LC docs

Cargo.lock

@@ -5,3 +5,61 @@ version = 3
 [[package]]
 name = "lc-to-iota"
 version = "0.1.0"
+dependencies = [
+ "thiserror",
+]
+
+[[package]]
+name = "proc-macro2"
+version = "1.0.89"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "f139b0662de085916d1fb67d2b4169d1addddda1919e696f3252b740b629986e"
+dependencies = [
+ "unicode-ident",
+]
+
+[[package]]
+name = "quote"
+version = "1.0.37"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "b5b9d34b8991d19d98081b46eacdd8eb58c6f2b201139f7c5f643cc155a633af"
+dependencies = [
+ "proc-macro2",
+]
+
+[[package]]
+name = "syn"
+version = "2.0.87"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "25aa4ce346d03a6dcd68dd8b4010bcb74e54e62c90c573f394c46eae99aba32d"
+dependencies = [
+ "proc-macro2",
+ "quote",
+ "unicode-ident",
+]
+
+[[package]]
+name = "thiserror"
+version = "2.0.3"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "c006c85c7651b3cf2ada4584faa36773bd07bac24acfb39f3c431b36d7e667aa"
+dependencies = [
+ "thiserror-impl",
+]
+
+[[package]]
+name = "thiserror-impl"
+version = "2.0.3"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "f077553d607adc1caf65430528a576c757a71ed73944b66ebb58ef2bbd243568"
+dependencies = [
+ "proc-macro2",
+ "quote",
+ "syn",
+]
+
+[[package]]
+name = "unicode-ident"
+version = "1.0.13"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+checksum = "e91b56cd4cadaeb79bbf1a5645f6b4f8dc5bde8834ad5894a8db35fda9efa1fe"

Cargo.toml

@@ -4,3 +4,4 @@ version = "0.1.0"
 edition = "2021"
 
 [dependencies]
+thiserror = "2.0.3"

src/lib.rs

@@ -3,8 +3,12 @@
 //! to a tree of [Iota (ι) combinators](https://en.wikipedia.org/wiki/Iota_and_Jot),
 //! represented by the [`Iota`] type.
 
+#[cfg(test)]
+mod test;
+
 use core::fmt;
-use std::{collections::HashSet, rc::Rc};
+use std::rc::Rc;
+use thiserror::Error;
 
 #[derive(Debug, PartialEq, Eq)]
 pub enum Iota {
@@ -12,42 +16,96 @@ pub enum Iota {
     Iota,
 }
 
+#[derive(Debug, Error, PartialEq, Eq)]
+pub enum IotaCompileError {
+    #[error("LC term has a free variable")]
+    FreeVar,
+}
+
+impl TryFrom<LC> for Iota {
+    type Error = IotaCompileError;
+
+    fn try_from(value: LC) -> Result<Self, Self::Error> {
+        todo!()
+    }
+}
+
+/// A representation of the [lambda calculus](https://en.wikipedia.org/wiki/Lambda_calculus), with
+/// [de Bruijn indices](https://en.wikipedia.org/wiki/De_Bruijn_index).
 #[derive(Debug, PartialEq, Eq)]
 pub enum LC {
+    /// A lambda abstraction; binds a new variable.
     Abs(Rc<LC>),
+    /// An application of a function to an argument.
     App(Rc<LC>, Rc<LC>),
+    /// A variable represented by a
+    /// [de Bruijn index](https://en.wikipedia.org/wiki/De_Bruijn_index).
+    ///
+    /// Zero refers to the closest abstraction, and each successive number refers to a
+    /// nested abstraction, as shown in this diagram:
+    /// ```text
+    ///   ┌─────┐  
+    ///   │ ┌─┐ │  
+    /// λ λ λ 0 1 2
+    /// └─────────┘
+    /// ```
     Var(usize),
 }
 
 impl LC {
+    /// Applies this term to the given term.
+    ///
+    /// Often more ergonomic than [`LC::App`].
+    /// # examples
+    /// ```
+    /// # use lc_to_iota::LC::{Abs, App, Var};
+    /// assert_eq!(Var(0).app(1), App(Var(0).into(), Var(1).into()));
+    /// ```
+    #[must_use]
     pub fn app(self, x: impl Into<Self>) -> Self {
         Self::App(self.into(), x.into().into())
     }
 
