//! provides type-comparison
use std::cmp::Ordering;
use std::option::Option; // conflicting to Type::Option

use erg_type::constructors::or;
use erg_type::free::fresh_varname;
use erg_type::free::{Constraint, FreeKind, FreeTyVar};
use erg_type::typaram::{TyParam, TyParamOrdering};
use erg_type::value::ValueObj::Inf;
use erg_type::{Predicate, RefinementType, SubrKind, SubrType, Type};
use Predicate as Pred;

use erg_common::Str;
use erg_common::{assume_unreachable, enum_unwrap, log, set};
use TyParamOrdering::*;
use Type::*;

use crate::context::instantiate::TyVarContext;
use crate::context::{Context, TraitInstancePair, Variance};

#[derive(Debug, Clone, Copy, PartialEq, Eq, Hash)]
pub enum Credibility {
    Maybe,
    Absolutely,
}

use Credibility::*;

impl Context {
    pub(crate) fn eq_tp(&self, lhs: &TyParam, rhs: &TyParam) -> bool {
        match (lhs, rhs) {
            (TyParam::Type(lhs), TyParam::Type(rhs)) => {
                return self.structural_same_type_of(lhs, rhs)
            }
            (TyParam::Mono(l), TyParam::Mono(r)) => {
                if let (Some((l, _)), Some((r, _))) = (
                    self.types.iter().find(|(t, _)| &t.name() == l),
                    self.types.iter().find(|(t, _)| &t.name() == r),
                ) {
                    return self.structural_supertype_of(l, r) || self.structural_subtype_of(l, r);
                }
            }
            (TyParam::MonoQVar(name), _other) | (_other, TyParam::MonoQVar(name)) => {
                panic!("Not instantiated type parameter: {name}")
            }
            (
                TyParam::App {
                    name: ln,
                    args: largs,
                },
                TyParam::App {
                    name: rn,
                    args: rargs,
                },
            ) => {
                return ln == rn
                    && largs.len() == rargs.len()
                    && largs
                        .iter()
                        .zip(rargs.iter())
                        .all(|(l, r)| self.eq_tp(l, r))
            }
            (TyParam::FreeVar(fv), other) | (other, TyParam::FreeVar(fv)) => match &*fv.borrow() {
                FreeKind::Linked(tp) => return self.eq_tp(tp, other),
                FreeKind::Unbound { constraint, .. }
                | FreeKind::NamedUnbound { constraint, .. } => {
                    let t = constraint.get_type().unwrap();
                    let other_t = self.type_of(other);
                    return self.structural_supertype_of(t, &other_t);
                }
            },
            (l, r) if l == r => return true,
            _ => {}
        }
        self.eval.shallow_eq_tp(lhs, rhs, self)
    }

    /// e.g.
    /// ```erg
    /// super_traits_of(Nat) == [Eq(Nat), Add(Nat), ...]
    /// ```
    pub fn super_traits<'a>(&'a self, t: &'a Type) -> Vec<&'a TraitInstancePair> {
        log!("{}", self.name);
        let traits: Vec<_> = self
            .trait_impls
            .iter()
            .map(|(_, sub_and_sup)| {
                sub_and_sup.iter().filter_map(|pair| {
                    let t_name = pair.sub_type.name();
                    let sub_ctx = self.rec_type_ctx_by_name(&t_name).unwrap();
                    let bounds = sub_ctx.type_params_bounds();
                    let mut tv_ctx = TyVarContext::new(self.level, bounds, self);
                    let sub_type = Self::instantiate_t(pair.sub_type.clone(), &mut tv_ctx);
                    log!("{sub_type}, {t}");
                    if self.supertype_of(&sub_type, t) {
                        Some(pair)
                    } else {
                        None
                    }
                })
            })
            .flatten()
            .collect();
        if let Some(outer) = self.outer.as_ref() {
            [traits, outer.super_traits(t)].concat()
        } else {
            traits
        }
    }

    /// e.g.
    /// Named :> Module
    /// => Module.super_types == [Named]
    /// Seq(T) :> Range(T)
    /// => Range(T).super_types == [Eq, Mutate, Seq('T), Output('T)]
    pub(crate) fn rec_supertype_of(&self, lhs: &Type, rhs: &Type) -> bool {
        if self.supertype_of(lhs, rhs) {
            return true;
        }
        if let Some(outer) = &self.outer {
            if outer.rec_supertype_of(lhs, rhs) {
                return true;
            }
        }
        false
    }

    pub(crate) fn rec_subtype_of(&self, lhs: &Type, rhs: &Type) -> bool {
        self.rec_supertype_of(rhs, lhs)
    }

    pub(crate) fn rec_same_type_of(&self, lhs: &Type, rhs: &Type) -> bool {
        self.rec_supertype_of(lhs, rhs) && self.rec_subtype_of(lhs, rhs)
    }

    pub(crate) fn _rec_related(&self, lhs: &Type, rhs: &Type) -> bool {
        self.rec_supertype_of(lhs, rhs) || self.rec_subtype_of(lhs, rhs)
    }

