1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
|
structure CPS =
struct
fun toCPS (e : Syntax.lexp) (cont : Syntax.value -> Syntax.cexp) : Syntax.cexp =
case e of
Syntax.LVar v => cont (Syntax.VVar v)
| Syntax.LFn (v, expr) =>
let
val fnName = Gensym.new ()
val k = Gensym.new ()
in
Syntax.CFix
([(fnName, [v, k], toCPS expr (fn ret => Syntax.CApp (Syntax.VVar k, [ret])))],
cont (Syntax.VVar fnName))
end
| Syntax.LFix (decls, body) =>
Syntax.CFix
( map
(fn (name, arg, expr) =>
let val w = Gensym.new ()
in
( name
, [arg, w]
, toCPS expr (fn z => Syntax.CApp (Syntax.VVar w, [z]))
)
end)
decls
, toCPS body cont
)
| Syntax.LApp (Syntax.LPrim primop, Syntax.LRecord args) =>
let
val temp = Gensym.new ()
fun go [] acc = Syntax.CPrimop (primop, rev acc, [temp], [cont (Syntax.VVar temp)])
| go (arg :: args) acc = toCPS arg (fn arg' => go args (arg' :: acc))
in go args []
end
| Syntax.LApp (Syntax.LPrim primop, arg) => toCPS (Syntax.LApp (Syntax.LPrim primop, Syntax.LRecord [arg])) cont
| Syntax.LApp (f, x) =>
let
val addr = Gensym.new ()
val arg = Gensym.new ()
in Syntax.CFix
([(addr, [arg], cont (Syntax.VVar arg))],
toCPS f (fn f' =>
toCPS x (fn x' =>
Syntax.CApp (f', [x', Syntax.VVar addr]))))
end
| Syntax.LInt i => cont (Syntax.VInt i)
| Syntax.LString s =>
let val temp = Gensym.new ()
in
Syntax.CRecord
( [(map (fn c => (Syntax.VInt (Char.ord c), [])) (String.explode s), temp)]
, cont (Syntax.VVar temp)
)
end
| Syntax.LRecord [] => cont (Syntax.VInt 0)
| Syntax.LSelect (i, expr) =>
let val temp = Gensym.new ()
in toCPS expr (fn x => Syntax.CSelect (i, x, temp, cont (Syntax.VVar temp)))
end
| Syntax.LRecord exprs =>
let
fun go [] vars =
let val temp = Gensym.new ()
in Syntax.CRecord ([(map (fn v => (v, [])) (rev vars), temp)], cont (Syntax.VVar temp))
end
| go (expr :: exprs) vars =
toCPS expr (fn v => go exprs (v :: vars))
in go exprs []
end
| Syntax.LSwitch (expr, arms, otherwise) =>
let
val sortedArms = Sort.sort (fn ((x, _), (y, _)) => Int.compare (x, y)) arms
val contAddr = Gensym.new ()
val otherwiseAddr = Gensym.new ()
val arg = Gensym.new ()
fun go _ [] cont = Syntax.CApp (Syntax.VVar otherwiseAddr, [])
| go v [(x, arm)] cont =
(case otherwise of
NONE => toCPS arm cont
| SOME _ =>
let val b = Gensym.new ()
in
Syntax.CPrimop
( Syntax.PEq
, [v, Syntax.VInt x]
, [b]
, [ Syntax.CPrimop
( Syntax.PIf
, [Syntax.VVar b]
, []
, [toCPS arm cont, Syntax.CApp (Syntax.VVar otherwiseAddr, [])]
)
]
)
end)
| go v arms cont =
let
val b = Gensym.new ()
val h = length arms div 2
val half1 = List.take (arms, h)
val half2 = List.drop (arms, h)
val (x, _) = hd half2
in
Syntax.CPrimop
( Syntax.PLess
, [v, Syntax.VInt x]
, [b]
, [ Syntax.CPrimop
( Syntax.PIf
, [Syntax.VVar b]
, []
, [go v half1 cont, go v half2 cont]
)
]
)
end
fun contFunc x = Syntax.CApp (Syntax.VVar contAddr, [x])
val fixFuncs = [(contAddr, [arg], cont (Syntax.VVar arg))]
val fixFuncs =
case otherwise of
NONE => fixFuncs
| SOME otherwise => (otherwiseAddr, [], toCPS otherwise contFunc) :: fixFuncs
in
Syntax.CFix
( fixFuncs
, toCPS expr (fn v => go v sortedArms contFunc)
)
end
| _ => raise Fail ("malformed expression " ^ Syntax.lexpToString e)
fun hoist (expr : Syntax.cexp) : Syntax.cexp =
let
fun exprs (Syntax.CRecord (records, k)) = Syntax.CRecord (records, exprs k)
| exprs (Syntax.CSelect (i, arg, res, k)) = Syntax.CSelect (i, arg, res, exprs k)
| exprs (expr as Syntax.CApp _) = expr
| exprs (Syntax.CFix (_, body)) = exprs body
| exprs (Syntax.CPrimop (p, args, res, ks)) = Syntax.CPrimop (p, args, res, (map exprs ks))
fun funs (Syntax.CRecord (_, k)) acc = funs k acc
| funs (Syntax.CSelect (_, _, _, k)) acc = funs k acc
| funs (Syntax.CApp _) acc = acc
| funs (Syntax.CFix (fs, body)) acc =
funs body (foldl (fn ((fName, fVars, fBody), acc) => (fName, fVars, exprs fBody) :: funs fBody acc) acc fs)
