ParserLibrary 1.4.3

ParserLibrary

No Other Expression Parser, Ever

About

I wanted to write my "custom terminal" that used interactive commands with expressions. Other Expression builders used only numbers as basic entities which I did not want; this is something too common. I wanted some variables to represent musical notes/chords, or even vectors and matrices and some other to represent numbers. The only way, was to build an Expression builder that could allow custom types. Obviously, the default capability of handling numerical values was needed as a start.

The library is frequently updated, so please check again for a newer version and the most recent README after a while 😃.

The library is based on modern programming tools and can be highly customized. Its basic features are:

• Default support for:
  • Double arithmetic via the DefaultParser
  • Complex arithmetic via the ComplexParser
  • Vector arithmetic via the Vector3Parser
• Logger customization (typically via the appsettings.json ).
• Full control of unary and binary operators via configuration files (typically appsettings.json).
• Support for custom data types and/or combination of custom data types with standard data types (such as int, double).
• Support for custom functions with arbitrary number of arguments. Each argument may be a custom type.

The library is built with modern tools:

• .NET 6.0
• Use of .NET Generic Host (i.e Dependency Inversion/Injection principles, Logging, Configuration) (see NET Generic Host for more). All derived Parsers are typically singletons.
• Support for custom loggers (Serilog is implemented by default)

There are 2 main classes: the Tokenizer and the Parser. Both of them are base classes and adapt to the corresponding interfaces ITokenizer and IParser. Let's uncover all the potential by giving examples with incrementally added functionality.

Simple Parser Examples

DefaultParser examples

//This is a simple expression, which uses variables and literals of type double, and the DefaultParser.
double result = (double)App.Evaluate( "-5.0+2*a", new() { { "a", 5.0 } });
Console.WriteLine(result);  //5

//2 variables example (spaces are obviously ignored)
double result2 = (double)App.Evaluate("-a + 500 * b + 2^3", new() { { "a", 5 }, { "b", 1 } });
Console.WriteLine(result2); //503

The first example is the same with the example below: the second way uses explicitly the DefaultParser, which can be later overriden in order to use a custom Parser.

//The example below uses explicitly the DefaultParser.
var app = App.GetParserApp<DefaultParser>();
var parser = app.Services.GetParser();
double result = (double)parser.Evaluate("-5.0+2*a", new() { { "a", 5.0 } });

Let's use some functions already defined in the DefaultParser:

double result3 = (double)App.Evaluate("cosd(ph)^2+sind(ph)^2", new() { { "ph", 45 } });
Console.WriteLine(result3); //  1.0000000000000002

...and some constants used in the DefaultParser:

Console.WriteLine(App.Evaluate("5+2*cos(pi)+3*ln(e)")); //will return 5 - 2 + 3 -> 6

DefaultParser examples #2 (custom functions)

That was the boring stuff, let's start adding some custom functionality. Let's add a custom function add3 that takes 3 arguments. For this purpose, we create a new subclass of DefaultParser. Note that we can add custom logging via dependency injection (some more examples will follow on this). For the moment, ignore the constructor. We assume that the add3 functions sums its 3 arguments with a specific weight.

private class SimpleFunctionParser : DefaultParser
{
    public SimpleFunctionParser(ILogger<Parser> logger, ITokenizer tokenizer, IOptions<TokenizerOptions> options) : base(logger, tokenizer, options)
    {
    }

    protected override object EvaluateFunction(Node<Token> functionNode, Dictionary<Node<Token>, object> nodeValueDictionary)
    {
        double[] a = GetDoubleFunctionArguments(functionNode, nodeValueDictionary);

        return functionNode.Text.ToLower() switch
        {
            "add3" => a[0] + 2 * a[1] + 3 * a[2],
            //for all other functions use the base class stuff (DefaultParser)
            _ => base.EvaluateFunction(functionNode, nodeValueDictionary)
        };
    }
}

Let's use our first customized Parser:

var parser = App.GetCustomParser<SimpleFunctionParser>();
double result = (double)parser.Evaluate("8 + add3(5.0,g,3.0)", new() { { "g", 3 } }); // will return 8 + (5 + 2 * 3 + 3 * 3.0) i.e -> 28

Single type parsing

If we want to parse an expression that deals with a single data type, then we can avoid the use of creating a custom parser, using the Parser.Evaluate function. In the example below, we assume that the expression contains only int data types.

