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#![deny(missing_docs)] //! # Path-Iter //! A cocategory enumeration library based on path semantics //! //! Implementation based on paper [Cocategory Enumeration](https://github.com/advancedresearch/path_semantics/blob/master/papers-wip/cocategory-enumeration.pdf). //! //! For an introduction to Path Semantics, //! see [this paper](https://github.com/advancedresearch/path_semantics/blob/master/papers-wip/introduction-to-path-semantics-for-computer-scientists.pdf). //! //! ### Sub-types in Path Semantics //! //! In normal Path Semantics, one uses //! [normal paths](https://github.com/advancedresearch/path_semantics/blob/master/papers-wip/normal-paths.pdf) //! in theorem proving. //! Normal paths is a derivation from functions with sub-types. //! //! This library focuses on sub-types, not on the more general case of normal paths. //! //! A sub-type in Path Semantics is written in this form: //! //! ```text //! x : [f] a //! ``` //! //! Where `x` is some input, `f` is a function and `a` is the output of `f`. //! //! This library is for enumerating such sub-types efficiently. //! //! ### Example: AND //! //! The `path!` macro is used to write in the standard notation of Path Semantics. //! It constructs a type using `Path` that implements `IntoIterator`: //! //! ```rust //! use path_iter::*; //! //! fn main() { //! for a in path!([And] true) { //! // Prints `(true, true)` //! println!("{:?}", a); //! } //! } //! ``` //! //! It prints `(true, true)` because that is the only input value to `And` //! which produces `true` as output. //! //! ### Example: AND 2 //! //! You can decide the output value at runtime: //! //! ```rust //! use path_iter::*; //! //! fn main() { //! for &b in &[false, true] { //! for a in path!([And] b) { //! println!("{:?}", a); //! } //! println!(""); //! } //! } //! ``` //! //! This prints: //! //! ```text //! (false, false) //! (false, true) //! (true, false) //! //! (true, true) //! ``` //! //! ### Example: AND-NOT //! //! You can chain path sub-types together: //! //! ```rust //! use path_iter::*; //! //! fn main() { //! for a in path!([And] [Not] true) { //! println!("{:?}", a); //! } //! } //! ``` //! //! ### Example: Partial Application //! //! Partial application is a technique where //! a function reduces to another function //! when calling it with fewer arguments than the signature. //! //! For example, `And(true)` reduces to `Idb`. //! //! ```rust //! use path_iter::*; //! //! fn main() { //! for a in path!([And(true)] true) { //! println!("{:?}", a); //! } //! } //! ``` //! //! This should not be confused with function currying, //! which is extensionally equal to partial application, //! but captures the underlying function in a closure. //! //! The `path!` macro expands to partial application automatically, but it is very limited. //! Outside the macro `path!` or for complex cases, one must use `PApp::papp`. //! //! ### Example: AND 3 //! //! The standard notation for composing paths is not very friendly with Rust macros. //! Therefore, one can use a single bracket `[]` with functions separated by commas: //! //! ```rust //! use path_iter::*; //! //! fn main() { //! for a in path!([((And, And), (And, And)), (And, And), And] true) { //! println!("{:?}", a); //! } //! } //! ``` use std::iter::IntoIterator; pub use boolean::*; pub use range::*; /// Syntax sugar for a path sub-type. /// /// For example: /// ```rust /// use path_iter::*; /// /// fn main() { /// for a in path!([And] true) { /// // Prints `(true, true)` /// println!("{:?}", a); /// } /// } /// ``` #[macro_export] macro_rules! path( ([$x:ident ($y:expr)] $([$($z:tt)*])+ $w:expr) => { Path($crate::PApp::papp($x, $y), path!($([$($z)*])+ $w)) }; ([$x0:expr , $($x:expr),+ $(,)?] $z:expr) => { path($x0, path!([$($x),*] $z)) }; ([$x:expr] [$x1:expr] [$x2:expr] [$x3:expr] [$x4:expr] [$x5:expr] [$x6:expr] $z:expr) => { path($x, path!([$x1] [$x2] [$x3] [$x4] [$x5] [$x6] $z)) }; ([$x:expr] [$x1:expr] [$x2:expr] [$x3:expr] [$x4:expr] [$x5:expr] $z:expr) => { path($x, path!