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Evaluate logic expression contained in a passed in string based on a list of strings

So I am unsure how to word this question properly.
If you look below lets say I have a list of options (PG , PA, PM, TK, TD) that a customer has ordered. Now lets say I have some expression I need evaluate against the customers ordered options such as: PA OR PB where evaluates to customers list of options contains either option PA or PB. Seems simple enough but these expressions could grow quite a bit. Below in the code are some good examples of what I would like to accomplish.
I by no means claim to have knowledge about string parsing and comparing logical operations. I am looking for some general direction or what my options are. I saw some things about dynamic linq, rule engines, expression trees, etc. Its just a whole lot to absorb and am looking for some direction on which would accomplish what I want?
I am open to just about any approach. Any answers are appreciated!
Code:
class Program
{
static void Main(string[] args)
{
//Reprsents what the customer selected
List<string> CustomerSelectedOptins = new List<string> { "PG", "PA", "PM", "TK", "TD" };
string LogicOperation = "PA OR (PB AND PC)"; //Evaluates true since customer list contains PA
string LogicOperation2 = "PF OR (NOT PB AND PM)"; //Evaluates true since customer list does not contain PB but contain PM
string LogicOperation3 = "NOT PG AND NOT(PL AND TZ)"; //Evaluates false since the customer does have PG selected
}
}

There are a few different approaches you can take. One common one is to replace the option checks with true or false and then use one of the built-in expression evaluators to evaluate the resulting expression. Note: XOR is not available for these.
public static class Evaluator {
static Regex wordRE = new Regex(#"[A-Z]+", RegexOptions.Compiled);
static HashSet<string> Operators = new[] { "AND", "OR", "NOT" }.ToHashSet(StringComparer.OrdinalIgnoreCase);
public static bool Evaluate(this List<string> options, string op) {
var opListOfOptions = wordRE.Matches(op).Select(m => m.Value).Where(w => !Operators.Contains(w));
foreach (var option in opListOfOptions) {
var value = options.Contains(option).ToString();
op = op.Replace(option, value);
}
//return DTEval(op) == 1;
return CompEval(op);
//return XEval(op);
}
static double DTEval(string expression) {
var dt = new DataTable();
var loDataColumn = new DataColumn("Eval", typeof(double), expression);
dt.Columns.Add(loDataColumn);
dt.Rows.Add(0);
return (double)(dt.Rows[0]["Eval"]);
}
static DataTable cDT = new DataTable();
static bool CompEval(string expression) {
return (bool)cDT.Compute(expression, "");
}
public static bool XEval(string expression) {
expression = new System.Text.RegularExpressions.Regex(#"not +(true|false)").Replace(expression.ToLower(), " not(${1}) ");
expression = new System.Text.RegularExpressions.Regex(#"(true|false)").Replace(expression, " ${1}() ");
return (bool)new System.Xml.XPath.XPathDocument(new System.IO.StringReader("<r/>")).CreateNavigator()
.Evaluate(String.Format("boolean({0})", expression));
}
}
The Evaluate method comments show the different options you could use.
Alternatively, you could write your own expression evaluator. A simple one is a recursive descent evaluator that parses a simple grammar. This one uses C# precedence rules, having OR/XOR/AND binding left to right.
public class Evaluator {
// recursive descent boolean expression evaluator
// grammer:
// primary = id
// primary = ( expr )
// unop = primary
// unop = not unop
// andop = unop [ and unop ]*
// xorop = andop [ xor andop ]*
// orop = xorop [ or xorop ]*
// expr = orop
public class TokenList {
List<string> tokens;
int curTokenNum;
static Regex tokenRE = new Regex(#"\w+|[()]", RegexOptions.Compiled);
public TokenList(string expr) {
curTokenNum = 0;
tokens = tokenRE.Matches(expr).Select(m => m.Value).ToList();
}
public string CurToken => curTokenNum < tokens.Count ? tokens[curTokenNum] : String.Empty;
public void MoveNext() => ++curTokenNum;
public bool MoreTokens => curTokenNum < tokens.Count;
public void NextToken() {
MoveNext();
if (!MoreTokens)
throw new InvalidExpressionException("Expected token");
}
}
static List<string> OperatorStrings = new[] { "AND", "OR", "XOR", "NOT" }.ToList();
enum Operators { and, or, xor, not };
static List<string> ParenStrings = new[] { "(", ")" }.ToList();
enum Parens { open, close };
TokenList tokens;
List<string> trueOptions;
public Evaluator(List<string> trueOptions) {
this.trueOptions = trueOptions;
}
string curToken => tokens.CurToken;
bool curTokenValue => trueOptions.Contains(curToken);
bool isOperator => OperatorStrings.FindIndex(s => s.Equals(curToken, StringComparison.OrdinalIgnoreCase)) != -1;
Operators curOp => (Operators)OperatorStrings.FindIndex(s => s.Equals(curToken, StringComparison.OrdinalIgnoreCase));
bool isParen => ParenStrings.Contains(curToken);
Parens curParen => (Parens)(ParenStrings.IndexOf(curToken));
public bool id() {
if (isOperator)
throw new InvalidExpressionException("missing operand");
else {
var ans = curTokenValue;
tokens.MoveNext();
return ans;
}
}
bool primary() {
if (isParen)
if (curParen == Parens.open) {
tokens.NextToken();
var ans = expr();
if (!isParen || curParen != Parens.close)
throw new InvalidExpressionException($"missing ) at {curToken}");
else
tokens.MoveNext();
return ans;
}
else
throw new InvalidExpressionException("Invalid )");
else
return id();
}
bool unop() {
if (isOperator && curOp == Operators.not) {
tokens.NextToken();
return !unop();
}
else
return primary();
}
bool andop() {
var ans = unop();
while (tokens.MoreTokens && isOperator && curOp == Operators.and) {
tokens.NextToken();
ans = ans & unop();
}
return ans;
}
bool xorop() {
var ans = andop();
while (tokens.MoreTokens && isOperator && curOp == Operators.xor) {
tokens.NextToken();
ans = ans ^ andop();
}
return ans;
}
bool orop() {
var ans = xorop();
while (tokens.MoreTokens && isOperator && curOp == Operators.or) {
tokens.NextToken();
ans = ans | xorop();
}
return ans;
}
bool expr() => orop();
public bool Value(string exp) {
tokens = new TokenList(exp);
var ans = expr();
if (tokens.MoreTokens)
throw new InvalidExpressionException($"Unrecognized token {curToken} after expression");
return ans;
}
}
You can call it by creating an Evaluator and passing it an expression to evaluate:
var eval = new Evaluator(CustomerSelectedOptions);
var ans = eval.Value(LogicOperation);

