using System;
using System.Collections.Generic;
using UnityEngine;
using UnityEngine.Networking;
using Newtonsoft.Json;
using JsonSubTypes;
using System.Linq;
using REST_JSON_API;
using static SOMDocManager;
using UnityEngine.ProBuilder;
using Unity.Mathematics;
using System.Runtime.ExceptionServices;

public static class ParsingDictionary
{
    //TODO? get rid of this, use reflection? instead, if possible
    //TODO: docu

    public static Dictionary<string, Func<MMTDeclaration, Fact>> parseFactDictionary = new() {
        { MMT_OMS_URI.Point,
            PointFact.parseFact },
        { MMT_OMS_URI.Metric,
            LineFact.parseFact },
        { MMT_OMS_URI.Angle,
            AngleFact.parseFact },
        { MMT_OMS_URI.Eq,
            AngleFact.parseFact },
        { MMT_OMS_URI.RightAngle,
            RightAngleFact.parseFact },
        { MMT_OMS_URI.LineType,
            RayFact.parseFact },
        { MMT_OMS_URI.LineOf,
            RayFact.parseFact },
        { MMT_OMS_URI.OnLine,
            OnLineFact.parseFact },
        { MMT_OMS_URI.ParallelLine,
            ParallelLineFact.parseFact },
        { MMT_OMS_URI.CircleType3d,
            CircleFact.parseFact },
        { MMT_OMS_URI.OnCircle,
            OnCircleFact.parseFact },
        { MMT_OMS_URI.AnglePlaneLine,
            AngleCircleLineFact.parseFact },
        { MMT_OMS_URI.RadiusCircleMetric,
            RadiusFact.parseFact },
        { MMT_OMS_URI.AreaCircle,
            AreaCircleFact.parseFact },
        { MMT_OMS_URI.OrthoCircleLine,
            OrthogonalCircleLineFact.parseFact },
        { MMT_OMS_URI.VolumeCone,
            ConeVolumeFact.parseFact },
        { MMT_OMS_URI.TruncatedVolumeCone,
            TruncatedConeVolumeFact.parseFact },
        { MMT_OMS_URI.CylinderVolume,
            CylinderVolumeFact.parseFact },
        { MMT_OMS_URI.TestType,
            TestFact.parseFact },
        { MMT_OMS_URI.EqualityCircles,
            EqualCirclesFact.parseFact },
        { MMT_OMS_URI.UnEqualityCircles,
            UnEqualCirclesFact.parseFact },
        { MMT_OMS_URI.ListLiteral,
            ListFact.parseFact },
    };

    // TODO: get rid of this
    public static Dictionary<string, string> parseTermsToId = new();
}


/// <summary>
/// %Fact representation of Unity; mostly mirrors Facts of MMT.
/// </summary>
[JsonConverter(typeof(JsonSubtypes), "s_type")]
[JsonSubtypes.KnownSubType(typeof(PointFact), nameof(PointFact))]
[JsonSubtypes.KnownSubType(typeof(LineFact), nameof(LineFact))]
[JsonSubtypes.KnownSubType(typeof(RayFact), nameof(RayFact))]
[JsonSubtypes.KnownSubType(typeof(OnLineFact), nameof(OnLineFact))]
[JsonSubtypes.KnownSubType(typeof(AngleFact), nameof(AngleFact))]
[JsonSubtypes.KnownSubType(typeof(CircleFact), nameof(CircleFact))]
[JsonSubtypes.KnownSubType(typeof(ParallelLineFact), nameof(ParallelLineFact))]
[JsonSubtypes.KnownSubType(typeof(OnCircleFact), nameof(OnCircleFact))]
[JsonSubtypes.KnownSubType(typeof(AngleCircleLineFact), nameof(AngleCircleLineFact))]
[JsonSubtypes.KnownSubType(typeof(OrthogonalCircleLineFact), nameof(OrthogonalCircleLineFact))]
[JsonSubtypes.KnownSubType(typeof(AreaCircleFact), nameof(AreaCircleFact))]
[JsonSubtypes.KnownSubType(typeof(RadiusFact), nameof(RadiusFact))]
[JsonSubtypes.KnownSubType(typeof(ConeVolumeFact), nameof(ConeVolumeFact))]
[JsonSubtypes.KnownSubType(typeof(TruncatedConeVolumeFact), nameof(TruncatedConeVolumeFact))]
[JsonSubtypes.KnownSubType(typeof(RightAngleFact), nameof(RightAngleFact))]
[JsonSubtypes.KnownSubType(typeof(CylinderVolumeFact), nameof(CylinderVolumeFact))]
[JsonSubtypes.KnownSubType(typeof(TestFact), nameof(TestFact))]
[JsonSubtypes.KnownSubType(typeof(EqualCirclesFact), nameof(EqualCirclesFact))]
[JsonSubtypes.KnownSubType(typeof(UnEqualCirclesFact), nameof(UnEqualCirclesFact))]
[JsonSubtypes.KnownSubType(typeof(AttachedPositionFunction), nameof(AttachedPositionFunction))]
[JsonSubtypes.KnownSubType(typeof(FunctionFact), nameof(FunctionFact))]
[JsonSubtypes.KnownSubType(typeof(FunctionCallFact), nameof(FunctionCallFact))]
[JsonSubtypes.KnownSubType(typeof(ListFact), nameof(ListFact))]
[JsonSubtypes.KnownSubType(typeof(TupelFact), nameof(TupelFact))]
//[JsonSubtypes.KnownSubType(typeof(FunctionFact<T0, TResult>), "FunctionFact<T0, TResult>")] //TODO: generics? => nameof does not work (generic agnostic)
//[JsonSubtypes.KnownSubType(typeof(FunctionFactFloat<Vector3>), "FunctionFact<System.Single, UnityEngine.Vector3>")]
public abstract class Fact
{
    /// <summary>
    /// Reference to <c>GameObject</c> that represents this Fact in the GameWorld.
    /// </summary>
    /// <seealso cref="FactObject3D"/>
    [JsonIgnore]
    public FactWrapper WorldRepresentation;

    /// <summary>
    /// Collection of <c>Type</c>s of *all* available <see cref="Fact"/>s to choose from.
    /// </summary>
    [JsonIgnore]
    public static readonly Type[] Types = TypeExtensions<Fact>.UAssemblyInheritenceTypes;

    /// <value>
    /// [ClassName] for JSON de-/serialization.
    /// Automatically set in <see cref="Fact()"/> for <b>NON-Generiy-Types</b>!
    /// Also add JsonSubtypes.KnownSubType decorator for deserialization to Fact!
    /// </value>
    [JsonProperty]
    protected string s_type;

    /// <returns><see langword="true"/> if Fact depends on other \ref Fact "Facts"; equivalent to <see cref="getDependentFactIds"/> returns non empty array</returns>
    [JsonIgnore]
    public virtual bool HasDependentFacts => DependentFactIds.Length > 0;

    /// <returns> array of Fact <see cref="Id"> Ids </see> on which this Fact depends.</returns>
    /// <example><see cref="AngleFact"/> needs 3 <see cref="PointFact"/>s to be defined.</example>
    [JsonIgnore]
    public string[] DependentFactIds => _DependentFactIds ??= GetGetDependentFactIds();
    private string[] _DependentFactIds;

    /// <returns> array of Fact <see cref="Id"> Ids </see> on which this Fact depends.</returns>
    /// <example><see cref="AngleFact"/> needs 3 <see cref="PointFact"/>s to be defined.</example>
    protected abstract string[] GetGetDependentFactIds();

    /// <value>
    /// Unique Id. e.g.: MMT URI
    /// </value>
    [JsonIgnore]
    public string Id
    {
        get
        {
            //while (FetchURICoroutine.MoveNext()) ; //active wait for server
            return _URI;
        }
    }
    //private IEnumerator FetchURICoroutine = IEnumeratorExtensions.yield_break;

    /// <summary>
    /// MMT URI
    /// </summary>
    [JsonProperty]
    protected string _URI;

    /// <value>
    /// <c>get</c> initiates and subsequently updates a human readable name. <remarks>Should be called once a constructor call to be initiated.</remarks>
    /// <c>set</c> calls <see cref="rename(string)"/>
    /// </value>
    public string Label
    {
        get
        { // in case of renamed dependables
            return _Facts == null // JsonSerialization toggle (_Facts.GetNumberOfFacts() == 0 && this is not PointFact) // JsonSerialization toggle && allow first (Point)Fact to be created
                || (hasCustomLabel && _CustomLabel != null)
                ? _CustomLabel
                : generateLabel();
        }
        set
        {
            if (_Facts == null) // JsonSerialization toggle)
            {
                _CustomLabel = value;
                LabelId = -LabelId;
                return;
            }
            rename(value);
        }
    }

    /// <value>
    /// Is true if Fact has a custom <see cref="Label"/> which is not <c>null</c> or <c>""</c>.
    /// </value>
    public bool hasCustomLabel => LabelId < 0;

    /// <summary>
    /// Stores custom <see cref="Label"/> if set.
    /// </summary>
    protected string _CustomLabel = null;

    /// <summary>
    /// Counter to organize auto generated <see cref="Label"/>.
    /// Set to negative, if custom \ref Label is assigned.
    /// </summary>
    // property for JSON to set AFTER Label => declare AFTER Label
    public int LabelId { get; set; }

    /// <summary>
    /// Reference to <see cref="FactOrganizer"/> in which this Fact and all its <see cref="getDependentFactIds">depending Facts</see> are beeing organized.
    /// </summary>
    [JsonIgnore]
    protected FactOrganizer _Facts;

    [JsonIgnore]
    bool ForceRecalculateTransform = true;

    [JsonIgnore]
    public Vector3 Position
    {
        get
        {
            if (ForceRecalculateTransform)
                RecalculateTransform();
            return _Position;
        }
        protected set
        {
            ForceRecalculateTransform = false;
            _Position = value;
        }
    }
    private Vector3 _Position = Vector3.zero;

    [JsonIgnore]
    public Quaternion Rotation
    {
        get
        {
            if (ForceRecalculateTransform)
                RecalculateTransform();
            return _Rotation;
        }
        protected set
        {
            ForceRecalculateTransform = false;
            _Rotation = value;
        }
    }
    private Quaternion _Rotation = Quaternion.identity;

    [JsonIgnore]
    public Vector3 LocalScale
    {
        get
        {
            if (ForceRecalculateTransform)
                RecalculateTransform();
            return _LocalScale;
        }
        protected set
        {
            ForceRecalculateTransform = false;
            _LocalScale = value;
        }
    }
    private Vector3 _LocalScale = Vector3.one;

