JSONManager.cs

using System.Collections.Generic;
using Newtonsoft.Json;
using JsonSubTypes;
using System.Linq.Expressions;
using System.Reflection;
using UnityEngine.UIElements;
using System;
using static UnityEngine.Windows.Speech.PhraseRecognitionSystem;
using System.Linq;

public static class JSONManager
{

    public static class MMTURIs
    {
        public static readonly string Point = "http://mathhub.info/MitM/core/geometry?3DGeometry?point";
        public static readonly string Tuple = "http://gl.mathhub.info/MMT/LFX/Sigma?Symbols?Tuple";
        public static readonly string LineType = "http://mathhub.info/MitM/core/geometry?Geometry/Common?line_type";
        public static readonly string LineOf = "http://mathhub.info/MitM/core/geometry?Geometry/Common?lineOf";

        public static readonly string OnLine = "http://mathhub.info/MitM/core/geometry?Geometry/Common?onLine";
        public static readonly string Ded = "http://mathhub.info/MitM/Foundation?Logic?ded";
        public static readonly string Eq = "http://mathhub.info/MitM/Foundation?Logic?eq";
        public static readonly string Metric = "http://mathhub.info/MitM/core/geometry?Geometry/Common?metric";
        public static readonly string Angle = "http://mathhub.info/MitM/core/geometry?Geometry/Common?angle_between";
        public static readonly string Sketch = "http://mathhub.info/MitM/Foundation?InformalProofs?proofsketch";
        public static readonly string RealLit = "http://mathhub.info/MitM/Foundation?RealLiterals?real_lit";

        public static readonly string ParallelLine = "http://mathhub.info/MitM/core/geometry?Geometry/Common?parallelLine";
        //public static readonly string RectangleFact = "http://mathhub.info/FrameIT/frameworld?FrameITRectangles?rectangleType";
        //public static readonly string RectangleFactmk = "http://mathhub.info/FrameIT/frameworld?FrameITRectangles?mkRectangle";

        public static readonly string CircleType3d = "http://mathhub.info/FrameIT/frameworld?FrameITCircle?circleType3D";
        public static readonly string MkCircle3d = "http://mathhub.info/FrameIT/frameworld?FrameITCircle?circle3D";
        public static readonly string TriangleMiddlePoint = "http://mathhub.info/FrameIT/frameworld?FrameITTriangles?triangleMidPointWrapper";
        public static readonly string RadiusCircleMetric = "http://mathhub.info/FrameIT/frameworld?FrameITCircle?circleRadius";

        public static readonly string AreaCircle = "http://mathhub.info/FrameIT/frameworld?FrameITCircle?areaCircle";
        public static readonly string VolumeCone = "http://mathhub.info/FrameIT/frameworld?FrameITCone?volumeCone";
        public static readonly string ConeOfCircleApex = "http://mathhub.info/FrameIT/frameworld?FrameITCone?circleConeOf";

        public static readonly string ParametrizedPlane = "http://mathhub.info/MitM/core/geometry?Planes?ParametrizedPlane";
        public static readonly string pointNormalPlane = "http://mathhub.info/MitM/core/geometry?Planes?pointNormalPlane";
        public static readonly string OnCircle = "http://mathhub.info/FrameIT/frameworld?FrameITCircle?pointOnCircle";
        public static readonly string AnglePlaneLine = "http://mathhub.info/FrameIT/frameworld?FrameITCircle?angleCircleLine";
        public static readonly string OrthoCircleLine = "http://mathhub.info/FrameIT/frameworld?FrameITCircle?orthogonalCircleLine";

        public static readonly string TruncatedVolumeCone = "http://mathhub.info/FrameIT/frameworld?FrameITCone?truncatedConeVolume";
        public static readonly string CylinderVolume = "http://mathhub.info/FrameIT/frameworld?FrameITCylinder?cylinderVolume";
        public static readonly string EqualityCircles = "http://mathhub.info/FrameIT/frameworld?FrameITCircle?equalityCircles";
        public static readonly string UnEqualityCircles = "http://mathhub.info/FrameIT/frameworld?FrameITCircle?unequalityCircles";