    pub(crate) fn related(&self, lhs: &Type, rhs: &Type) -> bool {
        self.supertype_of(lhs, rhs) || self.subtype_of(lhs, rhs)
    }

    pub(crate) fn supertype_of(&self, lhs: &Type, rhs: &Type) -> bool {
        match self.cheap_supertype_of(lhs, rhs) {
            (Absolutely, judge) => judge,
            (Maybe, judge) => {
                judge
                    || self.structural_supertype_of(lhs, rhs)
                    || self.nominal_supertype_of(lhs, rhs)
            }
        }
    }

    pub(crate) fn subtype_of(&self, lhs: &Type, rhs: &Type) -> bool {
        match self.cheap_subtype_of(lhs, rhs) {
            (Absolutely, judge) => judge,
            (Maybe, judge) => {
                judge || self.structural_subtype_of(lhs, rhs) || self.nominal_subtype_of(lhs, rhs)
            }
        }
    }

    pub(crate) fn same_type_of(&self, lhs: &Type, rhs: &Type) -> bool {
        self.supertype_of(lhs, rhs) && self.subtype_of(lhs, rhs)
    }

    pub(crate) fn cheap_supertype_of(&self, lhs: &Type, rhs: &Type) -> (Credibility, bool) {
        if lhs == rhs {
            return (Absolutely, true);
        }
        match (lhs, rhs) {
            // FIXME: Obj/Neverはクラス、Top/Bottomは構造型
            (Obj, _) | (_, Never) => (Absolutely, true),
            (_, Obj) | (Never, _) => (Absolutely, false),
            (Float | Ratio | Int | Nat | Bool, Bool)
            | (Float | Ratio | Int | Nat, Nat)
            | (Float | Ratio | Int, Int)
            | (Float | Ratio, Ratio)
            | (Float, Float) => (Absolutely, true),
            (Type, Class | Trait) => (Absolutely, true),
            (Type, Record(rec)) => (
                Absolutely,
                rec.iter().all(|(_, attr)| self.supertype_of(&Type, attr)),
            ),
            (Type, Subr(subr)) => (
                Absolutely,
                subr.kind
                    .self_t()
                    .map(|t| self.supertype_of(&Type, t))
                    .unwrap_or(true)
                    && subr
                        .default_params
                        .iter()
                        .all(|pt| self.supertype_of(&Type, &pt.ty))
                    && subr
                        .non_default_params
                        .iter()
                        .all(|pt| self.supertype_of(&Type, &pt.ty))
                    && self.supertype_of(&Type, &subr.return_t),
            ),
            (
                Type::Mono(n),
                Subr(SubrType {
                    kind: SubrKind::Func,
                    ..
                }),
            ) if &n[..] == "GenericFunc" => (Absolutely, true),
            (
                Type::Mono(n),
                Subr(SubrType {
                    kind: SubrKind::Proc,
                    ..
                }),
            ) if &n[..] == "GenericProc" => (Absolutely, true),
            (
                Type::Mono(n),
                Subr(SubrType {
                    kind: SubrKind::FuncMethod(_),
                    ..
                }),
            ) if &n[..] == "GenericFuncMethod" => (Absolutely, true),
            (
                Type::Mono(n),
                Subr(SubrType {
                    kind: SubrKind::ProcMethod { .. },
                    ..
                }),
            ) if &n[..] == "GenericProcMethod" => (Absolutely, true),
            (Type::Mono(l), Type::Poly { name: r, .. })
                if &l[..] == "GenericArray" && &r[..] == "Array" =>
            {
                (Absolutely, true)
            }
            (Type::Mono(l), Type::Poly { name: r, .. })
                if &l[..] == "GenericDict" && &r[..] == "Dict" =>
            {
                (Absolutely, true)
            }
            (Type::Mono(l), Type::Mono(r))
                if &l[..] == "GenericCallable"
                    && (&r[..] == "GenericFunc"
                        || &r[..] == "GenericProc"
                        || &r[..] == "GenericFuncMethod"
                        || &r[..] == "GenericProcMethod") =>
            {
                (Absolutely, true)
            }
            (Type::Mono(n), Subr(_)) if &n[..] == "GenericCallable" => (Absolutely, true),
            (lhs, rhs) if lhs.is_basic_class() && rhs.is_basic_class() => (Absolutely, false),
            _ => (Maybe, false),
        }
    }

    fn cheap_subtype_of(&self, lhs: &Type, rhs: &Type) -> (Credibility, bool) {
        self.cheap_supertype_of(rhs, lhs)
    }

