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

Desugaring arrow commands

\begin{code}
module DsArrows ( dsProcExpr ) where

#include "HsVersions.h"

import Match
import DsUtils
import DsMonad

import HsSyn
import TcHsSyn

-- 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, dsLocalBinds )

import TcType
import Type
import CoreSyn
import CoreFVs
import CoreUtils

import Id
import Name
import PrelInfo
import DataCon
import TysWiredIn
import BasicTypes
import PrelNames
import Util

import HsUtils
import VarSet
import SrcLoc
\end{code}

\begin{code}
data DsCmdEnv = DsCmdEnv {
	meth_binds :: [CoreBind],
	arr_id, compose_id, first_id, app_id, choice_id, loop_id :: CoreExpr
    }

mkCmdEnv :: SyntaxTable Id -> DsM DsCmdEnv
mkCmdEnv ids
  = dsSyntaxTable ids			`thenDs` \ (meth_binds, ds_meths) ->
    return $ DsCmdEnv {
		meth_binds = meth_binds,
		arr_id	   = Var (lookupEvidence ds_meths arrAName),
		compose_id = Var (lookupEvidence ds_meths composeAName),
		first_id   = Var (lookupEvidence ds_meths firstAName),
		app_id	   = Var (lookupEvidence ds_meths appAName),
		choice_id  = Var (lookupEvidence ds_meths choiceAName),
		loop_id	   = Var (lookupEvidence ds_meths loopAName)
	    }

bindCmdEnv :: DsCmdEnv -> CoreExpr -> CoreExpr
bindCmdEnv ids body = foldr Let body (meth_binds ids)

-- 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]

-- map_arrow (f :: b -> c) (g :: a c d) = arr f >>> g :: a b d
do_map_arrow :: DsCmdEnv -> Type -> Type -> Type ->
		CoreExpr -> CoreExpr -> CoreExpr
do_map_arrow ids b_ty c_ty d_ty f c
  = do_compose ids b_ty c_ty d_ty (do_arr ids b_ty c_ty f) c

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) -> b
mkSndExpr :: Type -> Type -> DsM CoreExpr
mkSndExpr a_ty b_ty
  = newSysLocalDs a_ty			`thenDs` \ a_var ->
    newSysLocalDs b_ty			`thenDs` \ b_var ->
    newSysLocalDs (mkCorePairTy a_ty b_ty)	`thenDs` \ pair_var ->
    returnDs (Lam pair_var
		  (coreCasePair pair_var a_var b_var (Var b_var)))
\end{code}

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

\begin{code}
-- 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 (tupleCon Boxed 2), [var1, var2], body)]
\end{code}

\begin{code}
mkCorePairTy :: Type -> Type -> Type
mkCorePairTy t1 t2 = mkCoreTupTy [t1, t2]

mkCorePairExpr :: CoreExpr -> CoreExpr -> CoreExpr
mkCorePairExpr e1 e2 = mkCoreTup [e1, e2]
\end{code}

The input is divided into a local environment, which is a flat tuple
(unless it's too big), and a stack, each element of which is paired
with the stack in turn.  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.

\begin{code}
envStackType :: [Id] -> [Type] -> Type
envStackType ids stack_tys = foldl mkCorePairTy (mkTupleType ids) stack_tys

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

buildEnvStack :: [Id] -> [Id] -> CoreExpr
buildEnvStack env_ids stack_ids
  = foldl mkCorePairExpr (mkTupleExpr env_ids) (map Var stack_ids)

----------------------------------------------
-- 		matchEnvStack
--
--	\ (...((x1,...,xn),s1),...sk) -> e
--	=>
--	\ zk ->
--	case zk of (zk-1,sk) ->
--	...
--	case z1 of (z0,s1) ->
--	case z0 of (x1,...,xn) ->
--	e

matchEnvStack	:: [Id] 	-- x1..xn
		-> [Id] 	-- s1..sk
		-> CoreExpr 	-- e
		-> DsM CoreExpr
matchEnvStack env_ids stack_ids body
  = newUniqueSupply			`thenDs` \ uniqs ->
    newSysLocalDs (mkTupleType env_ids)	`thenDs` \ tup_var ->
    matchVarStack tup_var stack_ids 
		  (coreCaseTuple uniqs tup_var env_ids body)


----------------------------------------------
-- 		matchVarStack
--
--	\ (...(z0,s1),...sk) -> e
--	=>
--	\ zk ->
--	case zk of (zk-1,sk) ->
--	...
--	case z1 of (z0,s1) ->
--	e

matchVarStack :: Id 		-- z0
	      -> [Id] 		-- s1..sk
	      -> CoreExpr 	-- e
	      -> DsM CoreExpr
matchVarStack env_id [] body
  = returnDs (Lam env_id body)
matchVarStack env_id (stack_id:stack_ids) body
  = newSysLocalDs (mkCorePairTy (idType env_id) (idType stack_id))
					`thenDs` \ pair_id ->
    matchVarStack pair_id stack_ids 
		  (coreCasePair pair_id env_id stack_id body)
\end{code}

\begin{code}
mkHsTupleExpr :: [HsExpr Id] -> HsExpr Id
mkHsTupleExpr [e] = e
mkHsTupleExpr es = ExplicitTuple (map noLoc es) Boxed

mkHsPairExpr :: HsExpr Id -> HsExpr Id -> HsExpr Id
mkHsPairExpr e1 e2 = mkHsTupleExpr [e1, e2]

mkHsEnvStackExpr :: [Id] -> [Id] -> HsExpr Id
mkHsEnvStackExpr env_ids stack_ids
  = foldl mkHsPairExpr (mkHsTupleExpr (map HsVar env_ids)) (map HsVar stack_ids)
\end{code}

