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//! The type checker uses [`TcKey`](struct.TcKey.html) to refer to entities like variables or terms.  [`Constraint`](enum.Constraint.html) related different keys and abstract/concrete types.
//!
//! [`TcKey`](struct.TcKey.html)s are an inexpensive and simple indexing mechanism that can be copied, checked for equality, and hashed.  
//! A [`TcKey`](struct.TcKey.html) offers functions for relating them to other keys or types, symmetrically or asymmetrically.

use crate::types::{Abstract, Generalizable};
use std::hash::Hash;

/// Represents a constraint on one or several `TcKey`s and/or types.
///
/// Rather than creating these constraints directly, `TcKey` provides several convenient functions for this
/// purpose.  They can then be passed to the [`TypeChecker`](struct.TypeChecker.html) via the [`Typechecker::impose()`](struct.TypeChecker.html#method.impose) function.
#[must_use = "the creation of a `TypeConstraint` has no effect, it should be passed to a `TypeChecker`"]
#[derive(Debug, Clone)]
pub enum Constraint<AbsTy: Abstract> {
    /// Equates two keys, i.e., they refer to the same type and are thus symmetrically connected.  Refining one will refine the other as well.
    #[doc(hidden)]
    Equal(TcKey, TcKey),

    /// Connects two keys asymmetrically.  Refining `bound` refines `target` whereas refining `target` leaves `bound` unaffected.
    #[doc(hidden)]
    MoreConc {
        /// The more concrete key that is bound and thus affected by changes to `bound`.
        #[doc(hidden)]
        target: TcKey,
        /// The less concrete key that constitutes a bound for `target`.
        #[doc(hidden)]
        bound: TcKey,
    },
    /// An asymmetric relation between a key and a type.  Note that the type cannot change over time.
    #[doc(hidden)]
    MoreConcExplicit(TcKey, AbsTy),

    /// A conjunction of several constraints.
    #[doc(hidden)]
    Conjunction(Vec<Self>),

    /// Declares that the key needs to resolve to a type with the given variant.
    #[doc(hidden)]
    Variant(TcKey, AbsTy::VariantTag),
}