([$x1] [$x2] [$x3] [$x4] [$x5] $z)) }; ([$x:expr] [$x1:expr] [$x2:expr] [$x3:expr] [$x4:expr] $z:expr) => { path($x, path!([$x1] [$x2] [$x3] [$x4] $z)) }; ([$x:expr] [$x1:expr] [$x2:expr] [$x3:expr] $z:expr) => { path($x, path!([$x1] [$x2] [$x3] $z)) }; ([$x:expr] [$x1:expr] [$x2:expr] $z:expr) => { path($x, path!([$x1] [$x2] $z)) }; ([$x:expr] [$y:expr] $z:expr) => { path($x, path!([$y] $z)) }; ([$x:ident ($y:expr)] $z:expr) => { Path($crate::PApp::papp($x, $y), $crate::item($z)) }; ([$x:expr] $y:expr) => { Path($x, $crate::item($y)) }; ); /// Stores a path sub-type with either `[T] U` (left) or `[T] [V] ...` (right). #[derive(Clone)] pub struct Path<T, U, V>(pub T, pub Either<U, V>); /// Represents a terminal path `[T] U`. pub type PathEnd<T, U> = Path<T, U, Empty>; /// Represents a path composition. pub type PathComp<T, V> = Path<T, Empty, V>; mod boolean; mod range; /// Implemented for partial application. /// /// For example, `And::papp(true)` returns `Either::Left(Idb)`. pub trait PApp { /// The argument type. type Arg; /// The return type of partial application. type Ret; /// Applies argument to function, using partial application. fn papp(self, arg: Self::Arg) -> Self::Ret; } /// Iterates over two the sum type of two iterators. #[derive(Clone)] pub enum EitherIter<T, U> { /// The left iterator. Left(T), /// The right iterator. Right(U) } /// Used to lift iterator generators into a sum type. /// /// This is used in partial application, /// e.g. `And::papp(true)` returns `Either::Left(Idb)`. #[derive(Clone)] pub enum Either<T, U> { /// The left iterator generator. Left(T), /// The right iterator generator. Right(U) } /// A type that is impossible to construct. #[derive(Clone)] pub enum Empty {} /// Used to make end of path disambiguous from path composition. pub type Item<T> = Either<T, Empty>; /// Constructs an item. pub fn item<T>(a: T) -> Item<T> {Either::Left(a)} /// Construct a path composition. pub fn path<T, U>(a: T, b: U) -> PathComp<T, U> {Path(a, Either::Right(b))} impl<T> Item<T> { /// Gets the inner value. pub fn inner(self) -> T { if let Either::Left(a) = self { a } else { // This is unreachable because `Empty` can not be constructed. unreachable!() } } } impl<T> Either<Empty, T> { /// Gets the inner right value. pub fn inner_right(self) -> T { if let Either::Right(a) = self { a } else { // This is unreachable because `Empty` can not be constructed. unreachable!() } } } impl<T> IntoIterator for Item<T> { type Item = T; type IntoIter = <Option<T> as IntoIterator>::IntoIter; fn into_iter(self) -> Self::IntoIter { if let Either::Left(a) = self { Some(a).into_iter() } else { // This is unreachable because `Empty` can not be constructed. unreachable!() } } } impl<T, U, V> Iterator for EitherIter<T, U> where T: Iterator<Item = V>, U: Iterator<Item = V> { type Item = V; fn next(&mut self) -> Option<V> { match self { EitherIter::Left(a) => a.next(), EitherIter::Right(b) => b.next() } } } /// Iterates over a product of two iterator generators. /// /// For example, `[(And, Or)] (true, false)` /// iterates over the product of `[And] true` and `[Or] false`. pub struct ProductIter<T, U, V, W> { inner: T, outer: U, outer_ty: V, inner_vals: Vec<W>, inner_ind: usize, over_diagonal: Option<usize>, } impl<T, U, V, W1, W2> Iterator for ProductIter<T, U, V, W1> where T: Iterator<Item = W1>, U: Iterator<Item = W2>, V: Clone + IntoIterator<Item = W2, IntoIter = U>, W1: Clone { type Item = (W1, W2); fn next(&mut self) -> Option<Self::Item> { if let Some(max_len) = self.over_diagonal { if self.inner_vals.len() == 0 {return None}; if self.inner_ind > 0 { let u = self.inner_vals[self.inner_ind - 1].clone(); if let Some(v) = self.outer.next() { self.inner_ind -= 1; return Some((u.clone(), v)); } else { return None; } } // Remove one value. self.inner_vals.pop(); self.inner_ind = self.inner_vals.len(); self.outer = self.outer_ty.clone().into_iter(); // Skip the first values. for _ in self.inner_ind..max_len { if self.outer.next().is_none() {return None} } return self.next(); } if self.inner_ind > 0 { let u = self.inner_vals[self.inner_ind - 1].clone(); if let Some(v) = self.outer.next() { self.inner_ind -= 1; return Some((u.clone(), v)); } } self.outer = self.outer_ty.clone().into_iter(); if let Some(val) = self.inner.next() { self.inner_vals.push(val); } else { self.over_diagonal = Some(self.inner_vals.len()); self.inner_vals.reverse(); self.inner_ind = 0; return self.next(); } self.inner_ind = self.inner_vals.len(); self.next() } } /// Implemented by iterator generators. /// /// A function, e.g. `And` is a iterator generator /// with respect to the output, e.g. `[And] true`. /// This iterates over inputs that makes `And` return `true`. pub trait HigherIntoIterator<T> { /// The item type generated by the iterator. type Item; /// The iterator type. type IntoIter; /// Construct iterator from an argument. fn hinto_iter(self, a: T) -> Self::IntoIter; } impl<T1, T2, U1, U2, V1, V2, I1, I2> HigherIntoIterator<Item<(U1, U2)>> for (T1, T2) where T1: HigherIntoIterator<Item<U1>, Item = V1, IntoIter = I1>, T2: Clone + HigherIntoIterator<Item<U2>, Item = V2, IntoIter = I2>, I1: Iterator<Item = V1>, U2: Clone { type Item = (V1, V2); type IntoIter = ProductIter<I1, I2, PathEnd<T2, U2>, V1>; fn hinto_iter(self, arg: Item<(U1, U2)>) -> Self::IntoIter { let (u1, u2) = arg.inner(); let (a, b) = self; let inner = a.hinto_iter(item(u1)); let outer = b.clone().hinto_iter(item(u2.clone())); ProductIter { inner, inner_vals: vec![], outer, outer_ty: Path(b, item(u2)), inner_ind: 0, over_diagonal: None, } } } impl<T, U, V, I> HigherIntoIterator<Item<U>> for Item<T> where Item<T>: IntoIterator<Item = V, IntoIter = I>, I: Iterator<Item = V> { type Item = V; type IntoIter = I; fn hinto_iter(self, _: Item<U>) -> Self::IntoIter { <Self as IntoIterator>::into_iter(self) } } impl<T, U, V, W, I1, I2> HigherIntoIterator<Item<V>> for Either<T, U> where T: HigherIntoIterator<Item<V>, Item = W, IntoIter = I1>, U: HigherIntoIterator<Item<V>, Item = W, IntoIter = I2>, I1: Iterator<Item = W>, I2: Iterator<Item = W> { type Item = W; type IntoIter = EitherIter<I1, I2>; fn hinto_iter(self, arg: Item<V>) -> Self::IntoIter { match self { Either::Left(a) => EitherIter::Left(a.hinto_iter(arg)), Either::Right(b) => EitherIter::Right(b.hinto_iter(arg)) } } } impl<T, U, V, W> IntoIterator for PathEnd<T, U> where T: HigherIntoIterator<Item<U>, Item = W, IntoIter = V>, V: Iterator<Item = W> { type Item = W; type IntoIter = V; fn into_iter(self) -> Self::IntoIter { self.0.hinto_iter(self.1) } } impl<T, U, W, I, W2, I2> IntoIterator for PathComp<T, U> where U: IntoIterator<Item = W, IntoIter = I>, T: Clone + HigherIntoIterator<Item<W>, Item = W2, IntoIter = I2>, I: Iterator<Item = W>, I2: Iterator<Item = W2> { type Item = W2; type IntoIter = PathIter<I2, I, T>; fn into_iter(self) -> Self::IntoIter { let Path(a, b) = self; let in_iter = b.inner_right().into_iter(); PathIter { in_iter, out_iter: vec![], out_ind: 0, arg: a } } } /// Iterates over a path composition, e.g. `[f] [g] a`. pub struct PathIter<T, U, V> { out_iter: Vec<T>, in_iter: U, out_ind: usize, arg: V, } impl<T, U, V> Iterator for PathIter<T, U, V> where T: Iterator, U: Iterator, V: Clone, V: HigherIntoIterator<Item<U::Item>, Item = T::Item, IntoIter = T> { type Item = T::Item; fn next(&mut self) -> Option<T::Item> { loop { while self.out_ind < self.out_iter.len() { let v = self.out_iter[self.out_ind].next(); if v.is_some() { self.out_ind += 1; return v; } else { self.out_iter.swap_remove(self.out_ind); } } if let Some(u) = self.in_iter.next() { self.out_iter.push(self.arg.clone().hinto_iter(item(u))); } else if self.out_iter.len() == 0 { return None; } self.out_ind = 0; } } } #[cfg(test)] mod tests { use super::*; #[test] fn it_works() { assert_eq!(item(true).into_iter().next(), Some(true)); assert_eq!(item(false).into_iter().next(), Some(false)); assert_eq!(Path(Not, item(true)).into_iter().next(), Some(false)); assert_eq!(Path(Not, item(false)).into_iter().next(), Some(true)); assert_eq!(path(Not, Path(Not, item(true))).into_iter().next(), Some(true)); assert_eq!(path(Not, Path(Not, item(false))).into_iter().next(), Some(false)); } }