_ty'

    fail_expr <- mkFailExpr LambdaExpr in_ty'
    -- match the patterns against the parameters
    match_code <- matchSimplys (map Var param_ids) LambdaExpr pats core_expr
                    fail_expr
    -- match the parameters against the top of the old stack
    (stack_id, param_code) <- matchVarStack param_ids stack_id' match_code
    -- match the old environment and stack against the input
    select_code <- matchEnvStack env_ids stack_id param_code
    return (do_premap ids in_ty in_ty' res_ty select_code core_body,
            free_vars `uniqDSetMinusUniqSet` pat_vars)

dsCmd ids local_vars stack_ty res_ty (HsCmdPar _ cmd) env_ids
  = dsLCmd ids local_vars stack_ty res_ty cmd env_ids

-- D, xs |- e :: Bool
-- D; xs1 |-a c1 : stk --> t
-- D; xs2 |-a c2 : stk --> t
-- ----------------------------------------
-- D; xs |-a if e then c1 else c2 : stk --> t
--
--              ---> premap (\ ((xs),stk) ->
--                       if e then Left ((xs1),stk) else Right ((xs2),stk))
--                     (c1 ||| c2)

dsCmd ids local_vars stack_ty res_ty (HsCmdIf _ mb_fun cond then_cmd else_cmd)
        env_ids = do
    core_cond <- dsLExpr cond
    (core_then, fvs_then, then_ids)
       <- dsfixCmd ids local_vars stack_ty res_ty then_cmd
    (core_else, fvs_else, else_ids)
       <- dsfixCmd ids local_vars stack_ty res_ty else_cmd
    stack_id   <- newSysLocalDs stack_ty
    either_con <- dsLookupTyCon eitherTyConName
    left_con   <- dsLookupDataCon leftDataConName
    right_con  <- dsLookupDataCon rightDataConName

    let mk_left_expr ty1 ty2 e = mkCoreConApps left_con   [Type ty1,Type ty2, e]
        mk_right_expr ty1 ty2 e = mkCoreConApps right_con [Type ty1,Type ty2, e]

        in_ty = envStackType env_ids stack_ty
        then_ty = envStackType then_ids stack_ty
        else_ty = envStackType else_ids stack_ty
        sum_ty = mkTyConApp either_con [then_ty, else_ty]
        fvs_cond = exprFreeIdsDSet core_cond
                   `uniqDSetIntersectUniqSet` local_vars

        core_left  = mk_left_expr  then_ty else_ty
                       (buildEnvStack then_ids stack_id)
        core_right = mk_right_expr then_ty else_ty
                       (buildEnvStack else_ids stack_id)

    core_if <- case mb_fun of
       Just fun -> do { fun_apps <- dsSyntaxExpr fun
                                      [core_cond, core_left, core_right]
                      ; matchEnvStack env_ids stack_id fun_apps }
       Nothing  -> matchEnvStack env_ids stack_id $
                   mkIfThenElse core_cond core_left core_right

    return (do_premap ids in_ty sum_ty res_ty
                core_if
                (do_choice ids then_ty else_ty res_ty core_then core_else),
        fvs_cond `unionDVarSet` fvs_then `unionDVarSet` fvs_else)

{-
Case commands are treated in much the same way as if commands
(see above) except that there are more alternatives.  For example

        case e of { p1 -> c1; p2 -> c2; p3 -> c3 }

is translated to

        premap (\ ((xs)*ts) -> case e of
                p1 -> (Left (Left (xs1)*ts))
                p2 -> Left ((Right (xs2)*ts))
                p3 -> Right ((xs3)*ts))
        ((c1 ||| c2) ||| c3)

The idea is to extract the commands from the case, build a balanced tree
of choices, and replace the commands with expressions that build tagged
tuples, obtaining a case expression that can be desugared normally.
To build all this, we use triples describing segments of the list of
case bodies, containing the following fields:
 * a list of expressions of the form (Left|Right)* ((xs)*ts), to be put
   into the case replacing the commands
 * a sum type that is the common type of these expressions, and also the
   input type of the arrow
 * a CoreExpr for an arrow built by combining the translated command
   bodies with |||.
-}

dsCmd ids local_vars stack_ty res_ty
      (HsCmdCase _ exp (MG { mg_alts = (dL->L l matches)
                           , mg_ext = MatchGroupTc arg_tys _
                           , mg_origin = origin }))
      env_ids = do
    stack_id <- newSysLocalDs stack_ty

