erg_compiler 0.1.1

Centimetre: the Erg compiler
Documentation
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
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
//! defines type information for builtin objects (in `SymbolTable`)
//!
//! 組み込みオブジェクトの型情報を(記号表に)定義
use erg_common::{Str};
use erg_common::{set, debug_power_assert};
use erg_common::ty::{Type, TyParam, ConstObj};
use Type::*;
use erg_common::ty::type_constrs::*;
use ParamSpec as PS;

use erg_parser::ast::{VarName};

use crate::varinfo::{Mutability, Visibility, VarInfo, VarKind};
use crate::table::{SymbolTable, ParamSpec, DefaultInfo};
use Visibility::*;
use Mutability::*;
use VarKind::*;
use DefaultInfo::*;

// NOTE: TyParam::MonoQuantVarは生成時に型を指定する必要があるが、逆にそちらがあれば型境界を指定しなくてもよい
impl SymbolTable {
    fn register_decl(&mut self, name: &'static str, t: Type, vis: Visibility) {
        let name = VarName::from_static(name);
        if self.decls.get(&name).is_some() {
            panic!("already registered: {name}");
        } else {
            self.decls.insert(name, VarInfo::new(t, Immutable, vis, Builtin));
        }
    }

    fn register_impl(&mut self, name: &'static str, t: Type, muty: Mutability, vis: Visibility) {
        let name = VarName::from_static(name);
        if self.impls.get(&name).is_some() {
            panic!("already registered: {name}");
        } else {
            self.impls.insert(name, VarInfo::new(t, muty, vis, Builtin));
        }
    }

    fn register_const(&mut self, name: &'static str, obj: ConstObj) {
        if self.consts.get(name).is_some() {
            panic!("already registered: {name}");
        } else {
            self.consts.insert(Str::ever(name), obj);
        }
    }

    fn register_type(&mut self, t: Type, table: Self, muty: Mutability) {
        if self.types.contains_key(&t) {
            panic!("{} has already been registered", t.name());
        } else {
            let name = VarName::from_str(Str::rc(t.name()));
            self.impls.insert(name, VarInfo::new(Type, muty, Private, Builtin));
            self.types.insert(t, table);
        }
    }

    fn register_patch(&mut self, name: &'static str, table: Self, muty: Mutability) {
        if self.patches.contains_key(name) {
            panic!("{} has already been registered", name);
        } else {
            let name = VarName::from_static(name);
            self.impls.insert(name.clone(), VarInfo::new(Type, muty, Private, Builtin));
            for method_name in table.impls.keys() {
                if let Some(patches) = self._method_impl_patches.get_mut(method_name) {
                    patches.push(name.clone());
                } else {
                    self._method_impl_patches.insert(method_name.clone(), vec![name.clone()]);
                }
            }
            debug_power_assert!(table.super_classes.len(), ==, 1);
            if let Some(target_type) = table.super_classes.first() {
                for impl_trait in table.super_traits.iter() {
                    self.glue_patch_and_types.push(
                        (VarName::from_str(table.name.clone()), target_type.clone(), impl_trait.clone())
                    );
                }
            }
            self.patches.insert(name, table);
        }
    }