Translation of arrow abstraction

\begin{code}

--	A | xs |- c :: [] t'  	    ---> c'
--	--------------------------
--	A |- proc p -> c :: a t t'  ---> arr (\ p -> (xs)) >>> c'
--
--		where (xs) is the tuple of variables bound by p

dsProcExpr
	:: LPat Id
	-> LHsCmdTop Id
	-> DsM CoreExpr
dsProcExpr pat (L _ (HsCmdTop cmd [] cmd_ty ids))
  = mkCmdEnv ids			`thenDs` \ meth_ids ->
    let
	locals = mkVarSet (collectPatBinders pat)
    in
    dsfixCmd meth_ids locals [] cmd_ty cmd
				`thenDs` \ (core_cmd, free_vars, env_ids) ->
    let
	env_ty = mkTupleType env_ids
    in
    mkFailExpr ProcExpr env_ty		`thenDs` \ fail_expr ->
    selectSimpleMatchVarL pat		`thenDs` \ var ->
    matchSimply (Var var) ProcExpr pat (mkTupleExpr env_ids) fail_expr
					`thenDs` \ match_code ->
    let
	pat_ty = hsLPatType pat
	proc_code = do_map_arrow meth_ids pat_ty env_ty cmd_ty
		(Lam var match_code)
		core_cmd
    in
    returnDs (bindCmdEnv meth_ids proc_code)
\end{code}

Translation of command judgements of the form

	A | xs |- c :: [ts] t

\begin{code}
dsLCmd ids local_vars env_ids stack res_ty cmd
  = dsCmd ids local_vars env_ids stack res_ty (unLoc cmd)

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

--	A |- f :: a (t*ts) t'
--	A, xs |- arg :: t
--	-----------------------------
--	A | xs |- f -< arg :: [ts] t'
--
--		---> arr (\ ((xs)*ts) -> (arg*ts)) >>> f

dsCmd ids local_vars env_ids stack res_ty
	(HsArrApp arrow arg arrow_ty HsFirstOrderApp _)
  = let
	(a_arg_ty, _res_ty') = tcSplitAppTy arrow_ty
        (_a_ty, arg_ty) = tcSplitAppTy a_arg_ty
	env_ty = mkTupleType env_ids
    in
    dsLExpr arrow			`thenDs` \ core_arrow ->
    dsLExpr arg				`thenDs` \ core_arg ->
    mappM newSysLocalDs stack		`thenDs` \ stack_ids ->
    matchEnvStack env_ids stack_ids
	(foldl mkCorePairExpr core_arg (map Var stack_ids))
					`thenDs` \ core_make_arg ->
    returnDs (do_map_arrow ids
		(envStackType env_ids stack)
		arg_ty
		res_ty
		core_make_arg
		core_arrow,
	      exprFreeVars core_arg `intersectVarSet` local_vars)

--	A, xs |- f :: a (t*ts) t'
--	A, xs |- arg :: t
--	------------------------------
--	A | xs |- f -<< arg :: [ts] t'
--
--		---> arr (\ ((xs)*ts) -> (f,(arg*ts))) >>> app

dsCmd ids local_vars env_ids stack res_ty
	(HsArrApp arrow arg arrow_ty HsHigherOrderApp _)
  = let
	(a_arg_ty, _res_ty') = tcSplitAppTy arrow_ty
        (_a_ty, arg_ty) = tcSplitAppTy a_arg_ty
	env_ty = mkTupleType env_ids
    in
    dsLExpr arrow			`thenDs` \ core_arrow ->
    dsLExpr arg				`thenDs` \ core_arg ->
    mappM newSysLocalDs stack		`thenDs` \ stack_ids ->
    matchEnvStack env_ids stack_ids
	(mkCorePairExpr core_arrow
		(foldl mkCorePairExpr core_arg (map Var stack_ids)))
					`thenDs` \ core_make_pair ->
    returnDs (do_map_arrow ids
		(envStackType env_ids stack)
		(mkCorePairTy arrow_ty arg_ty)
		res_ty
		core_make_pair
		(do_app ids arg_ty res_ty),
	      (exprFreeVars core_arrow `unionVarSet` exprFreeVars core_arg)
		`intersectVarSet` local_vars)