//we use the base Parser here
var parserApp = App.GetParserApp<Parser>();
var parser = parserApp.Services.GetParser();

int result = parser.Evaluate<int>( //returns 860
    "a+f10(8+5) + f2(321+asd*2^2)",
    (s) => int.Parse(s),
    variables:  new () {
        { "a", 8 },
        { "asd", 10 } },
    binaryOperators: new () {
        { "+",(v1,v2)=>v1+v2} ,
        { "*", (v1, v2) => v1 * v2 },
        { "^",(v1,v2)=>(int)Math.Pow(v1,v2)}  },
    funcs1Arg:
    new () {
        { "f10", (v) => 10 * v } ,
        { "f2", (v) => 2 * v }}
    );

From the declaration of the function below, we can see that the Evaluate function supports functions from up to 3 arguments and the definition of custom operators. As shown in the example above, it is best to use the named parameters syntax.

 V Evaluate<V>(
        string s,
        Func<string, V> literalParser = null,
        Dictionary<string, V> variables = null,
        Dictionary<string, Func<V, V, V>> binaryOperators = null,
        Dictionary<string, Func<V, V>> unaryOperators = null,

        Dictionary<string, Func<V, V>>? funcs1Arg = null,
        Dictionary<string, Func<V, V, V>>? funcs2Arg = null,
        Dictionary<string, Func<V, V, V, V>>? funcs3Arg = null
        );

Custom Parsers

Any Parser that uses custom types should inherit the Parser base class. Each custom parser should override the methods:

• Evaluate: if there is at least one "constant" such as pi, which should be defined by default.
• EvaluateUnaryOperator : if there is at least one unary operator
• EvaluateLiteral: if there is at least one literal value such as 0.421. In most cases a simple parse function can be called for a double or int.
• EvaluateOperator: if there is at least one binary operator
• EvaluateFunction: if there is at least one function. It is best to understand how to override these functions in the example implementations below. Note that some Node functions are used, which are explained later in the text (namely the methods GetUnaryArgument, GetBinaryArguments, GetFunctionArguments).

Custom parser examples #1: ComplexParser

Another ready to use Parser is the ComplexParser for complex arithmetic. The application of the Parser for Complex numbers is a first application of a custom data type (i.e. other that double). Let's see the implementation of the ComplexParser to clarify how a generic custom parser is implemented:

using System.Numerics;

namespace ParserLibrary.Parsers;

public class ComplexParser : Parser
{
    public ComplexParser(ILogger<Parser> logger, ITokenizer tokenizer, IOptions<TokenizerOptions> options) : base(logger, tokenizer, options)
    { }

    protected override object Evaluate(List<Token> postfixTokens, Dictionary<string, object> variables = null)
    {
        if (variables is null) variables = new();

        //we define "constants" if they are not already defined
        if (!variables.ContainsKey("i")) variables.Add("i", Complex.ImaginaryOne);
        if (!variables.ContainsKey("j")) variables.Add("j", Complex.ImaginaryOne);
        if (!variables.ContainsKey("pi")) variables.Add("pi", new Complex(Math.PI, 0));
        if (!variables.ContainsKey("e")) variables.Add("e", new Complex(Math.E, 0));

        return base.Evaluate(postfixTokens, variables);
    }

    protected override object EvaluateLiteral(string s) =>
        double.Parse(s, CultureInfo.InvariantCulture);


    #region Auxiliary functions to get operands

    public Complex GetComplexUnaryOperand(Node<Token> operatorNode, Dictionary<Node<Token>, object> nodeValueDictionary)
    {
        var arg = operatorNode.GetUnaryArgument(
             _options.TokenPatterns.UnaryOperatorDictionary[operatorNode.Text].Prefix,
             nodeValueDictionary);

        if (arg is double || arg is int) return new Complex(Convert.ToDouble(arg), 0);
        else return (Complex)arg;
    }

    public (Complex Left, Complex Right) GetComplexBinaryOperands(Node<Token> operatorNode, Dictionary<Node<Token>, object> nodeValueDictionary)
    {
        var operands = operatorNode.GetBinaryArguments(nodeValueDictionary);

        return (Left: operands.LeftOperand is double || operands.LeftOperand is int ?
            new Complex(Convert.ToDouble(operands.LeftOperand), 0) : (Complex)operands.LeftOperand,
                 Right: operands.RightOperand is double || operands.RightOperand is int ?
            new Complex(Convert.ToDouble(operands.RightOperand), 0) : (Complex)operands.RightOperand);
    }

    public Complex[] GetComplexFunctionArguments(Node<Token> functionNode, Dictionary<Node<Token>, object> nodeValueDictionary)
    {
        return functionNode.GetFunctionArguments(
            _options.TokenPatterns.ArgumentSeparator,
            nodeValueDictionary).Select(arg =>
     {
         if (arg is double || arg is int) return new Complex(Convert.ToDouble(arg), 0);
         else return (Complex)arg;
     }).ToArray();
    }

