@@ -0,0 +1,351 @@
+// SPDX-License-Identifier: AGPL-3.0-or-later
+
+/**
+ * Modelica CAS bindings module.
+ *
+ * Provides a `ModelScript.CAS` package that exposes the CAS engine's
+ * capabilities as Modelica-callable functions. These functions operate
+ * on ModelicaExpression ASTs at compile-time (during flattening) and
+ * can be used in annotations, parameter evaluation, and symbolic
+ * transformations.
+ *
+ * Runtime bindings are registered via `registerCASFunctions()` which
+ * hooks into the ExpressionEvaluator's `functionLookup` callback.
+ */
+
+import type { ModelicaExpression } from "../dae.js";
+import { ModelicaFunctionCallExpression, ModelicaNameExpression, ModelicaRealLiteral } from "../dae.js";
+import { differentiateExpr, simplifyExpr } from "../symbolic-diff.js";
+import { egraphSimplify } from "./egraph.js";
+import { collectTerms, expandExpr, getLiteralValue, normalizeExpr } from "./expand.js";
+import { factorQuadratic, rationalRoots } from "./factor.js";
+import { integrateExpr, limit, nthDerivative, taylorSeries } from "./integrate.js";
+import { solveForVariable } from "./solve.js";
+import { trigExpand, trigSimplify } from "./trigsimp.js";
+
+// ─────────────────────────────────────────────────────────────────────
+// Compile-Time CAS Operations
+// ─────────────────────────────────────────────────────────────────────
+
+/**
+ * Registry of CAS functions that operate on ModelicaExpression ASTs.
+ * These are invoked at compile-time during flattening when the
+ * function name matches `ModelScript.CAS.*`.
+ */
+export const CAS_FUNCTIONS = new Map<string, (args: ModelicaExpression[]) => ModelicaExpression | null>([
+  // ── Simplification ──
+  [
+    "ModelScript.CAS.simplify",
+    (args) => {
+      if (args.length < 1 || !args[0]) return null;
+      return egraphSimplify(args[0]);
+    },
+  ],
+
+  [
+    "ModelScript.CAS.expand",
+    (args) => {
+      if (args.length < 1 || !args[0]) return null;
+      return expandExpr(args[0]);
+    },
+  ],
+
+  [
+    "ModelScript.CAS.normalize",
+    (args) => {
+      if (args.length < 1 || !args[0]) return null;
+      return normalizeExpr(args[0]);
+    },
+  ],
+
+  [
+    "ModelScript.CAS.trigSimplify",
+    (args) => {
+      if (args.length < 1 || !args[0]) return null;
+      return trigSimplify(args[0]);
+    },
+  ],
+
+  [
+    "ModelScript.CAS.trigExpand",
+    (args) => {
+      if (args.length < 1 || !args[0]) return null;
+      return trigExpand(args[0]);
+    },
+  ],
+
+  // ── Differentiation ──
+  [
+    "ModelScript.CAS.diff",
+    (args) => {
+      if (args.length < 2 || !args[0] || !args[1]) return null;
+      const varName = extractVarName(args[1]);
+      if (!varName) return null;
+      if (args.length >= 3 && args[2]) {
+        const n = getLiteralValue(args[2]);
+        if (n !== null && n > 0) return nthDerivative(args[0], varName, n);
+      }
+      return simplifyExpr(differentiateExpr(args[0], varName));
+    },
+  ],
+
+  // ── Integration ──
+  [
+    "ModelScript.CAS.integrate",
+    (args) => {
+      if (args.length < 2 || !args[0] || !args[1]) return null;
+      const varName = extractVarName(args[1]);
+      if (!varName) return null;
+      return integrateExpr(args[0], varName);
+    },
+  ],
+
+  // ── Solving ──
+  [
+    "ModelScript.CAS.solve",
+    (args) => {
+      if (args.length < 2 || !args[0] || !args[1]) return null;
+      const varName = extractVarName(args[1]);
+      if (!varName) return null;
+      const solutions = solveForVariable(args[0], varName);
+      // Return first solution (most useful for single-variable equations)