/// An inexpensive and simple indexing mechanism using during the type checking procedure.
///
/// It can that can be copied, checked for equality, and hashed, however, it is not ordered.
/// A [`TcKey`](struct.TcKey.html) offers functions for relating them to other keys or types, symmetrically or asymmetrically, by creating constraints.
/// These constraints only serve one purpose: They can be passed to the type checker's [`TypeChecker::impose`](struct.TypeChecker.html#method.impose) function.
///
/// # Example
/// There are several kinds of constraints that can be generated for a key.
/// Assume the following data structures exist:
/// ```
/// use rusttyc::{types::Abstract, TcKey, TypeChecker, TcVar, TcErr};
///
/// #[derive(Debug, Clone, Copy, PartialEq, Eq)]
/// enum MyVariant {
///     U8,
///     String,
/// }
///
/// #[derive(Debug, Clone, Copy, PartialEq, Eq)]
/// enum MyType {
///     Top,
///     Numeric,
///     UInt,
///     U8,
///     String,
/// }
///
/// impl Abstract for MyType {
///     type Err = String;
///     type VariantTag = MyVariant;
///     fn from_tag(tag: Self::VariantTag, children: Vec<Self>) -> Self {
///         assert!(children.is_empty());
///         match tag {
///             MyVariant::String => MyType::String,
///             MyVariant::U8 => MyType::U8,
///         }
///     }
///     fn variant_arity(_tag: Self::VariantTag) -> usize {
///         0
///     }
///     fn meet(&self, other: &Self) -> Result<Self, Self::Err> {
///         use MyType::*;
///         match (*self, *other) {
///             (Top, x) | (x, Top) => Ok(x),
///             (String, String) => Ok(String),
///             (String, _) | (_, String) => Err("string can only be met with string.".to_string()),
///             (Numeric, x) | (x, Numeric) => Ok(x), // x can only be Numeric, UInt, or U8.
///             (UInt, x) | (x, UInt) => Ok(x),       // x can only be UInt or U8.
///             (U8, U8) => Ok(U8),
///         }
///     }
///     fn unconstrained() -> Self {
///         Self::Top
///     }
///     fn variant(&self) -> Option<Self::VariantTag> {
///         match self {
///             Self::String => Some(MyVariant::String),
///             Self::U8 => Some(MyVariant::U8),
///             _ => None,
///         }
///     }
/// }
/// #[derive(PartialEq, Eq, Hash, Clone, Copy, Debug)]
/// struct MyVar(u8);
/// impl TcVar for MyVar {}
/// ```
///
/// The type checking procedure can then proceed as follows.
/// ```
/// # use rusttyc::{types::Abstract, TcKey, TypeChecker, TcVar, TcErr};
/// #
/// # #[derive(Debug, Clone, Copy, PartialEq, Eq)]
/// # enum MyVariant {
/// #     U8,
/// #     String,
/// # }
/// #
/// # #[derive(Debug, Clone, Copy, PartialEq, Eq)]
/// # enum MyType {
/// #     Top,
/// #     Numeric,
/// #     UInt,
/// #     U8,
/// #     String,
/// # }
/// #
/// # impl Abstract for MyType {
/// #     type Err = String;
/// #     type VariantTag = MyVariant;
/// #     fn from_tag(tag: Self::VariantTag, children: Vec<Self>) -> Self {
/// #         assert!(children.is_empty());
/// #         match tag {
/// #             MyVariant::String => MyType::String,
/// #             MyVariant::U8 => MyType::U8,
/// #         }
/// #     }
/// #     fn variant_arity(_tag: Self::VariantTag) -> usize {
/// #         0
/// #     }
/// #     fn meet(&self, other: &Self) -> Result<Self, Self::Err> {
/// #         use MyType::*;
/// #         match (*self, *other) {
/// #             (Top, x) | (x, Top) => Ok(x),
/// #             (String, String) => Ok(String),
/// #             (String, _) | (_, String) => Err("string can only be met with string.".to_string()),
/// #             (Numeric, x) | (x, Numeric) => Ok(x), // x can only be Numeric, UInt, or U8.
/// #             (UInt, x) | (x, UInt) => Ok(x),       // x can only be UInt or U8.
/// #             (U8, U8) => Ok(U8),
/// #         }
/// #     }
/// #     fn unconstrained() -> Self {
/// #         Self::Top
/// #     }
/// #     fn variant(&self) -> Option<Self::VariantTag> {
/// #         match self {
/// #             Self::String => Some(MyVariant::String),
/// #             Self::U8 => Some(MyVariant::U8),
/// #             _ => None,
/// #         }
/// #     }
/// # }
/// # #[derive(PartialEq, Eq, Hash, Clone, Copy, Debug)]
/// # struct MyVar(u8);
/// # impl TcVar for MyVar {}
/// #
/// # fn main() -> Result<(), TcErr<MyType>> {
/// let mut tc: TypeChecker<MyType, MyVar> = TypeChecker::new();
/// let key1 = tc.new_term_key();
/// let key2 = tc.new_term_key();
/// let key3 = tc.new_term_key();
/// let key4 = tc.new_term_key();
///
/// tc.impose(key1.more_concrete_than_explicit(MyType::Numeric))?;  // key1 is numeric.
/// // key2 is at least as concrete as k1, i.e. it will also be numeric.
/// tc.impose(key2.more_concrete_than(key1))?;
/// tc.impose(key3.equate(key2))?; // key3 is the same type as key2, i.e., numeric
///
/// let tt = tc.clone().type_check()?;
/// assert_eq!(tt[key1], MyType::Numeric);
/// assert_eq!(tt[key2], MyType::Numeric);
/// assert_eq!(tt[key3], MyType::Numeric);
/// // we did not impose a constraint on it, yet, so its the top element.
/// assert_eq!(tt[key4], MyType::Top);
///
/// // Concretize key3 to be a UInt.  Also affects key2 due to unification.  
/// // key1 is unaffected because of the asymmetric relation between key1 and key2,
/// // which translates to an asymmetric relation between key1 and key3 as well.
/// tc.impose(key3.more_concrete_than_explicit(MyType::UInt))?;
///
/// let tt = tc.clone().type_check()?;
/// assert_eq!(tt[key1], MyType::Numeric);
/// assert_eq!(tt[key2], MyType::UInt);
/// assert_eq!(tt[key3], MyType::UInt);
/// assert_eq!(tt[key4], MyType::Top);
///
/// // key4 is more concrete than both key2 (and transitively key3), and key1, so it becomes a UInt.
/// tc.impose(key4.is_meet_of(key2, key1))?;
/// // Make key2 and key3 U8.  key4 depends on them, so it becomes U8 as well.  key1 is unaffected.
/// tc.impose(key2.more_concrete_than_explicit(MyType::U8))?;
/// let key5 = tc.new_term_key();
/// tc.impose(key5.more_concrete_than_explicit(MyType::String))?; // key5 is a string.
///
/// let tt = tc.clone().type_check()?;
/// assert_eq!(tt[key1], MyType::Numeric);
/// assert_eq!(tt[key2], MyType::U8);
/// assert_eq!(tt[key3], MyType::U8);
/// assert_eq!(tt[key4], MyType::U8);
/// assert_eq!(tt[key5], MyType::String);
///
/// let key6 = tc.new_term_key();
/// // key6 is the meet of all other keys.
/// tc.impose(key6.is_meet_of_all(&[key1, key2, key3, key4, key5]))?;
///
/// let res = tc.clone().type_check();
/// // The meet of numeric types and strings will fail, so key6 cannot be resolved.
/// assert!(res.is_err());  
/// # Ok(())
/// # }
/// ```
#[derive(Debug, Clone, Copy, Hash, PartialEq, Eq)]
pub struct TcKey {
    pub(crate) ix: usize,
}