    /// <summary>
    /// Only being used by [JsonReader](https://www.newtonsoft.com/json/help/html/T_Newtonsoft_Json_JsonReader.htm) to initiate empty \ref Fact "Facts".
    /// <seealso cref="SOMDocManager"/>
    /// </summary>
    protected Fact()
    {
        this._Facts = null; // new FactOrganizer();
        LabelId = 0;

        s_type = this.GetType().Name;
    }

    /// <summary>
    /// Standard base-constructor.
    /// </summary>
    /// <param name="organizer"><see cref="_Facts"/></param>
    protected Fact(FactOrganizer organizer) : this()
    {
        this._Facts = organizer;
    }

    /// <summary>
    /// Copies <paramref name="fact"/> by initiating new MMT %Fact.
    /// </summary>
    /// <param name="fact">Fact to be copied</param>
    /// <param name="old_to_new"><c>Dictionary</c> mapping <paramref name="fact"/>.<see cref="getDependentFactIds"/> in <paramref name="fact"/>.<see cref="Fact._Facts"/> to corresponding <see cref="Fact.Id"/> in <paramref name="organizer"/> </param>
    /// <param name="organizer"><see cref="_Facts"/></param>
    public Fact ReInitializeMe(Dictionary<string, string> old_to_new, FactOrganizer organizer)
    {
        Fact ret = _ReInitializeMe(old_to_new, organizer);

        ret.LabelId = this.LabelId;
        if (ret.hasCustomLabel)
            ret._CustomLabel = this.Label;

        return ret;
    }
    protected abstract Fact _ReInitializeMe(Dictionary<string, string> old_to_new, FactOrganizer organizer);

    /// <summary>
    /// Assignes a custom <see cref="Label"/>, if <paramref name="newLabel"/> is not yet taken;
    /// or clears custom <see cref="Label"/>.
    /// </summary>
    /// <param name="newLabel">To be new <see cref="Label"/>. To reset to auto-generation set to <c>null</c> or <c>""</c>.</param>
    /// <returns></returns>

    //TODO: notify about updated dependable Labelnames for UI
    //TODO: check for colissions with not yet generated names
    public bool rename(string newLabel)
    // returns true if succeded
    {
        if (string.IsNullOrEmpty(newLabel) && _Facts.GetNumberOfFacts() != 0)
        // switch back to autogenerated
        {
            generateLabel();
            _CustomLabel = null;
            return true;
        }
        else
        // set CustomLabel if available
        {
            if (_Facts.ContainsLabel(newLabel))
                return false;

            freeAutoLabel();
            _CustomLabel = newLabel;

            return true;
        }
    }

    protected abstract void RecalculateTransform();

    public abstract MMTDeclaration MakeMMTDeclaration();

    /// <summary>
    /// Frees ressources e.g. <see cref="Label"/> and will eventually delete %Fact Server-Side in far-near future when feature is supported.
    /// </summary>
    ~Fact()
    {
        //TODO: MMT: delete over there

        freeAutoLabel();

        if (CommunicationEvents.VerboseURI)
            Debug.Log("Server removed Fact:\n" + this.Id);
    }

    /// <summary>
    /// Compares \ref Fact "this" against <paramref name="f2"/>.
    /// </summary>
    /// <param name="f2">Fact to compare to</param>
    /// <returns><c>true</c> if <paramref name="f2"/> is semantical very similar to \ref Fact "this"</returns>
    public abstract bool Equivalent(Fact f2);

    /// <summary>
    /// Compares <paramref name="f1"/> against <paramref name="f2"/>.
    /// </summary>
    /// <param name="f1">Fact to compare to</param>
    /// <param name="f2">Fact to compare to</param>
    /// <returns><c>true</c> if <paramref name="f2"/> is semantical very similar to <paramref name="f1"/></returns>
    public abstract bool Equivalent(Fact f1, Fact f2);

    /// <summary>
    /// canonical
    /// </summary>
    /// <returns>unique-ish Hash</returns>
    public new virtual int GetHashCode()
        => DependentFactIds
            .Select(id => id.GetHashCode())
            .Aggregate((hash1, hash2) => hash1 ^ hash2);

    /// <summary>
    /// auto-generates <see cref="Label"/> using generation variable(s) e.g. <see cref="LabelId"/>;
    /// if custom <see cref="Label"/> is set, tries to restore original generated <see cref="Label"/> **without** resetting <see cref="_CustomLabel"/>. If original <see cref="Label"/> is already taken, a new one will be generated.
    /// </summary>
    /// <returns>auto-generated <see cref="Label"/></returns>
    protected virtual string generateLabel()
    {
        if (LabelId < 0)
            // reload Label if possible
            LabelId = _Facts.UnusedLabelIds.Remove(-LabelId) ? -LabelId : 0;

        if (LabelId == 0)
            if (_Facts.UnusedLabelIds.Count == 0)
                LabelId = ++_Facts.MaxLabelId;
            else
            {
                LabelId = _Facts.UnusedLabelIds.Min;
                _Facts.UnusedLabelIds.Remove(LabelId);
            }

        return ((char)(64 + LabelId)).ToString();
    }

    /// <summary>
    /// Parses <see cref="MMTDeclaration"/> to actual Fact
    /// </summary>
    /// <param name="fact">instance to be parsed</param>
    /// <returns>parsed Fact</returns>
    public static Fact parseFact(MMTDeclaration fact)
        => null;

    /// <summary>
    /// Tells <see cref="_Facts"/> that \ref Fact "this" no longer uses auto-generated <see cref="Label"/>, but remembers current generation variable(s).
    /// </summary>

    // TODO? only get _Fact to freeLabel/
    public /*protected internal*/ void freeAutoLabel()
    {
        if (LabelId > 0)
        {
            _Facts.UnusedLabelIds.Add(LabelId);
            // store Label for name-persistance
            LabelId = -LabelId;
        }
    }

    /// <summary>
    /// 
    /// </summary>
    /// <remarks>Asynchron version has proofen inefficent, since <see cref="Fact.Id"/> is usually called in close proximity.</remarks>
    // Asynchron version in comments
    public void SendToMMT()
    {
        MMTDeclaration mmtDecl = MakeMMTDeclaration();

        //GlobalBehaviour.Instance.StartCoroutine(
        //    FetchURICoroutine = 
        _URI =
            _SendAdd(
                CommunicationEvents.ServerAdress + "/fact/add",
                mmtDecl.ToJson()
        //,(string uri) => _SendURICallback(mmtDecl, uri)
        );//);

        //return;

        //void _SendURICallback(MMTDeclaration mmtDecl, string uri)
        //{
        //    _URI = uri;

        if (mmtDecl is MMTSymbolDeclaration mMTSymbol && mMTSymbol.defines != null)
            ParsingDictionary.parseTermsToId[mMTSymbol.defines.ToString()] = _URI;
        //}

        /*IEnumerator*/
        string _SendAdd(string path, string body)//, Action<string> uriCallback)
        {
            if (!CommunicationEvents.ServerRunning)
            {
                Debug.LogWarning("Server not running");
                //uriCallback(null);
                return null; // yield break;
            }

            if (CommunicationEvents.VerboseURI)
                Debug.Log("Sending to Server:\n" + body);

            //Put constructor parses stringbody to byteArray internally  (goofy workaround)
            using UnityWebRequest www = UnityWebRequest.Put(path, body);
            www.method = UnityWebRequest.kHttpVerbPOST;
            www.SetRequestHeader("Content-Type", "application/json");
            www.timeout = 1;

            //yield return 
            UnityWebRequestAsyncOperation web =
                www.SendWebRequest();

            while (!web.isDone) ;

            if (www.result == UnityWebRequest.Result.ConnectionError
             || www.result == UnityWebRequest.Result.ProtocolError)
            {
                Debug.LogWarning(www.error);
                //uriCallback(null);
                return null; // yield break;
            }
            else
            {
                while (!www.downloadHandler.isDone)
                    //yield return null
                    ;

                FactReference res = JsonUtility.FromJson<FactReference>(www.downloadHandler.text);

                if (CommunicationEvents.VerboseURI)
                    Debug.Log("Server added Fact:\n" + res.uri);

                //uriCallback(res.uri);
                return res.uri; // yield break;
            }
        }
    }
}

/// <summary>
/// Implements CRTP for <see cref="Fact"/>; Escalates constructors;
/// </summary>
/// <typeparam name="T">class, which inherits from FactWrappedCRTP</typeparam>
public abstract class FactWrappedCRTP<T> : Fact where T : FactWrappedCRTP<T>
{
    /// <summary>\copydoc Fact.Fact()</summary>
    protected FactWrappedCRTP() : base() { }

    /// <summary>\copydoc Fact.Fact(FactOrganizer)</summary>
    protected FactWrappedCRTP(FactOrganizer organizer) : base(organizer) { }

    /// \copydoc Fact.Equivalent(Fact)
    public override bool Equivalent(Fact f2)
        => Equivalent(this, f2);

    /// \copydoc Fact.Equivalent(Fact, Fact)
    public override bool Equivalent(Fact f1, Fact f2)
        => f1.GetType() == f2.GetType() && EquivalentWrapped((T)f1, (T)f2);

    /// <summary>CRTP step of <see cref="Equivalent(Fact)"/> and <see cref="Equivalent(Fact, Fact)"/></summary>
    protected abstract bool EquivalentWrapped(T f1, T f2);

    protected bool DependentFactsEquivalent(T f1, T f2)
        => f1.DependentFactIds
            .Zip(f2.DependentFactIds,
                (id1, id2) =>
                    id1 == id2
                    || FactOrganizer.AllFacts[id1].Equivalent(FactOrganizer.AllFacts[id2])
            )
            .All(b => b);
}

/// <summary>
/// Point in 3D Space
/// </summary>
public class PointFact : FactWrappedCRTP<PointFact>
{
    /// <summary> Position </summary>
    public Vector3 Point;
    /// <summary> Orientation for <see cref="Fact.WorldRepresentation"/> </summary>
    [JsonProperty]
    private Vector3 Normal;

    /// <summary> \copydoc Fact.Fact </summary>
    public PointFact() : base()
    {
        this.Point = Vector3.zero;
        this.Normal = Vector3.up;
    }

