2 files changed, 55 insertions, 4 deletions
diff --git a/semiring/src/counting.rs b/semiring/src/counting.rs
new file mode 100644
index 0000000..9095888
--- /dev/null
+++ b/semiring/src/counting.rs
@@ -0,0 +1,43 @@
+//! This module implements the "counting semiring", which counts the
+//! number of ways a sentence can be derived by a grammar.
+
+use super::*;
+
+/// The counting semiring is a thin wrapper around the natural numbers
+/// with the usual addition and multiplication.
+#[derive(Copy, Clone, Debug, Ord, PartialOrd, Hash, Eq, PartialEq)]
+pub struct Count(usize);
+
+impl Count {
+    /// Wrap the count in the wrapper.
+    pub fn new(count: usize) -> Self {
+        Self(count)
+    }
+
+    /// Extract the count out.
+    pub fn value(&self) -> usize {
+        self.0
+    }
+}
+
+impl Semiring for Count {
+    fn zero() -> Self {
+        Self::new(0)
+    }
+
+    fn one() -> Self {
+        Self::new(1)
+    }
+
+    fn add(&mut self, other: &Self) {
+        self.0 = self.value() + other.value();
+    }
+
+    fn mul(&mut self, other: &Self) {
+        self.0 = self.value() * other.value();
+    }
+
+    fn valuation(_pos: usize, _grammar: &Grammar) -> Self {
+        Self::new(1)
+    }
+}
diff --git a/semiring/src/lib.rs b/semiring/src/lib.rs
index 9d096db..6c0e0d5 100644
--- a/semiring/src/lib.rs
+++ b/semiring/src/lib.rs
@@ -15,6 +15,8 @@
 //! description.  Specifically, it will produce items as it parses the
 //! input string.  Then we can execute these items by any interpreter.
 
+use grammar::Grammar;
+
 /// A semiring is equipped with two operations: the addition and the
 /// multiplication.  It also has additive and multiplicative
 /// identities.  Also the two operations are supposed to be
@@ -29,14 +31,20 @@ pub trait Semiring {
     fn one() -> Self;
 
     /// The addition.
-    fn add(&mut self, other: impl AsRef<Self>);
+    fn add(&mut self, other: &Self);
 
     /// The multiplication.
-    fn mul(&mut self, other: impl AsRef<Self>);
+    fn mul(&mut self, other: &Self);
+
+    /// A valuation associates a semiring value from a rule position.
+    ///
+    /// Since a position is not complete without a grammar, we also
+    /// give it a grammar.
+    fn valuation(pos: usize, grammar: &Grammar) -> Self;
 }
 
-// TODO: Implement boolean semiring
-// TODO: Implement counting semiring
+pub mod counting;
+
 // TODO: Implement derivation forest semiring
 
 #[cfg(test)]