    /// see std/prelude.er
    // 型境界はすべて各サブルーチンで定義する
    // push_subtype_boundなどはユーザー定義APIの型境界決定のために使用する
    fn init_builtin_traits(&mut self) {
        let mut eq = Self::poly_trait("Eq", vec![PS::t("R", WithDefault)], vec![], Self::TOP_LEVEL);
        // __eq__: |Self <: Eq; R <: Eq()| Self(R).(R) -> Bool
        let op_t = fn1_met(poly("Self", vec![mono_q_tp("R")]), mono_q("R"), Bool);
        let op_t = quant(op_t, set!{subtype(mono_q("Self"), mono("Eq")), subtype(mono_q("R"), poly("Eq", vec![]))});
        eq.register_decl("__eq__", op_t.clone(), Public);
        let mut ord = Self::poly_trait("Ord", vec![PS::t("R", WithDefault)], vec![mono("Eq")], Self::TOP_LEVEL);
        let op_t = fn1_met(poly("Self", vec![mono_q_tp("R")]), mono_q("R"), Bool);
        let op_t = quant(op_t, set!{subtype(mono_q("Self"), mono("Ord")), subtype(mono_q("R"), poly("Ord", vec![]))});
        ord.register_decl("__lt__", op_t.clone(), Public);
        let mut seq = Self::poly_trait("Seq", vec![PS::t("T", NonDefault)], vec![], Self::TOP_LEVEL);
        let self_t = poly_q("Self", vec![TyParam::t(mono_q("T"))]);
        let t = fn0_met(self_t.clone(), Nat);
        let t = quant(t, set!{subtype(self_t.clone(), mono("Seq"))});
        seq.register_decl("__len__", t, Public);
        let t = Type::fn1_met(self_t.clone(), Nat, mono_q("T"));
        let t = quant(t, set!{subtype(self_t, mono("Seq")), static_instance("T", Type)});
        seq.register_decl("get", t, Public);
        let (r, o) = (mono_q("R"), mono_q("O"));
        let (r_bound, o_bound) = (static_instance("R", Type), static_instance("O", Type));
        let params = vec![PS::t("R", WithDefault), PS::t("O", WithDefault)];
        let ty_params = vec![mono_q_tp("R"), mono_q_tp("O")];
        let mut add_ro = Self::poly_trait("Add", params.clone(), vec![], Self::TOP_LEVEL);
        let self_bound = subtype(poly_q("Self", ty_params.clone()), poly("Add", ty_params.clone()));
        let op_t = fn1_met(poly_q("Self", ty_params.clone()), r.clone(), o.clone());
        let op_t = quant(op_t, set!{r_bound.clone(), o_bound.clone(), self_bound});
        add_ro.register_decl("__add__", op_t, Public);
        let mut sub_ro = Self::poly_trait("Sub", params.clone(), vec![], Self::TOP_LEVEL);
        let self_bound = subtype(poly_q("Self", ty_params.clone()), poly("Sub", ty_params.clone()));
        let op_t = fn1_met(poly_q("Self", ty_params.clone()), r.clone(), o.clone());
        let op_t = quant(op_t, set!{r_bound.clone(), o_bound.clone(), self_bound});
        sub_ro.register_decl("__sub__", op_t, Public);
        let mut mul_ro = Self::poly_trait("Mul", params.clone(), vec![], Self::TOP_LEVEL);
        let op_t = fn1_met(poly("Mul", ty_params.clone()), r.clone(), o.clone());
        mul_ro.register_decl("__mul__", op_t, Public);
        let mut div_ro = Self::poly_trait("Div", params.clone(), vec![], Self::TOP_LEVEL);
        let op_t = fn1_met(poly("Div", ty_params.clone()), r, o);
        div_ro.register_decl("__div__", op_t, Public);
        let sup = poly("Add", vec![mono_q_tp("Self"), TyParam::mono_proj(mono_q_tp("Self"), "AddO")]);
        let mut add = Self::mono_trait("Add", vec![sup], Self::TOP_LEVEL);
        add.register_decl("AddO", Type, Public);
        let sup = poly("Sub", vec![mono_q_tp("Self"), TyParam::mono_proj(mono_q_tp("Self"), "SubO")]);
        let mut sub = Self::mono_trait("Sub", vec![sup], Self::TOP_LEVEL);
        sub.register_decl("SubO", Type, Public);
        let sup = poly("Mul", vec![mono_q_tp("Self"), TyParam::mono_proj(mono_q_tp("Self"), "MulO")]);
        let mut mul = Self::mono_trait("Mul", vec![sup], Self::TOP_LEVEL);
        mul.register_decl("MulO", Type, Public);
        let sup = Type::poly("Div", vec![mono_q_tp("Self"), TyParam::mono_proj(mono_q_tp("Self"), "DivO")]);
        let mut div = Self::mono_trait("Div", vec![sup], Self::TOP_LEVEL);
        div.register_decl("DivO", Type, Public);
        let num = Self::mono_trait("Num", vec![
            mono("Eq"),
            mono("Add"), mono("Sub"), mono("Mul"),
        ], Self::TOP_LEVEL);
        self.register_type(mono("Eq"), eq, Const);
        self.register_type(mono("Ord"), ord, Const);
        self.register_type(mono("Seq"), seq, Const);
        self.register_type(poly("Add", ty_params.clone()), add_ro, Const);
        self.register_type(poly("Sub", ty_params.clone()), sub_ro, Const);
        self.register_type(poly("Mul", ty_params.clone()), mul_ro, Const);
        self.register_type(poly("Div", ty_params),         div_ro, Const);
        self.register_type(mono("Num"), num, Const);
    }