Evaluating complex expression tree

I have a basic rule engine that I've built in a very similar way to the route suggested here:
How to implement a rule engine?
Ive extended it based on further requirements, and now I need to evaluate complex classes eg
EvaluateRule("Transaction.IsOpen", "Equals", "true")
The code in its most basic form is:
var param = inputMessageType;
left = Expression.Property(param, memberName);
tProp = typeof(T).GetProperty(r.MemberName).PropertyType;
right = Expression.Constant(Convert.ChangeType(r.TargetValue, tProp));
return Expression.MakeBinary(tBinary, left, right);
In order to evaluate complex classes I used a method similar to here:
https://stackoverflow.com/questions/16544672/dynamically-evaluating-a-property-string-with-expressions
The problem that Im having is that when I try to evaluate the rule with a property of a class (Transaction.IsOpen), I get it with the type of the root type on the right hand side of the expression but the type of the complex object on the left hand side of the expression.
This results in the error:
System.InvalidOperationException: The binary operator Equal is not defined for the types 'System.Func`2[Transaction,System.Boolean]' and 'System.Boolean'.
How do I overcome this problem? I am no expert using Expression Trees, and many of the concepts are proving difficult to grasp when the example strays from the standard documentation.
Edit: Here is the code(Ive omitted some stuff that is environment specific so as keep focus with the problem)
public Actions EvaluateRulesFromMessage(ClientEventQueueMessage message)
{
var ruleGroups = _ruleRepository.GetRuleList();
var actions = new Actions();
foreach (var ruleGroup in ruleGroups)
{
if (message.MessageType == "UI_UPDATE")
{
// clean up json object
JObject dsPayload = (JObject.Parse(message.Payload));
var msgParams = JsonConvert.DeserializeObject<UiTransactionUpdate>(message.Payload);
msgParams.RulesCompleted = msgParams.RulesCompleted ?? new List<int>();
var conditionsMet = false;
// process the rules filtering out the rules that have already been evaluated
var filteredRules = ruleGroup.Rules.Where(item =>
!msgParams.RulesCompleted.Any(r => r.Equals(item.Id)));
foreach (var rule in filteredRules)
{
Func<UiTransactionUpdate, bool> compiledRule = CompileRule<UiTransactionUpdate>(rule, msgParams);
if (compiledRule(msgParams))
{
conditionsMet = true;
}
else
{
conditionsMet = false;
break;
}
}
if (conditionsMet)
{
actions = AddAction(message, ruleGroup);
break;
}
}
}
return actions;
}
public Func<UiTransactionUpdate, bool> CompileRule<T>(Rule r, UiTransactionUpdate msg)
{
var expression = Expression.Parameter(typeof(UiTransactionUpdate));
Expression expr = BuildExpr<UiTransactionUpdate>(r, expression, msg);
// build a lambda function UiTransactionUpdate->bool and compile it
return Expression.Lambda<Func<UiTransactionUpdate, bool>>(expr, expression).Compile();
}
static Expression Eval(object root, string propertyString, out Type tProp)
{
Type type = null;
var propertyNames = propertyString.Split('.');
ParameterExpression param = Expression.Parameter(root.GetType());
Expression property = param;
string propName = "";
foreach (var prop in propertyNames)
{
property = MemberExpression.PropertyOrField(property, prop);
type = property.Type;
propName = prop;
}
tProp = Type.GetType(type.UnderlyingSystemType.AssemblyQualifiedName);
var param2 = MemberExpression.Parameter(tProp);
var e = Expression.Lambda(property, param);
return e;
}
static Expression BuildExpr<T>(Rule r, ParameterExpression param, UiTransactionUpdate msg)
{
Expression left;
Type tProp;
string memberName = r.MemberName;
if (memberName.Contains("."))
{
left = Eval(msg, memberName, out tProp);
}
else
{
left = Expression.Property(param, memberName);
tProp = typeof(T).GetProperty(r.MemberName).PropertyType;
}
ExpressionType tBinary;
if (ExpressionType.TryParse(r.Operator, out tBinary))
{
Expression right=null;
switch (r.ValueType) ///todo: this needs to be refactored to be type independent
{
case TargetValueType.Value:
right = Expression.Constant(Convert.ChangeType(r.TargetValue, tProp));
break;
}
// use a binary operation ie true/false
return Expression.MakeBinary(tBinary, left, right);
}
else
{
var method = tProp.GetMethod(r.Operator);
var tParam = method.GetParameters()[0].ParameterType;
var right = Expression.Constant(Convert.ChangeType(r.TargetValue, tParam));
// use a method call, e.g. 'Contains' -> 'u.Tags.Contains(some_tag)'
return Expression.Call(left, method, right);
}
}