--	A | ys |- c :: [t:ts] t'
--	A, xs  |- e :: t
--	------------------------
--	A | xs |- c e :: [ts] t'
--
--		---> arr (\ ((xs)*ts) -> let z = e in (((ys),z)*ts)) >>> c

dsCmd ids local_vars env_ids stack res_ty (HsApp cmd arg)
  = dsLExpr arg			`thenDs` \ core_arg ->
    let
	arg_ty = exprType core_arg
	stack' = arg_ty:stack
    in
    dsfixCmd ids local_vars stack' res_ty cmd
				`thenDs` \ (core_cmd, free_vars, env_ids') ->
    mappM newSysLocalDs stack	`thenDs` \ stack_ids ->
    newSysLocalDs arg_ty	`thenDs` \ arg_id ->
    -- push the argument expression onto the stack
    let
	core_body = bindNonRec arg_id core_arg
			(buildEnvStack env_ids' (arg_id:stack_ids))
    in
    -- match the environment and stack against the input
    matchEnvStack env_ids stack_ids core_body
				`thenDs` \ core_map ->
    returnDs (do_map_arrow ids
			(envStackType env_ids stack)
			(envStackType env_ids' stack')
			res_ty
			core_map
			core_cmd,
	(exprFreeVars core_arg `intersectVarSet` local_vars)
		`unionVarSet` free_vars)

--	A | ys |- c :: [ts] t'
--	-----------------------------------------------
--	A | xs |- \ p1 ... pk -> c :: [t1:...:tk:ts] t'
--
--		---> arr (\ ((((xs), p1), ... pk)*ts) -> ((ys)*ts)) >>> c

dsCmd ids local_vars env_ids stack res_ty
    (HsLam (MatchGroup [L _ (Match pats _ (GRHSs [L _ (GRHS [] body)] _ ))] _))
  = let
	pat_vars = mkVarSet (collectPatsBinders pats)
	local_vars' = local_vars `unionVarSet` pat_vars
	stack' = drop (length pats) stack
    in
    dsfixCmd ids local_vars' stack' res_ty body
				`thenDs` \ (core_body, free_vars, env_ids') ->
    mappM newSysLocalDs stack	`thenDs` \ stack_ids ->

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

    let
        (actual_ids, stack_ids') = splitAt (length pats) stack_ids
	-- build a new environment, plus what's left of the stack
	core_expr = buildEnvStack env_ids' stack_ids'
	in_ty = envStackType env_ids stack
	in_ty' = envStackType env_ids' stack'
    in
    mkFailExpr LambdaExpr in_ty'	`thenDs` \ fail_expr ->
    -- match the patterns against the top of the old stack
    matchSimplys (map Var actual_ids) LambdaExpr pats core_expr fail_expr
					`thenDs` \ match_code ->
    -- match the old environment and stack against the input
    matchEnvStack env_ids stack_ids match_code
					`thenDs` \ select_code ->
    returnDs (do_map_arrow ids in_ty in_ty' res_ty select_code core_body,
	     free_vars `minusVarSet` pat_vars)

dsCmd ids local_vars env_ids stack res_ty (HsPar cmd)
  = dsLCmd ids local_vars env_ids stack res_ty cmd

--	A, xs |- e :: Bool
--	A | xs1 |- c1 :: [ts] t
--	A | xs2 |- c2 :: [ts] t
--	----------------------------------------
--	A | xs |- if e then c1 else c2 :: [ts] t
--
--		---> arr (\ ((xs)*ts) ->
--			if e then Left ((xs1)*ts) else Right ((xs2)*ts)) >>>
--		     c1 ||| c2

dsCmd ids local_vars env_ids stack res_ty (HsIf cond then_cmd else_cmd)
  = dsLExpr cond			`thenDs` \ core_cond ->
    dsfixCmd ids local_vars stack res_ty then_cmd
				`thenDs` \ (core_then, fvs_then, then_ids) ->
    dsfixCmd ids local_vars stack res_ty else_cmd
				`thenDs` \ (core_else, fvs_else, else_ids) ->
    mappM newSysLocalDs stack		`thenDs` \ stack_ids ->
    dsLookupTyCon eitherTyConName	`thenDs` \ either_con ->
    dsLookupDataCon leftDataConName	`thenDs` \ left_con ->
    dsLookupDataCon rightDataConName	`thenDs` \ right_con ->
    let
	left_expr ty1 ty2 e = mkConApp left_con [Type ty1, Type ty2, e]
	right_expr ty1 ty2 e = mkConApp right_con [Type ty1, Type ty2, e]

	in_ty = envStackType env_ids stack
	then_ty = envStackType then_ids stack
	else_ty = envStackType else_ids stack
	sum_ty = mkTyConApp either_con [then_ty, else_ty]
	fvs_cond = exprFreeVars core_cond `intersectVarSet` local_vars
    in
    matchEnvStack env_ids stack_ids
	(mkIfThenElse core_cond
	    (left_expr then_ty else_ty (buildEnvStack then_ids stack_ids))
	    (right_expr then_ty else_ty (buildEnvStack else_ids stack_ids)))
					`thenDs` \ core_if ->
    returnDs(do_map_arrow ids in_ty sum_ty res_ty
		core_if
		(do_choice ids then_ty else_ty res_ty core_then core_else),
	fvs_cond `unionVarSet` fvs_then `unionVarSet` fvs_else)
\end{code}