    /// make judgments that include supertypes in the same namespace & take into account glue patches
    /// 同一名前空間にある上位型を含めた判定&接着パッチを考慮した判定を行う
    fn nominal_supertype_of(&self, lhs: &Type, rhs: &Type) -> bool {
        log!("{lhs}, {rhs}");
        for rhs_ctx in self.sorted_sup_type_ctxs(rhs) {
            log!("{lhs}, {}", rhs_ctx.name);
            if lhs.has_qvar() {
                let r_bounds = rhs_ctx.type_params_bounds();
                let bounds = if let Some((_, lhs_ctx)) = self._just_type_ctxs(lhs) {
                    lhs_ctx.type_params_bounds().concat(r_bounds)
                } else {
                    r_bounds
                };
                let mut tv_ctx = TyVarContext::new(self.level, bounds, self);
                let lhs = Self::instantiate_t(lhs.clone(), &mut tv_ctx);
                if rhs_ctx
                    .super_classes
                    .iter()
                    .chain(rhs_ctx.super_traits.iter())
                    .any(|sup| {
                        if sup.has_qvar() {
                            let sup = Self::instantiate_t(sup.clone(), &mut tv_ctx);
                            self.supertype_of(&lhs, &sup)
                        } else {
                            self.supertype_of(&lhs, &sup)
                        }
                    })
                {
                    return true;
                }
            } else {
                let r_bounds = rhs_ctx.type_params_bounds();
                let mut tv_ctx = TyVarContext::new(self.level, r_bounds, self);
                if rhs_ctx
                    .super_classes
                    .iter()
                    .chain(rhs_ctx.super_traits.iter())
                    .any(|sup| {
                        if sup.has_qvar() {
                            let sup = Self::instantiate_t(sup.clone(), &mut tv_ctx);
                            log!("{lhs}, {sup}");
                            self.supertype_of(&lhs, &sup)
                        } else {
                            log!("{lhs}, {sup}");
                            self.supertype_of(&lhs, &sup)
                        }
                    })
                {
                    return true;
                }
            }
        }
        log!("{lhs}, {rhs}",);
        for (patch_name, pair) in self.glue_patch_and_types.iter() {
            let patch = self
                .rec_get_patch(patch_name)
                .unwrap_or_else(|| panic!("{patch_name} not found"));
            log!("{patch_name}, {pair}",);
            if pair.sub_type.has_qvar() || pair.sup_trait.has_qvar() {
                let bounds = patch.type_params_bounds();
                let mut tv_ctx = TyVarContext::new(self.level, bounds, self);
                let sub_type = Self::instantiate_t(pair.sub_type.clone(), &mut tv_ctx);
                let sup_trait = Self::instantiate_t(pair.sup_trait.clone(), &mut tv_ctx);
                // e.g.
                // P = Patch X, Impl: Ord
                // Rhs <: X => Rhs <: Ord
                // Ord <: Lhs => Rhs <: Ord <: Lhs
                if self.supertype_of(&sub_type, rhs) && self.subtype_of(&sup_trait, lhs) {
                    return true;
                }
            } else {
                if self.supertype_of(&pair.sub_type, rhs) && self.subtype_of(&pair.sup_trait, lhs) {
                    return true;
                }
            }
        }
        false
    }

    fn nominal_subtype_of(&self, lhs: &Type, rhs: &Type) -> bool {
        self.nominal_supertype_of(rhs, lhs)
    }

    /// assert!(sup_conforms(?E(<: Eq(?E)), {Nat, Eq(Nat)}))
    /// assert!(sup_conforms(?E(<: Eq(?R)), {Nat, Eq(T)}))
    fn sup_conforms(&self, free: &FreeTyVar, inst_pair: &TraitInstancePair) -> bool {
        // 一旦汎化して、自由にlinkできるようにする
        let generalized = self.generalize_t(Type::FreeVar(free.clone()));
        let quant = enum_unwrap!(generalized, Type::Quantified);
        let mut ctx = TyVarContext::new(self.level, quant.bounds, self);
        let inst = Self::instantiate_t(*quant.unbound_callable, &mut ctx);
        let free = enum_unwrap!(inst, Type::FreeVar);
        let (_sub, sup) = free.crack_bound_types().unwrap();
        free.link(&inst_pair.sub_type);
        self.supertype_of(&sup, &inst_pair.sup_trait)
    }

    /// assert!(sup_conforms(?E(<: Eq(?E)), {Nat, Eq(Nat)}))
    /// assert!(sup_conforms(?E(<: Eq(?R)), {Nat, Eq(T)}))
    fn sub_conforms(&self, free: &FreeTyVar, inst_pair: &TraitInstancePair) -> bool {
        let generalized = self.generalize_t(Type::FreeVar(free.clone()));
        let quant = enum_unwrap!(generalized, Type::Quantified);
        let mut ctx = TyVarContext::new(self.level, quant.bounds, self);
        let inst = Self::instantiate_t(*quant.unbound_callable, &mut ctx);
        let free = enum_unwrap!(inst, Type::FreeVar);
        let (_sub, sup) = free.crack_bound_types().unwrap();
        free.link(&inst_pair.sub_type);
        self.subtype_of(&sup, &inst_pair.sup_trait)
    }