The sample code does not cover all data types used in your scenario, so it's hard to tell where it breaks exactly, but from the exception System.Func'2[Transaction,System.Boolean]' and 'System.Boolean it's obvious that on left hand you have a delegate that takes in Transaction and returns bool (Func<Transaction, bool>), and on the right hand you just have bool.
It's not possible to compare Func<Transaction, bool> to bool, but it's possible to call the function and compare its result:
Func<Transaction, bool> func = ...;
bool comparand = ...;
Transaction transaction = ...;
if (func(transaction) == comparand) { ... }
What translated to expression tree:
Expression funcExpression = ... /*LambdaExpression<Func<Transaction,bool>>*/;
Expression comparandExpression = Expression.Constant(true);
Expression transactionArg = /*e.g.*/Expression.Constant(transaction);
Expression funcResultExpression = Expression.Call(funcExpression, "Invoke", null, transactionArg);
Expression equalityTestExpression = Expression.Equal(funcResultExpression, comparandExpression);

Create expression for a simple math formula

I have some fun with Expressions and a question appears: it throws an exception that I didn't suppose.
I have an input - simple math formula, for example 2*x+3, and I want to create an expression tree for it. So I write this code
using System;
using System.Linq.Expressions;
namespace ConsoleApplication50
{
class Program
{
static void Main()
{
string s = "3*x^2+2/5*x+4";
Expression<Func<double, double>> expr = MathExpressionGenerator.GetExpression(s);
Console.WriteLine(expr);
var del = expr.Compile();
Console.WriteLine(del(10));
}
}
static class MathExpressionGenerator
{
public const string SupportedOps = "+-*/^";
private static readonly ParameterExpression Parameter = Expression.Parameter(typeof(double), "x");
public static Expression<Func<double, double>> GetExpression(string s)
{
ParameterExpression parameterExpression = Expression.Parameter(typeof(double), "x");
Expression result = GetExpressionInternal(s);
return Expression.Lambda<Func<double, double>>(result, parameterExpression);
}
private static Expression GetExpressionInternal(string s)
{
double constant;
if (s == "x")
return Parameter;
if (double.TryParse(s, out constant))
return Expression.Constant(constant, typeof(double));
foreach (char op in SupportedOps)
{
var split = s.Split(new[] { op }, StringSplitOptions.RemoveEmptyEntries);
if (split.Length > 1)
{
var expression = GetExpressionInternal(split[0]);
for (int i = 1; i < split.Length; i++)
{
expression = RunOp(expression, GetExpressionInternal(split[i]), op);
}
return expression;
}
}
throw new NotImplementedException("never throws");
}
private static Expression RunOp(Expression a, Expression b, char op)
{
switch (op)
{
case '+':
return Expression.Add(a, b);
case '-':
return Expression.Subtract(a, b);
case '/':
return Expression.Divide(a, b);
case '*':
return Expression.Multiply(a, b);
case '^':
return Expression.Power(a, b);
}
throw new NotSupportedException();
}
}
}
but I get an error:
Unhandled Exception: System.InvalidOperationException: variable 'x' of
type 'Sys tem.Double' referenced from scope '', but it is not defined
at
System.Linq.Expressions.Compiler.VariableBinder.Reference(ParameterExpress
ion node, VariableStorageKind storage) at
System.Linq.Expressions.Compiler.VariableBinder.VisitParameter(ParameterEx
pression node) at
System.Linq.Expressions.ParameterExpression.Accept(ExpressionVisitor
visit or) at ... and so on
Please, advice, how can it be fixed? Here I have a single global parameter and referencing it so I have no idea, why it says this stuff.