    #endregion

    protected override object EvaluateUnaryOperator(Node<Token> operatorNode, Dictionary<Node<Token>, object> nodeValueDictionary)
    {
        Complex operand = GetComplexUnaryOperand(operatorNode, nodeValueDictionary);

        switch (operatorNode.Text)
        {
            case "-": return -operand;
            case "+": return operand;
            default: return base.EvaluateUnaryOperator(operatorNode, nodeValueDictionary);
        }
    }


    protected override object EvaluateOperator(Node<Token> operatorNode, Dictionary<Node<Token>, object> nodeValueDictionary)
    {
        (Complex left, Complex right) = GetComplexBinaryOperands(operatorNode, nodeValueDictionary);

        switch (operatorNode.Text)
        {
            case "+": return Complex.Add(left, right);
            case "-": return left - right;
            case "*": return left * right;
            case "/": return left / right;
            case "^": return Complex.Pow(left, right);
            default: return base.EvaluateOperator(operatorNode, nodeValueDictionary);

        }
    }

    protected const double TORAD = Math.PI / 180.0, TODEG = 180.0 * Math.PI;

    //HashSet<string> funcsWith2Args = new() { "logn", "pow", "round" };

    protected override object EvaluateFunction(Node<Token> functionNode, Dictionary<Node<Token>, object> nodeValueDictionary)
    {
        string functionName = functionNode.Text.ToLower();

        Complex[] a = GetComplexFunctionArguments(functionNode, nodeValueDictionary);

        switch (functionName)
        {
            case "abs": return Complex.Abs(a[0]);
            case "acos": return Complex.Acos(a[0]);
            case "acosd": return Complex.Acos(a[0]) * TODEG;
            case "asin": return Complex.Asin(a[0]);
            case "asind": return Complex.Asin(a[0]) * TODEG;
            case "atan": return Complex.Atan(a[0]);
            case "atand": return Complex.Atan(a[0]) * TODEG;
            case "cos": return Complex.Cos(a[0]);
            case "cosd": return Complex.Cos(a[0] * TORAD);
            case "cosh": return Complex.Cosh(a[0]);
            case "exp": return Complex.Exp(a[0]);
            case "log":
            case "ln": return Complex.Log(a[0]);
            case "log10": return Complex.Log10(a[0]);
            case "log2": return Complex.Log(a[0]) / Complex.Log(2);
            case "logn": return Complex.Log(a[0]) / Complex.Log(a[1]);
            case "pow": return Complex.Pow(a[0], a[1]);
            case "round": return new Complex(Math.Round(a[0].Real, (int)a[1].Real), Math.Round(a[0].Imaginary, (int)a[1].Real));
            case "sin": return Complex.Sin(a[0]);
            case "sind": return Complex.Sin(a[0] * TORAD);
            case "sinh": return Complex.Sinh(a[0]);
            case "sqr":
            case "sqrt": return Complex.Sqrt(a[0]);
            case "tan": return Complex.Tan(a[0]);
            case "tand": return Complex.Tan(a[0] * TORAD);
            case "tanh": return Complex.Tanh(a[0]);
        }

        return base.EvaluateFunction(functionNode, nodeValueDictionary);
    }

}

Below is an example of usage of the ComplexParser:

using System.Numerics; //needed if we want to further use the result
...
var cparser = App.GetCustomParser<ComplexParser>();

//unless we override the i or j variables, both are considered to correspond to the imaginary unit
//NOTE: because i is used as a variable (internally), the syntax for the imaginary part should be 3*i, NOT 3i
Complex result = (Complex)cparser.Evaluate("(1+3*i)/(2-3*i)"); 
Console.WriteLine(result); // (-0.5384615384615385, 0.6923076923076924)

//another one with a variable (should give the same result) 
Complex result2 = (Complex)cparser.Evaluate("(1+3*i)/b", new() { { "b", new Complex(2,-3)} });
Console.WriteLine(result2); //same result

//and something more "complex", using nested functions: note that the complex number is returned as a string in the form (real, imaginary) 
Console.WriteLine(cparser.Evaluate("cos((1+i)/(8+i))")); //(0.9961783779071353, -0.014892390041785901)
Console.WriteLine(cparser.Evaluate("round(cos((1+i)/(8+i)),4)")); //(0.9962, -0.0149)

Console.WriteLine(cparser.Evaluate("round(exp(i*pi),8)")); //(-1, 0)  (Euler is correct!)