+      return solutions.length > 0 ? (solutions[0] ?? null) : null;
+    },
+  ],
+
+  [
+    "ModelScript.CAS.solveAll",
+    (args) => {
+      if (args.length < 2 || !args[0] || !args[1]) return null;
+      const varName = extractVarName(args[1]);
+      if (!varName) return null;
+      const solutions = solveForVariable(args[0], varName);
+      if (solutions.length === 0) return null;
+      // Return as an array-like nested expression
+      return solutions.length === 1 ? (solutions[0] ?? null) : buildArray(solutions);
+    },
+  ],
+
+  // ── Factoring ──
+  [
+    "ModelScript.CAS.factor",
+    (args) => {
+      if (args.length < 2 || !args[0] || !args[1]) return null;
+      const varName = extractVarName(args[1]);
+      if (!varName) return null;
+      return factorQuadratic(args[0], varName);
+    },
+  ],
+
+  // ── Taylor Series ──
+  [
+    "ModelScript.CAS.taylor",
+    (args) => {
+      if (args.length < 4 || !args[0] || !args[1] || !args[2] || !args[3]) return null;
+      const varName = extractVarName(args[1]);
+      if (!varName) return null;
+      const point = getLiteralValue(args[2]);
+      const order = getLiteralValue(args[3]);
+      if (point === null || order === null) return null;
+      return taylorSeries(args[0], varName, point, Math.round(order));
+    },
+  ],
+
+  // ── Limit ──
+  [
+    "ModelScript.CAS.limit",
+    (args) => {
+      if (args.length < 3 || !args[0] || !args[1] || !args[2]) return null;
+      const varName = extractVarName(args[1]);
+      if (!varName) return null;
+      const point = getLiteralValue(args[2]);
+      if (point === null) return null;
+      const result = limit(args[0], varName, point);
+      return result !== null ? new ModelicaRealLiteral(result) : null;
+    },
+  ],
+
+  // ── Degree ──
+  [
+    "ModelScript.CAS.degree",
+    (args) => {
+      if (args.length < 2 || !args[0] || !args[1]) return null;
+      const varName = extractVarName(args[1]);
+      if (!varName) return null;
+      const terms = collectTerms(args[0], varName);
+      const maxDeg = Math.max(0, ...terms.keys());
+      return new ModelicaRealLiteral(maxDeg);
+    },
+  ],
+
+  // ── Rational Roots ──
+  [
+    "ModelScript.CAS.roots",
+    (args) => {
+      if (args.length < 2 || !args[0] || !args[1]) return null;
+      const varName = extractVarName(args[1]);
+      if (!varName) return null;
+      const roots = rationalRoots(args[0], varName);
+      if (roots.length === 0) return null;
+      return buildArray(roots.map((r) => new ModelicaRealLiteral(r)));
+    },
+  ],
+]);
+
+// ─────────────────────────────────────────────────────────────────────
+// Compile-Time Dispatch
+// ─────────────────────────────────────────────────────────────────────
+
+/**
+ * Attempt to evaluate a CAS function call at compile-time.
+ * Returns the result expression, or null if the function is not a CAS function.
+ */
+export function evaluateCASFunction(functionName: string, args: ModelicaExpression[]): ModelicaExpression | null {
+  const fn = CAS_FUNCTIONS.get(functionName);
+  if (!fn) return null;
+  try {
+    return fn(args);
+  } catch {
+    return null; // CAS operation failed gracefully
+  }
+}
+
+/**
+ * Check if a function name is a CAS function.
+ */
+export function isCASFunction(name: string): boolean {
+  return CAS_FUNCTIONS.has(name);
+}
+
+// ─────────────────────────────────────────────────────────────────────
+// Modelica Package Declaration
+// ─────────────────────────────────────────────────────────────────────
+
+/**
+ * The Modelica source for the ModelScript.CAS package.