Problem with your code is that you have two instances of x parameter. One of them is private static field that is used across expression generation, and second one is that you create and use in Lambda creation.
If you have ParameterExpression, then you should use the same instance in expression and pass the same instance into Lambda generation, otherwise it will fail like in your example.
it will work fine if you remove parameterExpression and will use private Parameter field like this:
public static Expression<Func<double, double>> GetExpression(string s)
{
Expression result = GetExpressionInternal(s);
return Expression.Lambda<Func<double, double>>(result, Parameter);
}
Working example in .NetFiddle - https://dotnetfiddle.net/Onw0Hy

static void Main(string[] args)
{
var str = #"3*x^2+2/5*x+4";
str = Transform(str);
var param = Expression.Parameter(typeof (double), "x");
var expression = System.Linq.Dynamic.DynamicExpression.ParseLambda(new[] {param}, null, str);
var exp10 = expression.Compile().DynamicInvoke(10);
Console.WriteLine(exp10);
}
public const string SupportedOps = "+-*/";//separators without ^
private static string Transform(string expression)
{
//replace x^y with Math.Pow(x,y)
var toBeReplaced = expression.Split(SupportedOps.ToCharArray()).Where(s => s.Contains("^"));
var result = expression;
return toBeReplaced.Aggregate(expression, (current, str) => current.Replace(str, string.Format("Math.Pow({0})", str.Replace('^', ','))));
//OR
//foreach (var str in toBeReplaced)
//{
// result =result.Replace(str, string.Format("Math.Pow({0})", str.Replace('^', ',')));
//}
//return result;
}