    fn init_builtin_classes(&mut self) {
        let mut obj = Self::mono_class("Obj", vec![], vec![], Self::TOP_LEVEL);
        let t = fn0_met(mono_q("Self"), mono_q("Self"));
        let t = quant(t, set!{subtype(mono_q("Self"), mono("Obj"))});
        obj.register_impl("clone", t, Const, Public);
        obj.register_impl("__module__", Str, Const, Public);
        obj.register_impl("__sizeof__", fn0_met(Obj, Nat), Const, Public);
        obj.register_impl("__repr__", fn0_met(Obj, Str), Immutable, Public);
        obj.register_impl("__str__", fn0_met(Obj, Str), Immutable, Public);
        obj.register_impl(
            "__dict__",
            fn0_met(Obj, Type::dict(Str, Obj)),
            Immutable,
            Public,
        );
        obj.register_impl(
            "__bytes__",
            fn0_met(Obj, Type::mono("Bytes")),
            Immutable,
            Public,
        );
        // let mut record = Self::mono_trait("Record", vec![Obj], Self::TOP_LEVEL);
        // let mut class = Self::mono_class("Class", vec![Type, Obj], Self::TOP_LEVEL);
        let mut float = Self::mono_class("Float", vec![Obj], vec![
            mono("Num"),
            mono("Ord"), mono("Eq"),
            mono("Add"), mono("Sub"), mono("Mul"), mono("Div"),
            mono("Mutate"),
        ], Self::TOP_LEVEL);
        let op_t = fn1_met(Float, Float, Float);
        float.register_impl("__add__", op_t.clone(), Const, Public);
        float.register_impl("__sub__", op_t.clone(), Const, Public);
        float.register_impl("__mul__", op_t.clone(), Const, Public);
        float.register_impl("__div__", op_t        , Const, Public);
        float.register_impl("Real", Int, Const, Public);
        float.register_impl("Imag", Int, Const, Public);
        let mut int = Self::mono_class("Int", vec![Obj], vec![
            mono("Num"),
            mono("Rational"), mono("Integral"),
            mono("Ord"), mono("Eq"),
            mono("Add"), mono("Sub"), mono("Mul"), mono("Div"),
            mono("Mutate"),
        ], Self::TOP_LEVEL);
        int.register_impl("abs", fn0_met(Int, Nat), Immutable, Public);
        // __div__ is not included in Int (cast to Float)
        let op_t = fn1_met(Int, Int, Int);
        int.register_impl("__add__", op_t.clone(), Const, Public);
        int.register_impl("__sub__", op_t.clone(), Const, Public);
        int.register_impl("__mul__", op_t,         Const, Public);
        int.register_impl("Real", Int, Const, Public);
        int.register_impl("Imag", Int, Const, Public);
        int.super_traits.push(poly("Add", vec![ty_tp(Int), ty_tp(Int)]));
        int.super_traits.push(poly("Sub", vec![ty_tp(Int), ty_tp(Int)]));
        int.super_traits.push(poly("Mul", vec![ty_tp(Int), ty_tp(Int)]));
        int.super_traits.push(poly("Div", vec![ty_tp(Int), ty_tp(Ratio)]));
        let mut nat = Self::mono_class("Nat", vec![Int, Obj], vec![
            mono("Num"),
            mono("Rational"), mono("Integral"),
            mono("Ord"), mono("Eq"),
            mono("Add"), mono("Sub"), mono("Mul"), mono("Div"),
            mono("Mutate"),
            Obj,
        ], Self::TOP_LEVEL);
        // __sub__, __div__ is not included in Nat (cast to Int)
        let op_t = fn1_met(Nat, Nat, Nat);
        nat.register_impl("__add__", op_t.clone(), Const, Public);
        nat.register_impl("__mul__", op_t,         Const, Public);
        nat.register_impl(
            "times!",
            Type::pr_met(Nat, None, vec![param_t("p", nd_proc(vec![], NoneType))], vec![], NoneType),
            Immutable,
            Public
        );
        nat.register_impl("Real", Int, Const, Public);
        nat.register_impl("Imag", Int, Const, Public);
        nat.super_traits.push(poly("Add", vec![ty_tp(Nat), ty_tp(Nat)]));