    /// lhs :> rhs?
    /// ```erg
    /// assert supertype_of(Int, Nat) # i: Int = 1 as Nat
    /// assert supertype_of(Bool, Bool)
    /// ```
    /// This function does not consider the nominal subtype relation.
    /// Use `rec_full_supertype_of` for complete judgement.
    /// 単一化、評価等はここでは行わない、スーパータイプになる可能性があるかだけ判定する
    /// ので、lhsが(未連携)型変数の場合は単一化せずにtrueを返す
    pub(crate) fn structural_supertype_of(&self, lhs: &Type, rhs: &Type) -> bool {
        match (lhs, rhs) {
            (Subr(ls), Subr(rs))
                if ls.kind.same_kind_as(&rs.kind)
                    && (ls.kind == SubrKind::Func || ls.kind == SubrKind::Proc) =>
            {
                // () -> Never <: () -> Int <: () -> Object
                // (Object) -> Int <: (Int) -> Int <: (Never) -> Int
                ls.non_default_params.len() == rs.non_default_params.len()
                && ls.default_params.len() == rs.default_params.len()
                && self.supertype_of(&ls.return_t, &rs.return_t) // covariant
                && ls.non_default_params.iter()
                    .zip(rs.non_default_params.iter())
                    .all(|(l, r)| self.subtype_of(&l.ty, &r.ty))
                && ls.default_params.iter()
                    .zip(rs.default_params.iter())
                    .all(|(l, r)| self.subtype_of(&l.ty, &r.ty))
                // contravariant
            }
            // RefMut, OptionMut are invariant
            (Ref(lhs), Ref(rhs)) | (VarArgs(lhs), VarArgs(rhs)) => self.supertype_of(lhs, rhs),
            (FreeVar(lfv), rhs) if lfv.is_linked() => self.supertype_of(&lfv.crack(), rhs),
            // true if it can be a supertype, false if it cannot (due to type constraints)
            // No type constraints are imposed here, as subsequent type decisions are made according to the possibilities
            (FreeVar(lfv), rhs) => {
                log!("here: {lfv}, {rhs}");
                let super_traits = self.super_traits(rhs);
                log!("super_traits: {}", erg_common::fmt_vec(&super_traits));
                for inst_pair in super_traits.into_iter() {
                    if self.sup_conforms(&lfv, inst_pair) {
                        return true;
                    }
                }
                false
            }
            (lhs, FreeVar(lfv)) if lfv.is_linked() => self.supertype_of(lhs, &lfv.crack()),
            (lhs, FreeVar(rfv)) => {
                log!("here: {rfv}, {lhs}");
                let super_traits = self.super_traits(lhs);
                for inst_pair in super_traits.into_iter() {
                    if self.sub_conforms(&rfv, inst_pair) {
                        return true;
                    }
                }
                false
            }
            (Type, Record(rec)) => {
                for (_, t) in rec.iter() {
                    if !self.supertype_of(&Type, t) {
                        return false;
                    }
                }
                true
            }
            // (MonoQuantVar(_), _) | (_, MonoQuantVar(_)) => true,
            // REVIEW: maybe this is incomplete
            // ({I: Int | I >= 0} :> {N: Int | N >= 0}) == true,
            // ({I: Int | I >= 0} :> {I: Int | I >= 1}) == true,
            // ({I: Int | I >= 0} :> {N: Nat | N >= 1}) == true,
            // ({I: Int | I > 1 or I < -1} :> {I: Int | I >= 0}) == false,
            (Refinement(l), Refinement(r)) => {
                if !self.supertype_of(&l.t, &r.t) {
                    return false;
                }
                let mut r_preds_clone = r.preds.clone();
                for l_pred in l.preds.iter() {
                    for r_pred in r.preds.iter() {
                        if l_pred.subject().unwrap_or("") == &l.var[..]
                            && r_pred.subject().unwrap_or("") == &r.var[..]
                            && self.rec_is_super_pred_of(l_pred, r_pred)
                        {
                            r_preds_clone.remove(r_pred);
                        }
                    }
                }
                r_preds_clone.is_empty()
            }
            (Nat, re @ Refinement(_)) => {
                let nat = Type::Refinement(self.into_refinement(Nat));
                self.structural_supertype_of(&nat, re)
            }