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

	arr (\ ((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 quadruples decribing segments of the list of
case bodies, containing the following fields:
1. an IdSet containing the environment variables free in the case bodies
2. a list of expressions of the form (Left|Right)* ((xs)*ts), to be put
   into the case replacing the commands
3. a sum type that is the common type of these expressions, and also the
   input type of the arrow
4. a CoreExpr for an arrow built by combining the translated command
   bodies with |||.

\begin{code}
dsCmd ids local_vars env_ids stack res_ty (HsCase exp (MatchGroup matches match_ty))
  = dsLExpr exp				`thenDs` \ core_exp ->
    mappM newSysLocalDs stack		`thenDs` \ stack_ids ->

    -- 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)
	  = dsfixCmd ids (local_vars `unionVarSet` bound_vars) stack res_ty leaf
			   `thenDs` \ (core_leaf, fvs, leaf_ids) ->
	    returnDs (fvs `minusVarSet` bound_vars,
		      [noLoc $ mkHsEnvStackExpr leaf_ids stack_ids],
		      envStackType leaf_ids stack,
		      core_leaf)
    in
    mappM make_branch leaves		`thenDs` \ branches ->
    dsLookupTyCon eitherTyConName	`thenDs` \ either_con ->
    dsLookupDataCon leftDataConName	`thenDs` \ left_con ->
    dsLookupDataCon rightDataConName	`thenDs` \ right_con ->
    let
	left_id  = HsVar (dataConWrapId left_con)
	right_id = HsVar (dataConWrapId right_con)
	left_expr  ty1 ty2 e = noLoc $ HsApp (noLoc $ HsWrap (mkWpTyApps [ty1, ty2]) left_id ) e
	right_expr ty1 ty2 e = noLoc $ HsApp (noLoc $ HsWrap (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 (fvs1, builds1, in_ty1, core_exp1)
		       (fvs2, builds2, in_ty2, core_exp2) 
	  = (fvs1 `unionVarSet` fvs2,
	     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)
	(fvs_alts, 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
	fvs_exp = exprFreeVars core_exp `intersectVarSet` local_vars

	pat_ty    = funArgTy match_ty
	match_ty' = mkFunTy pat_ty sum_ty
	-- Note that we replace the HsCase result type by sum_ty,
	-- which is the type of matches'
    in
    dsExpr (HsCase exp (MatchGroup matches' match_ty')) `thenDs` \ core_body ->
    matchEnvStack env_ids stack_ids core_body
					`thenDs` \ core_matches ->
    returnDs(do_map_arrow ids in_ty sum_ty res_ty core_matches core_choices,
	     fvs_exp `unionVarSet` fvs_alts)

--	A | ys |- c :: [ts] t
--	----------------------------------
--	A | xs |- let binds in c :: [ts] t
--
--		---> arr (\ ((xs)*ts) -> let binds in ((ys)*ts)) >>> c

dsCmd ids local_vars env_ids stack res_ty (HsLet binds body)
  = let
	defined_vars = mkVarSet (map unLoc (collectLocalBinders binds))
	local_vars' = local_vars `unionVarSet` defined_vars
    in
    dsfixCmd ids local_vars' stack res_ty body
				`thenDs` \ (core_body, free_vars, env_ids') ->
    mappM newSysLocalDs stack		`thenDs` \ stack_ids ->
    -- build a new environment, plus the stack, using the let bindings
    dsLocalBinds binds (buildEnvStack env_ids' stack_ids)
					`thenDs` \ core_binds ->
    -- match the old environment and stack against the input
    matchEnvStack env_ids stack_ids core_binds
					`thenDs` \ core_map ->
    returnDs (do_map_arrow ids
			(envStackType env_ids stack)
			(envStackType env_ids' stack)
			res_ty
			core_map
			core_body,
	exprFreeVars core_binds `intersectVarSet` local_vars)

dsCmd ids local_vars env_ids [] res_ty (HsDo _ctxt stmts body _)
  = dsCmdDo ids local_vars env_ids res_ty stmts body

--	A |- e :: forall e. a1 (e*ts1) t1 -> ... an (e*tsn) tn -> a (e*ts) t
--	A | xs |- ci :: [tsi] ti
--	-----------------------------------
--	A | xs |- (|e c1 ... cn|) :: [ts] t	---> e [t_xs] c1 ... cn

dsCmd _ids local_vars env_ids _stack _res_ty (HsArrForm op _ args)
  = let
	env_ty = mkTupleType env_ids
    in
    dsLExpr op				`thenDs` \ core_op ->
    mapAndUnzipDs (dsTrimCmdArg local_vars env_ids) args
					`thenDs` \ (core_args, fv_sets) ->
    returnDs (mkApps (App core_op (Type env_ty)) core_args,
	      unionVarSets fv_sets)


dsCmd ids local_vars env_ids stack res_ty (HsTick ix vars expr)
  = dsLCmd ids local_vars env_ids stack res_ty expr `thenDs` \ (expr1,id_set) ->
    mkTickBox ix vars expr1                    	    `thenDs` \ expr2 ->
    return (expr2,id_set)