        nat.super_traits.push(poly("Sub", vec![ty_tp(Nat), ty_tp(Nat)]));
        nat.super_traits.push(poly("Mul", vec![ty_tp(Nat), ty_tp(Nat)]));
        nat.super_traits.push(poly("Div", vec![ty_tp(Nat), ty_tp(Ratio)]));
        let mut bool_ = Self::mono_class("Bool", vec![Nat, Int, Obj], vec![
            mono("Num"),
            mono("Rational"), mono("Integral"),
            mono("Ord"), mono("Eq"),
            mono("Add"), mono("Sub"), mono("Mul"), mono("Div"),
            mono("Mutate"),
            Obj,
        ], Self::TOP_LEVEL);
        bool_.register_impl("__and__", fn1_met(Bool, Bool, Bool), Const, Public);
        bool_.register_impl("__or__",  fn1_met(Bool, Bool, Bool), Const, Public);
        let mut str_ = Self::mono_class("Str", vec![Obj], vec![
            mono("Eq"), mono("Seq"), mono("Mutate"),
        ], Self::TOP_LEVEL);
        str_.register_impl("__add__", fn1_met(Str, Str, Str), Const, Public);
        str_.register_impl("replace", Type::fn_met(
            Str,
            vec![param_t("pat", Str), param_t("into", Str)],
            vec![], Str),
            Immutable,
            Public
        );
        str_.super_traits.push(poly("Add", vec![ty_tp(Str), ty_tp(Str)]));
        let mut array = Self::poly_class("Array", vec![PS::t_nd("T"), PS::named_nd("N", Nat)], vec![Obj], vec![
            mono("Eq"), mono("Seq"), mono("Mutate"), poly("Output", vec![ty_tp(mono_q("T"))])
        ], Self::TOP_LEVEL);
        let n = mono_q_tp("N");
        let m = mono_q_tp("M");
        let array_t = Type::array(mono_q("T"), n.clone());
        let t = Type::fn_met(
            array_t.clone(),
            vec![param_t("rhs", Type::array(mono_q("T"), m.clone()))],
            vec![],
            Type::array(mono_q("T"), n + m)
        );
        let t = quant(t, set!{static_instance("N", Nat), static_instance("M", Nat)});
        array.register_impl("concat", t, Immutable, Public);
        let mut_type = ConstObj::t(Type::poly("Array!", vec![
            TyParam::t(mono_q("T")),
            TyParam::mono_q("N").mutate(),
        ]));
        // [T; N].MutType! = [T; !N] (neither [T!; N] nor [T; N]!)
        array.register_const("MutType!", mut_type);
        let mut type_ = Self::mono_class("Type", vec![Obj], vec![mono("Eq")], Self::TOP_LEVEL);
        type_.register_impl("mro", Type::array(Type, TyParam::erased(Nat)), Immutable, Public);
        let array_mut_t = Type::poly("Array!", vec![TyParam::t(mono_q("T")), mono_q_tp("N")]);
        let mut array_mut = Self::poly_class("Array!", vec![PS::t_nd("T"), PS::named_nd("N", NatMut)], vec![Obj], vec![
            mono("Eq"), mono("Seq"), mono("Mutate"),
        ], Self::TOP_LEVEL);
        let t = Type::pr_met(
            Type::ref_mut(array_mut_t.clone()),
            Some(Type::ref_mut(poly("Array!", vec![TyParam::t(mono_q("T")), mono_q_tp("N") + value(1)]))),
            vec![param_t("elem", mono_q("T"))],
            vec![],
            Type::NoneType,
        );
        let t = quant(t, set!{static_instance("T", Type), static_instance("N", NatMut)});
        array_mut.register_impl("push!", t, Immutable, Public);
        self.register_type(Obj, obj, Const);
        // self.register_type(Type::mono("Record"), vec![], record, Const);
        // self.register_type(Type::mono("Class"), vec![], class, Const);
        self.register_type(Float, float, Const);
        self.register_type(Int, int, Const);
        self.register_type(Nat, nat, Const);
        self.register_type(Bool, bool_, Const);
        self.register_type(Str, str_, Const);
        self.register_type(array_t, array, Const);
        self.register_type(array_mut_t, array_mut, Const);
        self.register_type(Type, type_, Const);
    }

