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//! # Compile-Time Evaluation //! //! We all know Rust's trait system is Turing complete, so tell me, why aren't we exploiting //! this??? //! //! Who needs `const-fn` when we've got a crate like this?! //! //! ## Example //! //! Here's an eminently readable example where we play FizzBuzz at compile-time! //! //! ```rust //! # use trait_eval::*; //! # use std::fmt::Display; //! trait FizzBuzzType { //! fn show() -> String; // Don't worry about this -- it's just so we can print the result //! } //! //! struct Fizz; //! //! impl FizzBuzzType for Fizz { //! fn show() -> String { //! "Fizz".to_string() //! } //! } //! //! struct Buzz; //! //! impl FizzBuzzType for Buzz { //! fn show() -> String { //! "Buzz".to_string() //! } //! } //! //! struct FizzBuzz; //! //! impl FizzBuzzType for FizzBuzz { //! fn show() -> String { //! "FizzBuzz".to_string() //! } //! } //! //! impl<T: Nat> FizzBuzzType for T //! where //! T: Eval, //! <T as Eval>::Output: Display, //! { //! fn show() -> String { //! format!("{}", T::eval()) //! } //! } //! //! trait FizzBuzzEval: Nat { //! type Result: FizzBuzzType; //! } //! //! impl<T: Nat, //! Mod3: Nat, //! Mod5: Nat, //! ShouldFizz: Bool, //! ShouldBuzz: Bool, //! ShouldFizzBuzz: Bool, //! DidBuzz: FizzBuzzType, //! DidFizz: FizzBuzzType, //! DidFizzBuzz: FizzBuzzType> FizzBuzzEval for T //! where //! T: Mod<Three, Result = Mod3> + Mod<Five, Result = Mod5>, //! Mod3: Equals<Zero, Result = ShouldFizz>, //! Mod5: Equals<Zero, Result = ShouldBuzz>, //! ShouldFizz: AndAlso<ShouldBuzz, Result = ShouldFizzBuzz>, //! (Fizz, T): If<ShouldFizz, Result = DidFizz>, //! (Buzz, DidFizz): If<ShouldBuzz, Result = DidBuzz>, //! (FizzBuzz, DidBuzz): If<ShouldFizzBuzz, Result = DidFizzBuzz>, //! { //! type Result = DidFizzBuzz; //! } //! //! assert_eq!(<One as FizzBuzzEval>::Result::show(), "1"); //! assert_eq!(<Two as FizzBuzzEval>::Result::show(), "2"); //! assert_eq!(<Three as FizzBuzzEval>::Result::show(), "Fizz"); //! assert_eq!(<Four as FizzBuzzEval>::Result::show(), "4"); //! assert_eq!(<Five as FizzBuzzEval>::Result::show(), "Buzz"); //! assert_eq!(<Six as FizzBuzzEval>::Result::show(), "Fizz"); //! assert_eq!(<Seven as FizzBuzzEval>::Result::show(), "7"); //! assert_eq!(<Eight as FizzBuzzEval>::Result::show(), "8"); //! assert_eq!(<Nine as FizzBuzzEval>::Result::show(), "Fizz"); //! assert_eq!(<Ten as FizzBuzzEval>::Result::show(), "Buzz"); //! //! type Fifteen = <Three as Times<Five>>::Result; //! assert_eq!(<Fifteen as FizzBuzzEval>::Result::show(), "FizzBuzz"); // !!! //! ``` use std::marker::PhantomData; /// The type of natural numbers (`0..`) pub trait Nat {} /// Constant zero (`0`) pub struct Zero {} impl Nat for Zero {} impl<T: Nat> Nat for Succ<T> {} /// Constant one (`1`) pub type One = Succ<Zero>; /// Constant two (`2`) pub type Two = Succ<One>; /// Constant three (`3`) pub type Three = Succ<Two>; /// Constant four (`4`) pub type Four = Succ<Three>; /// Constant five (`5`) pub type Five = Succ<Four>; /// Constant six (`6`) pub type Six = Succ<Five>; /// Constant seven (`7`) pub type Seven = Succ<Six>; /// Constant eight (`8`) pub type Eight = Succ<Seven>; /// Constant nine (`9`) pub type Nine = Succ<Eight>; /// Constant ten (`10`) pub type Ten = Succ<Nine>; /// # Peano-style increment operator /// /// ```rust /// # use trait_eval::*; /// assert_eq!