            (re @ Refinement(_), Nat) => {
                let nat = Type::Refinement(self.into_refinement(Nat));
                self.structural_supertype_of(re, &nat)
            }
            // Int :> {I: Int | ...} == true
            // Real :> {I: Int | ...} == false
            // Int :> {I: Str| ...} == false
            (l, Refinement(r)) => self.supertype_of(l, &r.t),
            // ({I: Int | True} :> Int) == true, ({N: Nat | ...} :> Int) == false, ({I: Int | I >= 0} :> Int) == false
            (Refinement(l), r) => {
                if l.preds
                    .iter()
                    .any(|p| p.mentions(&l.var) && p.can_be_false())
                {
                    return false;
                }
                self.supertype_of(&l.t, r)
            }
            (Quantified(l), Quantified(r)) => {
                // REVIEW: maybe this should be `unreachable`
                let mut l_tv_ctx = TyVarContext::new(self.level, l.bounds.clone(), self);
                let mut r_tv_ctx = TyVarContext::new(self.level, r.bounds.clone(), self);
                let l_callable =
                    Self::instantiate_t(l.unbound_callable.as_ref().clone(), &mut l_tv_ctx);
                let r_callable =
                    Self::instantiate_t(r.unbound_callable.as_ref().clone(), &mut r_tv_ctx);
                self.structural_supertype_of(&l_callable, &r_callable)
            }
            (Quantified(q), r) => {
                // REVIEW: maybe this should be `unreachable`
                let mut tv_ctx = TyVarContext::new(self.level, q.bounds.clone(), self);
                let q_callable =
                    Self::instantiate_t(q.unbound_callable.as_ref().clone(), &mut tv_ctx);
                self.structural_supertype_of(&q_callable, r)
            }
            (Or(l_or, r_or), rhs) => self.supertype_of(l_or, rhs) || self.supertype_of(r_or, rhs),
            (lhs, Or(or_l, or_r)) => self.supertype_of(lhs, or_l) && self.supertype_of(lhs, or_r),
            (And(l_and, r_and), rhs) => {
                self.supertype_of(l_and, rhs) && self.supertype_of(r_and, rhs)
            }
            (lhs, And(l_and, r_and)) => {
                self.supertype_of(lhs, l_and) || self.supertype_of(lhs, r_and)
            }
            (_lhs, Not(_, _)) => todo!(),
            (Not(_, _), _rhs) => todo!(),
            (VarArgs(lhs), rhs) => self.supertype_of(lhs, rhs),
            // TはすべてのRef(T)のメソッドを持つので、Ref(T)のサブタイプ
            (Ref(lhs), rhs) | (RefMut(lhs), rhs) => self.supertype_of(lhs, rhs),
            (
                Poly {
                    name: ln,
                    params: lps,
                },
                Poly {
                    name: rn,
                    params: rps,
                },
            ) => {
                if ln != rn || lps.len() != rps.len() {
                    return false;
                }
                let ctx = self
                    .rec_type_ctx_by_name(ln)
                    .unwrap_or_else(|| panic!("{ln} is not found"));
                let variances = ctx.type_params_variance();
                debug_assert_eq!(lps.len(), variances.len());
                lps.iter()
                    .zip(rps.iter())
                    .zip(variances.iter())
                    .all(|((lp, rp), variance)| match (lp, rp, variance) {
                        (TyParam::Type(l), TyParam::Type(r), Variance::Contravariant) => {
                            self.subtype_of(l, r)
                        }
                        (TyParam::Type(l), TyParam::Type(r), Variance::Covariant) => {
                            // if matches!(r.as_ref(), &Type::Refinement(_)) { log!("{l}, {r}, {}", self.structural_supertype_of(l, r, bounds, Some(lhs_variance))); }
                            self.supertype_of(l, r)
                        }
                        // Invariant
                        _ => self.eq_tp(lp, rp),
                    })
            }
            (MonoQVar(name), r) | (PolyQVar { name, .. }, r) => {
                panic!("Not instantiated type variable: {name}, r: {r}")
            }
            (l, MonoQVar(name)) | (l, PolyQVar { name, .. }) => {
                panic!("Not instantiated type variable: {name}, l: {l}")
            }
            (_l, _r) => false,
        }
    }