Parse string into int32 using expressions in C#

Basically I've wrote my own parser and I'm parsing a string into and expression and then compiling and storing to be reused later on.
For (an odd) example the type of string I'm parsing is this:-
if #name == 'max' and #legs > 5 and #ears > 5 then shoot()
The hash parts in the string are telling my parser to look at the properties on the object of type T that I pass in, if not found to look in a Dictionary that also gets passed in as extra.
I parse up the string into parts create an expression and join the expressions using methods from the PredicateBuilder.
I get the left value from where ever it may be and then the right value and turn it into an int32 or a string based on if it's wrapped in single quotes.. for now, then pass both into Expression.Equals/Expression.GreaterThan etc. dependant on the operator.
So far this works fine for equals and strings but take for example #ears which isn't a property on the object but is in the dictionary I end up with "does string equal int32" and it throws an exception.
I need to be able to parse the string from the dictionary into and int32 and then try the equal/greater/less than method.
Hopefully someone could shed some light on this as I haven't found anything yet that will do it and its driving me mad.
Here is the CreateExpression method I'm using to create an expression from the string.
private Expression<Func<T, IDictionary<string, string>, bool>> CreateExpression<T>(string condition)
{
string[] parts = condition.Split(new char[] { ' ' }, 3, StringSplitOptions.RemoveEmptyEntries);
if (parts.Length == 3)
{
var typeCache = _cache[typeof(T).FullName];
var param = Expression.Parameter(typeCache.T, "o");
var param2 = Expression.Parameter(typeof(IDictionary<string, string>), "d");
/* Convert right hand side into correct value type
*/
Expression right = null;
if (parts[2][0] == '\'' && parts[2][parts[2].Length - 1] == '\'')
right = Expression.Constant(parts[2].Trim(new char[] { '\'' }), typeof(string));
else
{
int x = 0;
right = (int.TryParse(parts[2].Trim(), out x))
? Expression.Constant(x)
: Expression.Constant(parts[2].Trim(new char[] { '\'' }), typeof(string));
}
/* Get the left hand side value from object T or IDictionary and then attempt to convert it
* into the right hand side value type
*/
Expression left = null;
var key = (parts[0][0] == '#') ? parts[0].TrimStart('#') : parts[0];
if (_cache[typeCache.T.FullName].Properties.Find(key, true) == null)
{
var m = typeof(ExpressionExtensions).GetMethod("GetValue");
left = Expression.Call(null, m, new Expression[] { param2, Expression.Constant(key) });
}
else
left = Expression.PropertyOrField(param, key);
/* Find the operator and return the correct expression
*/
if (parts[1] == "==")
{
return Expression.Lambda<Func<T, IDictionary<string, string>, bool>>(
Expression.Equal(left, right), new ParameterExpression[] { param, param2 });
}
else if (parts[1] == ">")
{
return Expression.Lambda<Func<T, IDictionary<string, string>, bool>>(
Expression.GreaterThan(left, right), new ParameterExpression[] { param, param2 });
}
}
return null;
}
And here is the method to parse the whole string into parts and build up the expression.
public Func<T, IDictionary<string, string>, bool> Parse<T>(string rule)
{
var type = typeof(T);
if (!_cache.ContainsKey(type.FullName))
_cache[type.FullName] = new TypeCacheItem()
{
T = type,
Properties = TypeDescriptor.GetProperties(type)
};
Expression<Func<T, IDictionary<string, string>, bool>> exp = null;
var actionIndex = rule.IndexOf("then");
if (rule.IndexOf("if") == 0 && actionIndex > 0)
{
var conditionStatement = rule.Substring(2, actionIndex - 2).Trim();
var actionStatement = rule.Substring(actionIndex + 4).Trim();
var startIndex = 0;
var endIndex = 0;
var conditionalOperator = "";
var lastConditionalOperator = "";
do
{
endIndex = FindConditionalOperator(conditionStatement, out conditionalOperator, startIndex);
var condition = (endIndex == -1) ? conditionStatement.Substring(startIndex) : conditionStatement.Substring(startIndex, endIndex - startIndex);
var x = CreateExpression<T>(condition.Trim());
if (x != null)
{
if (exp != null)
{
switch (lastConditionalOperator)
{
case "or":
exp = exp.Or<T>(x);
break;
case "and":
exp = exp.And<T>(x);
break;
default:
exp = x;
break;
}
}
else
exp = x;
}
lastConditionalOperator = conditionalOperator;
startIndex = endIndex + conditionalOperator.Length;
} while (endIndex > -1);
}
else
throw new ArgumentException("Rule must start with 'if' and contain 'then'.");
return (exp == null) ? null : exp.Compile();
}
My eyes are open to suggestions or advice on this but the idea of parsing that string as is to return true or false has to be,
EDIT:
I've now alter my method that retrieves the value from the dictionary to a generic one as Fahad suggested to this:-
public static T GetValue<T>(this IDictionary<string, string> dictionary, string key)
{
string x = string.Empty;
dictionary.TryGetValue(key, out x);
if (typeof(T) == typeof(int))
{
int i = 0;
if (int.TryParse(x, out i))
return (T)(i as object);
}
return default(T);
//throw new ArgumentException("Failed to convert dictionary value to type.");
}
And this works fine but I would rather return null than a default value for the type i've tried using Nullable ... where T : struct and returning null when not found or can't convert but I don't know how to use the null result in my expression.

I think you should redo your problem analysis and try another way. One way I would propose is to have a generic method that would give you the value from a IDictionary or IList etc., and use this method to wrap around your Expression's. The Expression would only want the "Type" of the object to be satisfied, if that is done correctly, then you could easily do it. If you know the "Type" then you can implement it with generic methods, otherwise, you could still use reflection and do generics.
So all you have to think is how to get the value from the dictionary or any other list through expressions.
Hope that helps.
-Fahad

You could use Expression.Call(null, typeof(int), "Parse", Type.EmptyTypes, yourTextExpression)