(Succ::<Six>::eval(), 7); /// ``` pub struct Succ<T> where T: Nat { _marker: PhantomData<T>, } /// The bool type (`true`, `false`) pub trait Bool {} /// True (`true`) pub struct True {} impl Bool for True {} /// False (`false`) pub struct False {} impl Bool for False {} /// # Conditional execution! /// /// The syntax is kind of clunky, but write `<(Then, Else) as If<Cond>::Result`. The condition can /// be any boolean expression built using [`True`](struct.True.html), [`False`](struct.False.html), /// [`AndAlso`](trait.AndAlso.html), [`OrElse`](trait.OrElse.html) and [`Not`](trait.Not.html). /// Talk about feature complete. /// /// ```rust /// # use trait_eval::*; /// assert_eq!(<(Three, Four) as If<True>>::Result::eval(), 3); /// assert_eq!(<(Three, Four) as If<False>>::Result::eval(), 4); /// ``` pub trait If<T: Bool> { type Result; } impl<U, V> If<True> for (U, V) { type Result = U; } impl<U, V> If<False> for (U, V) { type Result = V; } /// # Addition /// /// Addition at compile-time. That's right. Only limited by your imagination (and maybe your /// `#[recursion_limit]`). /// /// ```rust /// # use trait_eval::*; /// assert_eq!(<Four as Plus<Three>>::Result::eval(), 7); /// assert_eq!(<Seven as Plus<One>>::Result::eval(), 8); /// assert_eq!(<Three as Plus<Three>>::Result::eval(), 6); /// assert_eq!(<Two as Plus<Three>>::Result::eval(), 5); /// ``` pub trait Plus<T: Nat>: Nat { type Result: Nat; } impl<T: Nat> Plus<T> for Zero { type Result = T; } impl<T: Nat, U: Nat> Plus<T> for Succ<U> where U: Plus<T>, { type Result = Succ<U::Result>; } /// # Multiplication /// /// It's time to get timesing at compile-time! That sounded way cooler in my head. /// /// ```rust /// # use trait_eval::*; /// assert_eq!(<Four as Times<Three>>::Result::eval(), 12); /// assert_eq!(<Seven as Times<One>>::Result::eval(), 7); /// assert_eq!(<Three as Times<Three>>::Result::eval(), 9); /// assert_eq!(<Two as Times<Three>>::Result::eval(), 6); /// assert_eq!(<Six as Times<Seven>>::Result::eval(), 42); /// ``` pub trait Times<T: Nat>: Nat { type Result: Nat; } impl<T: Nat> Times<T> for Zero { type Result = Zero; } impl<T: Nat, U: Nat, V: Nat> Times<T> for Succ<U> where U: Times<T, Result = V>, V: Plus<T>, { type Result = V::Result; } /// # Factorial! /// /// Did I hear shouting? Or was that just this epic compile-time factorial operator?! /// /// ```rust /// # #![recursion_limit = "20000000"] /// # use trait_eval::*; /// assert_eq!(<Zero as Fact>::Result::eval(), 1); /// assert_eq!(<One as Fact>::Result::eval(), 1); /// assert_eq!(<Two as Fact>::Result::eval(), 2); /// assert_eq!(<Three as Fact>::Result::eval(), 6); /// assert_eq!(<Four as Fact>::Result::eval(), 24); /// assert_eq!(<Five as Fact>::Result::eval(), 120); /// // assert_eq!(<Six as Fact>::Result::eval(), 720); -- `rustc` gives up about here :(( /// ``` /// /// (Ok, fine, yes, the recursion limit is on like 20,000,000.) pub trait Fact: Nat { type Result: Nat; } impl Fact for Zero { type Result = One; } impl<T: Nat, U: Nat> Fact for Succ<T> where T: Fact<Result = U>, U: Times<Succ<T>>, { type Result = U::Result; } /// # Saturating Decrement /// /// See, this is engineering at its finest, compile-time execution and no undefined behaviour! /// /// ```rust /// # use trait_eval::*; /// assert_eq!(<Zero as Pred>::Result::eval(), 0); /// assert_eq!(<One as Pred>::Result::eval(), 0); /// assert_eq!(<Two as Pred>::Result::eval(), 1); /// assert_eq!(<Three as Pred>::Result::eval(), 2); /// assert_eq!(<Four as Pred>::Result::eval(), 3); /// assert_eq!(<Five as Pred>::Result::eval(), 4); /// assert_eq!(<Six as Pred>::Result::eval(), 5); /// assert_eq!(<Seven as Pred>::Result::eval(), 6); /// assert_eq!