+ * This declares all CAS functions with their signatures for use
+ * in Modelica models.
+ */
+export const MODELSCRIPT_CAS_PACKAGE = `
+package ModelScript
+  package CAS "Computer Algebra System"
+
+    function simplify "Simplify an expression using E-Graph equality saturation"
+      input Real expr;
+      output Real result;
+      external "builtin";
+    end simplify;
+
+    function expand "Expand polynomial expressions (distribute multiplication)"
+      input Real expr;
+      output Real result;
+      external "builtin";
+    end expand;
+
+    function normalize "Normalize to canonical form via E-Graph"
+      input Real expr;
+      output Real result;
+      external "builtin";
+    end normalize;
+
+    function trigSimplify "Simplify using trigonometric identities"
+      input Real expr;
+      output Real result;
+      external "builtin";
+    end trigSimplify;
+
+    function trigExpand "Expand trig expressions using addition formulas"
+      input Real expr;
+      output Real result;
+      external "builtin";
+    end trigExpand;
+
+    function diff "Symbolic differentiation"
+      input Real expr;
+      input Real var "Variable to differentiate with respect to";
+      input Integer n = 1 "Order of derivative";
+      output Real result;
+      external "builtin";
+    end diff;
+
+    function integrate "Symbolic anti-differentiation"
+      input Real expr;
+      input Real var "Variable to integrate with respect to";
+      output Real result;
+      external "builtin";
+    end integrate;
+
+    function solve "Solve expr = 0 for var (returns first solution)"
+      input Real expr;
+      input Real var "Variable to solve for";
+      output Real result;
+      external "builtin";
+    end solve;
+
+    function solveAll "Solve expr = 0 for var (returns all solutions)"
+      input Real expr;
+      input Real var "Variable to solve for";
+      output Real[:] result;
+      external "builtin";
+    end solveAll;
+
+    function factor "Factor a quadratic polynomial"
+      input Real expr;
+      input Real var;
+      output Real result;
+      external "builtin";
+    end factor;
+
+    function taylor "Taylor series expansion"
+      input Real expr;
+      input Real var;
+      input Real point;
+      input Integer order;
+      output Real result;
+      external "builtin";
+    end taylor;
+
+    function limit "Evaluate limit of expr as var -> point"
+      input Real expr;
+      input Real var;
+      input Real point;
+      output Real result;
+      external "builtin";
+    end limit;
+
+    function degree "Get polynomial degree of expr in var"
+      input Real expr;
+      input Real var;
+      output Integer result;
+      external "builtin";
+    end degree;
+
+    function roots "Find rational roots of polynomial expr in var"
+      input Real expr;
+      input Real var;
+      output Real[:] result;
+      external "builtin";
+    end roots;
+
+  end CAS;
+end ModelScript;
+`;
+
+// ─────────────────────────────────────────────────────────────────────
+// Utilities
+// ─────────────────────────────────────────────────────────────────────
+
+function extractVarName(expr: ModelicaExpression): string | null {
+  if (expr instanceof ModelicaNameExpression) return expr.name;
+  if (expr && typeof expr === "object" && "name" in expr) {
+    return (expr as { name: string }).name;
+  }
+  return null;
+}
+
+function buildArray(exprs: ModelicaExpression[]): ModelicaExpression {
+  // For simplicity, return first element if only one, or construct
+  // a function call to "array" with all elements
+  if (exprs.length === 1) return exprs[0] ?? new ModelicaRealLiteral(0);
+  return new ModelicaFunctionCallExpression("array", exprs);
+}
@@ -63,3 +63,6 @@ export { integrateExpr, limit, nthDerivative, taylorSeries } from "./integrate.j
 
 // Gröbner basis
 export { Polynomial, Term, TermOrder, computeGroebnerBasis, sPolynomial } from "./groebner.js";
+
+// Modelica CAS bindings
+export { CAS_FUNCTIONS, MODELSCRIPT_CAS_PACKAGE, evaluateCASFunction, isCASFunction } from "./cas-bindings.js";