    /// <summary>
    /// Standard Constructor:
    /// Initiates <see cref="Point"/>, <see cref="Normal"/>, <see cref="Fact._URI"/> and creates MMT %Fact Server-Side
    /// </summary>
    /// <param name="P">sets <see cref="Point"/></param>
    /// <param name="N">sets <see cref="Normal"/></param>
    /// <param name="organizer">sets <see cref="Fact._Facts"/></param>
    public PointFact(Vector3 P, Vector3 N, FactOrganizer organizer) : base(organizer)
    {
        this.Point = P;
        this.Normal = N;

        SendToMMT();
    }

    protected override void RecalculateTransform()
    {
        Position = Point;
        { // Rotation
            Vector3 notNormal = Vector3.forward != Normal ? Vector3.forward : Vector3.up;
            Rotation = Quaternion.LookRotation(
                Vector3.Cross(Normal, notNormal),
                Normal
            );
        }
    }

    /// <summary>
    /// Bypasses initialization of new MMT %Fact by using existend URI, _which is not checked for existence_.
    /// <see cref="Normal"/> set to <c>Vector3.up</c>
    /// </summary>
    /// <param name="point">sets <see cref="Point"/></param>
    /// <param name="uri">MMT URI</param>
    /// <param name="organizer">sets <see cref="Fact._Facts"/></param>
    public PointFact(Vector3 point, string uri, FactOrganizer organizer) : base(organizer)
    {
        this.Point = point;
        this.Normal = Vector3.up;
        this._URI = uri;
        _ = this.Label;
    }

    /// \copydoc Fact.parseFact(ScrollFact)
    public new static PointFact parseFact(MMTDeclaration fact)
    {
        if (((MMTSymbolDeclaration)fact).defines is not OMA defines)
            return null;
        ParsingDictionary.parseTermsToId.TryAdd(defines.ToString(), fact.@ref.uri);

        Vector3 point = (defines.GetLambdaExpression().Compile() as Func<Vector3>)();
        return new PointFact(point, fact.@ref.uri, StageStatic.stage.factState);
    }

    /// \copydoc Fact.hasDependentFacts
    public override bool HasDependentFacts => false;

    /// \copydoc Fact.getDependentFactIds
    protected override string[] GetGetDependentFactIds()
        => new string[] { };

    /// \copydoc Fact.GetHashCode
    public override int GetHashCode()
        => this.Point.GetHashCode();

    /// \copydoc Fact.Equivalent(Fact, Fact)
    protected override bool EquivalentWrapped(PointFact f1, PointFact f2)
        => Math3d.IsApproximatelyEqual(f1.Point, f2.Point);

    protected override Fact _ReInitializeMe(Dictionary<string, string> old_to_new, FactOrganizer organizer)
        => new PointFact(this.Point, this.Normal, organizer);

    public override MMTDeclaration MakeMMTDeclaration()
    {
        SOMDoc tp = new OMS(MMT_OMS_URI.Point);
        SOMDoc df = new OMA(
                new OMS(MMT_OMS_URI.Tuple),
                new[] {
                        new OMF(Point.x),
                        new OMF(Point.y),
                        new OMF(Point.z),
                }
            );

        return new MMTSymbolDeclaration(Label, tp, df);
    }
}

/// <summary>
/// A <see cref="PointFact"/> on a <see cref="AbstractLineFact"/>
/// </summary>
public class OnLineFact : FactWrappedCRTP<OnLineFact>
{
    /// <summary> <see cref="PointFact"/>.<see cref="Fact.Id">Id</see> </summary>
    public string Pid;
    [JsonIgnore]
    public PointFact Point { get => (PointFact)FactOrganizer.AllFacts[Pid]; }

    /// <summary> <see cref="AbstractLineFact"/>.<see cref="Fact.Id">Id</see> </summary>
    public string Rid;
    [JsonIgnore]
    public AbstractLineFact Ray { get => (AbstractLineFact)FactOrganizer.AllFacts[Rid]; }

    /// <summary> \copydoc Fact.Fact </summary>
    public OnLineFact() : base()
    {
        this.Pid = null;
        this.Rid = null;
    }

    /// <summary>
    /// Standard Constructor:
    /// Initiates <see cref="Pid"/>, <see cref="Rid"/>, <see cref="Fact._URI"/> and creates MMT %Fact Server-Side
    /// </summary>
    /// <param name="pid">sets <see cref="Pid"/></param>
    /// <param name="rid">sets <see cref="Rid"/></param>
    /// <param name="organizer">sets <see cref="Fact._Facts"/></param>
    public OnLineFact(string pid, string rid, FactOrganizer organizer) : base(organizer)
    {
        this.Pid = pid;
        this.Rid = rid;

        SendToMMT();
    }

    protected override void RecalculateTransform()
    {
        Position = Point.Position;
        { //Rotation
            Vector3 up = Point.Rotation * Vector3.up;
            Vector3 forward = Ray.Dir;

            if (Math3d.IsApproximatelyEqual(up, forward))
            {
                Vector3 arbitary = Math3d.IsApproximatelyEqual(forward, Vector3.forward)
                    ? Vector3.right
                    : Vector3.forward;

                up = Vector3.Cross(arbitary, forward);
            }

            Rotation = Quaternion.LookRotation(forward, up);
        }
    }

    /// <summary>
    /// Bypasses initialization of new MMT %Fact by using existend URI, _which is not checked for existence_.
    /// </summary>
    /// <param name="pid">sets <see cref="Pid"/></param>
    /// <param name="rid">sets <see cref="Rid"/></param>
    /// <param name="uri">MMT URI</param>
    /// <param name="organizer">sets <see cref="Fact._Facts"/></param>
    public OnLineFact(string pid, string rid, string uri, FactOrganizer organizer) : base(organizer)
    {
        this.Pid = pid;
        this.Rid = rid;
        this._URI = uri;
        _ = this.Label;
    }

    /// \copydoc Fact.parseFact(ScrollFact)
    public new static OnLineFact parseFact(MMTDeclaration fact)
    {
        string pointUri = ((OMS)((OMA)((OMA)((MMTSymbolDeclaration)fact).type).arguments[0]).arguments[1]).uri;
        string lineUri = ((OMA)((OMA)((MMTSymbolDeclaration)fact).type).arguments[0]).arguments[0] is OMS
            // standard case
            ? ((OMS)((OMA)((OMA)((MMTSymbolDeclaration)fact).type).arguments[0]).arguments[0]).uri
            // case when line Uri has a projl on the line Argument 
            : ((OMS)((OMA)((OMA)((OMA)((MMTSymbolDeclaration)fact).type).arguments[0]).arguments[0]).arguments[0]).uri;

        if (!FactOrganizer.AllFacts.ContainsKey(pointUri)
         || !FactOrganizer.AllFacts.ContainsKey(lineUri))
            return null;

        return new OnLineFact(pointUri, lineUri, fact.@ref.uri, StageStatic.stage.factState);
    }

    /// \copydoc Fact.generateLabel
    protected override string generateLabel()
        => Point.Label + "∈" + Ray.Label;

    /// \copydoc Fact.hasDependentFacts
    public override bool HasDependentFacts => true;

    /// \copydoc Fact.getDependentFactIds
    protected override string[] GetGetDependentFactIds()
        => new string[] { Pid, Rid };

    protected override bool EquivalentWrapped(OnLineFact f1, OnLineFact f2)
        => DependentFactsEquivalent(f1, f2);

    protected override Fact _ReInitializeMe(Dictionary<string, string> old_to_new, FactOrganizer organizer)
        => new OnLineFact(old_to_new[this.Pid], old_to_new[this.Rid], organizer);

    public override MMTDeclaration MakeMMTDeclaration()
    {
        SOMDoc tp = new OMA(
            new OMS(MMT_OMS_URI.Ded),
            new[] {
                new OMA(
                    new OMS(MMT_OMS_URI.OnLine),
                    new[]  {
                        new OMS(Rid),
                        new OMS(Pid)
        }),});

        SOMDoc df = null;

        return new MMTSymbolDeclaration(this.Label, tp, df);
    }
}

/// <summary>
/// Two parallel Lines comprised of two <see cref="LineFact">LineFacts</see> 
/// </summary>
public class ParallelLineFact : FactWrappedCRTP<ParallelLineFact>
{
    /// @{ <summary>
    /// One <see cref="Fact.Id">Id</see> of two <see cref="LineFact"/> that are parallel [<see cref="Lid1"/>, <see cref="Lid2"/>].
    /// </summary>
    public string Lid1, Lid2;
    /// @}

    [JsonIgnore]
    public AbstractLineFact Ray1 { get => (AbstractLineFact)FactOrganizer.AllFacts[Lid1]; }
    [JsonIgnore]
    public AbstractLineFact Ray2 { get => (AbstractLineFact)FactOrganizer.AllFacts[Lid2]; }

    /// <summary> \copydoc Fact.Fact </summary>
    public ParallelLineFact() : base()
    {
        this.Lid1 = null;
        this.Lid2 = null;
    }

    /// <summary>
    /// Standard Constructor
    /// </summary>
    /// <param name="lid1">sets <see cref="Lid1"/></param>
    /// <param name="lid2">sets <see cref="Lid2"/></param>
    /// <param name="organizer">sets <see cref="Fact._Facts"/></param>
    public ParallelLineFact(string lid1, string lid2, FactOrganizer organizer) : base(organizer)
    {
        this.Lid1 = lid1;
        this.Lid2 = lid2;

        SendToMMT();
    }

    protected override void RecalculateTransform() { }

    /// <summary>
    /// Bypasses initialization of new MMT %Fact by using existend URI, _which is not checked for existence_.
    /// </summary>
    /// <param name="Lid1">sets <see cref="Lid1"/></param>
    /// <param name="Lid2">sets <see cref="Lid2"/></param>
    /// <param name="backendURI">MMT URI</param>
    /// <param name="organizer">sets <see cref="Fact._Facts"/></param>
    public ParallelLineFact(string Lid1, string Lid2, string backendURI, FactOrganizer organizer) : base(organizer)
    {
        this.Lid1 = Lid1;
        this.Lid2 = Lid2;

        this._URI = backendURI;
        _ = this.Label;
    }

    /// \copydoc Fact.parseFact(ScrollFact)
    public new static ParallelLineFact parseFact(MMTDeclaration fact)
    {
        if (((MMTSymbolDeclaration)fact).type is not OMA type) // proof DED
            return null;