    -- Extract and desugar the leaf commands in the case, building tuple
    -- expressions that will (after tagging) replace these leaves

    let
        leaves = concatMap leavesMatch matches
        make_branch (leaf, bound_vars) = do
            (core_leaf, _fvs, leaf_ids)
               <- dsfixCmd ids (bound_vars `unionVarSet` local_vars) stack_ty
                    res_ty leaf
            return ([mkHsEnvStackExpr leaf_ids stack_id],
                    envStackType leaf_ids stack_ty,
                    core_leaf)

    branches <- mapM make_branch leaves
    either_con <- dsLookupTyCon eitherTyConName
    left_con <- dsLookupDataCon leftDataConName
    right_con <- dsLookupDataCon rightDataConName
    let
        left_id  = HsConLikeOut noExtField (RealDataCon left_con)
        right_id = HsConLikeOut noExtField (RealDataCon right_con)
        left_expr  ty1 ty2 e = noLoc $ HsApp noExtField
                           (noLoc $ mkHsWrap (mkWpTyApps [ty1, ty2]) left_id ) e
        right_expr ty1 ty2 e = noLoc $ HsApp noExtField
                           (noLoc $ mkHsWrap (mkWpTyApps [ty1, ty2]) right_id) e

        -- Prefix each tuple with a distinct series of Left's and Right's,
        -- in a balanced way, keeping track of the types.

        merge_branches (builds1, in_ty1, core_exp1)
                       (builds2, in_ty2, core_exp2)
          = (map (left_expr in_ty1 in_ty2) builds1 ++
                map (right_expr in_ty1 in_ty2) builds2,
             mkTyConApp either_con [in_ty1, in_ty2],
             do_choice ids in_ty1 in_ty2 res_ty core_exp1 core_exp2)
        (leaves', sum_ty, core_choices) = foldb merge_branches branches

        -- Replace the commands in the case with these tagged tuples,
        -- yielding a HsExpr Id we can feed to dsExpr.

        (_, matches') = mapAccumL (replaceLeavesMatch res_ty) leaves' matches
        in_ty = envStackType env_ids stack_ty

    core_body <- dsExpr (HsCase noExtField exp
                         (MG { mg_alts = cL l matches'
                             , mg_ext = MatchGroupTc arg_tys sum_ty
                             , mg_origin = origin }))
        -- Note that we replace the HsCase result type by sum_ty,
        -- which is the type of matches'

    core_matches <- matchEnvStack env_ids stack_id core_body
    return (do_premap ids in_ty sum_ty res_ty core_matches core_choices,
            exprFreeIdsDSet core_body `uniqDSetIntersectUniqSet` local_vars)

-- D; ys |-a cmd : stk --> t
-- ----------------------------------
-- D; xs |-a let binds in cmd : stk --> t
--
--              ---> premap (\ ((xs),stk) -> let binds in ((ys),stk)) c

dsCmd ids local_vars stack_ty res_ty (HsCmdLet _ lbinds@(dL->L _ binds) body)
                                                                    env_ids = do
    let
        defined_vars = mkVarSet (collectLocalBinders binds)
        local_vars' = defined_vars `unionVarSet` local_vars

    (core_body, _free_vars, env_ids')
       <- dsfixCmd ids local_vars' stack_ty res_ty body
    stack_id <- newSysLocalDs stack_ty
    -- build a new environment, plus the stack, using the let bindings
    core_binds <- dsLocalBinds lbinds (buildEnvStack env_ids' stack_id)
    -- match the old environment and stack against the input
    core_map <- matchEnvStack env_ids stack_id core_binds
    return (do_premap ids
                        (envStackType env_ids stack_ty)
                        (envStackType env_ids' stack_ty)
                        res_ty
                        core_map
                        core_body,
        exprFreeIdsDSet core_binds `uniqDSetIntersectUniqSet` local_vars)

-- D; xs |-a ss : t
-- ----------------------------------
-- D; xs |-a do { ss } : () --> t
--
--              ---> premap (\ (env,stk) -> env) c

dsCmd ids local_vars stack_ty res_ty do_block@(HsCmdDo stmts_ty
                                               (dL->L loc stmts))
                                                                   env_ids = do
    putSrcSpanDs loc $
      dsNoLevPoly stmts_ty
        (text "In the do-command:" <+> ppr do_block)
    (core_stmts, env_ids') <- dsCmdDo ids local_vars res_ty stmts env_ids
    let env_ty = mkBigCoreVarTupTy env_ids
    core_fst <- mkFstExpr env_ty stack_ty
    return (do_premap ids
                (mkCorePairTy env_ty stack_ty)
                env_ty
                res_ty
                core_fst
                core_stmts,
        env_ids')

-- D |- e :: forall e. a1 (e,stk1) t1 -> ... an (e,stkn) tn -> a (e,stk) t
-- D; xs |-a ci :: stki --> ti
-- -----------------------------------
-- D; xs |-a (|e c1 ... cn|) :: stk --> t       ---> e [t_xs] c1 ... cn

dsCmd _ local_vars _stack_ty _res_ty (HsCmdArrForm _ op _ _ args) env_ids = do
    let env_ty = mkBigCoreVarTupTy env_ids
    core_op <- dsLExpr op
    (core_args, fv_sets) <- mapAndUnzipM (dsTrimCmdArg local_vars env_ids) args
    return (mkApps (App core_op (Type env_ty)) core_args,
            unionDVarSets fv_sets)

dsCmd ids local_vars stack_ty res_ty (HsCmdWrap _ wrap cmd) env_ids = do
    (core_cmd, env_ids') <- dsCmd ids local_vars stack_ty res_ty cmd env_ids
    core_wrap <- dsHsWrapper wrap
    return (core_wrap core_cmd, env_ids')

dsCmd _ _ _ _ _ c = pprPanic "dsCmd" (ppr c)

