//! defines type information for builtin objects (in `Context`)
//!
//! 組み込みオブジェクトの型情報を(Context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::context::{Context, 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 Context {
    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, ctx: 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, ctx);
        }
    }

    fn register_patch(&mut self, name: &'static str, ctx: 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 ctx.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!(ctx.super_classes.len(), ==, 1);
            if let Some(target_type) = ctx.super_classes.first() {
                for impl_trait in ctx.super_traits.iter() {
                    self.glue_patch_and_types.push(
                        (VarName::from_str(ctx.name.clone()), target_type.clone(), impl_trait.clone())
                    );
                }
            }
            self.patches.insert(name, ctx);
        }
    }

    /// 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", Float, Const, Public);
        float.register_impl("Imag", Float, Const, Public);
        let mut ratio = Self::mono_class("Ratio", 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(Ratio, Ratio, Ratio);
        ratio.register_impl("__add__", op_t.clone(), Const, Public);
        ratio.register_impl("__sub__", op_t.clone(), Const, Public);
        ratio.register_impl("__mul__", op_t.clone(), Const, Public);
        ratio.register_impl("__div__", op_t        , Const, Public);
        ratio.register_impl("Real", Ratio, Const, Public);
        ratio.register_impl("Imag", Ratio, 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", Nat, Const, Public);
        nat.register_impl("Imag", Nat, 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("Mutate"), poly("Seq", vec![ty_tp(Str)]),
        ], 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("Mutate"),
            poly("Seq", vec![ty_tp(mono_q("T"))]), 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"), mono("Named")], Self::TOP_LEVEL);
        type_.register_impl("mro", Type::array(Type, TyParam::erased(Nat)), Immutable, Public);
        let module = Self::mono_class("Module", vec![Obj], vec![mono("Eq"), mono("Named")], Self::TOP_LEVEL);
        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("Mutate"), poly("Seq", vec![ty_tp(mono_q("T"))])
        ], 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);
        let range_t = Type::poly("Range", vec![TyParam::t(mono_q("T"))]);
        let range = Self::poly_class("Range", vec![PS::t_nd("T")], vec![Obj], vec![
            mono("Eq"), mono("Mutate"),
            poly("Seq", vec![ty_tp(mono_q("T"))]), poly("Output", vec![ty_tp(mono_q("T"))])
        ], Self::TOP_LEVEL);
        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(Ratio, ratio, 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(Type, type_, Const);
        self.register_type(Module, module, Const);
        self.register_type(array_t, array, Const);
        self.register_type(range_t, range, Const);
        self.register_type(array_mut_t, array_mut, 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 = Type::func2(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.clone(), Private);
        self.register_decl("__lorng__", op_t.clone(), Private);
        self.register_decl("__rorng__", op_t.clone(), Private);
        self.register_decl("__orng__", 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_py_math_mod() -> Self {
        let mut math = Context::module("math".into(), 10);
        math.register_impl("pi", Type::Float, Immutable, Public);
        math.register_impl("tau", Type::Float, Immutable, Public);
        math.register_impl("e", Type::Float, Immutable, Public);
        math.register_impl("sin", Type::func1(Float, Float), Immutable, Public);
        math.register_impl("cos", Type::func1(Float, Float), Immutable, Public);
        math.register_impl("tan", Type::func1(Float, Float), Immutable, Public);
        math
    }

    pub(crate) fn init_py_random_mod() -> Self {
        let mut random = Context::module("random".into(), 10);
        random.register_impl("seed!", Type::proc(vec![], vec![
            param_t("a", Type::mono("Num")), // TODO: NoneType, int, float, str, bytes, bytearray
            param_t("version", Type::Int),
        ], NoneType), Immutable, Public);
        random.register_impl("randint!", nd_proc(vec![param_t("a", Int), param_t("b", Int)], Int), Immutable, Public);
        let t = nd_proc(vec![param_t("seq", Type::poly("Seq", vec![ty_tp(mono_q("T"))]))], mono_q("T"));
        let t = quant(t, set!{static_instance("T", Type)});
        random.register_impl("choice!", t, Immutable, Public);
        random
    }

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