(<Eight as Pred>::Result::eval(), 7); /// assert_eq!(<Nine as Pred>::Result::eval(), 8); /// assert_eq!(<Ten as Pred>::Result::eval(), 9); /// ``` pub trait Pred: Nat { type Result: Nat; } impl Pred for Zero { type Result = Zero; } impl<T: Nat> Pred for Succ<T> { type Result = T; } /// # Saturating Subtraction /// /// It's 2:30AM and I've completely run out of snappy sales pitches. It's subtraction - wow. /// /// ```rust /// # use trait_eval::*; /// assert_eq!(<Ten as Minus<Three>>::Result::eval(), 7); /// assert_eq!(<Seven as Minus<One>>::Result::eval(), 6); /// assert_eq!(<Three as Minus<Three>>::Result::eval(), 0); /// assert_eq!(<Two as Minus<Three>>::Result::eval(), 0); /// ``` pub trait Minus<T: Nat>: Nat { type Result: Nat; } impl<T: Nat> Minus<Zero> for T { type Result = T; } impl<T: Nat, U: Nat, V: Nat> Minus<Succ<T>> for U where U: Minus<T, Result = V>, V: Pred, { type Result = V::Result; } /// # Remainders /// /// GCD is left as an exercise for the reader... /// /// ```rust /// # use trait_eval::*; /// assert_eq!(<Five as Mod<Three>>::Result::eval(), 2); /// assert_eq!(<Ten as Mod<Two>>::Result::eval(), 0); /// assert_eq!(<Seven as Mod<Nine>>::Result::eval(), 7); /// assert_eq!(<Six as Mod<Six>>::Result::eval(), 0); /// ``` pub trait Mod<T: Nat>: Nat { type Result: Nat; } impl<T: Nat> Mod<T> for Zero { type Result = Zero; } impl<T: Nat, U: Nat, V: Nat, W: Nat, C: Bool> Mod<T> for Succ<U> where Self: Minus<T, Result = V> + LessThan<T, Result = C>, V: Mod<T>, (Self, <V as Mod<T>>::Result): If<C, Result = W>, { type Result = W; } /// # Equality testing /// /// ```rust /// # use trait_eval::*; /// type TwoPlusTwo = <Two as Plus<Two>>::Result; /// type IsFour = <TwoPlusTwo as Equals<Four>>::Result; /// assert_eq!(IsFour::eval(), true); /// type MinusOne = <TwoPlusTwo as Minus<One>>::Result; /// type ThatsThree = <MinusOne as Equals<Three>>::Result; /// assert_eq!(ThatsThree::eval(), true); // quick maffs /// /// assert_eq!(<Zero as Equals<One>>::Result::eval(), false); /// ``` pub trait Equals<T: Nat> { type Result: Bool; } impl Equals<Zero> for Zero { type Result = True; } impl<T: Nat> Equals<Succ<T>> for Zero { type Result = False; } impl<T: Nat> Equals<Zero> for Succ<T> { type Result = False; } impl<T: Nat, U: Nat> Equals<Succ<T>> for Succ<U> where T: Equals<U>, { type Result = T::Result; } /// # Integer comparison /// /// I honestly can't be bothered to implement `<=`, `>=` and `>`, so you're just going to have to make /// do with this and [`Not`](trait.Not.html). /// /// ```rust /// # use trait_eval::*; /// assert_eq!(<Three as LessThan<Five>>::Result::eval(), true); /// assert_eq!(<Five as LessThan<Five>>::Result::eval(), false); /// assert_eq!(<Ten as LessThan<Five>>::Result::eval(), false); /// ``` pub trait LessThan<T: Nat> { type Result: Bool; } impl LessThan<Zero> for Zero { type Result = False; } impl<T: Nat> LessThan<Succ<T>> for Zero { type Result = True; } impl<T: Nat> LessThan<Zero> for Succ<T> { type Result = False; } impl<T: Nat, U: Nat> LessThan<Succ<T>> for Succ<U> where U: LessThan<T>, { type Result = U::Result; } /// # Built-in Fibonacci sequence /// /// Of course, every programmer uses the Fibonacci sequence on the daily, so we've built it right /// into the library. Now you don't need to worry about what the nth Fibonacci number is at /// runtime. We've got you covered. /// /// ```rust /// # use trait_eval::*; /// assert_eq!(<One as Fib>::Result::eval(), 1); /// assert_eq!(<Two as Fib>::Result::eval(), 1); /// assert_eq!(<Three as Fib>::Result::eval(), 2); /// assert_eq!