        OMA parallel_lines_OMA = (OMA)type.arguments[0]; // parallel

        string lineAUri = ((OMS)parallel_lines_OMA.arguments[0]).uri;
        string lineBUri = ((OMS)parallel_lines_OMA.arguments[1]).uri;

        if (!FactOrganizer.AllFacts.ContainsKey(lineAUri)
         || !FactOrganizer.AllFacts.ContainsKey(lineBUri))
            return null;

        return new ParallelLineFact(lineAUri, lineBUri, fact.@ref.uri, StageStatic.stage.factState);
    }

    /// \copydoc Fact.generateLabel
    protected override string generateLabel()
        => Ray1.Label + "||" + Ray2.Label;

    public override MMTDeclaration MakeMMTDeclaration()
    {
        SOMDoc tp = new OMA(
            new OMS(MMT_OMS_URI.Ded),
            new[] {
                new OMA(
                    new OMS(MMT_OMS_URI.ParallelLine),
                    new[]  {
                        new OMS(Lid1),
                        new OMS(Lid2),
                    }
                ),
            }
        );

        SOMDoc df = null;

        return new MMTSymbolDeclaration(this.Label, tp, df);
    }

    /// \copydoc Fact.hasDependentFacts
    public override bool HasDependentFacts => true;

    /// \copydoc Fact.getDependentFactIds
    protected override string[] GetGetDependentFactIds()
        => new string[] { Lid1, Lid2 };

    /// \copydoc Fact.Equivalent(Fact, Fact)
    protected override bool EquivalentWrapped(ParallelLineFact f1, ParallelLineFact f2)
        => DependentFactsEquivalent(f1, f2);

    protected override Fact _ReInitializeMe(Dictionary<string, string> old_to_new, FactOrganizer organizer)
        => new ParallelLineFact(old_to_new[this.Lid1], old_to_new[this.Lid2], organizer);
}

/// <summary>
/// A Circle that is made out of a middle point, a plane and a radius
/// </summary>
public class CircleFact : FactWrappedCRTP<CircleFact>
{
    /// <summary> defining the middle point of the circle  </summary>
    public string Pid1;
    /// <summary>  defining the base point of the circle plane </summary>
    public string Pid2;

    [JsonIgnore]
    public PointFact Point1 { get => (PointFact)FactOrganizer.AllFacts[Pid1]; }
    [JsonIgnore]
    public PointFact Point2 { get => (PointFact)FactOrganizer.AllFacts[Pid2]; }

    /// <summary>  radius of the circle </summary>
    public float radius;
    /// <summary> normal vector of the plane </summary>
    public Vector3 normal;

    /// <summary> \copydoc Fact.Fact </summary>
    public CircleFact() : base()
    {
        this.normal = Vector3.zero;
        this.Pid1 = null;
        this.Pid2 = null;
        this.radius = 0;
    }

    /// <summary>
    /// Standard Constructor:
    /// Initiates <see cref="Pid1"/>, <see cref="Pid2"/>, <see cref="radius"/>,<see cref="dir1"/>,<see cref="dir2"/>, <see cref="Fact._URI"/> and creates MMT %Fact Server-Side
    /// </summary>
    /// <param name="pid1">sets <see cref="Pid1"/></param>
    /// <param name="pid2">sets <see cref="Pid2"/></param>
    /// <param name="radius">sets <see cref="radius"/></param>
    /// <param name="normal">sets <see cref="normal"/></param>
    /// <param name="organizer">sets <see cref="Fact._Facts"/></param>
    public CircleFact(string pid1, string pid2, float radius, Vector3 normal, FactOrganizer organizer) : base(organizer)
    {
        this.Pid1 = pid1;
        this.Pid2 = pid2;

        this.radius = radius;
        this.normal = normal;

        SendToMMT();
    }

    protected override void RecalculateTransform()
    {
        Position = Point1.Position;
        { //Rotation
            Vector3 arbitary_not_normal = normal == Vector3.forward ? Vector3.right : Vector3.forward;
            Vector3 forwoard = Vector3.Cross(arbitary_not_normal, normal);

            Rotation = Quaternion.LookRotation(forwoard, normal);
        }
        LocalScale = new Vector3(radius, 1, radius);
    }

    /// <summary>
    /// Bypasses initialization of new MMT %Fact by using existend URI, _which is not checked for existence_.
    /// </summary>
    /// <param name="Pid1">sets <see cref="Pid1"/></param>
    /// <param name="Pid2">sets <see cref="Pid2"/></param>
    /// <param name="radius">sets <see cref="radius"/></param>
    /// <param name="normal">sets <see cref="normal"/></param>
    /// <param name="backendURI">MMT URI</param>
    /// <param name="organizer">sets <see cref="Fact._Facts"/></param>
    public CircleFact(string Pid1, string Pid2, float radius, Vector3 normal, string backendURI, FactOrganizer organizer) : base(organizer)
    {
        this.Pid1 = Pid1;
        this.Pid2 = Pid2;

        this.radius = radius;
        this.normal = normal;

        this._URI = backendURI;
        _ = this.Label;
    }

    /// <summary>
    /// parses the Circlefact response of the MMT-Server
    /// </summary>
    /// \copydoc Fact.parseFact(ScrollFact) 
    public new static CircleFact parseFact(MMTDeclaration fact)
    {
        if (((MMTSymbolDeclaration)fact).defines is not OMA df)
            return null;

        OMA planeOMA = (OMA)df.arguments[0];
        string planeApplicant = ((OMS)planeOMA.applicant).uri;

        Vector3 normal;
        // Getting the plane
        // IN case of a normale plane
        if (planeApplicant.Equals(MMT_OMS_URI.pointNormalPlane))
        {
            //OMA pointAOMA = (OMA)planeOMA.arguments[0];
            normal = (planeOMA.arguments[1].GetLambdaExpression().Compile() as Func<Vector3>)();
        }
        // In case of parametrized plane
        else if (planeApplicant.Equals(MMT_OMS_URI.ParametrizedPlane))
        {
            Vector3 v = (planeOMA.arguments[1].GetLambdaExpression().Compile() as Func<Vector3>)();
            Vector3 w = (planeOMA.arguments[2].GetLambdaExpression().Compile() as Func<Vector3>)();

            normal = Vector3.Cross(v, w).normalized;
        }
        // incase of smth else. Shouldn't hapepen unless there is an error
        else throw new ArgumentException("Invalid planeApplicant: " + planeApplicant);

        // get the mid point uri
        string parse_id_M = df.arguments[1].ToString();
        string M_uri = ParsingDictionary.parseTermsToId[parse_id_M];
        string A_uri = ParsingDictionary.parseTermsToId[planeOMA.arguments[0].ToString()];
        float radius = ((OMF)df.arguments[2]).@float;

        if (!FactOrganizer.AllFacts.ContainsKey(M_uri)
         || !FactOrganizer.AllFacts.ContainsKey(A_uri))
            return null; //If dependent facts do not exist return null

        return new CircleFact(M_uri, A_uri, radius, normal, fact.@ref.uri, StageStatic.stage.factState);
    }

    /// \copydoc Fact.generateLabel
    protected override string generateLabel()
        => "○" + Point1.Label;

    /// <summary>
    /// Constructs struct for right-angled MMT %Fact <see cref="AddFactResponse"/>
    /// </summary>
    /// <param name="Pid1"> <see cref="Pid1"/></param>
    /// <param name="p2URI"> <see cref="Pid2"/></param>
    /// <param name="radius"> <see cref="radius"/></param>
    /// <returns>struct for <see cref="AddFactResponse"/></returns>
    public override MMTDeclaration MakeMMTDeclaration()
    {
        SOMDoc[] outerArguments = new SOMDoc[]
        {
           //CirclePlane,
           new OMA(
               //PointNormalPlane,
               new OMS(MMT_OMS_URI.pointNormalPlane), 
               //planeArgs,
               new SOMDoc[] {
                    //base point of the circle plane?,
                    new OMS(Pid2),
                    //NormalVector,
                    new OMA(
                        //"Vector"
                        new OMS(MMT_OMS_URI.Tuple),
                        //normalArgs,
                        new[]  {
                            new OMF(normal.x),
                            new OMF(normal.y),
                            new OMF(normal.z)
                        }
                    ),
                }
            ),
           //middlePoint,
           new OMS(Pid1),
           //Radius,
           new OMF(radius),
        };

        // Do i need this here? doubt 
        SOMDoc tp = new OMS(MMT_OMS_URI.CircleType3d);
        SOMDoc df = new OMA(new OMS(MMT_OMS_URI.MkCircle3d), outerArguments);

        return new MMTSymbolDeclaration(Label, tp, df);
    }

    /// \copydoc Fact.hasDependentFacts
    public override bool HasDependentFacts => true;

    /// \copydoc Fact.getDependentFactIds
    protected override string[] GetGetDependentFactIds()
        => new string[] { Pid1, Pid2 };

    /// \copydoc Fact.Equivalent(Fact, Fact)
    protected override bool EquivalentWrapped(CircleFact f1, CircleFact f2)
        => DependentFactsEquivalent(f1, f2)
        && Math3d.IsApproximatelyEqual(f1.normal, f2.normal)
        && Mathf.Approximately(f1.radius, f2.radius);

    protected override Fact _ReInitializeMe(Dictionary<string, string> old_to_new, FactOrganizer organizer)
        => new CircleFact(old_to_new[this.Pid1], old_to_new[this.Pid2], this.radius, this.normal, organizer);
}

/// <summary>
/// A <see cref="PointFact"/> on a <see cref="CircleFact"/>
/// </summary>
public class OnCircleFact : FactWrappedCRTP<OnCircleFact>
{
    /// <summary> the point on the circle  </summary>
    public string Pid;
    /// <summary> the circle, which the point is on  </summary>
    public string Cid;

    [JsonIgnore]
    public PointFact Point { get => (PointFact)FactOrganizer.AllFacts[Pid]; }
    [JsonIgnore]
    public CircleFact Circle { get => (CircleFact)FactOrganizer.AllFacts[Cid]; }

    /// <summary> \copydoc Fact.Fact </summary>
    public OnCircleFact() : base()
    {
        this.Pid = null;
        this.Cid = null;
    }

    /// <summary>
    /// Standard Constructor:
    /// Initiates <see cref="Pid"/>, <see cref="Rid"/>, <see cref="Fact._URI"/> and creates MMT %Fact Server-Side
    /// </summary>
    /// <param name="pid">sets <see cref="Pid"/></param>
    /// <param name="cid">sets <see cref="Cid"/></param>
    /// <param name="organizer">sets <see cref="Fact._Facts"/></param>
    public OnCircleFact(string pid, string cid, FactOrganizer organizer) : base(organizer)
    {
        this.Pid = pid;
        this.Cid = cid; ;