        public static readonly string ParallelCircles = "http://mathhub.info/FrameIT/frameworld?FrameITCone?parallelCircles";
        public static readonly string RightAngle = "http://mathhub.info/FrameIT/frameworld?FrameITBasics?rightAngle";

        public static readonly string TestType = "http://mathhub.info/FrameIT/frameworld?FrameITCircle?xcircleType3D";
    }


    public static class MMTtoLambdaExpression<T>
    {
        private static LambdaExpression @default = Expression.Lambda(Expression.Default(typeof(T)), null);
        // TODO: Populate Dictionaries
        #region ExpressionDictionaries

        private static Dictionary<string, Func<LambdaExpression>> MMTtoLambdaMaker = new()
        {
            { "sin", 
                MakeSin},
            { "cos", 
                MakeCos},
        };

        private static Dictionary<string, ExpressionType> MMTtoBinaryExpressionType = new()
        {
            { "Add", 
                ExpressionType.Add},
            { "AddAssign", 
                ExpressionType.AddAssign},
            { "AddAssignChecked", 
                ExpressionType.AddAssignChecked},
            { "AddChecked", 
                ExpressionType.AddChecked},
            { "And", 
                ExpressionType.And},
            { "AndAlso", 
                ExpressionType.AndAlso},
            { "AndAssign", 
                ExpressionType.AndAssign},
            { "Assign", 
                ExpressionType.Assign},
            { "Divide", 
                ExpressionType.Divide},
            { "DivideAssign", 
                ExpressionType.DivideAssign},
            { "Equal", 
                ExpressionType.Equal},
            { "ExclusiveOr", 
                ExpressionType.ExclusiveOr},
            { "ExclusiveOrAssign", 
                ExpressionType.ExclusiveOrAssign},
            { "GreaterThan", 
                ExpressionType.GreaterThan},
            { "GreaterThanOrEqual", 
                ExpressionType.GreaterThanOrEqual},
            { "LeftShift", 
                ExpressionType.LeftShift},
            { "LeftShiftAssign", 
                ExpressionType.LeftShiftAssign},
            { "LessThan", 
                ExpressionType.LessThan},
            { "LessThanOrEqual", 
                ExpressionType.LessThanOrEqual},
            { "Modulo", 
                ExpressionType.Modulo},
            { "ModuloAssign", 
                ExpressionType.ModuloAssign},
            { "Multiply", 
                ExpressionType.Multiply},
            { "MultiplyAssign", 
                ExpressionType.MultiplyAssign},
            { "MultiplyAssignChecked", 
                ExpressionType.MultiplyAssignChecked},
            { "MultiplyChecked", 
                ExpressionType.MultiplyChecked},
            { "NotEqual", 
                ExpressionType.NotEqual},
            { "Or", 
                ExpressionType.Or},
            { "OrAssign", 
                ExpressionType.OrAssign},
            { "OrElse", 
                ExpressionType.OrElse},
            { "Power", 
                ExpressionType.Power},
            { "PowerAssign", 
                ExpressionType.PowerAssign},
            { "RightShift", 
                ExpressionType.RightShift},
            { "RightShiftAssign", 
                ExpressionType.RightShiftAssign},
            { "Subtract", 
                ExpressionType.Subtract},
            { "SubtractAssign", 
                ExpressionType.SubtractAssign},
            { "SubtractAssignChecked", 
                ExpressionType.SubtractAssignChecked},
            { "SubtractChecked", 
                ExpressionType.SubtractChecked},
        };