--	A | ys |- c :: [ts] t	(ys <= xs)
--	---------------------
--	A | xs |- c :: [ts] t	---> arr_ts (\ (xs) -> (ys)) >>> c

dsTrimCmdArg
	:: IdSet		-- set of local vars available to this command
	-> [Id]			-- list of vars in the input to this command
	-> LHsCmdTop Id	-- command argument to desugar
	-> DsM (CoreExpr,	-- desugared expression
		IdSet)		-- set of local vars that occur free
dsTrimCmdArg local_vars env_ids (L _ (HsCmdTop cmd stack cmd_ty ids))
  = mkCmdEnv ids			`thenDs` \ meth_ids ->
    dsfixCmd meth_ids local_vars stack cmd_ty cmd
				`thenDs` \ (core_cmd, free_vars, env_ids') ->
    mappM newSysLocalDs stack		`thenDs` \ stack_ids ->
    matchEnvStack env_ids stack_ids (buildEnvStack env_ids' stack_ids)
					`thenDs` \ trim_code ->
    let
	in_ty = envStackType env_ids stack
	in_ty' = envStackType env_ids' stack
	arg_code = if env_ids' == env_ids then core_cmd else
		do_map_arrow meth_ids in_ty in_ty' cmd_ty trim_code core_cmd
    in
    returnDs (bindCmdEnv meth_ids arg_code, free_vars)

-- Given A | xs |- c :: [ts] t, builds c with xs fed back.
-- Typically needs to be prefixed with arr (\p -> ((xs)*ts))

dsfixCmd
	:: DsCmdEnv		-- arrow combinators
	-> IdSet		-- set of local vars available to this command
	-> [Type]		-- type of the stack
	-> Type			-- return type of the command
	-> LHsCmd Id		-- command to desugar
	-> DsM (CoreExpr,	-- desugared expression
		IdSet,		-- set of local vars that occur free
		[Id])		-- set as a list, fed back
dsfixCmd ids local_vars stack cmd_ty cmd
  = fixDs (\ ~(_,_,env_ids') ->
	dsLCmd ids local_vars env_ids' stack cmd_ty cmd
					`thenDs` \ (core_cmd, free_vars) ->
	returnDs (core_cmd, free_vars, varSetElems free_vars))

\end{code}

Translation of command judgements of the form

	A | xs |- do { ss } :: [] t

\begin{code}

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

--	A | xs |- c :: [] t
--	--------------------------
--	A | xs |- do { c } :: [] t

dsCmdDo ids local_vars env_ids res_ty [] body
  = dsLCmd ids local_vars env_ids [] res_ty body

dsCmdDo ids local_vars env_ids res_ty (stmt:stmts) body
  = let
	bound_vars = mkVarSet (map unLoc (collectLStmtBinders stmt))
	local_vars' = local_vars `unionVarSet` bound_vars
    in
    fixDs (\ ~(_,_,env_ids') ->
	dsCmdDo ids local_vars' env_ids' res_ty stmts body
					`thenDs` \ (core_stmts, fv_stmts) ->
	returnDs (core_stmts, fv_stmts, varSetElems fv_stmts))
				`thenDs` \ (core_stmts, fv_stmts, env_ids') ->
    dsCmdLStmt ids local_vars env_ids env_ids' stmt
				`thenDs` \ (core_stmt, fv_stmt) ->
    returnDs (do_compose ids
		(mkTupleType env_ids)
		(mkTupleType env_ids')
		res_ty
		core_stmt
		core_stmts,
	      fv_stmt)

\end{code}
A statement maps one local environment to another, and is represented
as an arrow from one tuple type to another.  A statement sequence is
translated to a composition of such arrows.
\begin{code}
dsCmdLStmt ids local_vars env_ids out_ids cmd
  = dsCmdStmt ids local_vars env_ids out_ids (unLoc cmd)

dsCmdStmt
	:: DsCmdEnv		-- arrow combinators
	-> IdSet		-- set of local vars available to this statement
	-> [Id]			-- list of vars in the input to this statement
				-- This is typically fed back,
				-- so don't pull on it too early
	-> [Id]			-- list of vars in the output of this statement
	-> Stmt Id	-- statement to desugar
	-> DsM (CoreExpr,	-- desugared expression
		IdSet)		-- set of local vars that occur free