        SendToMMT();
    }

    protected override void RecalculateTransform()
    {
        Position = Point.Position;
        Rotation = Circle.Rotation;
    }

    /// <summary>
    /// Bypasses initialization of new MMT %Fact by using existend URI, _which is not checked for existence_.
    /// </summary>
    /// <param name="pid">sets <see cref="Pid"/></param>
    /// <param name="cid">sets <see cref="Cid"/></param>
    /// <param name="uri">MMT URI</param>
    /// <param name="organizer">sets <see cref="Fact._Facts"/></param>
    public OnCircleFact(string pid, string cid, string uri, FactOrganizer organizer) : base(organizer)
    {
        this.Pid = pid;
        this.Cid = cid;
        this._URI = uri;
        _ = this.Label;
    }

    /// \copydoc Fact.parseFact(ScrollFact)
    public new static OnCircleFact parseFact(MMTDeclaration fact)
    {
        if (((MMTSymbolDeclaration)fact).type is not OMA type)
            return null;

        string circleUri = ((OMS)((OMA)type.arguments[0]).arguments[0]).uri;
        string pointUri = ((OMS)((OMA)type.arguments[0]).arguments[1]).uri;

        if (!FactOrganizer.AllFacts.ContainsKey(pointUri)
         || !FactOrganizer.AllFacts.ContainsKey(circleUri))
            return null;

        return new OnCircleFact(pointUri, circleUri, fact.@ref.uri, StageStatic.stage.factState);
    }

    /// \copydoc Fact.generateLabel
    protected override string generateLabel()
        => Point.Label + "∈" + Circle.Label;

    /// \copydoc Fact.hasDependentFacts
    public override bool HasDependentFacts => true;

    /// \copydoc Fact.getDependentFactIds
    protected override string[] GetGetDependentFactIds()
        => new string[] { Pid, Cid };

    /// \copydoc Fact.Equivalent(Fact, Fact)
    protected override bool EquivalentWrapped(OnCircleFact c1, OnCircleFact c2)
        => DependentFactsEquivalent(c1, c2);

    protected override Fact _ReInitializeMe(Dictionary<string, string> old_to_new, FactOrganizer organizer)
        => new OnCircleFact(old_to_new[this.Pid], old_to_new[this.Cid], organizer);

    public override MMTDeclaration MakeMMTDeclaration()
    {
        SOMDoc tp =
            new OMA(
                new OMS(MMT_OMS_URI.Ded),
                new[] {
                    new OMA(
                        new OMS(MMT_OMS_URI.OnCircle),
                        new[] {
                            new OMS(Cid),
                            new OMS(Pid),
        }),});

        SOMDoc df = null;

        return new MMTSymbolDeclaration(Label, tp, df);
    }
}

/// <summary>
/// Angle comprised of a line and a circle 
/// </summary>
public class AngleCircleLineFact : FactWrappedCRTP<AngleCircleLineFact>
{
    /// @{ <summary>
    /// One <see cref="Fact.Id">Id</see> of a <see cref="RayFact">RayFact</see> and a <see cref="CircleFact">CircleFact</see>  defining Angle [<see cref="Cid1"/>, <see cref="Rid2"/>].
    /// </summary>
    public string Cid1, Rid2;
    /// @}

    [JsonIgnore]
    public AbstractLineFact Ray { get => (AbstractLineFact)FactOrganizer.AllFacts[Rid2]; }
    [JsonIgnore]
    public CircleFact Circle { get => (CircleFact)FactOrganizer.AllFacts[Cid1]; }

    //TODO? deg or rad?
    [JsonIgnore]
    public float angle;

    [JsonIgnore]
    public Vector3 intersection;

    /// <summary> \copydoc Fact.Fact </summary>
    public AngleCircleLineFact() : base()
    {
        this.Cid1 = null;
        this.Rid2 = null;
        this.angle = 0.0f;
    }

    /// <summary>
    /// Standard Constructor:
    /// Initiates <see cref="Cid1"/>, <see cref="Rid2"/>, <see cref="angle"/> <see cref="Fact._URI"/> and creates MMT %Fact Server-Side
    /// </summary>
    /// <param name="cid1">sets <see cref="Cid1"/></param>
    /// <param name="rid2">sets <see cref="Rid2"/></param>
    /// <param name="angle"> sets the angle </param>
    /// <param name="organizer">sets <see cref="Fact._Facts"/></param>
    public AngleCircleLineFact(string cid1, string rid2, FactOrganizer organizer) : base(organizer)
    {
        this.Cid1 = cid1;
        this.Rid2 = rid2;
        this.angle = Math3d.AngleVectorPlane(Ray.Dir, Circle.normal).ToDegrees();
        Math3d.LinePlaneIntersection(out intersection, Ray.Point1.Position, Ray.Dir, Circle.normal, Circle.Position);

        SendToMMT();
    }

    protected override void RecalculateTransform()
    {
        Position = intersection;
        { //Rotation
            Vector3 from = (Circle.Position - Position).normalized;

            Vector3 angle_to = Math3d.IsApproximatelyEqual(intersection, Ray.Point1.Position)
                ? Ray.Point2.Position
                : Ray.Point1.Position;
            Vector3 to = (angle_to - Position).normalized;

            Vector3 up = Vector3.Cross(to, from);
            Vector3 forwoard = (from + to).normalized;

            if (up.sqrMagnitude < Math3d.vectorPrecission)
            { //Angle is 180° (or 0°)
                Vector3 arbitary = up.normalized == Vector3.forward ? Vector3.right : Vector3.forward;
                up = Vector3.Cross(arbitary, to);
                forwoard = Vector3.Cross(up, to);
            }

            Rotation = Quaternion.LookRotation(forwoard, up);
        }
    }

    /// <summary>
    /// Bypasses initialization of new MMT %Fact by using existend URI, _which is not checked for existence_.
    /// </summary>
    /// <param name="Cid1">sets <see cref="Cid1"/></param>
    /// <param name="´Rid2">sets <see cref="Rid2"/></param>
    /// <param name="angle"> sets the angle </param>
    /// <param name="backendURI">MMT URI</param>
    /// <param name="organizer">sets <see cref="Fact._Facts"/></param>
    public AngleCircleLineFact(string Cid1, string Rid2, float angle, string backendURI, FactOrganizer organizer) : base(organizer)
    {
        this.Cid1 = Cid1;
        this.Rid2 = Rid2;
        this.angle = angle;

        this._URI = backendURI;
        _ = this.Label;
    }

    /// \copydoc Fact.parseFact(ScrollFact)
    public new static AngleCircleLineFact parseFact(MMTDeclaration fact)
    {
        if (((MMTValueDeclaration)fact).lhs is not OMA lhs)
            return null;

        // init it with 0 degrees, so we don't accidentally generate orthogonalfacts 
        // and the parsing works correctly if smb ever adds a scroll for this
        float angle = 0.0f;

        if (((MMTValueDeclaration)fact).value is OMF oMFangle)
            angle = oMFangle.@float;

        string CircleUri = ((OMS)lhs.arguments[0]).uri;
        string RayUri = ((OMS)lhs.arguments[1]).uri;

        if (!FactOrganizer.AllFacts.ContainsKey(CircleUri)
         || !FactOrganizer.AllFacts.ContainsKey(RayUri))
            return null;

        return new AngleCircleLineFact(CircleUri, RayUri, angle, fact.@ref.uri, StageStatic.stage.factState);
    }

    /// \copydoc Fact.generateLabel
    protected override string generateLabel()
        => "∠" + Circle.Label + Ray.Label;

    public override MMTDeclaration MakeMMTDeclaration()
    {
        SOMDoc lhs =
            new OMA(
                new OMS(MMT_OMS_URI.AnglePlaneLine),
                new[] {
                    new OMS(Cid1),
                    new OMS(Rid2),
                }
            );

        SOMDoc valueTp = new OMS(MMT_OMS_URI.RealLit);
        SOMDoc value = new OMF(angle);

        return new MMTValueDeclaration(this.Label, lhs, valueTp, value);
    }

    /// \copydoc Fact.hasDependentFacts
    public override bool HasDependentFacts => true;

    /// \copydoc Fact.getDependentFactIds
    protected override string[] GetGetDependentFactIds()
        => new string[] { Cid1, Rid2 };

    /// \copydoc Fact.Equivalent(Fact, Fact)
    protected override bool EquivalentWrapped(AngleCircleLineFact f1, AngleCircleLineFact f2)
        => DependentFactsEquivalent(f1, f2);

    protected override Fact _ReInitializeMe(Dictionary<string, string> old_to_new, FactOrganizer organizer)
        => new AngleCircleLineFact(old_to_new[this.Cid1], old_to_new[this.Rid2], organizer);
}

/// <summary>
/// A RadiusFact that corresponds to a <see cref="CircleFact">PointFacts</see> and has a float value (the actual radius).
/// </summary>
public class RadiusFact : FactWrappedCRTP<RadiusFact>
{
    /// <summary> The circle corresponding to the radius </summary>
    public string Cid1;

    [JsonIgnore]
    public CircleFact Circle { get => (CircleFact)FactOrganizer.AllFacts[Cid1]; }

    /// <summary> The radius as a float </summary>
    public float rad;

    /// <summary> \copydoc Fact.Fact </summary>
    public RadiusFact() : base()
    {
        this.Cid1 = null;
        this.rad = 0.0f;
    }

    /// <summary>
    /// Standard Constructor:
    /// Initiates <see cref="Cid1"/> and <see cref="rad"/>
    /// </summary>
    /// <param name="cid1">sets <see cref="Cid1"/></param>
    /// <param name="organizer">sets <see cref="Fact._Facts"/></param>
    public RadiusFact(string cid1, FactOrganizer organizer) : base(organizer)
    {
        this.Cid1 = cid1;
        this.rad = Circle.radius;

        SendToMMT();
    }

    protected override void RecalculateTransform()
    {
        Position = Circle.Position;
        Rotation = Circle.Rotation;
    }

    /// <summary>
    /// Bypasses initialization of new MMT %Fact by using existend URI, _which is not checked for existence_.
    /// </summary>
    /// <param name="Cid1">sets <see cref="Cid1"/></param>
    /// <param name="backendURI">MMT URI</param>
    /// <param name="organizer">sets <see cref="Fact._Facts"/></param>
    public RadiusFact(string Cid1, string backendURI, FactOrganizer organizer) : base(organizer)
    {
        this.Cid1 = Cid1;

        this._URI = backendURI;
        _ = this.Label;
    }

    /// \copydoc Fact.parseFact(ScrollFact)
    public new static RadiusFact parseFact(MMTDeclaration fact)
    {
        string CircleUri = ((OMS)((OMA)((MMTValueDeclaration)fact).lhs).arguments[0]).uri;

        if (!FactOrganizer.AllFacts.ContainsKey(CircleUri))
            return null;

        return new RadiusFact(CircleUri, fact.@ref.uri, StageStatic.stage.factState);
    }