    /// lhs <: rhs?
    pub(crate) fn structural_subtype_of(&self, lhs: &Type, rhs: &Type) -> bool {
        self.structural_supertype_of(rhs, lhs)
    }

    pub(crate) fn structural_same_type_of(&self, lhs: &Type, rhs: &Type) -> bool {
        self.structural_supertype_of(lhs, rhs) && self.structural_subtype_of(lhs, rhs)
    }

    pub(crate) fn rec_try_cmp(&self, l: &TyParam, r: &TyParam) -> Option<TyParamOrdering> {
        match (l, r) {
            (TyParam::Value(l), TyParam::Value(r)) =>
                l.try_cmp(r).map(Into::into),
            // TODO: 型を見て判断する
            (TyParam::BinOp{ op, lhs, rhs }, r) => {
                if let Ok(l) = self.eval.eval_bin_tp(*op, lhs, rhs) {
                    self.rec_try_cmp(&l, r)
                } else { Some(Any) }
            },
            (TyParam::FreeVar(fv), p) if fv.is_linked() => {
                self.rec_try_cmp(&*fv.crack(), p)
            }
            (p, TyParam::FreeVar(fv)) if fv.is_linked() => {
                self.rec_try_cmp(p, &*fv.crack())
            }
            (
                l @ (TyParam::FreeVar(_) | TyParam::Erased(_) | TyParam::MonoQVar(_)),
                r @ (TyParam::FreeVar(_) | TyParam::Erased(_) | TyParam::MonoQVar(_)),
            ) /* if v.is_unbound() */ => {
                let l_t = self.eval.get_tp_t(l, self).unwrap();
                let r_t = self.eval.get_tp_t(r, self).unwrap();
                if self.rec_supertype_of(&l_t, &r_t) || self.rec_subtype_of(&l_t, &r_t) {
                    Some(Any)
                } else { Some(NotEqual) }
            },
            // Intervalとしてのl..rはl<=rであることが前提となっている
            // try_cmp((n: 1..10), 1) -> Some(GreaterEqual)
            // try_cmp((n: 0..2), 1) -> Some(Any)
            // try_cmp((n: 2.._), 1) -> Some(Greater)
            // try_cmp((n: -1.._), 1) -> Some(Any)
            (l @ (TyParam::Erased(_) | TyParam::FreeVar(_) | TyParam::MonoQVar(_)), p) => {
                let t = self.eval.get_tp_t(l, self).unwrap();
                let inf = self.rec_inf(&t);
                let sup = self.rec_sup(&t);
                if let (Some(inf), Some(sup)) = (inf, sup) {
                    // (n: Int, 1) -> (-inf..inf, 1) -> (cmp(-inf, 1), cmp(inf, 1)) -> (Less, Greater) -> Any
                    // (n: 5..10, 2) -> (cmp(5..10, 2), cmp(5..10, 2)) -> (Greater, Greater) -> Greater
                    match (
                        self.rec_try_cmp(&inf, p).unwrap(),
                        self.rec_try_cmp(&sup, p).unwrap()
                    ) {
                        (Less, Less) => Some(Less),
                        (Less, Equal) => Some(LessEqual),
                        (Less, LessEqual) => Some(LessEqual),
                        (Less, NotEqual) => Some(NotEqual),
                        (Less, Greater | GreaterEqual | Any) => Some(Any),
                        (Equal, Less) => assume_unreachable!(),
                        (Equal, Equal) => Some(Equal),
                        (Equal, Greater) => Some(GreaterEqual),
                        (Equal, LessEqual) => Some(Equal),
                        (Equal, NotEqual) => Some(GreaterEqual),
                        (Equal, GreaterEqual | Any) => Some(GreaterEqual),
                        (Greater, Less) => assume_unreachable!(),
                        (Greater, Equal) => assume_unreachable!(),
                        (Greater, Greater | NotEqual | GreaterEqual | Any) => Some(Greater),
                        (Greater, LessEqual) => assume_unreachable!(),
                        (LessEqual, Less) => assume_unreachable!(),
                        (LessEqual, Equal | LessEqual) => Some(LessEqual),
                        (LessEqual, Greater | NotEqual | GreaterEqual | Any) => Some(Any),
                        (NotEqual, Less) => Some(Less),
                        (NotEqual, Equal | LessEqual) => Some(LessEqual),
                        (NotEqual, Greater | GreaterEqual | Any) => Some(Any),
                        (NotEqual, NotEqual) => Some(NotEqual),
                        (GreaterEqual, Less) => assume_unreachable!(),
                        (GreaterEqual, Equal | LessEqual) => Some(Equal),
                        (GreaterEqual, Greater | NotEqual | GreaterEqual | Any) => Some(GreaterEqual),
                        (Any, Less) => Some(Less),
                        (Any, Equal | LessEqual) => Some(LessEqual),
                        (Any, Greater | NotEqual | GreaterEqual | Any) => Some(Any),
                        (l, r) =>
                            todo!("cmp({inf}, {sup}) = {l:?}, cmp({inf}, {sup}) = {r:?}"),
                    }
                } else { None }
            }
            (l, r @ (TyParam::Erased(_) | TyParam::MonoQVar(_) | TyParam::FreeVar(_))) =>
                self.rec_try_cmp(r, l).map(|ord| ord.reverse()),
            (_l, _r) => {
                erg_common::fmt_dbg!(_l, _r,);
                None
            },
        }
    }

    pub(crate) fn into_refinement(&self, t: Type) -> RefinementType {
        match t {
            Nat => {
                let var = Str::from(fresh_varname());
                RefinementType::new(
                    var.clone(),
                    Int,
                    set! {Predicate::ge(var, TyParam::value(0))},
                )
            }
            Refinement(r) => r,
            t => {
                let var = Str::from(fresh_varname());
                RefinementType::new(var, t, set! {})
            }
        }
    }

    /// 和集合(A or B)を返す
    pub(crate) fn rec_union(&self, lhs: &Type, rhs: &Type) -> Type {
        match (
            self.rec_supertype_of(lhs, rhs),
            self.rec_subtype_of(lhs, rhs),
        ) {
            (true, true) => return lhs.clone(),  // lhs = rhs
            (true, false) => return lhs.clone(), // lhs :> rhs
            (false, true) => return rhs.clone(),
            (false, false) => {}
        }
        match (lhs, rhs) {
            (Refinement(l), Refinement(r)) => Type::Refinement(self.union_refinement(l, r)),
            (t, Type::Never) | (Type::Never, t) => t.clone(),
            (t, Refinement(r)) | (Refinement(r), t) => {
                let t = self.into_refinement(t.clone());
                Type::Refinement(self.union_refinement(&t, r))
            }
            (l, r) => or(l.clone(), r.clone()),
        }
    }

    fn union_refinement(&self, lhs: &RefinementType, rhs: &RefinementType) -> RefinementType {
        if !self.structural_supertype_of(&lhs.t, &rhs.t)
            && !self.structural_subtype_of(&lhs.t, &rhs.t)
        {
            log!("{lhs}\n{rhs}");
            todo!()
        } else {
            let name = lhs.var.clone();
            let rhs_preds = rhs
                .preds
                .iter()
                .map(|p| p.clone().change_subject_name(name.clone()))
                .collect();
            // FIXME: predの包含関係も考慮する
            RefinementType::new(
                lhs.var.clone(),
                *lhs.t.clone(),
                lhs.preds.clone().concat(rhs_preds),
            )
        }
    }

