SOMDocManager.cs

using System.Collections.Generic;
using Newtonsoft.Json;
using JsonSubTypes;
using System.Linq.Expressions;
using System;
using System.Linq;
using MoreLinq;
using UnityEngine;
using static UnityEditor.PlayerSettings;

public static class SOMDocManager
{
    public static class MMT_OMS_URI
    {
        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 readonly string Sin = "Sin";
        public static readonly string Cos = "Cos";
        public static readonly string Add = "Add";
        public static readonly string Divide = "Divide";
        public static readonly string Multiply = "Multiply";
        public static readonly string Subtract = "Subtract";
        public static readonly string SquareRoot = "SquareRoot";
        public static readonly string MakeUnityEngineVector3 = "UnityEngine.Vector3";
    }


    public static class SOMDoctoLambdaExpression<T>
    {
        public static readonly LambdaExpression @default = Expression.Lambda(Expression.Default(typeof(T)), null);

        private static uint param_counter = 0; //for better debugs

        // TODO: Populate Dictionaries
        #region ExpressionDictionaries

        delegate LambdaExpression CustomFunction(LambdaExpression[] args_lamda);
        private static readonly Dictionary<string, CustomFunction> MMTtoLambdaMaker = new()
        {
            { MMT_OMS_URI.Sin,
                MakeSin},
            { MMT_OMS_URI.Cos,
                MakeCos},
            { MMT_OMS_URI.SquareRoot,
                MakeCos},
            { MMT_OMS_URI.MakeUnityEngineVector3,
                MakeUnityEngineVector3},
        };

        private static readonly Dictionary<string, ExpressionType> MMTtoBinaryExpressionType = new()
        {
            { MMT_OMS_URI.Add,
                ExpressionType.Add},
            { "AddAssign",
                ExpressionType.AddAssign},
            { "AddAssignChecked",
                ExpressionType.AddAssignChecked},
            { "AddChecked",
                ExpressionType.AddChecked},
            { "And",
                ExpressionType.And},
            { "AndAlso",
                ExpressionType.AndAlso},
            { "AndAssign",
                ExpressionType.AndAssign},
            { "Assign",
                ExpressionType.Assign},
            { MMT_OMS_URI.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},
            { MMT_OMS_URI.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},
            { MMT_OMS_URI.Subtract,
                ExpressionType.Subtract},
            { "SubtractAssign",
                ExpressionType.SubtractAssign},
            { "SubtractAssignChecked",
                ExpressionType.SubtractAssignChecked},
            { "SubtractChecked",
                ExpressionType.SubtractChecked},
        };

        private static readonly Dictionary<string, ExpressionType> MMTtoUnaryExpressionType = new()
        {
            //{ "Constant", // Not Unary
            //    ExpressionType.Constant},
            { "Convert",
                ExpressionType.Convert},
            { "ConvertChecked",
                ExpressionType.ConvertChecked},
            { "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, LambdaExpression[] args_lamda = null)
        {
            void ThrowArgumentException(ExpressionType expression_cast, int expected)
            {
                throw new ArgumentException(string.Format(
                    "\"Wrong number of Arguments. Required: {2}. Supplied: {3}.\\n\\tFor URI:\\\"{0}\\\"\\n\\tmapped to:\\\"{1}\\\"\"",
                    URI, expression_cast, expected, args_lamda.Count()
                ));
            }
            //TODO distinct! (in args_lamda and duplicate?)
            ParameterExpression[] args_param = args_lamda?.SelectMany(l => l.Parameters).ToArray(); //.DistinctBy(p => p.Name).ToArray();

            if (MMTtoUnaryExpressionType.TryGetValue(URI, out var unnary_type))
            {
                if (args_lamda == null)
                {
                    ParameterExpression[] args = new ParameterExpression[] {
                        Expression.Parameter(typeof(T), "PNamed_" + param_counter++.ToString()),
                    };
                    return Expression.Lambda(Expression.MakeUnary(unnary_type, args[0], typeof(T)), args);
                }
                else
                {
                    if (args_lamda.Count() < 1)
                        ThrowArgumentException(unnary_type, 1);