--	A | xs1 |- c :: [] t
--	A | xs' |- do { ss } :: [] t'
--	------------------------------
--	A | xs |- do { c; ss } :: [] t'
--
--		---> arr (\ (xs) -> ((xs1),(xs'))) >>> first c >>>
--			arr snd >>> ss

dsCmdStmt ids local_vars env_ids out_ids (ExprStmt cmd _ c_ty)
  = dsfixCmd ids local_vars [] c_ty cmd
				`thenDs` \ (core_cmd, fv_cmd, env_ids1) ->
    matchEnvStack env_ids []
	(mkCorePairExpr (mkTupleExpr env_ids1) (mkTupleExpr out_ids))
					`thenDs` \ core_mux ->
    let
	in_ty = mkTupleType env_ids
	in_ty1 = mkTupleType env_ids1
	out_ty = mkTupleType out_ids
	before_c_ty = mkCorePairTy in_ty1 out_ty
	after_c_ty = mkCorePairTy c_ty out_ty
    in
    mkSndExpr c_ty out_ty		`thenDs` \ snd_fn ->
    returnDs (do_map_arrow ids in_ty before_c_ty out_ty core_mux $
		do_compose ids before_c_ty after_c_ty out_ty
			(do_first ids in_ty1 c_ty out_ty core_cmd) $
		do_arr ids after_c_ty out_ty snd_fn,
	      extendVarSetList fv_cmd out_ids)
  where

--	A | xs1 |- c :: [] t
--	A | xs' |- do { ss } :: [] t'		xs2 = xs' - defs(p)
--	-----------------------------------
--	A | xs |- do { p <- c; ss } :: [] t'
--
--		---> arr (\ (xs) -> ((xs1),(xs2))) >>> first c >>>
--			arr (\ (p, (xs2)) -> (xs')) >>> ss
--
-- It would be simpler and more consistent to do this using second,
-- but that's likely to be defined in terms of first.

dsCmdStmt ids local_vars env_ids out_ids (BindStmt pat cmd _ _)
  = dsfixCmd ids local_vars [] (hsLPatType pat) cmd
				`thenDs` \ (core_cmd, fv_cmd, env_ids1) ->
    let
	pat_ty = hsLPatType pat
	pat_vars = mkVarSet (collectPatBinders pat)
	env_ids2 = varSetElems (mkVarSet out_ids `minusVarSet` pat_vars)
	env_ty2 = mkTupleType env_ids2
    in

    -- multiplexing function
    --		\ (xs) -> ((xs1),(xs2))

    matchEnvStack env_ids []
	(mkCorePairExpr (mkTupleExpr env_ids1) (mkTupleExpr env_ids2))
					`thenDs` \ core_mux ->

    -- projection function
    --		\ (p, (xs2)) -> (zs)

    newSysLocalDs env_ty2		`thenDs` \ env_id ->
    newUniqueSupply			`thenDs` \ uniqs ->
    let
	after_c_ty = mkCorePairTy pat_ty env_ty2
	out_ty = mkTupleType out_ids
	body_expr = coreCaseTuple uniqs env_id env_ids2 (mkTupleExpr out_ids)
    in
    mkFailExpr (StmtCtxt DoExpr) out_ty	`thenDs` \ fail_expr ->
    selectSimpleMatchVarL pat		`thenDs` \ pat_id ->
    matchSimply (Var pat_id) (StmtCtxt DoExpr) pat body_expr fail_expr
					`thenDs` \ match_code ->
    newSysLocalDs after_c_ty		`thenDs` \ pair_id ->
    let
	proj_expr = Lam pair_id (coreCasePair pair_id pat_id env_id match_code)
    in

    -- put it all together
    let
	in_ty = mkTupleType env_ids
	in_ty1 = mkTupleType env_ids1
	in_ty2 = mkTupleType env_ids2
	before_c_ty = mkCorePairTy in_ty1 in_ty2
    in
    returnDs (do_map_arrow ids in_ty before_c_ty out_ty core_mux $
		do_compose ids before_c_ty after_c_ty out_ty
			(do_first ids in_ty1 pat_ty in_ty2 core_cmd) $
		do_arr ids after_c_ty out_ty proj_expr,
	      fv_cmd `unionVarSet` (mkVarSet out_ids `minusVarSet` pat_vars))

--	A | xs' |- do { ss } :: [] t
--	--------------------------------------
--	A | xs |- do { let binds; ss } :: [] t
--
--		---> arr (\ (xs) -> let binds in (xs')) >>> ss

dsCmdStmt ids local_vars env_ids out_ids (LetStmt binds)
    -- build a new environment using the let bindings
  = dsLocalBinds binds (mkTupleExpr out_ids)	`thenDs` \ core_binds ->
    -- match the old environment against the input
    matchEnvStack env_ids [] core_binds	`thenDs` \ core_map ->
    returnDs (do_arr ids
			(mkTupleType env_ids)
			(mkTupleType out_ids)
			core_map,
	exprFreeVars core_binds `intersectVarSet` local_vars)