    /// \copydoc Fact.generateLabel
    protected override string generateLabel()
        => "r " + Circle.Label;

    /// <summary>
    /// Constructs struct for not-right-angled MMT %Fact <see cref="AddFactResponse"/>
    /// </summary>
    /// <param name="rad"> see <see cref="rad"/></param>
    /// <param name="c1URI"> see <see cref="Cid1"/></param>

    public override MMTDeclaration MakeMMTDeclaration()
    {
        SOMDoc lhs =
            new OMA(
                new OMS(MMT_OMS_URI.RadiusCircleMetric),
                new[] {
                    new OMS(Cid1),
                }
            );

        SOMDoc valueTp = new OMS(MMT_OMS_URI.RealLit);
        SOMDoc value = new OMF(rad);

        return new MMTValueDeclaration(this.Label, lhs, valueTp, value);
    }

    /// \copydoc Fact.hasDependentFacts
    public override bool HasDependentFacts => true;

    /// \copydoc Fact.getDependentFactIds
    protected override string[] GetGetDependentFactIds()
        => new string[] { Cid1 };

    /// \copydoc Fact.Equivalent(Fact, Fact)
    protected override bool EquivalentWrapped(RadiusFact f1, RadiusFact f2)
        => DependentFactsEquivalent(f1, f2);

    protected override Fact _ReInitializeMe(Dictionary<string, string> old_to_new, FactOrganizer organizer)
        => new RadiusFact(old_to_new[this.Cid1], organizer);
}

/// <summary>
/// Area of a <see cref="CircleFact">CircleFact</see> 
/// </summary>
public class AreaCircleFact : FactWrappedCRTP<AreaCircleFact>
{
    /// <summary> the circle <see cref="CircleFact">CircleFact</see>  </summary>
    public string Cid1;

    [JsonIgnore]
    public CircleFact Circle { get => (CircleFact)FactOrganizer.AllFacts[Cid1]; }

    /// <summary> the area which is contained by the circle </summary>
    public float A;


    /// <summary> \copydoc Fact.Fact </summary>
    public AreaCircleFact() : base()
    {
        this.Cid1 = null;
        this.A = 0.0f;
    }

    /// <summary>
    /// Standard Constructor:
    /// Initiates <see cref="Cid1"/> and creates MMT %Fact Server-Side
    /// </summary>
    /// <param name="cid1">sets <see cref="Cid1"/></param>
    /// <param name="organizer">sets <see cref="Fact._Facts"/></param>
    public AreaCircleFact(string cid1, FactOrganizer organizer) : base(organizer)
    {
        this.Cid1 = cid1;

        this.A = Circle.radius * Circle.radius * ((float)System.Math.PI);

        SendToMMT();
    }

    protected override void RecalculateTransform()
    {
        Position = Circle.Position;
        Rotation = Circle.Rotation;
    }

    /// <summary>
    /// Bypasses initialization of new MMT %Fact by using existend URI, _which is not checked for existence_.
    /// </summary>
    /// <param name="Cid1">sets <see cref="Cid1"/></param>
    /// <param name="backendURI">MMT URI</param>
    /// <param name="organizer">sets <see cref="Fact._Facts"/></param>
    public AreaCircleFact(string Cid1, string backendURI, FactOrganizer organizer) : base(organizer)
    {
        this.Cid1 = Cid1;

        this._URI = backendURI;
        _ = this.Label;
    }

    /// \copydoc Fact.parseFact(ScrollFact)
    public new static AreaCircleFact parseFact(MMTDeclaration fact)
    {
        string CircleUri = ((OMS)((OMA)((MMTValueDeclaration)fact).lhs).arguments[0]).uri;

        if (!FactOrganizer.AllFacts.ContainsKey(CircleUri))
            return null;

        return new AreaCircleFact(CircleUri, fact.@ref.uri, StageStatic.stage.factState);
    }

    /// \copydoc Fact.generateLabel
    protected override string generateLabel()
        => "A(" + Circle.Label + ")";

    public override MMTDeclaration MakeMMTDeclaration()
    {
        SOMDoc lhs =
            new OMA(
                new OMS(MMT_OMS_URI.AreaCircle),
                new[] {
                    new OMS(Cid1),
                }
            );

        SOMDoc valueTp = new OMS(MMT_OMS_URI.RealLit);
        SOMDoc value = new OMF(A);

        return new MMTValueDeclaration(this.Label, lhs, valueTp, value);
    }

    /// \copydoc Fact.hasDependentFacts
    public override bool HasDependentFacts => true;

    /// \copydoc Fact.getDependentFactIds
    protected override string[] GetGetDependentFactIds()
        => new string[] { Cid1 };

    /// \copydoc Fact.GetHashCode
    public override int GetHashCode()
        => base.GetHashCode() ^ A.GetHashCode();

    /// \copydoc Fact.Equivalent(Fact, Fact)
    protected override bool EquivalentWrapped(AreaCircleFact f1, AreaCircleFact f2)
        => DependentFactsEquivalent(f1, f2);

    protected override Fact _ReInitializeMe(Dictionary<string, string> old_to_new, FactOrganizer organizer)
        => new AreaCircleFact(old_to_new[this.Cid1], organizer);
}

/// <summary>
/// The volume of a cone A  defined by a base area  <see cref="CircleFact">CircleFact</see>, an apex <see cref="PointFact">PointFact</see> and the volume as float
/// </summary>
public class ConeVolumeFact : FactWrappedCRTP<ConeVolumeFact>
{
    ///  <summary> a <see cref="CircleFact">CircleFact</see> describing the base area </summary>
    public string Cid1;
    [JsonIgnore]
    public CircleFact Circle { get => (CircleFact)FactOrganizer.AllFacts[Cid1]; }

    ///  <summary> a <see cref="PointFact">PointFact</see> describing the apex point  </summary>
    public string Pid1;
    [JsonIgnore]
    public PointFact Point { get => (PointFact)FactOrganizer.AllFacts[Pid1]; }

    ///  <summary> the volume of the cone as a float </summary>
    public float vol;

    /// <summary> \copydoc Fact.Fact </summary>
    public ConeVolumeFact() : base()
    {
        this.Cid1 = null;
        this.Pid1 = null;
        this.vol = 0.0f;
    }

    /// <summary>
    /// Standard Constructor:
    /// Initiates members and creates MMT %Fact Server-Side
    /// </summary>
    /// <param name="cid1">sets <see cref="Cid1"/></param>
    /// <param name="pid1">sets <see cref="Pid1"/></param>
    /// <param name="vol">sets <see cref="vol"/></param>
    /// <param name="organizer">sets <see cref="Fact._Facts"/></param>
    public ConeVolumeFact(string cid1, string pid1, float vol, FactOrganizer organizer) : base(organizer)
    {
        this.Cid1 = cid1;
        this.Pid1 = pid1;
        this.vol = vol;

        SendToMMT();
    }

    protected override void RecalculateTransform()
    {
        Position = Point.Position;
        Rotation = Circle.Rotation;
    }

    /// <summary>
    /// Bypasses initialization of new MMT %Fact by using existend URI, _which is not checked for existence_.
    /// </summary>
    /// <param name="Cid1">sets <see cref="Cid1"/></param>
    /// <param name="Pid1">sets <see cref="Pid1"/></param>
    /// <param name="volume">sets <see cref="vol"/></param>
    /// <param name="backendURI">MMT URI</param>
    /// <param name="organizer">sets <see cref="Fact._Facts"/></param>
    public ConeVolumeFact(string Cid1, string Pid1, float volume, string backendURI, FactOrganizer organizer) : base(organizer)
    {
        this.Cid1 = Cid1;
        this.Pid1 = Pid1;
        this.vol = volume;

        this._URI = backendURI;
        _ = this.Label;
    }

    /// \copydoc Fact.parseFact(ScrollFact)
    public new static ConeVolumeFact parseFact(MMTDeclaration fact)
    {
        if (((MMTValueDeclaration)fact).lhs is not OMA lhs)
            return null;

        string CircleUri = ((OMS)((OMA)lhs.arguments[0]).arguments[0]).uri;
        string PointUri = ((OMS)((OMA)lhs.arguments[0]).arguments[1]).uri;

        float volume = 0.0f;
        if (((MMTValueDeclaration)fact).value is OMF oMFvolume)
            volume = oMFvolume.@float;

        if (!FactOrganizer.AllFacts.ContainsKey(CircleUri)
         || !FactOrganizer.AllFacts.ContainsKey(PointUri))
            return null;

        return new ConeVolumeFact(CircleUri, PointUri, volume, fact.@ref.uri, StageStatic.stage.factState);
    }

    /// \copydoc Fact.generateLabel
    protected override string generateLabel()
        => "V(" + Circle.Label + "," + Point.Label + ")";

    public override MMTDeclaration MakeMMTDeclaration()
    {
        SOMDoc lhs =
            new OMA(
                new OMS(MMT_OMS_URI.VolumeCone),

                new[] {
                    new OMA(new OMS(MMT_OMS_URI.ConeOfCircleApex),
                        new[]  {
                            new OMS(Cid1),
                            new OMS(Pid1),
                         }
                    ),
                }
            );

        SOMDoc valueTp = new OMS(MMT_OMS_URI.RealLit);
        SOMDoc value = new OMF(vol);

        return new MMTValueDeclaration(this.Label, lhs, valueTp, value);
    }

    /// \copydoc Fact.hasDependentFacts
    public override bool HasDependentFacts => true;

    /// \copydoc Fact.getDependentFactIds
    protected override string[] GetGetDependentFactIds()
        => new string[] { Cid1, Pid1 };

    /// \copydoc Fact.Equivalent(Fact, Fact)
    protected override bool EquivalentWrapped(ConeVolumeFact f1, ConeVolumeFact f2)
        => DependentFactsEquivalent(f1, f2);

    protected override Fact _ReInitializeMe(Dictionary<string, string> old_to_new, FactOrganizer organizer)
        => new ConeVolumeFact(old_to_new[this.Cid1], old_to_new[this.Pid1], this.vol, organizer);
}