Generated methods for polynomial evaluation

I'm trying to come up with an elegant way to handle some generated polynomials. Here's the situation we'll focus on (exclusively) for this question:
order is a parameter in generating an nth order polynomial, where n:=order + 1.
i is an integer parameter in the range 0..n
The polynomial has zeros at x_j, where j = 1..n and j ≠ i (it should be clear at this point that StackOverflow needs a new feature or it's present and I don't know it)
The polynomial evaluates to 1 at x_i.
Since this particular code example generates x_1 .. x_n, I'll explain how they're found in the code. The points are evenly spaced x_j = j * elementSize / order apart, where n = order + 1.
I generate a Func<double, double> to evaluate this polynomial¹.
private static Func<double, double> GeneratePsi(double elementSize, int order, int i)
{
if (order < 1)
throw new ArgumentOutOfRangeException("order", "order must be greater than 0.");
if (i < 0)
throw new ArgumentOutOfRangeException("i", "i cannot be less than zero.");
if (i > order)
throw new ArgumentException("i", "i cannot be greater than order");
ParameterExpression xp = Expression.Parameter(typeof(double), "x");
// generate the terms of the factored polynomial in form (x_j - x)
List<Expression> factors = new List<Expression>();
for (int j = 0; j <= order; j++)
{
if (j == i)
continue;
double p = j * elementSize / order;
factors.Add(Expression.Subtract(Expression.Constant(p), xp));
}
// evaluate the result at the point x_i to get scaleInv=1.0/scale.
double xi = i * elementSize / order;
double scaleInv = Enumerable.Range(0, order + 1).Aggregate(0.0, (product, j) => product * (j == i ? 1.0 : (j * elementSize / order - xi)));
/* generate an expression to evaluate
* (x_0 - x) * (x_1 - x) .. (x_n - x) / (x_i - x)
* obviously the term (x_i - x) is cancelled in this result, but included here to make the result clear
*/
Expression expr = factors.Skip(1).Aggregate(factors[0], Expression.Multiply);
// multiplying by scale forces the condition f(x_i)=1
expr = Expression.Multiply(Expression.Constant(1.0 / scaleInv), expr);
Expression<Func<double, double>> lambdaMethod = Expression.Lambda<Func<double, double>>(expr, xp);
return lambdaMethod.Compile();
}
The problem: I also need to evaluate ψ′=dψ/dx. To do this, I can rewrite ψ=scale×(x_0 - x)(x_1 - x)×..×(x_n - x)/(x_i - x) in the form ψ=α_n×x^n + α_n×x^(n-1) + .. + α_1×x + α_0. This gives ψ′=n×α_n×x^(n-1) + (n-1)×α_n×x^(n-2) + .. + 1×α_1.
For computational reasons, we can rewrite the final answer without calls to Math.Pow by writing ψ′=x×(x×(x×(..) - β_2) - β_1) - β_0.
To do all this "trickery" (all very basic algebra), I need a clean way to:
Expand a factored Expression containing ConstantExpression and ParameterExpression leaves and basic mathematical operations (end up either BinaryExpression with the NodeType set to the operation) - the result here can include InvocationExpression elements to the MethodInfo for Math.Pow which we'll handle in a special manner throughout.
Then I take the derivative with respect to some specified ParameterExpression. Terms in the result where the right hand side parameter to an invocation of Math.Pow was the constant 2 are replaced by the ConstantExpression(2) multiplied by what was the left hand side (the invocation of Math.Pow(x,1) is removed). Terms in the result that become zero because they were constant with respect to x are removed.
Then factor out the instances of some specific ParameterExpression where they occur as the left hand side parameter to an invocation of Math.Pow. When the right hand side of the invocation becomes a ConstantExpression with the value 1, we replace the invocation with just the ParameterExpression itself.
¹ In the future, I'd like the method to take a ParameterExpression and return an Expression that evaluates based on that parameter. That way I can aggregate generated functions. I'm not there yet.
² In the future, I hope to release a general library for working with LINQ Expressions as symbolic math.