--	A | ys |- do { ss; returnA -< ((xs1), (ys2)) } :: [] ...
--	A | xs' |- do { ss' } :: [] t
--	------------------------------------
--	A | xs |- do { rec ss; ss' } :: [] t
--
--			xs1 = xs' /\ defs(ss)
--			xs2 = xs' - defs(ss)
--			ys1 = ys - defs(ss)
--			ys2 = ys /\ defs(ss)
--
--		---> arr (\(xs) -> ((ys1),(xs2))) >>>
--			first (loop (arr (\((ys1),~(ys2)) -> (ys)) >>> ss)) >>>
--			arr (\((xs1),(xs2)) -> (xs')) >>> ss'

dsCmdStmt ids local_vars env_ids out_ids (RecStmt stmts later_ids rec_ids rhss binds)
  = let		-- ToDo: ****** binds not desugared; ROSS PLEASE FIX ********
	env2_id_set = mkVarSet out_ids `minusVarSet` mkVarSet later_ids
	env2_ids = varSetElems env2_id_set
	env2_ty = mkTupleType env2_ids
    in

    -- post_loop_fn = \((later_ids),(env2_ids)) -> (out_ids)

    newUniqueSupply		`thenDs` \ uniqs ->
    newSysLocalDs env2_ty	`thenDs` \ env2_id ->
    let
	later_ty = mkTupleType later_ids
	post_pair_ty = mkCorePairTy later_ty env2_ty
	post_loop_body = coreCaseTuple uniqs env2_id env2_ids (mkTupleExpr out_ids)
    in
    matchEnvStack later_ids [env2_id] post_loop_body
				`thenDs` \ post_loop_fn ->

    --- loop (...)

    dsRecCmd ids local_vars stmts later_ids rec_ids rhss
				`thenDs` \ (core_loop, env1_id_set, env1_ids) ->

    -- pre_loop_fn = \(env_ids) -> ((env1_ids),(env2_ids))

    let
	env1_ty = mkTupleType env1_ids
	pre_pair_ty = mkCorePairTy env1_ty env2_ty
	pre_loop_body = mkCorePairExpr (mkTupleExpr env1_ids)
					(mkTupleExpr env2_ids)

    in
    matchEnvStack env_ids [] pre_loop_body
				`thenDs` \ pre_loop_fn ->

    -- arr pre_loop_fn >>> first (loop (...)) >>> arr post_loop_fn

    let
	env_ty = mkTupleType env_ids
	out_ty = mkTupleType out_ids
	core_body = do_map_arrow ids env_ty pre_pair_ty out_ty
		pre_loop_fn
		(do_compose ids pre_pair_ty post_pair_ty out_ty
			(do_first ids env1_ty later_ty env2_ty
				core_loop)
			(do_arr ids post_pair_ty out_ty
				post_loop_fn))
    in
    returnDs (core_body, env1_id_set `unionVarSet` env2_id_set)

--	loop (arr (\ ((env1_ids), ~(rec_ids)) -> (env_ids)) >>>
--	      ss >>>
--	      arr (\ (out_ids) -> ((later_ids),(rhss))) >>>

dsRecCmd ids local_vars stmts later_ids rec_ids rhss
  = let
	rec_id_set = mkVarSet rec_ids
	out_ids = varSetElems (mkVarSet later_ids `unionVarSet` rec_id_set)
	out_ty = mkTupleType out_ids
	local_vars' = local_vars `unionVarSet` rec_id_set
    in

    -- mk_pair_fn = \ (out_ids) -> ((later_ids),(rhss))

    mappM dsExpr rhss		`thenDs` \ core_rhss ->
    let
	later_tuple = mkTupleExpr later_ids
	later_ty = mkTupleType later_ids
	rec_tuple = mkBigCoreTup core_rhss
	rec_ty = mkTupleType rec_ids
	out_pair = mkCorePairExpr later_tuple rec_tuple
	out_pair_ty = mkCorePairTy later_ty rec_ty
    in
	matchEnvStack out_ids [] out_pair
				`thenDs` \ mk_pair_fn ->

    -- ss

    dsfixCmdStmts ids local_vars' out_ids stmts
				`thenDs` \ (core_stmts, fv_stmts, env_ids) ->

    -- squash_pair_fn = \ ((env1_ids), ~(rec_ids)) -> (env_ids)

    newSysLocalDs rec_ty	`thenDs` \ rec_id ->
    let
	env1_id_set = fv_stmts `minusVarSet` rec_id_set
	env1_ids = varSetElems env1_id_set
	env1_ty = mkTupleType env1_ids
	in_pair_ty = mkCorePairTy env1_ty rec_ty
	core_body = mkBigCoreTup (map selectVar env_ids)
	  where
	    selectVar v
		| v `elemVarSet` rec_id_set
		  = mkTupleSelector rec_ids v rec_id (Var rec_id)
		| otherwise = Var v
    in
    matchEnvStack env1_ids [rec_id] core_body
				`thenDs` \ squash_pair_fn ->

    -- loop (arr squash_pair_fn >>> ss >>> arr mk_pair_fn)

    let
	env_ty = mkTupleType env_ids
	core_loop = do_loop ids env1_ty later_ty rec_ty
		(do_map_arrow ids in_pair_ty env_ty out_pair_ty
			squash_pair_fn
			(do_compose ids env_ty out_ty out_pair_ty
				core_stmts
				(do_arr ids out_ty out_pair_ty mk_pair_fn)))
    in
    returnDs (core_loop, env1_id_set, env1_ids)