                    Type UnarySecondArgument = args_lamda.Count() < 2 ? null : args_lamda[1].ReturnType;

                    return Expression.Lambda(Expression.MakeUnary(unnary_type, args_lamda[0].Body, UnarySecondArgument), args_param);
                }
            }
            else if (MMTtoBinaryExpressionType.TryGetValue(URI, out var binary_type))
            {
                if (args_lamda == null)
                {
                    ParameterExpression[] args = new ParameterExpression[] {
                        Expression.Parameter(typeof(T), "PNamed_" + param_counter++.ToString()),
                        Expression.Parameter(typeof(T), "PNamed_" + param_counter++.ToString()),
                    };
                    return Expression.Lambda(Expression.MakeBinary(binary_type, args[0], args[1]), args);
                }
                else
                {
                    if (args_lamda.Count() != 2)
                        ThrowArgumentException(binary_type, 2);

                    return Expression.Lambda(Expression.MakeBinary(binary_type, args_lamda[0].Body, args_lamda[1].Body), args_param);
                }
            }
            else if (MMTtoLambdaMaker.TryGetValue(URI, out var lamda_maker))
            {
                return lamda_maker(args_lamda ?? null); //args_lamda == null ok
            }

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

        private static LambdaExpression ExpresionFuncToLambda(LambdaExpression func, string name, 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), name, args);
        }

        private static LambdaExpression ExpresionFuncToLambda(LambdaExpression func, string name, LambdaExpression[] args_lamda, uint nTargs_fallback)
            => args_lamda == null || args_lamda.Count() == 0
                ? ExpresionFuncToLambda(func, name, nTargs_fallback)
                : Expression.Lambda(Expression.Invoke(func, args_lamda.Select(l => l.Body)), name, args_lamda.SelectMany(l => l.Parameters));

        private static LambdaExpression ParseFuncUUToExpression<U>(Func<U, U> func)
            => (Expression<Func<U, U>>)((x) => func(x));

        private static LambdaExpression MakeSin(LambdaExpression[] args_lamda)
            => ExpresionFuncToLambda(
                    default(T) switch // TODO? cleaner switch
                    {
                        float => ParseFuncUUToExpression<float>(MathF.Sin),
                        double => ParseFuncUUToExpression<double>(Math.Sin),
                        _ => throw new NotImplementedException("Sinus for " + typeof(T))
                    },
                    "Sin", args_lamda, 1
                );

        private static LambdaExpression MakeCos(LambdaExpression[] args_lamda)
            => ExpresionFuncToLambda(
                    default(T) switch // TODO? cleaner switch
                    {
                        float => ParseFuncUUToExpression<float>(MathF.Cos),
                        double => ParseFuncUUToExpression<double>(Math.Cos),
                        _ => throw new NotImplementedException("Cosinus for " + typeof(T))
                    },
                    "Cos", args_lamda, 1
                );

        private static LambdaExpression MakeUnityEngineVector3(LambdaExpression[] args_lamda)
            => ExpresionFuncToLambda(
                    (Expression<Func<float, float, float, Vector3>>)((x, y, z) => new Vector3(x, y, z)),
                    "UnityEngineVector3", args_lamda, 3
                );
    }


    [JsonConverter(typeof(JsonSubtypes), "kind")]
    [JsonSubtypes.KnownSubType(typeof(OMA), "OMA")]
    [JsonSubtypes.KnownSubType(typeof(OMS), "OMS")]
    [JsonSubtypes.KnownSubType(typeof(OMSTR), "OMSTR")]
    [JsonSubtypes.KnownSubType(typeof(OMF), "OMF")]
    [JsonSubtypes.KnownSubType(typeof(OMV), "OMV")]
    //[JsonSubtypes.KnownSubType(typeof(OMC<T>), "OMC<" + typeof(T) + ">")]
    [JsonSubtypes.KnownSubType(typeof(OMC<Vector3>), "OMC<UnityEngine.Vector3>")]
    [JsonSubtypes.KnownSubType(typeof(OMC<float>), "OMC<System.Single>")]
    [JsonSubtypes.KnownSubType(typeof(OMC<double>), "OMC<System.Double>")]
    abstract public class SOMDoc
    {
        string kind;