Custom parser examples #2: Vector3Parser

Vector3Parser is the corresponding parser for vector arithmetic. The Vector3 is also included in the System.Numerics namespace. The implementation of the Vector3Parser is similar to the implementation of the ComplexParser. The same methods from the Parser base class are overriden.

namespace ParserLibrary.Parsers;

using ParserLibrary.Tokenizers;
using System.Numerics;

public class Vector3Parser : Parser
{
    public Vector3Parser(ILogger<Parser> logger, ITokenizer tokenizer, IOptions<TokenizerOptions> options) : base(logger, tokenizer, options)
    { }

    protect override object Evaluate(List<Token> postfixTokens, Dictionary<string, object> variables = null)
    {
        if (variables is null) variables = new();

        if (!variables.ContainsKey("pi")) variables.Add("pi", DoubleToVector3((float)Math.PI));
        if (!variables.ContainsKey("e")) variables.Add("e", DoubleToVector3((float)Math.E));

        if (!variables.ContainsKey("ux")) variables.Add("ux", Vector3.UnitX);
        if (!variables.ContainsKey("uy")) variables.Add("uy", Vector3.UnitY);
        if (!variables.ContainsKey("uz")) variables.Add("uz", Vector3.UnitZ);

        return base.Evaluate(postfixTokens, variables);
    }

    protected override object EvaluateLiteral(string s) =>
        float.Parse(s, CultureInfo.InvariantCulture);


    #region Auxiliary functions to get operands

    public static Vector3 DoubleToVector3(object arg)
        => new Vector3(Convert.ToSingle(arg), Convert.ToSingle(arg), Convert.ToSingle(arg));


    public static bool IsNumeric(object arg) =>
           arg is double || arg is int || arg is float;

    public static Vector3 GetVector3(object arg) =>
            IsNumeric(arg) ? DoubleToVector3(arg) : (Vector3)arg;

    public Vector3 GetVector3UnaryOperand(Node<Token> operatorNode, Dictionary<Node<Token>, object> nodeValueDictionary)
    {
        var arg = operatorNode.GetUnaryArgument(
             _options.TokenPatterns.UnaryOperatorDictionary[operatorNode.Text].Prefix,
             nodeValueDictionary);

        return GetVector3(arg);
    }

    public (Vector3 Left, Vector3 Right) GetVector3BinaryOperands(Node<Token> operatorNode, Dictionary<Node<Token>, object> nodeValueDictionary)
    {
        var operands = operatorNode.GetBinaryArguments(nodeValueDictionary);

        return (Left: GetVector3(operands.LeftOperand),
                 Right: GetVector3(operands.RightOperand));
    }

    public Vector3[] GetVector3FunctionArguments(Node<Token> functionNode, Dictionary<Node<Token>, object> nodeValueDictionary)
    {
        return functionNode
            .GetFunctionArguments(_options.TokenPatterns.ArgumentSeparator, nodeValueDictionary)
            .Select(arg => GetVector3(arg)).ToArray();
    }

    #endregion

    protected override object EvaluateUnaryOperator(Node<Token> operatorNode, Dictionary<Node<Token>, object> nodeValueDictionary)
    {
        Vector3 operand = GetVector3UnaryOperand(operatorNode, nodeValueDictionary);

        return operatorNode.Text switch
        {
            "-" => -operand,
            "+" => operand,
            "!" => Vector3.Normalize(operand),
            _ => base.EvaluateUnaryOperator(operatorNode, nodeValueDictionary)
        };
    }


    protected override object EvaluateOperator(Node<Token> operatorNode, Dictionary<Node<Token>, object> nodeValueDictionary)
    {
        (Vector3 left, Vector3 right) = GetVector3BinaryOperands(operatorNode, nodeValueDictionary);

        return operatorNode.Text switch
        {
            "+" => left + right,
            "-" => left - right,
            "*" => left * right,
            "/" => left / right,
            "^" => Vector3.Cross(left, right),
            "@" => Vector3.Dot(left, right),
            _ => base.EvaluateOperator(operatorNode, nodeValueDictionary)
        };
    }

    protected override object EvaluateFunction(Node<Token> functionNode, Dictionary<Node<Token>, object> nodeValueDictionary)
    {
        string functionName = functionNode.Text.ToLower();
        Vector3[] a = GetVector3FunctionArguments( functionNode, nodeValueDictionary);

        switch (functionName)
        {
            case "abs": return Vector3.Abs(a[0]);
            case "cross": return Vector3.Cross(a[0], a[1]);
            case "dot": return Vector3.Dot(a[0], a[1]);
            case "dist": return Vector3.Distance(a[0], a[1]);
            case "dist2": return Vector3.DistanceSquared(a[0], a[1]);
            case "lerp": return Vector3.Lerp(a[0], a[1], a[2].X);
            case "length": return a[0].Length();
            case "length2": return a[0].LengthSquared();
            case "norm": return Vector3.Normalize(a[0]);
            case "sqr":
            case "sqrt": return Vector3.SquareRoot(a[0]);
            case "round":
                return new Vector3(
                (float)Math.Round(a[0].X, (int)a[1].X),
                (float)Math.Round(a[0].Y, (int)a[1].X),
                (float)Math.Round(a[0].Z, (int)a[1].X));
        }
        return base.EvaluateFunction(functionNode, nodeValueDictionary);
    }
}

Let's see some example usage too:

using System.Numerics; //needed if we want to further use the result
...
var vparser = App.GetCustomParser<Vector3Parser>();

