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//- // Copyright 2018 Mazdak Farrokhzad // // Licensed under the Apache License, Version 2.0 <LICENSE-APACHE or // http://www.apache.org/licenses/LICENSE-2.0> or the MIT license // <LICENSE-MIT or http://opensource.org/licenses/MIT>, at your // option. This file may not be copied, modified, or distributed // except according to those terms. //! Provides a `refl` encoding which you can use to provide a proof //! witness that one type is equivalent (identical) to another type. //! You can use this to encode a subset of what GADTs allow you to in Haskell. //! //! This is encoded as: //! //! ```rust //! use std::mem; //! use std::marker::PhantomData; //! //! pub struct Id<S: ?Sized, T: ?Sized>(PhantomData<(*mut S, *mut T)>); //! //! impl<T: ?Sized> Id<T, T> { pub const REFL: Self = Id(PhantomData); } //! //! pub fn refl<T: ?Sized>() -> Id<T, T> { Id::REFL } //! //! impl<S: ?Sized, T: ?Sized> Id<S, T> { //! /// Casts a value of type `S` to `T`. //! /// //! /// This is safe because the `Id` type is always guaranteed to //! /// only be inhabited by `Id<T, T>` types by construction. //! pub fn cast(self, value: S) -> T where S: Sized, T: Sized { //! unsafe { //! // Transmute the value; //! // This is safe since we know by construction that //! // S == T (including lifetime invariance) always holds. //! let cast_value = mem::transmute_copy(&value); //! //! // Forget the value; //! // otherwise the destructor of S would be run. //! mem::forget(value); //! //! cast_value //! } //! } //! //! // .. //! } //! ``` //! //! In Haskell, the `Id<A, B>` type corresponds to: //! //! ```haskell //! data a :~: b where //! Refl :: a :~: a //! ``` //! //! However, note that you must do the casting manually with `refl.cast(val)`. //! Rust will not know that `S == T` by just pattern matching on `Id<S, T>` //! (which you can't do). //! //! # Limitations //! //! Please note that Rust has no concept of higher kinded types (HKTs) and so //! we can not provide the general transformation `F<S> -> F<T>` given that //! `S == T`. With the introduction of generic associated types (GATs), it //! may be possible to introduce more transformations. //! //! # Example - A GADT-encoded expression type //! //! ```rust //! extern crate refl; //! use refl::*; //! //! trait Ty { type Repr: Copy + ::std::fmt::Debug; } //! //! #[derive(Debug)] //! struct Int; //! impl Ty for Int { type Repr = usize; } //! //! #[derive(Debug)] //! struct Bool; //! impl Ty for Bool { type Repr = bool; } //! //! #[derive(Debug)] //! enum Expr<T: Ty> { //! Lit(T::Repr), //! Add(Id<usize, T::Repr>, Box<Expr<Int>>, Box<Expr<Int>>), //! If(Box<Expr<Bool>>, Box<Expr<T>>, Box<Expr<T>>), //! } //! //! fn eval<T: Ty>(expr: &Expr<T>) -> T::Repr { //! match *expr { //! Expr::Lit(ref val) => //! *val, //! Expr::Add(ref refl, ref l, ref r) => //! refl.cast(eval(&*l) + eval(&*r)), //! Expr::If(ref c, ref i, ref e) => //! if eval(&*c) { eval(&*i) } else { eval(&*e) }, //! } //! } //! //! fn main() { //! let expr: Expr<Int> = //! Expr::If( //! Box::new(Expr::Lit(false)), //! Box::new(Expr::Lit(1)), //! Box::new(Expr::Add( //! refl(), //! Box::new(Expr::Lit(2)), //! Box::new(Expr::Lit(3)), //! )) //! ); //! //! assert_eq!