        [JsonIgnore]
        public static readonly Dictionary<string, Type> allowedTypes =
            new Type[] { typeof(float), typeof(double), typeof(string), typeof(UnityEngine.Vector3) }
            .ToDictionary(t => t.ToString());

        protected SOMDoc() { }

        public static LambdaExpression ReduceArguments(LambdaExpression expr)
        {
            var reduced_params = expr.Parameters.GroupBy(p => p.Name).Select(p => p.First()).ToArray();
            var name_to_params = reduced_params.ToDictionary(p => p.Name);

            return
                Expression.Lambda(
                    Expression.Invoke(
                        expr,
                        expr.Parameters.Select(p => name_to_params[p.Name])),
                    reduced_params);
        }

        public static bool Equivalent(SOMDoc sd1, SOMDoc sd2)
            => sd1.Equivalent(sd2);

        public abstract bool Equivalent(SOMDoc sd2);

        public LambdaExpression GetReducedLambdaExpression()
            => ReduceArguments(this.GetLambdaExpression());

        public abstract LambdaExpression GetLambdaExpression(LambdaExpression[] args = null);

        public abstract override string ToString();

        public abstract SOMDoc MapURIs(Dictionary<string, string> old_to_new);

        #region MakeMMT_OMS_URItoSOMDoc

        public static SOMDoc MakeUnityEngineVector3(Vector3 vec)
            => new OMA(
                new OMS(MMT_OMS_URI.MakeUnityEngineVector3),
                    new() {
                        new OMF(vec.x),
                        new OMF(vec.y),
                        new OMF(vec.z),
                    }
                );

        #endregion MakeMMT_OMS_URItoSOMDoc
    }

    public abstract class SOMDocCRTP<T> : SOMDoc where T : SOMDocCRTP<T>
    {
        protected SOMDocCRTP() : base() { }

        /// \copydoc Fact.Equivalent(Fact)
        public override bool Equivalent(SOMDoc sd2)
            => this.GetType() == sd2.GetType() && (this as T).EquivalentWrapped(sd2 as T);

        protected abstract bool EquivalentWrapped(T sd2);

        public override SOMDoc MapURIs(Dictionary<string, string> old_to_new)
            => MapURIsWrapped(old_to_new);

        public abstract T MapURIsWrapped(Dictionary<string, string> old_to_new);
    }

    public class OMA : SOMDocCRTP<OMA>
    {
        public string kind = "OMA";

        public SOMDoc applicant;
        public List<SOMDoc> arguments;

        [JsonConstructor]
        public OMA(SOMDoc applicant, List<SOMDoc> arguments) : base()
        {
            this.applicant = applicant;
            this.arguments = arguments;
        }

        protected override bool EquivalentWrapped(OMA sd2)
            => Equivalent(this.applicant, sd2.applicant)
            && this.arguments
                .Zip(sd2.arguments, (arg1, arg2) => Equivalent(arg1, arg2))
                .All(b => b);

        public override LambdaExpression GetLambdaExpression(LambdaExpression[] args = null)
            => applicant.GetLambdaExpression(arguments?.Select(mmt => mmt.GetLambdaExpression()).ToArray());

        public override string ToString()
            => applicant.ToString() + "(" + string.Join(", ", arguments.Select(a => a.ToString())) + ")";

        public override OMA MapURIsWrapped(Dictionary<string, string> old_to_new)
            => new OMA(
                applicant.MapURIs(old_to_new),
                arguments.Select(arg => arg.MapURIs(old_to_new)).ToList()
            );
    }

    public class OMS : SOMDocCRTP<OMS> //OMSTR?
    {
        public string kind = "OMS";

        public string uri;