        private static Dictionary<string, ExpressionType> MMTtoUnaryExpressionType = new()
        {
            //{ "Constant", // Not Unary
            //    ExpressionType.Constant},
            { "Decrement", 
                ExpressionType.Decrement},
            { "Increment", 
                ExpressionType.Increment},
            { "Negate", 
                ExpressionType.Negate},
            { "NegateChecked", 
                ExpressionType.NegateChecked},
            { "Not", 
                ExpressionType.Not},
            { "OnesComplement", 
                ExpressionType.OnesComplement},
            { "PostDecrementAssign", 
                ExpressionType.PostDecrementAssign},
            { "PostIncrementAssign", 
                ExpressionType.PostIncrementAssign},
            { "PreDecrementAssign", 
                ExpressionType.PreDecrementAssign},
            { "PreIncrementAssign", 
                ExpressionType.PreIncrementAssign},
            { "UnaryPlus", 
                ExpressionType.UnaryPlus},
        };

        #endregion ExpressionDictionaries

        public static LambdaExpression MakeLambdaExpression(string URI)
        {
            if (MMTtoUnaryExpressionType.TryGetValue(URI, out var unnary_type))
            {
                ParameterExpression[] args = new ParameterExpression[] {
                    Expression.Parameter(typeof(T))
                };
                return Expression.Lambda(Expression.MakeUnary(unnary_type, args[0], typeof(T)), args);
            }
            else if (MMTtoBinaryExpressionType.TryGetValue(URI, out var binary_type))
            {
                ParameterExpression[] args = new ParameterExpression[] { 
                    Expression.Parameter(typeof(T)),
                    Expression.Parameter(typeof(T)) 
                };
                return Expression.Lambda(Expression.MakeBinary(binary_type, args[0], args[1]), args);
            }
            else if (MMTtoLambdaMaker.TryGetValue(URI, out var lamda_maker))
            {
                return lamda_maker();
            }

            throw new NotImplementedException("Could not map URI: \"" + URI + "\"");
        }

        private static Expression<Func<T, T>> ParseFuncTUUT<U>(Func<U,U> func)
            => (T x) => 
                (T) Convert.ChangeType(
                        func(
                            (U) Convert.ChangeType(
                                x, 
                                typeof(U)
                            )
                        ), 
                        typeof(T)
                    );

        private static LambdaExpression ExpresionFuncToLambda(Expression func, uint nTargs)
        {   
            ParameterExpression[] args = new ParameterExpression[nTargs];
            for (int i = 0; i < nTargs; i++)
                args[i] = Expression.Parameter(typeof(T));

            return Expression.Lambda(Expression.Invoke(func, args), args);
        }

        //TODO? more general/generics
        private static LambdaExpression ParseFuncTUUTToLambda<U>(Func<U, U> func)
            => ExpresionFuncToLambda(ParseFuncTUUT<U>(func), 1);

        private static LambdaExpression MakeSin()
            => default(T) switch // TODO? cleaner switch
            {
                float  => ParseFuncTUUTToLambda<float>(MathF.Sin),
                double => ParseFuncTUUTToLambda<double>(Math.Sin),
                _ => throw new NotImplementedException("Sinus for " + typeof(T))
            };

        private static LambdaExpression MakeCos()
            => default(T) switch
            {
                float  => ParseFuncTUUTToLambda<float>(MathF.Cos),
                double => ParseFuncTUUTToLambda<double>(Math.Cos),
                _ => throw new NotImplementedException("Sinus for " + typeof(T))
            };
    }


    public class URI
    {
        public string uri;

        public URI(string uri)
        {
            this.uri = uri;
        }
    }
    
    [JsonConverter(typeof(JsonSubtypes), "kind")]
    public class MMTTerm
    {
        string kind;

        virtual public LambdaExpression GetLambdaExpression()
            => Expression.Lambda(Expression.Empty(), null);
    }

    public class OMA : MMTTerm
    {
        public MMTTerm applicant;
        public List<MMTTerm> arguments;
        public string kind = "OMA";

        public OMA(MMTTerm applicant, List<MMTTerm> arguments)
        {
            this.applicant = applicant;
            this.arguments = arguments;
        }

        override public LambdaExpression GetLambdaExpression()
        {
            // local variable for each arguments
            ParameterExpression[] line_variable = new ParameterExpression[arguments.Count];