/// <summary>
/// The fact that the plane of a <see cref="CircleFact">CircleFact</see> and the line <see cref="RayFact>RayFact</see> are orthogonal
/// </summary>
public class OrthogonalCircleLineFact : FactWrappedCRTP<OrthogonalCircleLineFact>
{
    ///  <summary> a <see cref="CircleFact">CircleFact</see> describing the base area </summary>
    public string Cid1;
    [JsonIgnore]
    public CircleFact Circle { get => (CircleFact)FactOrganizer.AllFacts[Cid1]; }

    ///  <summary> a <see cref="RayFact">Rayfact</see> describing the line </summary>
    public string Lid1;
    [JsonIgnore]
    public AbstractLineFact Ray { get => (AbstractLineFact)FactOrganizer.AllFacts[Lid1]; }

    //TODO? deg or rad?
    [JsonIgnore]
    public float angle = 90f;

    [JsonIgnore]
    public Vector3 intersection;


    /// <summary> \copydoc Fact.Fact </summary>
    public OrthogonalCircleLineFact() : base()
    {
        this.Cid1 = null;
        this.Lid1 = null;
    }

    /// <summary>
    /// Standard Constructor:
    /// Initiates members and creates MMT %Fact Server-Side
    /// </summary>
    /// <param name="cid1">sets <see cref="Cid1"/></param>
    /// <param name="lid1">sets <see cref="Lid1"/></param>
    /// <param name="organizer">sets <see cref="Fact._Facts"/></param>
    public OrthogonalCircleLineFact(string cid1, string lid1, FactOrganizer organizer) : base(organizer)
    {
        this.Cid1 = cid1;
        this.Lid1 = lid1;
        Math3d.LinePlaneIntersection(out intersection, Ray.Point1.Position, Ray.Dir, Circle.normal, Circle.Position);

        SendToMMT();
    }

    protected override void RecalculateTransform()
    {
        Position = intersection;
        { //Rotation
            Vector3 from = (Circle.Position - Position).normalized;

            Vector3 angle_to = Math3d.IsApproximatelyEqual(intersection, Ray.Point1.Position)
                ? Ray.Point2.Position
                : Ray.Point1.Position;
            Vector3 to = (angle_to - Position).normalized;

            Vector3 up = Vector3.Cross(to, from);
            Vector3 forward = (from + to).normalized;
            Rotation = Quaternion.LookRotation(forward, up);
        }
    }

    /// <summary>
    /// Bypasses initialization of new MMT %Fact by using existend URI, _which is not checked for existence_.
    /// </summary>
    /// <param name="Cid1">sets <see cref="Cid1"/></param>
    /// <param name="Lid1">sets <see cref="Lid1"/></param>
    /// <param name="backendURI">MMT URI</param>
    /// <param name="organizer">sets <see cref="Fact._Facts"/></param>
    public OrthogonalCircleLineFact(string Cid1, string Lid1, string backendURI, FactOrganizer organizer) : base(organizer)
    {
        this.Cid1 = Cid1;
        this.Lid1 = Lid1;

        this._URI = backendURI;
        _ = this.Label;
    }

    /// \copydoc Fact.parseFact(ScrollFact)
    public new static OrthogonalCircleLineFact parseFact(MMTDeclaration fact)
    {
        if (((MMTSymbolDeclaration)fact).type is not OMA type)
            return null;

        string CircleUri = ((OMS)((OMA)type.arguments[0]).arguments[0]).uri;
        string LineUri = ((OMS)((OMA)type.arguments[0]).arguments[1]).uri;

        if (!FactOrganizer.AllFacts.ContainsKey(CircleUri)
         || !FactOrganizer.AllFacts.ContainsKey(LineUri))
            return null;

        return new OrthogonalCircleLineFact(CircleUri, LineUri, fact.@ref.uri, StageStatic.stage.factState);
    }

    /// \copydoc Fact.generateLabel
    protected override string generateLabel()
        => Circle.Label + "⊥" + Ray.Label;

    public override MMTDeclaration MakeMMTDeclaration()
    {
        SOMDoc tp = new OMA(
            new OMS(MMT_OMS_URI.Ded),
            new[]{
                new OMA(
                    new OMS(MMT_OMS_URI.OrthoCircleLine),
                    new[] {
                        new OMS(Cid1),
                        new OMS(Lid1),
                    }
                ),
            }
        );

        SOMDoc df = null;

        return new MMTSymbolDeclaration(this.Label, tp, df);
    }

    /// \copydoc Fact.hasDependentFacts
    public override bool HasDependentFacts => true;

    /// \copydoc Fact.getDependentFactIds
    protected override string[] GetGetDependentFactIds()
        => new string[] { Cid1, Lid1 };

    /// \copydoc Fact.Equivalent(Fact, Fact)
    protected override bool EquivalentWrapped(OrthogonalCircleLineFact f1, OrthogonalCircleLineFact f2)
        => DependentFactsEquivalent(f1, f2);

    protected override Fact _ReInitializeMe(Dictionary<string, string> old_to_new, FactOrganizer organizer)
        => new OrthogonalCircleLineFact(old_to_new[this.Cid1], old_to_new[this.Lid1], organizer);
}

/// <summary>
/// The volume of a cone A  defined by a base area  <see cref="CircleFact">CircleFact</see>, a top area <see cref="CircleFact">CircleFact</see> and the volume as float
/// </summary>
public class TruncatedConeVolumeFact : FactWrappedCRTP<TruncatedConeVolumeFact>
{
    ///  <summary> a <see cref="CircleFact">CircleFact</see> describing the base area </summary>
    public string Cid1;
    [JsonIgnore]
    public CircleFact Circle1 { get => (CircleFact)FactOrganizer.AllFacts[Cid1]; }

    ///  <summary> a <see cref="CircleFact">CircleFact</see> describing the top area  </summary>
    public string Cid2;
    [JsonIgnore]
    public CircleFact Circle2 { get => (CircleFact)FactOrganizer.AllFacts[Cid2]; }

    ///  <summary> the volume of Truncated the cone as a float </summary>
    public float vol;
    /// <summary> a proof that both circles have not the same size </summary>
    public string unequalCirclesProof;
    ///  <summary> OMA proof that the two circles are parallel  </summary>
    public OMA proof;


    /// <summary> \copydoc Fact.Fact </summary>
    public TruncatedConeVolumeFact() : base()
    {
        this.Cid1 = null;
        this.Cid2 = null;
        this.vol = 0.0f;
        this.unequalCirclesProof = null;
        this.proof = null;
    }

    /// <summary>
    /// Standard Constructor:
    /// Initiates members and creates MMT %Fact Server-Side
    /// </summary>
    /// <param name="cid1">sets <see cref="Cid1"/></param>
    /// <param name="cid2">sets <see cref="Cid2"/></param>
    /// <param name="vol">sets <see cref="vol"/></param>
    /// <param name="proof">sets <see cref="proof"/></param>
    /// <param name="organizer">sets <see cref="Fact._Facts"/></param>
    public TruncatedConeVolumeFact(string cid1, string cid2, float vol, string unequalproof, OMA proof, FactOrganizer organizer) : base(organizer)
    {
        this.Cid1 = cid1;
        this.Cid2 = cid2;
        this.proof = proof;
        this.unequalCirclesProof = unequalproof;
        this.vol = vol;

        SendToMMT();
    }

    protected override void RecalculateTransform()
    {
        Position = Circle2.Position;
        Rotation = Circle2.Rotation;
    }

    /// <summary>
    /// Bypasses initialization of new MMT %Fact by using existend URI, _which is not checked for existence_.
    /// </summary>
    /// <param name="Cid1">sets <see cref="Cid1"/></param>
    /// <param name="Cid2">sets <see cref="Cid2"/></param>
    /// <param name="volume">sets <see cref="vol"/></param>
    /// <param name="proof">sets <see cref="proof"/></param>
    /// <param name="backendURI">MMT URI</param>
    /// <param name="organizer">sets <see cref="Fact._Facts"/></param>
    public TruncatedConeVolumeFact(string Cid1, string Cid2, float volume, string unequalproof, OMA proof, string backendURI, FactOrganizer organizer) : base(organizer)
    {
        this.Cid1 = Cid1;
        this.Cid2 = Cid2;
        this.vol = volume;
        this.proof = proof;
        this.unequalCirclesProof = unequalproof;

        this._URI = backendURI;
        _ = this.Label;
    }

    /// \copydoc Fact.parseFact(ScrollFact)
    public new static TruncatedConeVolumeFact parseFact(MMTDeclaration fact)
    {
        string Circle1Uri = ((OMS)((OMA)((OMA)((MMTValueDeclaration)fact).lhs).arguments[0]).arguments[0]).uri;
        string Circle2Uri = ((OMS)((OMA)((OMA)((MMTValueDeclaration)fact).lhs).arguments[0]).arguments[1]).uri;
        float volume = ((OMF)((MMTValueDeclaration)fact).value).@float;

        string UnEqualCirclesProof = ((OMS)(((OMA)((OMA)((MMTValueDeclaration)fact).lhs).arguments[0]).arguments[2])).uri;
        OMA proof = (OMA)(((OMA)((OMA)((MMTValueDeclaration)fact).lhs).arguments[0]).arguments[3]);

        if (!FactOrganizer.AllFacts.ContainsKey(Circle1Uri)
         || !FactOrganizer.AllFacts.ContainsKey(Circle2Uri))
            return null;

        return new TruncatedConeVolumeFact(Circle1Uri, Circle2Uri, volume, UnEqualCirclesProof, proof, fact.@ref.uri, StageStatic.stage.factState);
    }

    /// \copydoc Fact.generateLabel
    protected override string generateLabel()
        => "V(" + Circle1.Label + "," + Circle2.Label + ")";

    public override MMTDeclaration MakeMMTDeclaration()
    {
        SOMDoc lhs =
            new OMA(
                new OMS(MMT_OMS_URI.TruncatedVolumeCone),
                new SOMDoc[] {
                    new OMS(Cid1),
                    new OMS(Cid2),
                    new OMS(unequalCirclesProof),
                    proof,
                }
            );

        SOMDoc valueTp = new OMS(MMT_OMS_URI.RealLit);
        SOMDoc value = new OMF(vol);

        return new MMTValueDeclaration(this.Label, lhs, valueTp, value);
    }

    /// \copydoc Fact.hasDependentFacts
    public override bool HasDependentFacts => true;

    /// \copydoc Fact.getDependentFactIds
    protected override string[] GetGetDependentFactIds()
        => new string[] { Cid1, Cid2 };