impl TcKey {
    pub(crate) fn new(ix: usize) -> TcKey {
        TcKey { ix }
    }
}

impl TcKey {
    /// Connects two keys asymmetrically.  Refining `bound` refines `self` whereas refining `self` leaves `bound` unaffected.
    pub fn more_concrete_than<AbsTy: Abstract>(self, bound: Self) -> Constraint<AbsTy> {
        Constraint::MoreConc { target: self, bound }
    }
    /// Equates two keys, i.e., they refer to the same type and are thus symmetrically connected.  Refining one will refine the other as well.
    pub fn equate<AbsTy: Abstract>(self, other: Self) -> Constraint<AbsTy> {
        Constraint::Equal(self, other)
    }
    /// Declares that `self` is at least as concrete as `bound`.
    pub fn more_concrete_than_explicit<AbsTy: Abstract>(self, bound: AbsTy) -> Constraint<AbsTy> {
        Constraint::MoreConcExplicit(self, bound)
    }
    /// Declares that `self` is the meet of `left` and `right`.  
    /// This binds `self` to both `left` and `right` asymmetrically.
    pub fn is_meet_of<AbsTy: Abstract>(self, left: Self, right: Self) -> Constraint<AbsTy> {
        self.is_meet_of_all(&[left, right])
    }
    /// Declares that `self` is the meet of all elements contained in `elems`.  
    /// This binds `self` to all of these keys asymmetrically.
    pub fn is_meet_of_all<AbsTy: Abstract>(self, elems: &[Self]) -> Constraint<AbsTy> {
        Constraint::Conjunction(elems.iter().map(|e| self.more_concrete_than(*e)).collect())
    }
    /// Declares that `self` is at least as concrete as the abstracted version of `conc`.
    pub fn captures_concrete<AbsTy: Abstract, CT>(self, conc: CT) -> Constraint<AbsTy>
    where
        CT: Generalizable<Generalized = AbsTy>,
    {
        self.more_concrete_than_explicit(conc.generalize())
    }
}