| funs (Syntax.CPrimop (_, _, _, ks)) acc = foldl (fn (x, acc) => funs x acc) acc ks
val entryPoint = Gensym.new ()
in
Syntax.CFix ((entryPoint, [], exprs expr) :: funs expr [], Syntax.CApp (Syntax.VLabel entryPoint, []))
end
structure VarMap = Map (type k = Syntax.var
val cmp = Int.compare)
fun varSet (l : Syntax.var list) : unit VarMap.map = VarMap.fromList (map (fn x => (x, ())) l)
fun freeVars (expr : Syntax.cexp) : unit VarMap.map =
case expr of
Syntax.CRecord (records, k) =>
let
val kFreeVars = freeVars k
val argFreeVars =
foldl
(fn ((args, _), acc) =>
VarMap.union acc (varSet (List.mapPartial (fn (Syntax.VVar v, _) => SOME v | _ => NONE) args)))
VarMap.empty
records
val results =
foldl
(fn ((_, res), acc) =>
VarMap.insert res () acc)
VarMap.empty
records
in
VarMap.difference (VarMap.union kFreeVars argFreeVars) results
end
| Syntax.CSelect (_, arg, res, k) =>
let
val argFreeVars =
case arg of
Syntax.VVar v => varSet [v]
| _ => VarMap.empty
val kFreeVars = VarMap.delete res (freeVars k)
in
VarMap.union argFreeVars kFreeVars
end
| Syntax.CApp (func, args) =>
let
val funcFreeVars =
case func of
Syntax.VVar v => varSet [v]
| _ => VarMap.empty
val argFreeVars = varSet (List.mapPartial (fn Syntax.VVar v => SOME v | _ => NONE) args)
in
VarMap.union funcFreeVars argFreeVars
end
| Syntax.CFix (funs, body) =>
let
val names = varSet (map (fn (name, _, _) => name) funs)
val funsFreeVars = map (fn (name, args, fixBody) => VarMap.difference (freeVars fixBody) (varSet args)) funs
val bodyFreeVars = freeVars body
in
foldl (fn (x, acc) => VarMap.union acc (VarMap.difference x names)) VarMap.empty (bodyFreeVars :: funsFreeVars)
end
| Syntax.CPrimop (_, args, res, ks) =>
let
val argFreeVars = varSet (List.mapPartial (fn Syntax.VVar v => SOME v | _ => NONE) args)
val boundVars = varSet res
val kFreeVars = foldl (fn (x, acc) => VarMap.union acc x) VarMap.empty (map (fn k => VarMap.difference (freeVars k) boundVars) ks)
in
VarMap.union argFreeVars kFreeVars
end
fun freeVarsClosure (name, args, body) = map (fn (x, _) => x) (VarMap.toList (VarMap.difference (freeVars body) (varSet args)))
fun enumerate l = ListPair.zip (List.tabulate (length l, (fn x => x)), l)
fun convertExpr varMap expr =
let
fun translate var = getOpt (VarMap.lookup var varMap, var)
fun translateValue (Syntax.VVar v) = Syntax.VVar (translate v)
| translateValue v = v
in
case expr of
Syntax.CRecord (records, k) =>
Syntax.CRecord (map (fn (args, res) => (map (fn (v, p) => (translateValue v, p)) args, res)) records, convertExpr varMap k)
| Syntax.CSelect (i, arg, res, k) =>
Syntax.CSelect (i, translateValue arg, res, convertExpr varMap k)
| Syntax.CApp (func, args) =>
let
val temp = Gensym.new ()
val f = translateValue func
in Syntax.CSelect (0, f, temp,
Syntax.CApp (Syntax.VVar temp, f :: map translateValue args))
end
| Syntax.CFix (funcs, body) =>
let
val convertedFuncs =
map
(fn this as (name, args, body) =>
let
val funcFreeVars = freeVarsClosure this
val varMap' = VarMap.union varMap (VarMap.fromList (map (fn v => (v, Gensym.new ())) funcFreeVars))
val closure = Gensym.new ()
val newBody =
foldl
(fn ((i, x), acc) => Syntax.CSelect (i + 1, Syntax.VVar closure, valOf (VarMap.lookup x varMap'), acc))
(convertExpr varMap' body)
(enumerate funcFreeVars)
in
(Gensym.new (), closure :: args, newBody)
end)
funcs
val newBody =
Syntax.CRecord
( map
(fn (old as (oldName, args, body), (newName, _, _)) =>
let val funcFreeVars = freeVarsClosure old
in ((Syntax.VLabel newName, []) :: map (fn v => (Syntax.VVar (translate v), [])) funcFreeVars, oldName)
end)
(ListPair.zip (funcs, convertedFuncs))
, convertExpr varMap body
)
in
Syntax.CFix (convertedFuncs, newBody)
end
| Syntax.CPrimop (p, args, res, ks) =>
Syntax.CPrimop (p, map translateValue args, res, map (convertExpr varMap) ks)
end
fun convertClosures (expr : Syntax.cexp) : Syntax.cexp = hoist (convertExpr VarMap.empty expr)
end
|
