### Introduction

This is first part of a series about writing expression evaluator in C#. Even though there are several of them available already I decided to write my own as this
one is based on expression trees and is very simple. The evaluator supports numeric expressions as well as expression with parameters.

In this part we will build a simple expression evaluator which will support expressions like this: “2+2″, “2.7+3.2″, “1.7+2.9+14.24+6.58″,
“84+15+4-4*3*9+24+4-54/3-5-7+47″, “25/3+1.34*2.56+1.49+2.36/1.48″, etc. It will however not be able to parse expression with parentheses or with variables.
These features will be implemented in the coming posts.

### Getting Started

As the evaluator is based on expression trees it you should have a basic understanding of how they work. I will not cover them here as there
are many good
articles available out there.

The first thing we need to do is to make the following to tests pass:

[TestFixture]
class ExpressionEvaluatorTests
{
private BasicExpressionEvaluator evaluator;
private Random generator;
[TestFixtureSetUp]
public void SetUp()
{
evaluator = new BasicExpressionEvaluator();
generator = new Random();
}
[Test]
public void Empty_String_Is_Zero()
{
Assert.That(evaluator.Evaluate(" "), Is.EqualTo(0));
}
[Test]
public void Decimal_Is_Treated_As_Decimal()
{
var left = generator.Next(1, 100);
var right = generator.Next(1, 100);
decimal input = left + right / 100m;
Assert.That(evaluator.Evaluate(input.ToString()), Is.EqualTo(input));
}
}

The tests are very simple and the necessary code to make them pass is quite straightforward too:

public class BasicExpressionEvaluator
{
public decimal Evaluate(string expression)
{
decimal value = 0;
decimal.TryParse(expression, out value);
return value;
}
}

Let’s add support for adding to decimal numbers. Here is the test we need to pass:

[Test]
public void Can_Add_Two_Decimal_Numbers()
{
Assert.That(evaluator.Evaluate("2.7+3.2"), Is.EqualTo(2.7m + 3.2m));
}

Implementation is again quite easy. All we have to do it parse the operands and construct corresponding Expression by calling the `Expression.Add`

method.

public decimal Evaluate(string expression)
{
if (expression.Contains('+'))
{
var parts = expression.Split('+');
Expression sum = Expression.Add(
Expression.Constant(decimal.Parse(parts[0])),
Expression.Constant(decimal.Parse(parts[1])));
var lambda = Expression.Lambda<Func<decimal>>(sum);
var compiled = lambda.Compile();
return compiled();
}
decimal value = 0;
decimal.TryParse(expression, out value);
return value;
}

We can also extend it and implement adding multiple numbers:

public decimal Evaluate(string expression)
{
if (expression.Contains('+'))
{
var parts = expression.Split('+');
Expression sum = Expression.Constant(decimal.Parse(parts[0]));
for (int i = 1; i < parts.Length; i++)
{
sum = Expression.Add(sum, Expression.Constant(decimal.Parse(parts[i])));
}
var lambda = Expression.Lambda<Func<decimal>>(sum);
var compiled = lambda.Compile();
return compiled();
}
decimal value = 0;
decimal.TryParse(expression, out value);
return value;
}

We can take advantage of Enumerable.Aggregate method and refactor the above snippet like this:

public decimal Evaluate(string expression)
{
if (expression.Contains('+'))
{
var parts = expression.Split('+');
var sum = parts.Aggregate(Expression.Constant(0m) as Expression,
(current, next) =>
Expression.Add(current, Expression.Constant(decimal.Parse(next))));
var lambda = Expression.Lambda<Func<decimal>>(sum);
var compiled = lambda.Compile();
return compiled();
}
decimal value = 0;
decimal.TryParse(expression, out value);
return value;
}

Next step is to support subtraction. First we will process expressions like “5-2″ and “15.2-2.3-4.8-0.58″. As with additions we will split the string and subtract the terms:

public decimal Evaluate(string expression)
{
if (expression.Contains('+'))
{
var parts = expression.Split('+');
var sum = parts.Aggregate(Expression.Constant(0m) as Expression,
(current, next) => Expression.Add(current, Expression.Constant(decimal.Parse(next))));
var lambda = Expression.Lambda<Func<decimal>>(sum);
var compiled = lambda.Compile();
return compiled();
}
if (expression.Contains('-'))
{
var parts = expression.Split('-');
Expression sum = Expression.Constant(decimal.Parse(parts[0]));
for (int i = 1; i < parts.Length; i++)
{
sum = Expression.Subtract(sum, Expression.Constant(decimal.Parse(parts[i])));
}
var lambda = Expression.Lambda<Func<decimal>>(sum);
var compiled = lambda.Compile();
return compiled();
}
decimal value = 0;
decimal.TryParse(expression, out value);
return value;
}

We can refactor it again by using the Aggregate method again. However with subtraction we cannot start subtracting from zero as we did with addition.
Instead we have to start subtracting from the first term:

public decimal Evaluate(string expression)
{
if (expression.Contains('+'))
{
var parts = expression.Split('+');
var sum = parts.Aggregate(Expression.Constant(0m) as Expression,
(current, next) => Expression.Add(current,
Expression.Constant(decimal.Parse(next))));
var lambda = Expression.Lambda<Func<decimal>>(sum);
var compiled = lambda.Compile();
return compiled();
}
if (expression.Contains('-'))
{
var parts = expression.Split('-');
Expression sum = Expression.Constant(decimal.Parse(parts[0]));
sum = parts.Skip(1).Aggregate(sum, (current, next) =>
Expression.Subtract(current, Expression.Constant(decimal.Parse(next))));
var lambda = Expression.Lambda<Func<decimal>>(sum);
var compiled = lambda.Compile();
return compiled();
}
decimal value = 0;
decimal.TryParse(expression, out value);
return value;
}