+    /// Adds an abstration around this term.
+    ///
+    /// Often more ergonomic than [`LC::Abs`], but is somewhat backwards.
+    /// # examples
+    /// ```
+    /// # use lc_to_iota::LC::{Abs, App, Var};
+    /// assert_eq!(Var(0).abs(), Abs(Var(0).into()));
+    /// ```
+    #[must_use]
     pub fn abs(self) -> Self {
         Self::Abs(self.into())
     }
 
-    pub fn has_free_vars(&self) -> bool {
-        // TODO: faster
-        !self.free_vars().is_empty()
+    /// Returns whether any variables are
+    /// [free](https://en.wikipedia.org/wiki/Free_variables_and_bound_variables) in self;
+    /// that is, whether any variables occur that are not bound by an abstraction.
+    ///
+    /// # Examples
+    /// ```
+    /// # use lc_to_iota::LC::{Abs, App, Var};
+    /// // x
+    /// let x = Var(0);
+    /// assert!(x.has_free());
+    /// // λx.x
+    /// assert!(!x.abs().has_free());
+    /// // λfx.f x
+    /// let apply = Var(1).app(0).abs().abs();
+    /// assert!(!apply.has_free());
+    /// ```
+    #[must_use]
+    pub fn has_free(&self) -> bool {
+        self.has_free_past(0)
     }
 
-    // contextless free vars aren't that useful?
-    pub fn free_vars(&self) -> HashSet<usize> {
-        self.free_vars_past(0)
-    }
-
-    fn free_vars_past(&self, bound: usize) -> HashSet<usize> {
-        // TODO: faster
+    fn has_free_past(&self, bound: usize) -> bool {
         match self {
-            LC::Abs(x) => x.free_vars_past(bound + 1),
-            LC::App(f, x) => {
-                let f_vars = f.free_vars_past(bound);
-                let x_vars = x.free_vars_past(bound);
-                &f_vars | &x_vars
-            }
-            LC::Var(_) => todo!(),
+            LC::Abs(x) => x.has_free_past(bound + 1),
+            LC::App(f, x) => f.has_free_past(bound) || x.has_free_past(bound),
+            // if nothing is bound (bound = 0), x is always free
+            LC::Var(x) => *x >= bound,
         }
     }
 }
@@ -67,12 +125,3 @@ impl fmt::Display for LC {
         }
     }
 }
-
-#[test]
-fn lc_display() {
-    let identity = LC::Var(0).abs();
-    assert_eq!(identity.to_string(), "(λ 0)");
-
-    let apply = LC::Var(1).app(0).abs().abs();
-    assert_eq!(apply.to_string(), "(λ (λ (1 0)))");
-}

src/test.rs

@@ -0,0 +1,33 @@
+use crate::*;
+
+#[test]
+fn lc_display() {
+    use LC::*;
+    let identity = Var(0).abs();
+    assert_eq!(identity.to_string(), "(λ 0)");
+
+    let apply = Var(1).app(0).abs().abs();
+    assert_eq!(apply.to_string(), "(λ (λ (1 0)))");
+    assert_eq!(apply.to_string(), "(λ (λ (1 0)))");
+}
+
+#[test]
+fn lc_free() {
+    use LC::*;
+    assert!(Var(0).has_free());
+    assert!(!Var(0).abs().has_free());
+    assert!(Var(1).app(0).abs().has_free());
+    assert!(!Var(1).app(0).abs().abs().has_free());
+    assert!(Var(0).app(1).abs().has_free());
+
+    for i in 0..10 {
+        assert!(Var(i).has_free());
+        let mut term = Var(i);
+
+        for _ in 0..=i {
+            term = term.abs();
+        }
+        // var `n` with `n+1` abstractions is bound.
+        assert!(!term.has_free());
+    }
+}