Vector3 v1 = new Vector3(1, 4, 2),
    v2 = new Vector3(2, -2, 0);

Console.WriteLine(vparser.Evaluate("!(v1+3*v2)", //! means normalize vector
   new() { { "v1", v1 }, { "v2", v2 } })); //<0.92717266. -0.26490647. 0.26490647>

Console.WriteLine(vparser.Evaluate("10 + 3 * v1^v2", // ^ means cross product
   new() { { "v1", v1 }, { "v2", v2 } })); //<22. 22. -20>


Console.WriteLine(vparser.Evaluate("v1@v2", // @ means dot product
   new() { { "v1", v1 }, { "v2", v2 } })); //-6

Console.WriteLine(vparser.Evaluate("lerp(v1, v2, 0.5)", // lerp (linear combination of vectors)
   new() { { "v1", v1 }, { "v2", v2 } })); //<1.5, 1. 1>

Console.WriteLine(vparser.Evaluate("6*ux -12*uy + 14*uz")); //<6. -12. 14>

Custom parser examples #3: CustomTypeParser

Let's assume that we have a class named Item, which we want to interact with integer numbers and with other Item objects:

public class Item
{
    public string Name { get; set; }

    public int Value { get; set; } = 0;

    //we define a custom operator for the type to simplify the evaluateoperator example later
    //this is not 100% needed, but it keeps the code in the CustomTypeParser simpler
    public static Item operator +(int v1, Item v2) =>
        new Item { Name = v2.Name , Value = v2.Value + v1 };
    public static Item operator +(Item v2, int v1) =>
        new Item { Name = v2.Name, Value = v2.Value + v1 };

    public static Item operator +(Item v1, Item v2) =>
        new Item { Name = $"{v1.Name} {v2.Name}", Value = v2.Value + v1.Value };

    public override string ToString() => $"{Name} {Value}";

}

A custom parser that uses custom types derives from the Parser class. Because the Parser class does not assume any type in advance, we should override the EvaluateLiteral function which is used to parse the integer numbers in the string. In the following example we define the + operator, which can take an Item object or an int for its operands. We also define the add function, which assumes that the first argument is an Item and the second argument is an int. In practice, the Function syntax is usually stricter regarding the type of the arguments, so it is easier to write its implementation:

public class CustomTypeParser : Parser
{
    public CustomTypeParser(ILogger<Parser> logger, ITokenizer tokenizer, IOptions<TokenizerOptions> options) : base(logger, tokenizer, options)
    { }


    //we assume that literals are integer numbers only
    protected override object EvaluateLiteral(string s) => int.Parse(s);

    protected override object EvaluateOperator(Node<Token> operatorNode, Dictionary<Node<Token>, object> nodeValueDictionary)
    {
        (object LeftOperand, object RightOperand) = operatorNode.GetBinaryArguments(nodeValueDictionary);

        //we assume that the + operator is supported 
        if (operatorNode.Text == "+")
        {
            //we manage all combinations of Item/Item, Item/int, int/Item combinations here
            if (LeftOperand is Item && RightOperand is Item)
                return (Item)LeftOperand + (Item)RightOperand;

            return LeftOperand is Item ?  (Item)LeftOperand + (int)RightOperand : (int)LeftOperand + (Item)RightOperand;
        }

        return base.EvaluateOperator(operatorNode, nodeValueDictionary);
    }

    protected override object EvaluateFunction(Node<Token> functionNode, Dictionary<Node<Token>, object> nodeValueDictionary)
    {
        var a = functionNode.GetFunctionArguments(count: 2, nodeValueDictionary);

        return functionNode.Text switch
        {
            "add" => (Item)a[0] + (int)a[1],
            _ => base.EvaluateFunction(functionNode, nodeValueDictionary)
        };
    }

}

Now we can use the CustomTypeParser for parsing our custom expression:

var parser = App.GetCustomParser<CustomTypeParser>();
Item result = (Item)parser.Evaluate("a + add(b,4) + 5",
    new() {
        {"a", new Item { Name="foo", Value = 3}  },
        {"b", new Item { Name="bar"}  }
    });
Console.WriteLine(result); // foo bar 12

more examples to follow soon...