            // expression of computing arguments and assigning to corresponding variable
            Expression[] line_expression = new Expression[arguments.Count + 1];

            // unbound parameters a.k.a. all params of arguments
            List<ParameterExpression> father_param = new();

            for (int i = 0; i < arguments.Count; i++)
            {
                LambdaExpression
                    child_lambda = arguments[i].GetLambdaExpression();
                List<ParameterExpression>
                    child_params = child_lambda.Parameters.ToList();

                line_variable[i] = Expression.Variable(child_lambda.ReturnType);
                line_expression[i] = Expression.Assign(line_variable[i], Expression.Invoke(child_lambda, child_params));

                foreach (ParameterExpression arg in child_params)
                    father_param.Add(arg);
            }

            // invoke applicant with computed arguments
            line_expression[arguments.Count] = Expression.Invoke(applicant.GetLambdaExpression(), line_variable);

            // compile all this into LambdaExpression
            return Expression.Lambda(Expression.Block(line_variable, line_expression), father_param);
        }
    }

    public class OMS : MMTTerm
    {
        public string uri;
        public string kind = "OMS";

        public OMS(string uri)
        {
            this.uri = uri;
        }

        override public LambdaExpression GetLambdaExpression() 
            => MMTtoLambdaExpression<float>.MakeLambdaExpression(uri);
    }

    public class OMSTR : MMTTerm
    {
        [JsonProperty("float")]
        public string s;
        public string kind = "OMSTR";

        public OMSTR(string s)
        {
            this.s = s;
        }

        override public LambdaExpression GetLambdaExpression()
            => Expression.Lambda(Expression.Constant(s, typeof(string)), null);
    }

    public class OMF : MMTTerm
    {
        [JsonProperty("float")]
        public float f;
        public string kind = "OMF";

        public OMF(float f)
        {
            this.f = f;
        }

        override public LambdaExpression GetLambdaExpression()
            => Expression.Lambda(Expression.Constant(f, typeof(float)), null);
    }

    public class MMTDeclaration
    {
        public string label;

        public static MMTDeclaration FromJson(string json)
        {
            MMTDeclaration mmtDecl = JsonConvert.DeserializeObject<MMTDeclaration>(json);
            if (mmtDecl.label == null)
                mmtDecl.label = string.Empty;

            return mmtDecl;
        }

        public static string ToJson(MMTDeclaration mmtDecl)
        {
            if (mmtDecl.label == null)
                mmtDecl.label = string.Empty;

            string json = JsonConvert.SerializeObject(mmtDecl);
            return json;
        }
    }

    /**
     * MMTSymbolDeclaration: Class for facts without values, e.g. Points
     */ 
    public class MMTSymbolDeclaration : MMTDeclaration
    {
        public string kind = "general";
        public MMTTerm tp;
        public MMTTerm df;

        /**
         * Constructor used for sending new declarations to mmt
         */
        public MMTSymbolDeclaration(string label, MMTTerm tp, MMTTerm df)
        {
            this.label = label;
            this.tp = tp;
            this.df = df;
        }
    }

    /**
     * MMTValueDeclaration: Class for facts with values, e.g. Distances or Angles
     */
    public class MMTValueDeclaration : MMTDeclaration
    {
        public string kind = "veq";
        public MMTTerm lhs;
        public MMTTerm valueTp;
        public MMTTerm value;

        /**
         * Constructor used for sending new declarations to mmt
         */
        public MMTValueDeclaration(string label, MMTTerm lhs, MMTTerm valueTp, MMTTerm value)
        {
            this.label = label;
            this.lhs = lhs;
            this.valueTp = valueTp;
            this.value = value;
        }
    }
}