add SKI

src/lib.rs

@@ -1,7 +1,9 @@
 //! Compiles the [lambda calculus](https://en.wikipedia.org/wiki/Lambda_calculus),
 //! represented by the [`LC`] type,
 //! to a tree of [Iota (ι) combinators](https://en.wikipedia.org/wiki/Iota_and_Jot),
-//! represented by the [`Iota`] type.
+//! represented by the [`Iota`] type, via the
+//! [SKI combinator calculus](https://en.wikipedia.org/wiki/SKI_combinator_calculus),
+//! represented by the [`SKI`] type.
 
 #[cfg(test)]
 mod test;
@@ -10,27 +12,8 @@ use core::fmt;
 use std::rc::Rc;
 use thiserror::Error;
 
-#[derive(Debug, PartialEq, Eq)]
-pub enum Iota {
-    App(Rc<Iota>, Rc<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
+/// A representation of a term of the
+/// [lambda calculus](https://en.wikipedia.org/wiki/Lambda_calculus), using
 /// [de Bruijn indices](https://en.wikipedia.org/wiki/De_Bruijn_index).
 #[derive(Debug, PartialEq, Eq)]
 pub enum LC {
@@ -56,7 +39,7 @@ impl LC {
     /// Applies this term to the given term.
     ///
     /// Often more ergonomic than [`LC::App`].
-    /// # examples
+    /// # Examples
     /// ```
     /// # use lc_to_iota::LC::{Abs, App, Var};
     /// assert_eq!(Var(0).app(1), App(Var(0).into(), Var(1).into()));
@@ -69,7 +52,7 @@ impl LC {
     /// Adds an abstration around this term.
     ///
     /// Often more ergonomic than [`LC::Abs`], but is somewhat backwards.
-    /// # examples
+    /// # Examples
     /// ```
     /// # use lc_to_iota::LC::{Abs, App, Var};
     /// assert_eq!(Var(0).abs(), Abs(Var(0).into()));
@@ -125,3 +108,80 @@ impl fmt::Display for LC {
         }
     }
 }
+
+/// A representation of a term of the
+/// [SKI combinator calculus](https://en.wikipedia.org/wiki/SKI_combinator_calculus).
+#[derive(Debug, PartialEq, Eq)]
+pub enum SKI {
+    /// The S (substitution) combinator.
+    ///
+    /// ```text
+    /// S x y z = x z (y z)
+    /// ```
+    S,
+    /// The K (constant) combinator.
+    ///
+    /// ```text
+    /// K x y = x
+    /// ```
+    K,
+    /// The I (identity) combinator.
+    ///
+    /// ```text
+    /// I x = x
+    /// ```
+    I,
+    /// Application of one combinator to another.
+    App(Rc<SKI>, Rc<SKI>),
+}
+
+impl SKI {
+    /// Applies this term to the given term.
+    ///
+    /// Often more ergonomic than [`SKI::App`].
+    /// # Examples
+    /// ```
+    /// # use lc_to_iota::SKI::*;
+    /// assert_eq!(I.app(I), App(I.into(), I.into()));
+    /// assert_eq!(I.app(I).app(K), App(App(I.into(), I.into()).into(), K.into()));
+    /// ```
+    #[must_use]
+    pub fn app(self, x: impl Into<SKI>) -> Self {
+        Self::App(self.into(), x.into().into())
+    }
+}
+
+impl fmt::Display for SKI {
+    fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result {
+        match self {
+            SKI::S => write!(f, "S"),
+            SKI::K => write!(f, "K"),
+            SKI::I => write!(f, "I"),
+            SKI::App(g, x) => write!(f, "({g} {x})"),
+        }
+    }
+}
+
+#[derive(Debug, PartialEq, Eq)]
+pub enum Iota {
+    Iota,
+    App(Rc<Iota>, Rc<Iota>),
+}
+
+#[derive(Debug, Error, PartialEq, Eq)]
+pub enum SKICompileError {
+    #[error("LC term has a free variable")]
+    FreeVar,
+}
+
+// explicit compile method is almost certainly better, but this is fun
+impl TryFrom<LC> for SKI {
+    type Error = SKICompileError;
+
+    fn try_from(term: LC) -> Result<Self, Self::Error> {
+        if term.has_free() {
+            return Err(SKICompileError::FreeVar);
+        }
+        todo!()
+    }
+}

src/test.rs

@@ -31,3 +31,14 @@ fn lc_free() {
         assert!(!term.has_free());
     }
 }
+
+#[test]
+fn ski_display() {
+    use SKI::*;
+    assert_eq!(S.to_string(), "S");
+    assert_eq!(K.to_string(), "K");
+    assert_eq!(I.to_string(), "I");
+    assert_eq!(I.app(I).to_string(), "(I I)");
+    assert_eq!(S.app(K).app(I).to_string(), "((S K) I)");
+    assert_eq!(S.app(K.app(I)).to_string(), "(S (K I))");
+}