    /// see doc/LANG/compiler/refinement_subtyping.md
    /// ```erg
    /// assert is_super_pred({I >= 0}, {I == 0})
    /// assert is_super_pred({T >= 0}, {I == 0})
    /// assert !is_super_pred({I < 0}, {I == 0})
    /// ```
    fn rec_is_super_pred_of(&self, lhs: &Predicate, rhs: &Predicate) -> bool {
        match (lhs, rhs) {
            (Pred::LessEqual { rhs, .. }, _) if !rhs.has_upper_bound() => true,
            (Pred::GreaterEqual { rhs, .. }, _) if !rhs.has_lower_bound() => true,
            (
                Pred::Equal { .. },
                Pred::GreaterEqual { .. } | Pred::LessEqual { .. } | Pred::NotEqual { .. },
            )
            | (Pred::LessEqual { .. }, Pred::GreaterEqual { .. })
            | (Pred::GreaterEqual { .. }, Pred::LessEqual { .. })
            | (Pred::NotEqual { .. }, Pred::Equal { .. }) => false,
            (Pred::Equal { rhs, .. }, Pred::Equal { rhs: rhs2, .. })
            | (Pred::NotEqual { rhs, .. }, Pred::NotEqual { rhs: rhs2, .. }) => {
                self.rec_try_cmp(rhs, rhs2).unwrap().is_eq()
            }
            // {T >= 0} :> {T >= 1}, {T >= 0} :> {T == 1}
            (
                Pred::GreaterEqual { rhs, .. },
                Pred::GreaterEqual { rhs: rhs2, .. } | Pred::Equal { rhs: rhs2, .. },
            ) => self.rec_try_cmp(rhs, rhs2).unwrap().is_le(),
            (
                Pred::LessEqual { rhs, .. },
                Pred::LessEqual { rhs: rhs2, .. } | Pred::Equal { rhs: rhs2, .. },
            ) => self.rec_try_cmp(rhs, rhs2).unwrap().is_ge(),
            (lhs @ (Pred::GreaterEqual { .. } | Pred::LessEqual { .. }), Pred::And(l, r)) => {
                self.rec_is_super_pred_of(lhs, l) || self.rec_is_super_pred_of(lhs, r)
            }
            (lhs, Pred::Or(l, r)) => {
                self.rec_is_super_pred_of(lhs, l) && self.rec_is_super_pred_of(lhs, r)
            }
            (Pred::Or(l, r), rhs @ (Pred::GreaterEqual { .. } | Pred::LessEqual { .. })) => {
                self.rec_is_super_pred_of(l, rhs) || self.rec_is_super_pred_of(r, rhs)
            }
            (Pred::And(l, r), rhs) => {
                self.rec_is_super_pred_of(l, rhs) && self.rec_is_super_pred_of(r, rhs)
            }
            (lhs, rhs) => todo!("{lhs}/{rhs}"),
        }
    }

    pub(crate) fn is_sub_constraint_of(&self, l: &Constraint, r: &Constraint) -> bool {
        match (l, r) {
            // |I: Nat| <: |I: Int|
            (Constraint::TypeOf(lhs), Constraint::TypeOf(rhs)) => self.rec_subtype_of(lhs, rhs),
            // |T <: Int| <: |T: Type|
            (Constraint::Sandwiched { sub: Never, .. }, Constraint::TypeOf(Type)) => true,
            // |Int <: T| <: |Nat <: T|
            // |T <: Nat| <: |T <: Int|
            // |Int <: T <: Ratio| <: |Nat <: T <: Complex|
            (
                Constraint::Sandwiched {
                    sub: lsub,
                    sup: lsup,
                },
                Constraint::Sandwiched {
                    sub: rsub,
                    sup: rsup,
                },
            ) => self.rec_supertype_of(lsub, rsub) && self.rec_subtype_of(lsup, rsup),
            _ => false,
        }
    }

    #[inline]
    fn type_of(&self, p: &TyParam) -> Type {
        self.eval.get_tp_t(p, self).unwrap()
    }

    // sup/inf({±∞}) = ±∞ではあるが、Inf/NegInfにはOrdを実装しない
    fn rec_sup(&self, t: &Type) -> Option<TyParam> {
        match t {
            Int | Nat | Float => Some(TyParam::value(Inf)),
            Refinement(refine) => {
                let mut maybe_max = None;
                for pred in refine.preds.iter() {
                    match pred {
                        Pred::LessEqual { lhs, rhs } | Pred::Equal { lhs, rhs }
                            if lhs == &refine.var =>
                        {
                            if let Some(max) = &maybe_max {
                                if self.rec_try_cmp(rhs, max).unwrap() == Greater {
                                    maybe_max = Some(rhs.clone());
                                }
                            } else {
                                maybe_max = Some(rhs.clone());
                            }
                        }
                        _ => {}
                    }
                }
                maybe_max
            }
            _other => None,
        }
    }