    fn init_builtin_funcs(&mut self) {
        let t_abs = nd_func(vec![param_t("n", mono("Num"))], Nat);
        let t_assert = func(vec![param_t("condition", Bool)], vec![param_t("err_message", Str)], NoneType);
        let t_classof = nd_func(vec![param_t("o", Obj)], Type::option(Class));
        let t_compile = nd_func(vec![param_t("src", Str)], Code);
        let t_cond = nd_func(
            vec![param_t("condition", Bool), param_t("then", mono_q("T")), param_t("else", mono_q("T"))],
            mono_q("T"),
        );
        let t_cond = quant(t_cond, set!{static_instance("T", Type)});
        let t_discard = nd_func(vec![param_t("o", Obj)], NoneType);
        let t_id = nd_func(vec![param_t("o", Obj)], Nat);
        // FIXME: quantify
        let t_if = func(
            vec![param_t("cond", Bool), param_t("then", nd_func(vec![], mono_q("T")))],
            vec![param_t("else", nd_func(vec![], mono_q("T")))],
            Type::option(mono_q("T")),
        );
        let t_if = quant(t_if, set!{static_instance("T", Type)});
        let t_import = nd_func(vec![param_t("path", Str)], Module);
        let t_log = nd_func(vec![param_t("objs", Type::var_args(Obj))], NoneType);
        let t_pyimport = nd_func(vec![param_t("path", Str)], Module);
        let t_quit = func(vec![], vec![param_t("code", Int)], NoneType);
        self.register_impl("abs", t_abs, Const, Private);
        self.register_impl("assert", t_assert, Const, Private);
        self.register_impl("classof", t_classof, Const, Private);
        self.register_impl("compile", t_compile, Const, Private);
        self.register_impl("cond", t_cond, Const, Private);
        self.register_impl("discard", t_discard, Const, Private);
        self.register_impl("id" , t_id, Const, Private);
        self.register_impl("if", t_if, Const, Private);
        self.register_impl("log", t_log, Const, Private);
        self.register_impl("import", t_import, Const, Private);
        self.register_impl("pyimport", t_pyimport, Const, Private);
        self.register_impl("quit", t_quit, Const, Private);
    }