(eval(&expr), 5); //! } //! ``` #![cfg_attr(feature = "no_std", no_std)] #[cfg(feature = "no_std")] extern crate core as std; //============================================================================== // Type equality witnesses for GADTs //============================================================================== use std::mem; use std::marker::PhantomData; /// Construct a proof witness of the fact that a type is equivalent to itself. /// /// For a `const` version of this, use `Id::REFL`. pub fn refl<T: ?Sized>() -> Id<T, T> { Id::REFL } impl<T: ?Sized> Id<T, T> { /// A proof witness of the fact that a type is equivalent to itself. /// /// The benefit of this version compared to `refl()` is that this /// is usable in `const` contexts while `refl()` can't. pub const REFL: Self = Id(PhantomData); } /// A proof term that `S` and `T` are the same type (type identity). /// This type is only every inhabited when S is nominally equivalent to T. /// /// ## A note on variance and safety /// /// S and T are invariant, here, this means that for two, possibly disjoint, /// lifetimes `'a`, `'b` we can not construct an `Id<&'a T, &'b T>`. If we /// could, which we would if we had covariance, we could define /// the following unsafe function in safe Rust: /// /// ```ignore /// fn transmute_lifetime<'a, 'b, T: 'a + 'b>(r: &'a T) -> &'b T { /// refl().cast(r) /// } /// ``` /// /// See /// /// - <https://doc.rust-lang.org/nightly/nomicon/phantom-data.html> /// - <https://doc.rust-lang.org/beta/nomicon/subtyping.html> /// /// for more information on variance. #[derive(Copy, Clone, Debug, Hash, PartialEq, Eq, PartialOrd, Ord)] pub struct Id<S: ?Sized, T: ?Sized>(PhantomData<(*mut S, *mut T)>); impl<S: ?Sized, T: ?Sized> Id<S, T> { //========================================================================== // Reflexivity, Symmetry, Transivity: //========================================================================== /// Casts a value of type `S` to `T`. /// /// This is safe because the `Id` type is always guaranteed to /// only be inhabited by `Id<T, T>` types by construction. pub fn cast(self, value: S) -> T where S: Sized, T: Sized { unsafe { // Transmute the value; // This is safe since we know by construction that // S == T (including lifetime invariance) always holds. let cast_value = mem::transmute_copy(&value); // Forget the value; // otherwise the destructor of S would be run. mem::forget(value); cast_value } } /// Converts `Id<S, T>` into `Id<T, S>` since type equality is symmetric. pub fn sym(self) -> Id<T, S> { Id(PhantomData) } /// If you have proofs `Id<S, T>` and `Id<T, U>` you can conclude `Id<S, U>` /// since type equality is transitive. pub fn trans<U: ?Sized>(self, _: Id<T, U>) -> Id<S, U> { Id(PhantomData) } /// Casts a value of type `&S` to `&T` where `S == T`. /// /// ```rust /// extern crate refl; /// use refl::*; /// /// fn main() { /// let x: Box<u8> = Box::new(1); /// let refl: Id<Box<u8>, Box<u8>> = refl(); /// assert_eq!(&x, refl.cast_ref(&x)); /// } /// ``` pub fn cast_ref<'a>(self, value: &'a S) -> &'a T { unsafe { // Transmute the value; // This is safe since we know by construction that // S == T (including lifetime invariance) always holds. mem::transmute_copy(&value) // mem::forget not needed since &'a S has a trivial destructor. } } /// Casts a value of type `&S` to `&T` where `S == T`. /// /// ```rust /// extern crate refl; /// use refl::*; /// /// fn main() { /// let mut x: Box<u8> = Box::new(1); /// let refl: Id<Box<u8>, Box<u8>> = refl(); /// **refl.cast_ref_mut(&mut x) += 1; /// assert_eq!(*x, 2); /// } /// ``` pub fn cast_ref_mut<'a>(self, value: &'a mut S) -> &'a mut T { unsafe { // Transmute the value; // This is safe since we know by construction that // S == T (including lifetime invariance) always holds. mem::transmute_copy(&value) // mem::forget not needed since &'a mut S has a trivial destructor. } } // We could define it for other functors, // but we can't do it for all functors... } impl<X: ?Sized> Default for Id<X, X> { fn default() -> Self { Id::REFL } } // Id only consists of a PhantomData, which is a ZST. // ZSTs can always be sent across threads and shared between them. unsafe impl<A: ?Sized, B: ?Sized> Sync for Id<A, B> {} unsafe impl<A: ?Sized, B: ?Sized> Send for Id<A, B> {}