Customizing ParserLibrary

appsettings.json configuration file

The appsettings.json configuration file is crucial, when the user wants to have precise control over the tokenizer and the logger as well. The library is configured to use Serilog for debugging and informational purposes. The Serilog section (see Serilog configuration for more) typically can be configured to output to the Console and/or to an external file. In order to show less messages in the case below, we can use "Information" instead of "Debug" for the Console output. The logger can be accessed via the _logger field in every Parser subclass, so we can output debug/informational/critical messages to the screen/to a file in a controlled manner. The _logger field is of type ILogger, so Serilog is not the only type of logger that can be used (although it is recommended). The tokenizer options include the following properties:

• caseSensitive : if false, then the tokenizer/parser should be case insensitive
• tokenPatterns : this includes the regular expression patterns or simple string characters for identifying any token
  • identifier : regular expression to identify variable and function names as tokens
  • literal : regular expresssion to identify all literal -typically numeric- values
  • openParenthesis, closeParenthesis, argumentSeparator : the characters which correspond to the parenthesis pair and the argument separator
  • unary : the unary array defines all unary operators. The priority of unary operator priority is in general higher than the binary operators
  • operators : the operators array defines all binary operators. All binary operators are left-to-right by default except if specified otherwise (just like the exponent operator '^') Operators with higher priority have higher precedence for the calculations. The priority is overriden as always via the use of parentheses, which are identified as defined above.

{
  "Serilog": {
    "MinimumLevel": "Debug",
    "WriteTo": [
      {
        "Name": "Console",
        "Args": {
          "restrictedToMinimumLevel": "Debug"
        }
      }
    ]
  },

  "tokenizer":  {
    "version": "1.0",
    "caseSensitive": false,
    "tokenPatterns": {
      "identifier": "[A-Za-z_]\\w*",
      "literal": "\\b(?:\\d+(?:\\.\\d*)?|\\.\\d+)\\b",
      "openParenthesis": "(",
      "closeParenthesis": ")",
      "argumentSeparator": ",",

      "unary": [
        {
          "name": "-",
          "priority": 3,
          "prefix": true
        },
        {
          "name": "+",
          "priority": 3,
          "prefix": true
        },
        {
          "name": "!",
          "priority": 3,
          "prefix": true
        },
        {
          "name": "%",
          "priority": 3,
          "prefix": false
        },
        {
          "name": "*",
          "priority": 3,
          "prefix": false
        }
      ],
      "operators": [
        {
          "name": ",",
          "priority": 0
        },
        {
          "name": "+",
          "priority": 1
        },
        {
          "name": "-",
          "priority": 1
        },
        {
          "name": "*",
          "priority": 2
        },
        {
          "name": "/",
          "priority": 2
        },
        {
          "name": "^",
          "priority": 4,
          "lefttoright": false
        },
        {
          "name": "@",
          "priority": 4
        }
      ]
    }
  }
}

The appsettings.json file should exist in the same folder with the executable, so be sure that the file is set to be copied to the output directory. For example, inside the project file, the following block should be included:

<ItemGroup>
    <EmbeddedResource Include="appsettings.json">
        <CopyToOutputDirectory>PreserveNewest</CopyToOutputDirectory>
    </EmbeddedResource>
</ItemGroup>

Note that we are not bound to use the specific name for the configuration file. For example, we might want to keep the appsettings.json file for the logger configuration, and have another file parsersettings.json for the tokenizer (which should be also in the same directory with the executable). In order to define the parsersettings.json file, we define it as an argument when retrieving the IHost app instance, or immediately the IParser parser instance via the following calls:

var app = App.GetParserApp<DefaultParser>("parsersettings.json");
var parser = app.Services.GetParser();

//or to immediately get the parser

var parser2 = App.GetCustomParser<DefaultParser>("parsersettings.json");

Note, that in both cases above, the appsettings.json is also read (if found). The parsersettings.json file has higher priority, in case there are some conflicting options.

An example of using the internal fields _options of type TokenizerOptions and _logger of type ILogger can be shown below, by modifying the CustomTypeParser slightly modifying the example above:

...
protected override object EvaluateOperator(Node<Token> operatorNode, Dictionary<Node<Token>, object> nodeValueDictionary)
{
    (object LeftOperand, object RightOperand) = operatorNode.GetBinaryArguments(nodeValueDictionary);

    if (operatorNode.Text == "+")
    {
        //ADDED:
        _logger.LogDebug("Adding with + operator {left} and {right}", LeftOperand, RightOperand);

        if (LeftOperand is Item && RightOperand is Item)
            return (Item)LeftOperand + (Item)RightOperand;

        return LeftOperand is Item ?  (Item)LeftOperand + (int)RightOperand : (int)LeftOperand + (Item)RightOperand;
    }

    return base.EvaluateOperator(operatorNode, nodeValueDictionary);
}

protected override object EvaluateFunction(Node<Token> functionNode, Dictionary<Node<Token>, object> nodeValueDictionary)
{
    var a = functionNode.GetFunctionArguments(2, nodeValueDictionary);

    //return functionNode.Text switch
    //MODIFIED: use the CaseSensitive property from the options in the configuration files
    return _options.CaseSensitive ? functionNode.Text : functionNode.Text.ToLower() switch
    {
        "add" => (Item)a[0] + (int)a[1],
        _ => base.EvaluateFunction(functionNode, nodeValueDictionary)
    };
}