I wrote the basics of several symbolic math features using the ExpressionVisitor type in .NET 4. It's not perfect, but it looks like the foundation of a viable solution.
Symbolic is a public static class exposing methods like Expand, Simplify, and PartialDerivative
ExpandVisitor is an internal helper type that expands expressions
SimplifyVisitor is an internal helper type that simplifies expressions
DerivativeVisitor is an internal helper type that takes the derivative of an expression
ListPrintVisitor is an internal helper type that converts an Expression to a prefix notation with a Lisp syntax
Symbolic
public static class Symbolic
{
public static Expression Expand(Expression expression)
{
return new ExpandVisitor().Visit(expression);
}
public static Expression Simplify(Expression expression)
{
return new SimplifyVisitor().Visit(expression);
}
public static Expression PartialDerivative(Expression expression, ParameterExpression parameter)
{
bool totalDerivative = false;
return new DerivativeVisitor(parameter, totalDerivative).Visit(expression);
}
public static string ToString(Expression expression)
{
ConstantExpression result = (ConstantExpression)new ListPrintVisitor().Visit(expression);
return result.Value.ToString();
}
}
Expanding expressions with ExpandVisitor
internal class ExpandVisitor : ExpressionVisitor
{
protected override Expression VisitBinary(BinaryExpression node)
{
var left = Visit(node.Left);
var right = Visit(node.Right);
if (node.NodeType == ExpressionType.Multiply)
{
Expression[] leftNodes = GetAddedNodes(left).ToArray();
Expression[] rightNodes = GetAddedNodes(right).ToArray();
var result =
leftNodes
.SelectMany(x => rightNodes.Select(y => Expression.Multiply(x, y)))
.Aggregate((sum, term) => Expression.Add(sum, term));
return result;
}
if (node.Left == left && node.Right == right)
return node;
return Expression.MakeBinary(node.NodeType, left, right, node.IsLiftedToNull, node.Method, node.Conversion);
}
/// <summary>
/// Treats the <paramref name="node"/> as the sum (or difference) of one or more child nodes and returns the
/// the individual addends in the sum.
/// </summary>
private static IEnumerable<Expression> GetAddedNodes(Expression node)
{
BinaryExpression binary = node as BinaryExpression;
if (binary != null)
{
switch (binary.NodeType)
{
case ExpressionType.Add:
foreach (var n in GetAddedNodes(binary.Left))
yield return n;
foreach (var n in GetAddedNodes(binary.Right))
yield return n;
yield break;
case ExpressionType.Subtract:
foreach (var n in GetAddedNodes(binary.Left))
yield return n;
foreach (var n in GetAddedNodes(binary.Right))
yield return Expression.Negate(n);
yield break;
default:
break;
}
}
yield return node;
}
}
Taking a derivative with DerivativeVisitor
internal class DerivativeVisitor : ExpressionVisitor
{
private ParameterExpression _parameter;
private bool _totalDerivative;
public DerivativeVisitor(ParameterExpression parameter, bool totalDerivative)
{
if (_totalDerivative)
throw new NotImplementedException();
_parameter = parameter;
_totalDerivative = totalDerivative;
}
protected override Expression VisitBinary(BinaryExpression node)
{
switch (node.NodeType)
{
case ExpressionType.Add:
case ExpressionType.Subtract:
return Expression.MakeBinary(node.NodeType, Visit(node.Left), Visit(node.Right));
case ExpressionType.Multiply:
return Expression.Add(Expression.Multiply(node.Left, Visit(node.Right)), Expression.Multiply(Visit(node.Left), node.Right));
case ExpressionType.Divide:
return Expression.Divide(Expression.Subtract(Expression.Multiply(Visit(node.Left), node.Right), Expression.Multiply(node.Left, Visit(node.Right))), Expression.Power(node.Right, Expression.Constant(2)));
case ExpressionType.Power:
if (node.Right is ConstantExpression)
{
return Expression.Multiply(node.Right, Expression.Multiply(Visit(node.Left), Expression.Subtract(node.Right, Expression.Constant(1))));
}
else if (node.Left is ConstantExpression)
{
return Expression.Multiply(node, MathExpressions.Log(node.Left));
}
else
{
return Expression.Multiply(node, Expression.Add(
Expression.Multiply(Visit(node.Left), Expression.Divide(node.Right, node.Left)),
Expression.Multiply(Visit(node.Right), MathExpressions.Log(node.Left))
));
}
default:
throw new NotImplementedException();
}
}
protected override Expression VisitConstant(ConstantExpression node)
{
return MathExpressions.Zero;
}
protected override Expression VisitInvocation(InvocationExpression node)
{
MemberExpression memberExpression = node.Expression as MemberExpression;
if (memberExpression != null)
{
var member = memberExpression.Member;
if (member.DeclaringType != typeof(Math))
throw new NotImplementedException();
switch (member.Name)
{
case "Log":
return Expression.Divide(Visit(node.Expression), node.Expression);
case "Log10":
return Expression.Divide(Visit(node.Expression), Expression.Multiply(Expression.Constant(Math.Log(10)), node.Expression));
case "Exp":
case "Sin":
case "Cos":
default:
throw new NotImplementedException();