    fn rec_inf(&self, t: &Type) -> Option<TyParam> {
        match t {
            Int | Float => Some(TyParam::value(-Inf)),
            Nat => Some(TyParam::value(0usize)),
            Refinement(refine) => {
                let mut maybe_min = None;
                for pred in refine.preds.iter() {
                    match pred {
                        Predicate::GreaterEqual { lhs, rhs } | Predicate::Equal { lhs, rhs }
                            if lhs == &refine.var =>
                        {
                            if let Some(min) = &maybe_min {
                                if self.rec_try_cmp(rhs, min).unwrap() == Less {
                                    maybe_min = Some(rhs.clone());
                                }
                            } else {
                                maybe_min = Some(rhs.clone());
                            }
                        }
                        _ => {}
                    }
                }
                maybe_min
            }
            _other => None,
        }
    }

    /// lhsとrhsが包含関係にあるとき小さいほうを返す
    /// 関係なければNoneを返す
    pub(crate) fn rec_min<'t>(&self, lhs: &'t Type, rhs: &'t Type) -> Option<&'t Type> {
        // 同じならどちらを返しても良い
        match (
            self.rec_supertype_of(lhs, rhs),
            self.rec_subtype_of(lhs, rhs),
        ) {
            (true, true) | (true, false) => Some(rhs),
            (false, true) => Some(lhs),
            (false, false) => None,
        }
    }

    pub(crate) fn rec_max<'t>(&self, lhs: &'t Type, rhs: &'t Type) -> Option<&'t Type> {
        // 同じならどちらを返しても良い
        match (
            self.rec_supertype_of(lhs, rhs),
            self.rec_subtype_of(lhs, rhs),
        ) {
            (true, true) | (true, false) => Some(lhs),
            (false, true) => Some(rhs),
            (false, false) => None,
        }
    }

    fn _rec_cmp_t<'t>(&self, lhs: &'t Type, rhs: &'t Type) -> TyParamOrdering {
        match self.rec_min(lhs, rhs) {
            Some(l) if l == lhs => TyParamOrdering::Less,
            Some(_) => TyParamOrdering::Greater,
            None => TyParamOrdering::NoRelation,
        }
    }

    pub(crate) fn min<'t>(&self, lhs: &'t Type, rhs: &'t Type) -> Option<&'t Type> {
        // 同じならどちらを返しても良い
        match (self.supertype_of(lhs, rhs), self.subtype_of(lhs, rhs)) {
            (true, true) | (true, false) => Some(rhs),
            (false, true) => Some(lhs),
            (false, false) => None,
        }
    }

    fn _max<'t>(&self, lhs: &'t Type, rhs: &'t Type) -> Option<&'t Type> {
        // 同じならどちらを返しても良い
        match (self.supertype_of(lhs, rhs), self.subtype_of(lhs, rhs)) {
            (true, true) | (true, false) => Some(lhs),
            (false, true) => Some(rhs),
            (false, false) => None,
        }
    }

    pub(crate) fn cmp_t<'t>(&self, lhs: &'t Type, rhs: &'t Type) -> TyParamOrdering {
        match self.min(lhs, rhs) {
            Some(l) if l == lhs => TyParamOrdering::Less,
            Some(_) => TyParamOrdering::Greater,
            None => TyParamOrdering::NoRelation,
        }
    }

    // TODO:
    pub(crate) fn smallest_pair<I: Iterator<Item = TraitInstancePair>>(
        &self,
        type_and_traits: I,
    ) -> Option<TraitInstancePair> {
        let mut type_and_traits = type_and_traits.collect::<Vec<_>>();
        // Avoid heavy sorting as much as possible for efficiency
        let mut cheap_sort_succeed = true;
        type_and_traits.sort_by(|lhs, rhs| {
            match self.cmp_t(&lhs.sup_trait, &rhs.sup_trait).try_into() {
                Ok(ord) => ord,
                Err(_) => {
                    cheap_sort_succeed = false;
                    Ordering::Equal
                }
            }
        });
        let mut sorted = if cheap_sort_succeed {
            type_and_traits
        } else {
            self.sort_type_pairs(type_and_traits.into_iter())
        };
        if sorted.first().is_some() {
            Some(sorted.remove(0))
        } else {
            None
        }
    }

    pub(crate) fn smallest_ref_t<'t, I: Iterator<Item = &'t Type>>(
        &self,
        ts: I,
    ) -> Option<&'t Type> {
        let mut ts = ts.collect::<Vec<_>>();
        // Avoid heavy sorting as much as possible for efficiency
        let mut cheap_sort_succeed = true;
        ts.sort_by(|lhs, rhs| match self.cmp_t(lhs, rhs).try_into() {
            Ok(ord) => ord,
            Err(_) => {
                cheap_sort_succeed = false;
                Ordering::Equal
            }
        });
        let mut sorted = if cheap_sort_succeed {
            ts
        } else {
            self.sort_types(ts.into_iter())
        };
        if sorted.first().is_some() {
            Some(sorted.remove(0))
        } else {
            None
        }
    }
}