(<Four as Fib>::Result::eval(), 3); /// assert_eq!(<Five as Fib>::Result::eval(), 5); /// assert_eq!(<Six as Fib>::Result::eval(), 8); /// assert_eq!(<Seven as Fib>::Result::eval(), 13); /// assert_eq!(<Eight as Fib>::Result::eval(), 21); /// assert_eq!(<Nine as Fib>::Result::eval(), 34); /// assert_eq!(<Ten as Fib>::Result::eval(), 55); /// ``` pub trait Fib: Nat { type Result: Nat; } impl Fib for Zero { type Result = Zero; } #[doc(hidden)] pub trait FibRecurse: Nat { type Result: Nat; } impl<T: Nat, U: Nat, V: Nat, W: Nat, X: Nat, Y: Nat> FibRecurse for T where T: Pred<Result = U> + Minus<Two, Result = V>, U: Fib<Result = W>, V: Fib<Result = X>, W: Plus<X, Result = Y>, { type Result = Y; } impl<T: Nat, U: Bool, V: Nat, W: Nat> Fib for Succ<T> where T: Equals<Zero, Result = U>, Succ<T>: FibRecurse<Result = V>, (One, V): If<U, Result = W>, { type Result = W; } /// # Logical Not /// /// Negate any boolean you like at compile-time. /// /// (`¬¬(P V ¬P)` - just saying.) /// /// ```rust /// # use trait_eval::*; /// assert_eq!(<True as Not>::Result::eval(), false); /// assert_eq!(<False as Not>::Result::eval(), true); /// ``` pub trait Not: Bool { type Result: Bool; } impl Not for True { type Result = False; } impl Not for False { type Result = True; } /// # Logical And /// /// A logical and operator for all you conjunctive needs. It would short circuit if that were /// possible, but here we are. /// /// ```rust /// # use trait_eval::*; /// assert_eq!(<False as AndAlso<False>>::Result::eval(), false); /// assert_eq!(<False as AndAlso<True>>::Result::eval(), false); /// assert_eq!(<True as AndAlso<False>>::Result::eval(), false); /// assert_eq!(<True as AndAlso<True>>::Result::eval(), true); /// ``` pub trait AndAlso<T: Bool> { type Result: Bool; } impl<T: Bool> AndAlso<T> for False { type Result = False; } impl AndAlso<False> for True { type Result = False; } impl AndAlso<True> for True { type Result = True; } /// # Logical Or /// /// A logical or operator for all you disjunctive needs. It would short circuit if that were /// possible, but here we are. /// /// ```rust /// # use trait_eval::*; /// assert_eq!(<False as OrElse<False>>::Result::eval(), false); /// assert_eq!(<False as OrElse<True>>::Result::eval(), true); /// assert_eq!(<True as OrElse<False>>::Result::eval(), true); /// assert_eq!(<True as OrElse<True>>::Result::eval(), true); /// ``` pub trait OrElse<T: Bool> { type Result: Bool; } impl<T: Bool> OrElse<T> for True { type Result = True; } impl OrElse<False> for False { type Result = False; } impl OrElse<True> for False { type Result = True; } /// # `trait_eval` to Rust conversion /// /// Here's a magic trait for getting your data out of `trait_eval` and into Rust. Don't worry - it /// doesn't actually evaluate anything at all, I just couldn't think of a better name. pub trait Eval { /// The Rust representation of our type. type Output; /// A static function to actually grab the data. /// /// ```rust /// # use trait_eval::*; /// assert_eq!(Three::eval(), 3); /// assert_eq!(<Six as Times<Seven>>::Result::eval(), 42); /// ``` fn eval() -> Self::Output; } impl Eval for Zero { type Output = usize; #[inline] fn eval() -> Self::Output { 0 } } impl<T: Nat> Eval for Succ<T> where T: Eval<Output = usize> { type Output = usize; #[inline] fn eval() -> Self::Output { 1 + T::eval() } } impl Eval for True { type Output = bool; #[inline] fn eval() -> Self::Output { true } } impl Eval for False where { type Output = bool; #[inline] fn eval() -> Self::Output { false } }