Now, let’s mix additions and subtractions in one expression. We want the following test to pass:

[Test]
public void Can_Add_And_Subtract_Multiple_Numbers()
{
Assert.That(evaluator.Evaluate("15+8-4-2+7"),
Is.EqualTo(15 + 8 - 4 - 2 + 7));
Assert.That(evaluator.Evaluate("17.89-2.47+7.16"),
Is.EqualTo(17.89m - 2.47m + 7.16m));
}

Currently the test fails with `FormatException`

being thrown as we are trying to parse strings. To avoid the exception and pass the test instead of parsing
the terms we will recursively evaluate the term and parse the result. This is how it looks:

public decimal Evaluate(string expression)
{
if (expression.Contains('+'))
{
var parts = expression.Split('+');
var sum = parts.Aggregate(Expression.Constant(0m) as Expression,
(current, next) =>
Expression.Add(current,
Expression.Constant(Evaluate(next))));
var lambda = Expression.Lambda<Func<decimal>>(sum);
var compiled = lambda.Compile();
return compiled();
}
if (expression.Contains('-'))
{
var parts = expression.Split('-');
Expression sum = Expression.Constant(decimal.Parse(parts[0]));
sum = parts.Skip(1).Aggregate(sum, (current, next) =>
Expression.Subtract(current, Expression.Constant(decimal.Parse(next))));
var lambda = Expression.Lambda<Func<decimal>>(sum);
var compiled = lambda.Compile();
return compiled();
}
decimal value = 0;
decimal.TryParse(expression, out value);
return value;
}

Notice that the only change is in the part of the code which processes additions.

### Adding multiplication and division

Now we are ready to add support for multiplication and division. Evaluating expressions which contain only multiplication or division is easy
so I will jump to expression which contain all operations. As we did with addition and subtraction we need to recursively evaluate the operands before
adding or subtracting them. Also, as multiplication and division have higher priority than addition and subtraction we first have to split the input string
by ‘+’ and ‘-’ and than split the result by ‘*’ and ‘/’. This way we will first perform higher priority operations first and than move up the stack to perform
operations with less priority. For example splitting 2+5*3 by ‘+’ will result in 2 and 5*3 which we will split by ‘*’ and as a result calculate 5*3 before
performing addition. With this in mind this is how the corresponding test looks like:

public decimal Evaluate(string expression)
{
if (expression.Contains('+'))
{
var parts = expression.Split('+');
Expression result = Expression.Constant(Evaluate(parts[0]));
result = parts.Skip(1).Aggregate(result, (current, next) =>
Expression.Add(current, Expression.Constant(Evaluate(next))));
var lambda = Expression.Lambda<Func<decimal>>(result);
var compiled = lambda.Compile();
return compiled();
}
if (expression.Contains('-'))
{
var parts = expression.Split('-');
Expression result = Expression.Constant(Evaluate(parts[0]));
result = parts.Skip(1).Aggregate(result, (current, next) =>
Expression.Subtract(current, Expression.Constant(Evaluate(next))));
var lambda = Expression.Lambda<Func<decimal>>(result);
var compiled = lambda.Compile();
return compiled();
}
if (expression.Contains('*'))
{
var parts = expression.Split('*');
Expression result = Expression.Constant(Evaluate(parts[0]));
result = parts.Skip(1).Aggregate(result, (current, next) => Expression.Multiply(current, Expression.Constant(Evaluate(next))));
var lambda = Expression.Lambda<Func<decimal>>(result);
var compiled = lambda.Compile();
return compiled();
}
if (expression.Contains('/'))
{
var parts = expression.Split('/');
Expression result = Expression.Constant(Evaluate(parts[0]));
result = parts.Skip(1).Aggregate(result, (current, next) => Expression.Divide(current, Expression.Constant(Evaluate(next))));
var lambda = Expression.Lambda<Func<decimal>>(result);
var compiled = lambda.Compile();
return compiled();
}
decimal value = 0;
decimal.TryParse(expression, out value);
return value;
}

You can notice that all if block have very similar code: The first term is evaluated and other terms are aggregated based on the current operation.
We can take advantage of this and refactor the above code in one small snippet. First, we will introduce a dictionary which maps operation to corresponding
expression tree building method. Using it we can replace all if statements with one `foreach`

loop:

private Dictionary<char, Func<Expression, Expression, Expression>> operations =
new Dictionary<char, Func<Expression, Expression, Expression>>
{
{ '+', (current, next) => Expression.Add(current, next) },
{ '-', (current, next) => Expression.Subtract(current, next) },
{ '*', (current, next) => Expression.Multiply(current, next) },
{ '/', (current, next) => Expression.Divide(current, next) }
};
public decimal Evaluate(string expression)
{
foreach (var operation in operations)
{
if (expression.Contains(operation.Key))
{
var parts = expression.Split(operation.Key);
Expression result = Expression.Constant(Evaluate(parts[0]));
result = parts.Skip(1).Aggregate(result,
(current, next) =>
operation.Value(current, Expression.Constant(Evaluate(next))));
var lambda = Expression.Lambda<Func<decimal>>(result);
var compiled = lambda.Compile();
return compiled();
}
}
decimal value = 0;
decimal.TryParse(expression, out value);
return value;
}

The above function finds the first operation in the given expression and starts recursively evaluating the terms. This in turn will find other operations and evaluate
them again recursively until all the operations are performed.

Using the above method you can evaluate any expression as long as it does not contain variables
or parentheses. This is also confirmed by the following test results:

### Conclusion

As you can see we can build a very simple expression evaluator very easily using very little lines of code. In the following posts we will add support
for expression with parentheses and expressions containing variables. Stay tuned!

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