-- D; ys |-a c : stk --> t      (ys <= xs)
-- ---------------------
-- D; xs |-a c : stk --> t      ---> premap (\ ((xs),stk) -> ((ys),stk)) c

dsTrimCmdArg
        :: IdSet                -- set of local vars available to this command
        -> [Id]           -- list of vars in the input to this command
        -> LHsCmdTop GhcTc       -- command argument to desugar
        -> DsM (CoreExpr,       -- desugared expression
                DIdSet)         -- subset of local vars that occur free
dsTrimCmdArg local_vars env_ids
                       (dL->L _ (HsCmdTop
                                 (CmdTopTc stack_ty cmd_ty ids) cmd )) = do
    (meth_binds, meth_ids) <- mkCmdEnv ids
    (core_cmd, free_vars, env_ids')
       <- dsfixCmd meth_ids local_vars stack_ty cmd_ty cmd
    stack_id <- newSysLocalDs stack_ty
    trim_code
      <- matchEnvStack env_ids stack_id (buildEnvStack env_ids' stack_id)
    let
        in_ty = envStackType env_ids stack_ty
        in_ty' = envStackType env_ids' stack_ty
        arg_code = if env_ids' == env_ids then core_cmd else
                do_premap meth_ids in_ty in_ty' cmd_ty trim_code core_cmd
    return (mkLets meth_binds arg_code, free_vars)
dsTrimCmdArg _ _ _ = panic "dsTrimCmdArg"

-- Given D; xs |-a c : stk --> t, builds c with xs fed back.
-- Typically needs to be prefixed with arr (\(p, stk) -> ((xs),stk))

dsfixCmd
        :: DsCmdEnv             -- arrow combinators
        -> IdSet                -- set of local vars available to this command
        -> Type                 -- type of the stack (right-nested tuple)
        -> Type                 -- return type of the command
        -> LHsCmd GhcTc         -- command to desugar
        -> DsM (CoreExpr,       -- desugared expression
                DIdSet,         -- subset of local vars that occur free
                [Id])           -- the same local vars as a list, fed back
dsfixCmd ids local_vars stk_ty cmd_ty cmd
  = do { putSrcSpanDs (getLoc cmd) $ dsNoLevPoly cmd_ty
           (text "When desugaring the command:" <+> ppr cmd)
       ; trimInput (dsLCmd ids local_vars stk_ty cmd_ty cmd) }

-- Feed back the list of local variables actually used a command,
-- for use as the input tuple of the generated arrow.

trimInput
        :: ([Id] -> DsM (CoreExpr, DIdSet))
        -> DsM (CoreExpr,       -- desugared expression
                DIdSet,         -- subset of local vars that occur free
                [Id])           -- same local vars as a list, fed back to
                                -- the inner function to form the tuple of
                                -- inputs to the arrow.
trimInput build_arrow
  = fixDs (\ ~(_,_,env_ids) -> do
        (core_cmd, free_vars) <- build_arrow env_ids
        return (core_cmd, free_vars, dVarSetElems free_vars))

{-
Translation of command judgements of the form

        D |-a do { ss } : t
-}

dsCmdDo :: DsCmdEnv             -- arrow combinators
        -> IdSet                -- set of local vars available to this statement
        -> Type                 -- return type of the statement
        -> [CmdLStmt GhcTc]     -- statements to desugar
        -> [Id]                 -- list of vars in the input to this statement
                                -- This is typically fed back,
                                -- so don't pull on it too early
        -> DsM (CoreExpr,       -- desugared expression
                DIdSet)         -- subset of local vars that occur free

dsCmdDo _ _ _ [] _ = panic "dsCmdDo"

-- D; xs |-a c : () --> t
-- --------------------------
-- D; xs |-a do { c } : t
--
--              ---> premap (\ (xs) -> ((xs), ())) c

dsCmdDo ids local_vars res_ty [dL->L loc (LastStmt _ body _ _)] env_ids = do
    putSrcSpanDs loc $ dsNoLevPoly res_ty
                         (text "In the command:" <+> ppr body)
    (core_body, env_ids') <- dsLCmd ids local_vars unitTy res_ty body env_ids
    let env_ty = mkBigCoreVarTupTy env_ids
    env_var <- newSysLocalDs env_ty
    let core_map = Lam env_var (mkCorePairExpr (Var env_var) mkCoreUnitExpr)
    return (do_premap ids
                        env_ty
                        (mkCorePairTy env_ty unitTy)