If you want to extend your own IHostBuilder then this is easily feasible via the AddParserLibrary extension method. This includes the ITokenizer, the IParser and the TokenizerOptions. Examples of using the extension methods are given below:

using Microsoft.Extensions.DependencyInjection;
using Microsoft.Extensions.Options;
using ParserLibrary;
...
 IHostBuilder builder = Host.CreateDefaultBuilder()
   ...
   .ConfigureServices((context, services) =>
    {
        services
        //NOTE: TParser should be one of the derived parsers such as DefaultParser
        .AddParserLibrary<TParser>(context) //extension method. 
        ...
        ;
    })
    ...
var app = builder.Build();
...

var parser1 = app.Services.GetService<IParser>(); 
//or
var parser2 = app.Services.GetParser(); //extension method

//sample calls if we want to retrieve instances of Tokenizer and TokenizerOptions outside a subclassed Parser
var tokenizer1 = app.Services.GetService<ITokenizer>();
//or
var tokenizer2 = app.Services.GetTokenizer(); //extension method

var tokenizerOptions = app.Services.GetService<IOptions<TokenizerOptions>>().Value;

Parsers

Every Parser subclass adapts to the IParser interface and typically every Parser derives from the Parser base class. All derived Parsers use parenthesis pairs ((, )) by default to override the operators priority. The priority of the operators is internally defined in the DefaultParser. A custom Parser can override the default operator priority and use other than the common operators using an external appsettings.json file, which will be analyzed in later examples.

DefaultParser

The DefaultParser class for the moment accepts the followig operators:

• +: plus sign (unary) and plus (binary)
• -: negative sign (unary) and minus (binary)
• *: multiplication
• /: division
• ^: power

and the following functions:

• abs(x): Absolute value
• acos(x): Inverse cosine (in radians)
• acosd(x): Inverse cosine (in degrees)
• acosh(x): Inverse hyperbolic cosine
• asin(x): Inverse sine (in radians)
• asind(x): Inverse sine (in degrees)
• asinh(x): Inverse hyperbolic sine
• atan(x): Inverse tangent (in radians)
• atand(x): Inverse tangent (in degrees)
• atan2(y,x): Inverse tangent (in radians)
• atan2d(y,x): Inverse tangent (in degrees)
• atanh(x): Inverse hyperbolic tangent
• cbrt(x): Cube root
• cos(x): Cosine (x in radians)
• cosd(x): Cosine (x in degrees)
• cosh(x): Hyperbolic cosine
• exp(x): Exponential function (e^x)
• log(x) / ln(x): Natural logarithm
• log10(x): Base 10 logarithm
• log2(x): Base 2 logarithm
• logn(x,n): Base n logarithm
• max(x,y): Maximum
• min(x,y): Minimum
• pow(x,y): Power function (x^y)
• round(x,y): Round to y decimal digits
• sin(x): Sine (x in radians)
• sind(x): Sine (x in degrees)
• sinh(x): Hyperbolic sine
• sqr(x) / sqrt(x): Square root
• tan(x): Tangent (x in radians)
• tand(x): Tangent (x in degrees)
• tanh(x): Hyperbolic tangent

The following constants are also defined unless the same names are overriden by the variables dictionary argument when calling the Evaluate function:

• pi : the number π (see π)
• e : the Euler's number (see e)
• phi : the golden ratio φ (see φ)

ComplexParser

The ComplexParser class for the moment accepts the followig operators:

• +: plus sign (unary) and plus (binary)
• -: negative sign (unary) and minus (binary)
• *: multiplication
• /: division
• ^: power

and the following functions:

• abs(z): Absolute value
• acos(z): Inverse cosine (in radians)
• acosd(z): Inverse cosine (in degrees)
• asin(z): Inverse sine (in radians)
• asind(z): Inverse sine (in degrees)
• atan(z): Inverse tangent (in radians)
• atand(z): Inverse tangent (in degrees)
• cos(z): Cosine (z in radians)
• cosd(z): Cosine (z in degrees)
• cosh(z): Hyperbolic cosine
• exp(z): Exponential function (e^z)
• log(z) / ln(z): Natural logarithm
• log10(z): Base 10 logarithm
• log2(z): Base 2 logarithm
• logn(z,n): Base n logarithm
• pow(z,y): Power function (z^y)
• round(z,y): Round to y decimal digits
• sin(z): Sine (z in radians)
• sind(z): Sine (z in degrees)
• sinh(z): Hyperbolic sine
• sqr(z) / sqrt(z): Square root
• tan(z): Tangent (z in radians)
• tand(z): Tangent (z in degrees)
• tanh(z): Hyperbolic tangent

The following constants are also defined unless the same names are overriden by the variables dictionary argument when calling the Evaluate function:

• i , j: the imaginary unit (see imaginary unit)
• pi: the number π (see π)
• e: the Euler's number (see e)

VectorParser

The Vector3Parser class for the moment accepts the followig operators:

• +: plus sign (unary) and plus (binary)
• -: negative sign (unary) and minus (binary)
• *: multiplication (element-wise)
• /: division (element-wise)
• ^: cross product (e.g. v1 ^ v2)
• @: dot vector (e.g. v1 @ v2)
• !: normalize vector (e.g. !v1)

and the following functions:

• abs(v): Absolute value
• cross(v1,v2): Cross product (same result with ^)
• dot(v1,v2): Dot product (same result with @)
• dist(v1,v2): Distance
• dist2(v1,v2): Distance squared
• lerp(v1,v2,f): Linear combination of v1, v2
• length(v): Vector length
• length2(v): Vector length squared
• norm(v): Normalize (same result with !)
• sqr(v) / sqrt(v): Square root
• round(v,f): Round to f decimal digits

The following constants are also defined unless the same names are overriden by the variables dictionary argument when calling the Evaluate function:

• pi: the number π (see π)
• e: the Euler's number (see e)
• ux: the unit vector X
• uy: the unit vector Y
• uz: the unit vector Z

The Expression Tree

The project is based on Expression binary trees. The classes Node<T>, NodeBase and Tree (all 3 in namespace ParserLibrary.ExpressionTree) are comprising everything we need about binary trees. In fact due to the fact that Node<T> is generic, we can use it for other uses as well. Each Parser uses a Tokenizer to facilitate any parsing. For the example below, we get the in-order, pre-order and post-order Nodes for the root node of the expression tree. For each Tree or a specific Node, we can print to the console a depiction of the binary tree. Visualizing the epressing tree is great for understanding the operations priorities

string expr = "a+tan(8+5) + sin(321+afsd*2^2)";
var parser = App.GetDefaultParser();
var tokenizer = app.Services.GetTokenizer();
var tree = parser.GetExpressionTree(expr);
Console.WriteLine("Post order traversal: " + string.Join(" ", tree.Root.PostOrderNodes().Select(n => n.Text)));
Console.WriteLine("Pre order traversal: " + string.Join(" ", tree.Root.PreOrderNodes().Select(n => n.Text)));
Console.WriteLine("In order traversal: " + string.Join(" ", tree.Root.InOrderNodes().Select(n => n.Text)));
tree.Print(withSlashes:false) ;

The code above prints the following to the Console:

Post order traversal: a 8 5 + tan + 321 afsd 2 2 ^ * + sin +
Pre order traversal: + + a tan + 8 5 sin + 321 * afsd ^ 2 2
In order traversal: a + tan 8 + 5 + sin 321 + afsd * 2 ^ 2


      +
   ┌──└───┐
   +     sin
  ┌└─┐     └┐
  a tan     +
      └┐  ┌─└─┐
       + 321  *
      ┌└┐   ┌─└┐
      8 5 afsd ^
              ┌└┐
              2 2

Tree<T>

The Tree<T> class contains the following important members:

• Root [Node<T>]: The Root Node of the tree. This the only node in the Tree which has no parent nodes.
• Print [void]: Prints the Tree to the console using 2 available variations controlled by the argument withSlashes.
• Count [int]: The total number of nodes in the tree.
• GetHeight() [int]: The height of the binary tree. For example a tree with a single root node and 2 leafs has a height of 1.
• GetLeafNodesCount() [int]: The number of leaf nodes.

NodeBase

The NodeBase class contains the core of the binary tree functionality:

• Text [string]: The text representation of the node
• Left [NodeBase]: The left child node
• Right [NodeBase]: The right child node
• PreOrderNodes [IEnumerable<NodeBase>): All nodes starting from the current node, in pre-order arrangement
• PostOrderNodes [IEnumerable<NodeBase>): All nodes starting from the current node, in post-order arrangement
• InOrderNodes [IEnumerable<NodeBase>): All nodes starting from the current node, in in-order arrangement

Node<T>

The Node<T> inherits NodeaBase and includes some additional members which are expression-oriented:

• Value<T>: The value of the node. The inherited Text property should be a string representation of this value. To facilitate the retrieval of child nodes depending on the type of each token, some methods of the Node<T> are very practical:
• GetUnaryArgument [object]: Retrieves the value of the child node, assuming that the token represents a unary operator (such as unary -).
• GetBinaryArguments [(object LeftOperand, object RightOperand)]: Retrieves the value of the two operand child nodes, assuming that the token represents a binary operator (such as * and ^).
• GetFunctionArguments [(object[]]: Retrieves the values of the function argument nodes, assuming that the token represents a function token operator (such as sin). Note, that we are not using any generic types for the node values. The array of objects allow the single returned array to return instances of different daa types.

more documentation to follow soon...