\end{code}
A sequence of statements (as in a rec) is desugared to an arrow between
two environments
\begin{code}

dsfixCmdStmts
	:: DsCmdEnv		-- arrow combinators
	-> IdSet		-- set of local vars available to this statement
	-> [Id]			-- output vars of these statements
	-> [LStmt Id]	-- statements to desugar
	-> DsM (CoreExpr,	-- desugared expression
		IdSet,		-- set of local vars that occur free
		[Id])		-- input vars

dsfixCmdStmts ids local_vars out_ids stmts
  = fixDs (\ ~(_,_,env_ids) ->
	dsCmdStmts ids local_vars env_ids out_ids stmts
					`thenDs` \ (core_stmts, fv_stmts) ->
	returnDs (core_stmts, fv_stmts, varSetElems fv_stmts))

dsCmdStmts
	:: DsCmdEnv		-- arrow combinators
	-> IdSet		-- set of local vars available to this statement
	-> [Id]			-- list of vars in the input to these statements
	-> [Id]			-- output vars of these statements
	-> [LStmt Id]	-- statements to desugar
	-> DsM (CoreExpr,	-- desugared expression
		IdSet)		-- set of local vars that occur free

dsCmdStmts ids local_vars env_ids out_ids [stmt]
  = dsCmdLStmt ids local_vars env_ids out_ids stmt

dsCmdStmts ids local_vars env_ids out_ids (stmt:stmts)
  = let
	bound_vars = mkVarSet (map unLoc (collectLStmtBinders stmt))
	local_vars' = local_vars `unionVarSet` bound_vars
    in
    dsfixCmdStmts ids local_vars' out_ids stmts
				`thenDs` \ (core_stmts, fv_stmts, env_ids') ->
    dsCmdLStmt ids local_vars env_ids env_ids' stmt
				`thenDs` \ (core_stmt, fv_stmt) ->
    returnDs (do_compose ids
		(mkTupleType env_ids)
		(mkTupleType env_ids')
		(mkTupleType out_ids)
		core_stmt
		core_stmts,
	      fv_stmt)

\end{code}

Match a list of expressions against a list of patterns, left-to-right.

\begin{code}
matchSimplys :: [CoreExpr]              -- Scrutinees
	     -> HsMatchContext Name	-- Match kind
	     -> [LPat Id]         	-- Patterns they should match
	     -> CoreExpr                -- Return this if they all match
	     -> CoreExpr                -- Return this if they don't
	     -> DsM CoreExpr
matchSimplys [] _ctxt [] result_expr _fail_expr = returnDs result_expr
matchSimplys (exp:exps) ctxt (pat:pats) result_expr fail_expr
  = matchSimplys exps ctxt pats result_expr fail_expr
					`thenDs` \ match_code ->
    matchSimply exp ctxt pat match_code fail_expr
\end{code}

List of leaf expressions, with set of variables bound in each

\begin{code}
leavesMatch :: LMatch Id -> [(LHsExpr Id, IdSet)]
leavesMatch (L _ (Match pats _ (GRHSs grhss binds)))
  = let
	defined_vars = mkVarSet (collectPatsBinders pats)
			`unionVarSet`
		       mkVarSet (map unLoc (collectLocalBinders binds))
    in
    [(expr, 
      mkVarSet (map unLoc (collectLStmtsBinders stmts)) 
	`unionVarSet` defined_vars) 
    | L _ (GRHS stmts expr) <- grhss]
\end{code}

Replace the leaf commands in a match

\begin{code}
replaceLeavesMatch
	:: Type			-- new result type
	-> [LHsExpr Id]	-- replacement leaf expressions of that type
	-> LMatch Id	-- the matches of a case command
	-> ([LHsExpr Id],-- remaining leaf expressions
	    LMatch Id)	-- updated match
replaceLeavesMatch res_ty leaves (L loc (Match pat mt (GRHSs grhss binds)))
  = let
	(leaves', grhss') = mapAccumL replaceLeavesGRHS leaves grhss
    in
    (leaves', L loc (Match pat mt (GRHSs grhss' binds)))

replaceLeavesGRHS
	:: [LHsExpr Id]	-- replacement leaf expressions of that type
	-> LGRHS Id	-- rhss of a case command
	-> ([LHsExpr Id],-- remaining leaf expressions
	    LGRHS Id)	-- updated GRHS
replaceLeavesGRHS (leaf:leaves) (L loc (GRHS stmts rhs))
  = (leaves, L loc (GRHS stmts leaf))
\end{code}

Balanced fold of a non-empty list.

\begin{code}
foldb :: (a -> a -> a) -> [a] -> a
foldb _ [] = error "foldb of empty list"
foldb _ [x] = x
foldb f xs = foldb f (fold_pairs xs)
  where
    fold_pairs [] = []
    fold_pairs [x] = [x]
    fold_pairs (x1:x2:xs) = f x1 x2:fold_pairs xs
\end{code}