    fn init_builtin_procs(&mut self) {
        let t_print = nd_proc(vec![param_t("objs", Type::var_args(Type::refer(Obj)))], NoneType);
        let t_input = nd_proc(vec![param_t("msg", Str)], Str);
        let t_if = proc(
            vec![param_t("cond", Bool), param_t("then", nd_proc(vec![], mono_q("T")))],
            vec![param_t("else", nd_proc(vec![], mono_q("T")))],
            Type::option(mono_q("T"))
        );
        let t_if = quant(t_if, set!{static_instance("T", Type)});
        let t_for = nd_proc(vec![param_t("iter", Type::iter(mono_q("T"))), param_t("p", nd_proc(vec![anon(mono_q("T"))], NoneType))], NoneType);
        let t_for = quant(t_for, set!{static_instance("T", Type)});
        let t_while = nd_proc(vec![param_t("cond", BoolMut), param_t("p", nd_proc(vec![], NoneType))], NoneType);
        self.register_impl("print!", t_print, Const, Private);
        self.register_impl("input!", t_input, Const, Private);
        self.register_impl("if!", t_if, Const, Private);
        self.register_impl("for!", t_for, Const, Private);
        self.register_impl("while!", t_while, Const, Private);
    }

    fn init_builtin_operators(&mut self) {
        /* binary */
        let l = mono_q("L");
        let r = mono_q("R");
        let o = mono_q("O");
        let params = vec![mono_q_tp("R"), mono_q_tp("O")];
        let op_t = Type::func2(l.clone(), r.clone(), o.clone());
        let op_t = quant(op_t, set!{
            static_instance("R", Type),
            static_instance("O", Type),
            subtype(l.clone(), poly("Add", params.clone()))
        });
        self.register_impl("__add__", op_t, Const, Private);
        let op_t = Type::func2(l.clone(), r.clone(), o.clone());
        let op_t = quant(op_t, set!{
            static_instance("R", Type),
            static_instance("O", Type),
            subtype(l.clone(), poly("Sub", params.clone()))
        });
        self.register_impl("__sub__", op_t, Const, Private);
        let op_t = Type::func2(l.clone(), r.clone(), o.clone());
        let op_t = quant(op_t, set!{subtype(l.clone(), poly("Mul", params.clone()))});
        self.register_impl("__mul__", op_t, Const, Private);
        let op_t = Type::func2(l.clone(), r.clone(), o.clone());
        let op_t = quant(op_t, set!{subtype(l, poly("Mul", params.clone()))});
        self.register_impl("__div__", op_t, Const, Private);
        let m = mono_q("M");
        let op_t = Type::func2(m.clone(), m.clone(), m.clone());
        let op_t = quant(op_t, set!{subtype(m, poly("Mul", vec![]))});
        self.register_impl("__pow__", op_t, Const, Private);
        let d = mono_q("D");
        let op_t = Type::func2(d.clone(), d.clone(), d.clone());
        let op_t = quant(op_t, set!{subtype(d, poly("Div", vec![]))});
        self.register_impl("__mod__", op_t, Const, Private);
        let e = mono_q("E");
        let op_t = Type::func2(e.clone(), e.clone(), Bool);
        let op_t = quant(op_t, set!{subtype(e, poly("Eq", vec![]))});
        self.register_impl("__eq__", op_t.clone(), Const, Private);
        self.register_impl("__ne__", op_t,         Const, Private);
        let o = mono_q("O");
        let op_t = Type::func2(o.clone(), o.clone(), Bool);
        let op_t = quant(op_t, set!{subtype(o, poly("Ord", vec![]))});
        self.register_impl("__lt__",  op_t.clone(), Const, Private);
        self.register_impl("__le__",  op_t.clone(), Const, Private);
        self.register_impl("__gt__",  op_t.clone(), Const, Private);
        self.register_impl("__ge__",  op_t,         Const, Private);
        self.register_impl("__and__", Type::func2(Bool, Bool, Bool), Const, Private);
        self.register_impl("__or__",  Type::func2(Bool, Bool, Bool), Const, Private);
        /* unary */
        // TODO: Boolの+/-は警告を出したい
        let n = mono_q("N");
        let op_t = fn0_met(n.clone(), n.clone());
        let op_t = quant(op_t, set!{subtype(n, mono("Num"))});
        self.register_decl("__pos__", op_t.clone(), Private);
        self.register_decl("__neg__", op_t,         Private);
        let t = mono_q("T");
        let op_t = fn1_met(t.clone(), t.clone(), Type::range(t.clone()));
        let op_t = quant(op_t, set!{subtype(t, mono("Ord"))});
        self.register_decl("__rng__", op_t, Private);
        let op_t = Type::func1(mono_q("T"), Type::mono_proj(mono_q("T"), "MutType!"));
        let op_t = quant(op_t, set!{subtype(mono_q("T"), mono("Mutate"))});
        self.register_impl("__mutate__", op_t, Const, Private);
    }

    fn init_builtin_patches(&mut self) {
        let m = mono_q_tp("M");
        let n = mono_q_tp("N");
        let o = mono_q_tp("O");
        let p = mono_q_tp("P");
        let params = vec![
            PS::named_nd("M", Int), PS::named_nd("N", Int),
            PS::named_nd("O", Int), PS::named_nd("P", Int),
        ];
        // Interval is a bounding patch connecting M..N and (Add(O..P, M+O..N..P), Sub(O..P, M-P..N-O))
        let mut interval = Self::poly_patch("Interval", params, vec![Type::from(&m..=&n)], vec![
            poly("Add", vec![TyParam::from(&o..=&p), TyParam::from(m.clone() + o.clone() ..= n.clone() + p.clone())]),
            poly("Sub", vec![TyParam::from(&o..=&p), TyParam::from(m.clone() - p.clone() ..= n.clone() - o.clone())]),
        ], Self::TOP_LEVEL);
        let op_t = fn1_met(
            Type::from(&m..=&n),
            Type::from(&o..=&p),
            Type::from(m.clone() + o.clone() ..= n.clone() + p.clone()),
        );
        interval.register_impl("__add__", op_t, Const, Public);
        let op_t = fn1_met(
            Type::from(&m..=&n),
            Type::from(&o..=&p),
            Type::from(m - p ..= n - o),
        );
        interval.register_impl("__sub__", op_t, Const, Public);
        self.register_patch("Interval", interval, Const);
        // eq.register_impl("__ne__", op_t,         Const, Public);
        // ord.register_impl("__le__", op_t.clone(), Const, Public);
        // ord.register_impl("__gt__", op_t.clone(), Const, Public);
        // ord.register_impl("__ge__", op_t,         Const, Public);
    }

    pub(crate) fn init_builtins() -> Self {
        // TODO: capacityを正確に把握する
        let mut table = SymbolTable::module("<builtins>".into(), 40);
        table.init_builtin_funcs();
        table.init_builtin_procs();
        table.init_builtin_operators();
        table.init_builtin_traits();
        table.init_builtin_classes();
        table.init_builtin_patches();
        table
    }
}