add algorithm for fixpoint calculation

tests/fixpoint.js

@@ -0,0 +1,74 @@
+import { fixer } from "../lib/util/fixpoint.js";
+
+const booleanLattice = {
+  isMaximal: (value) => value,
+  equality: (l, r) => l === r,
+  bottom: () => false,
+};
+
+const nullable = grammar => nonterminal => request => {
+  console.log(nonterminal);
+  const f = nt => {
+    return {
+      Epsilon: () => true,
+      T: () => false,
+      NT: () => request(nt.nt),
+      Seq: () => f(nt.l) && f(nt.r),
+      Alt: () => f(nt.l) || f(nt.r),
+    }[nt.kind]();  
+  }
+  return f(grammar[nonterminal]);
+}
+
+// S → A B C
+// A → a A | ε
+// B → b B | A C
+// C → c C | ε
+const exampleGrammar = {
+  S: {kind: "Seq",
+    l: {kind: "NT", nt: "A"},
+    r: {kind: "Seq",
+      l: {kind: "NT", nt: "B"},
+      r: {kind: "NT", nt: "C"},
+    },
+  },
+
+  A: {kind: "Alt",
+    l: {kind: "Seq",
+      l: {kind: "T", token: "a"},
+      r: {kind: "NT", nt: "A"}
+    },
+    r: {kind: "Epsilon"},
+  },
+
+  B: {kind: "Alt",
+    l: {kind: "Seq",
+      l: {kind: "T", token: "b"},
+      r: {kind: "NT", nt: "B"}
+    },
+    r: {kind: "Seq",
+      l: {kind: "NT", nt: "A"},
+      r: {kind: "NT", nt: "C"}
+    },
+  },
+
+  C: {kind: "Alt",
+    l: {kind: "Seq",
+      l: {kind: "T", token: "c"},
+      r: {kind: "NT", nt: "C"}
+    },
+    r: {kind: "Epsilon"},
+  },
+};
+// A is nullable because it has a production A → ε.
+// C is nullable because it has a production C → ε.
+// B is nullable because B → A C, and both A and C are nullable.
+// S is nullable because S → A B C, and A, B, and C are all nullable.
+
+
+const isNullable = fixer(nullable(exampleGrammar), booleanLattice);
+
+console.log(isNullable("S"));
+console.log(isNullable("A"));
+console.log(isNullable("B"));
+console.log(isNullable("C"));