        [JsonConstructor]
        public OMS(string uri) : base()
        {
            this.uri = uri;
        }

        protected override bool EquivalentWrapped(OMS sd2)
            => this.uri == sd2.uri;

        public override LambdaExpression GetLambdaExpression(LambdaExpression[] args)
            => SOMDoctoLambdaExpression<float>.MakeLambdaExpression(uri, args);

        public override string ToString()
            => uri;

        public override OMS MapURIsWrapped(Dictionary<string, string> old_to_new)
        {
            if (!old_to_new.TryGetValue(uri, out string new_uri))
                new_uri = uri;

            return new OMS(new_uri);
        }
    }

    public class OMSTR : SOMDocCRTP<OMSTR>
    {
        public string kind = "OMSTR";

        [JsonProperty("float")]
        public string s;

        [JsonConstructor]
        public OMSTR(string s) : base()
        {
            this.s = s;
        }

        protected override bool EquivalentWrapped(OMSTR sd2)
            => this.s == sd2.s;

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

        public override string ToString()
            => s;

        public override OMSTR MapURIsWrapped(Dictionary<string, string> old_to_new)
            => (OMSTR)this.MemberwiseClone();
    }

    public class OMF : SOMDocCRTP<OMF>
    {
        public string kind = "OMF";

        [JsonProperty("float")]
        public float f;

        [JsonConstructor]
        public OMF(float f) : base()
        {
            this.f = f;
        }

        protected override bool EquivalentWrapped(OMF sd2)
            => this.f.IsApproximatelyEqual(sd2.f);

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

        public override string ToString()
            => f.ToString();

        public override OMF MapURIsWrapped(Dictionary<string, string> old_to_new)
            => (OMF)this.MemberwiseClone();
    }

    public class OMC<T> : SOMDocCRTP<OMC<T>>
    {
        public string kind = "OMC<" + typeof(T) + ">";

        public T value;

        [JsonConstructor]
        public OMC(T value) : base()
        {
            this.value = value;
        }

        protected override bool EquivalentWrapped(OMC<T> sd2)
        {
            Debug.LogWarning("Cannot check Equivalency for " + this.GetType() + "; only whether it's exact!");
            return this.value.Equals(value);
        }

        public override LambdaExpression GetLambdaExpression(LambdaExpression[] args = null)
            => Expression.Lambda(Expression.Constant(value, typeof(T)), null);

        public override string ToString()
            => "C_" + typeof(T) + "(" + value.ToString() + ")";

        public override OMC<T> MapURIsWrapped(Dictionary<string, string> old_to_new)
            => (OMC<T>)this.MemberwiseClone();
    }

    public class OMV : SOMDocCRTP<OMV>
    {
        public string kind = "OMV";

        public string name;

        /// <summary>@Type of this variable</summary>
        [JsonIgnore]
        public Type type;

        /// <summary>Enables (especially <see cref="JsonConverter"/>) to read and set <see cref="type"/> by its <c>string</c> representation.</summary>
        public string typeString
        {
            get => type.ToString();
            set => type = allowedTypes[value];
        }

        [JsonConstructor]
        public OMV(string name, string typeString) : base()
        {
            this.name = name;
            this.typeString = typeString;
        }

        public OMV(string name, Type type) : base()
        {
            this.name = name;
            this.type = type;
        }

        protected override bool EquivalentWrapped(OMV sd2)
            => this.type == sd2.type;

        public override LambdaExpression GetLambdaExpression(LambdaExpression[] args = null)
        {
            ParameterExpression v = Expression.Parameter(type, name);
            return Expression.Lambda(v, new[] { v });
        }

        public override string ToString()
            => "V_" + name + "(" + typeString + ")";

        public override OMV MapURIsWrapped(Dictionary<string, string> old_to_new)
            => (OMV)this.MemberwiseClone();
    }


    public class MMTDeclaration
    {
        public string label;

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

            return mmtDecl;
        }

        public static string ToJson(MMTDeclaration mmtDecl)
        {
            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 SOMDoc tp;
        public SOMDoc df;

        /**
         * Constructor used for sending new declarations to mmt
         */
        public MMTSymbolDeclaration(string label, SOMDoc tp, SOMDoc 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 SOMDoc lhs;
        public SOMDoc valueTp;
        public SOMDoc value;

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