}
}
throw new NotImplementedException();
}
protected override Expression VisitParameter(ParameterExpression node)
{
if (node == _parameter)
return MathExpressions.One;
return MathExpressions.Zero;
}
}
Simplifying expressions with SimplifyVisitor
internal class SimplifyVisitor : ExpressionVisitor
{
protected override Expression VisitBinary(BinaryExpression node)
{
var left = Visit(node.Left);
var right = Visit(node.Right);
ConstantExpression leftConstant = left as ConstantExpression;
ConstantExpression rightConstant = right as ConstantExpression;
if (leftConstant != null && rightConstant != null
&& (leftConstant.Value is double) && (rightConstant.Value is double))
{
double leftValue = (double)leftConstant.Value;
double rightValue = (double)rightConstant.Value;
switch (node.NodeType)
{
case ExpressionType.Add:
return Expression.Constant(leftValue + rightValue);
case ExpressionType.Subtract:
return Expression.Constant(leftValue - rightValue);
case ExpressionType.Multiply:
return Expression.Constant(leftValue * rightValue);
case ExpressionType.Divide:
return Expression.Constant(leftValue / rightValue);
default:
throw new NotImplementedException();
}
}
switch (node.NodeType)
{
case ExpressionType.Add:
if (IsZero(left))
return right;
if (IsZero(right))
return left;
break;
case ExpressionType.Subtract:
if (IsZero(left))
return Expression.Negate(right);
if (IsZero(right))
return left;
break;
case ExpressionType.Multiply:
if (IsZero(left) || IsZero(right))
return MathExpressions.Zero;
if (IsOne(left))
return right;
if (IsOne(right))
return left;
break;
case ExpressionType.Divide:
if (IsZero(right))
throw new DivideByZeroException();
if (IsZero(left))
return MathExpressions.Zero;
if (IsOne(right))
return left;
break;
default:
throw new NotImplementedException();
}
return Expression.MakeBinary(node.NodeType, left, right);
}
protected override Expression VisitUnary(UnaryExpression node)
{
var operand = Visit(node.Operand);
ConstantExpression operandConstant = operand as ConstantExpression;
if (operandConstant != null && (operandConstant.Value is double))
{
double operandValue = (double)operandConstant.Value;
switch (node.NodeType)
{
case ExpressionType.Negate:
if (operandValue == 0.0)
return MathExpressions.Zero;
return Expression.Constant(-operandValue);
default:
throw new NotImplementedException();
}
}
switch (node.NodeType)
{
case ExpressionType.Negate:
if (operand.NodeType == ExpressionType.Negate)
{
return ((UnaryExpression)operand).Operand;
}
break;
default:
throw new NotImplementedException();
}
return Expression.MakeUnary(node.NodeType, operand, node.Type);
}
private static bool IsZero(Expression expression)
{
ConstantExpression constant = expression as ConstantExpression;
if (constant != null)
{
if (constant.Value.Equals(0.0))
return true;
}
return false;
}
private static bool IsOne(Expression expression)
{
ConstantExpression constant = expression as ConstantExpression;
if (constant != null)
{
if (constant.Value.Equals(1.0))
return true;
}
return false;
}
}
Formatting expressions for display with ListPrintVisitor
internal class ListPrintVisitor : ExpressionVisitor
{
protected override Expression VisitBinary(BinaryExpression node)
{
string op = null;
switch (node.NodeType)
{
case ExpressionType.Add:
op = "+";
break;
case ExpressionType.Subtract:
op = "-";
break;
case ExpressionType.Multiply:
op = "*";
break;
case ExpressionType.Divide:
op = "/";
break;
default:
throw new NotImplementedException();
}
var left = Visit(node.Left);
var right = Visit(node.Right);
string result = string.Format("({0} {1} {2})", op, ((ConstantExpression)left).Value, ((ConstantExpression)right).Value);
return Expression.Constant(result);
}
protected override Expression VisitConstant(ConstantExpression node)
{
if (node.Value is string)
return node;
return Expression.Constant(node.Value.ToString());
}
protected override Expression VisitParameter(ParameterExpression node)
{
return Expression.Constant(node.Name);
}
}
Testing the results
[TestMethod]
public void BasicSymbolicTest()
{
ParameterExpression x = Expression.Parameter(typeof(double), "x");
Expression linear = Expression.Add(Expression.Constant(3.0), x);
Assert.AreEqual("(+ 3 x)", Symbolic.ToString(linear));
Expression quadratic = Expression.Multiply(linear, Expression.Add(Expression.Constant(2.0), x));
Assert.AreEqual("(* (+ 3 x) (+ 2 x))", Symbolic.ToString(quadratic));
Expression expanded = Symbolic.Expand(quadratic);
Assert.AreEqual("(+ (+ (+ (* 3 2) (* 3 x)) (* x 2)) (* x x))", Symbolic.ToString(expanded));
Assert.AreEqual("(+ (+ (+ 6 (* 3 x)) (* x 2)) (* x x))", Symbolic.ToString(Symbolic.Simplify(expanded)));
Expression derivative = Symbolic.PartialDerivative(expanded, x);
Assert.AreEqual("(+ (+ (+ (+ (* 3 0) (* 0 2)) (+ (* 3 1) (* 0 x))) (+ (* x 0) (* 1 2))) (+ (* x 1) (* 1 x)))", Symbolic.ToString(derivative));
Expression simplified = Symbolic.Simplify(derivative);
Assert.AreEqual("(+ 5 (+ x x))", Symbolic.ToString(simplified));
}