    /// \copydoc Fact.Equivalent(Fact, Fact)
    protected override bool EquivalentWrapped(TruncatedConeVolumeFact f1, TruncatedConeVolumeFact f2)
        => DependentFactsEquivalent(f1, f2);

    protected override Fact _ReInitializeMe(Dictionary<string, string> old_to_new, FactOrganizer organizer)
        => new TruncatedConeVolumeFact(old_to_new[this.Cid1], old_to_new[this.Cid2], this.vol, old_to_new[this.unequalCirclesProof], this.proof, organizer);
}

/// <summary>
/// The volume of a cylinder defined by a base area  <see cref="CircleFact">CircleFact</see>, a top area <see cref="CircleFact">CircleFact</see> and the volume as float
/// </summary>
public class CylinderVolumeFact : FactWrappedCRTP<CylinderVolumeFact>
{
    ///  <summary> a <see cref="CircleFact">CircleFact</see> describing the base area </summary>
    public string Cid1;
    [JsonIgnore]
    public CircleFact Circle1 { get => (CircleFact)FactOrganizer.AllFacts[Cid1]; }

    ///  <summary> a <see cref="CircleFact">CircleFact</see> describing the top area  </summary>
    public string Cid2;
    [JsonIgnore]
    public CircleFact Circle2 { get => (CircleFact)FactOrganizer.AllFacts[Cid2]; }

    ///  <summary> the volume of the cylinder as a float </summary>
    public float vol;
    /// <summary> a proof that both circles have the same size </summary>
    public string equalCirclesProof;
    ///  <summary> OMA proof that the two circles are parallel  </summary>
    public OMA proof;

    /// <summary> \copydoc Fact.Fact </summary>
    public CylinderVolumeFact() : base()
    {
        this.Cid1 = null;
        this.Cid2 = null;
        this.vol = 0.0f;
        this.proof = null;
        this.equalCirclesProof = null;
    }

    /// <summary>
    /// Standard Constructor:
    /// Initiates members and creates MMT %Fact Server-Side
    /// </summary>
    /// <param name="cid1">sets <see cref="Cid1"/></param>
    /// <param name="cid2">sets <see cref="Cid2"/></param>
    /// <param name="vol">sets <see cref="vol"/></param>
    /// <param name="proof">sets <see cref="proof"/></param>
    /// <param name="organizer">sets <see cref="Fact._Facts"/></param>
    public CylinderVolumeFact(string cid1, string cid2, float vol, string eqProof, OMA proof, FactOrganizer organizer) : base(organizer)
    {
        this.Cid1 = cid1;
        this.Cid2 = cid2;
        this.proof = proof;
        this.equalCirclesProof = eqProof;
        this.vol = vol;

        SendToMMT();
    }

    protected override void RecalculateTransform()
    {
        Position = Circle2.Position;
        Rotation = Circle2.Rotation;
    }

    /// <summary>
    /// Bypasses initialization of new MMT %Fact by using existend URI, _which is not checked for existence_.
    /// </summary>
    /// <param name="Cid1">sets <see cref="Cid1"/></param>
    /// <param name="Cid2">sets <see cref="Cid2"/></param>
    /// <param name="volume">sets <see cref="vol"/></param>
    /// <param name="proof">sets <see cref="proof"/></param>
    /// <param name="backendURI">MMT URI</param>
    /// <param name="organizer">sets <see cref="Fact._Facts"/></param>
    public CylinderVolumeFact(string Cid1, string Cid2, float volume, string eqProof, OMA proof, string backendURI, FactOrganizer organizer) : base(organizer)
    {
        this.Cid1 = Cid1;
        this.Cid2 = Cid2;
        this.vol = volume;
        this.proof = proof;
        this.equalCirclesProof = eqProof;

        this._URI = backendURI;
        _ = this.Label;
    }

    /// \copydoc Fact.parseFact(ScrollFact)
    public new static CylinderVolumeFact parseFact(MMTDeclaration fact)
    {
        string Circle1Uri = ((OMS)((OMA)((OMA)((MMTValueDeclaration)fact).lhs).arguments[0]).arguments[0]).uri;
        string Circle2Uri = ((OMS)((OMA)((OMA)((MMTValueDeclaration)fact).lhs).arguments[0]).arguments[1]).uri;
        float volume = ((OMF)((MMTValueDeclaration)fact).value).@float;
        string EqualCirclesProof = ((OMS)(((OMA)((OMA)((MMTValueDeclaration)fact).lhs).arguments[0]).arguments[2])).uri;

        OMA proof = (OMA)(((OMA)((OMA)((MMTValueDeclaration)fact).lhs).arguments[0]).arguments[3]);

        if (!FactOrganizer.AllFacts.ContainsKey(Circle1Uri)
         || !FactOrganizer.AllFacts.ContainsKey(Circle2Uri))
            return null;

        return new CylinderVolumeFact(Circle1Uri, Circle2Uri, volume, EqualCirclesProof, proof, fact.@ref.uri, StageStatic.stage.factState);
    }

    /// \copydoc Fact.generateLabel
    protected override string generateLabel()
        => "V(" + Circle1.Label + "," + Circle2.Label + ")";

    public override MMTDeclaration MakeMMTDeclaration()
    {
        SOMDoc lhs =
            new OMA(
                new OMS(MMT_OMS_URI.CylinderVolume),

                new SOMDoc[] {
                    new OMS(Cid1),
                    new OMS(Cid2),
                    new OMS(equalCirclesProof),
                    proof,
                }
            );

        SOMDoc valueTp = new OMS(MMT_OMS_URI.RealLit);
        SOMDoc value = new OMF(vol);

        return new MMTValueDeclaration(this.Label, lhs, valueTp, value);
    }

    /// \copydoc Fact.hasDependentFacts
    public override bool HasDependentFacts => true;

    /// \copydoc Fact.getDependentFactIds
    protected override string[] GetGetDependentFactIds()
        => new string[] { Cid1, Cid2, equalCirclesProof };

    /// \copydoc Fact.Equivalent(Fact, Fact)
    protected override bool EquivalentWrapped(CylinderVolumeFact f1, CylinderVolumeFact f2)
        => DependentFactsEquivalent(f1, f2);

    protected override Fact _ReInitializeMe(Dictionary<string, string> old_to_new, FactOrganizer organizer)
        => new CylinderVolumeFact(old_to_new[this.Cid1], old_to_new[this.Cid2], this.vol, old_to_new[this.equalCirclesProof], this.proof, organizer);
}

/// <summary>
/// A fact that describes, that two circles have the same size and is comprised of two <see cref="CircleFact">CircleFacts</see> 
/// </summary>
public class EqualCirclesFact : FactWrappedCRTP<EqualCirclesFact>
{
    /// @{ <summary>
    /// two circles that are meant to be equal in area
    /// </summary>
    public string Cid1, Cid2;
    /// @}

    [JsonIgnore]
    public CircleFact Circle1 { get => (CircleFact)FactOrganizer.AllFacts[Cid1]; }
    [JsonIgnore]
    public CircleFact Circle2 { get => (CircleFact)FactOrganizer.AllFacts[Cid2]; }

    /// <summary> \copydoc Fact.Fact </summary>
    public EqualCirclesFact() : base()
    {
        this.Cid1 = null;
        this.Cid2 = null;
    }

    /// <summary>
    /// Standard Constructor:
    /// Initiates members and creates MMT %Fact Server-Side
    /// </summary>
    /// <param name="cid1">sets <see cref="Cid1"/></param>
    /// <param name="cid2">sets <see cref="Cid2"/></param>
    /// <param name="organizer">sets <see cref="Fact._Facts"/></param>
    public EqualCirclesFact(string cid1, string cid2, FactOrganizer organizer) : base(organizer)
    {
        this.Cid1 = cid1;
        this.Cid2 = cid2;

        SendToMMT();
    }

    protected override void RecalculateTransform()
    {
        Position = Circle1.Position;
        Rotation = Circle1.Rotation;
    }

    /// <summary>
    /// Bypasses initialization of new MMT %Fact by using existend URI, _which is not checked for existence_.
    /// </summary>
    /// <param name="Cid1">sets <see cref="Cid1"/></param>
    /// <param name="Cid2">sets <see cref="Cid2"/></param>
    /// <param name="backendURI">MMT URI</param>
    /// <param name="organizer">sets <see cref="Fact._Facts"/></param>
    public EqualCirclesFact(string Cid1, string Cid2, string backendURI, FactOrganizer organizer) : base(organizer)
    {
        this.Cid1 = Cid1;
        this.Cid2 = Cid2;

        this._URI = backendURI;
        _ = this.Label;
    }

    /// \copydoc Fact.parseFact(ScrollFact)
    public new static EqualCirclesFact parseFact(MMTDeclaration fact)
    {
        if (((MMTSymbolDeclaration)fact).type is not OMA proof_OMA) // proof DED
            return null;

        OMA parallel_circles_OMA = (OMA)proof_OMA.arguments[0]; // parallel

        string circleAUri = ((OMS)parallel_circles_OMA.arguments[0]).uri;
        string circleBUri = ((OMS)parallel_circles_OMA.arguments[1]).uri;

        if (!FactOrganizer.AllFacts.ContainsKey(circleAUri)
         || !FactOrganizer.AllFacts.ContainsKey(circleBUri))
            return null;

        return new EqualCirclesFact(circleAUri, circleBUri, fact.@ref.uri, StageStatic.stage.factState);
    }

    /// \copydoc Fact.generateLabel
    protected override string generateLabel()
        => Circle1.Label + " ≠ " + Circle2.Label;

    public override MMTDeclaration MakeMMTDeclaration()
    {
        SOMDoc tp = new OMA(
            new OMS(MMT_OMS_URI.Ded),
            new[] {
                new OMA(
                    new OMS(MMT_OMS_URI.EqualityCircles),
                    new[]  {
                        new OMS(Cid1),
                        new OMS(Cid2),
                    }
                )
            }
        );

        SOMDoc df = null;

        return new MMTSymbolDeclaration(this.Label, tp, df);
    }

    /// \copydoc Fact.hasDependentFacts
    public override bool HasDependentFacts => true;

    /// \copydoc Fact.getDependentFactIds
    protected override string[] GetGetDependentFactIds()
        => new string[] { Cid1, Cid2 };

    /// \copydoc Fact.Equivalent(Fact, Fact)
    protected override bool EquivalentWrapped(EqualCirclesFact f1, EqualCirclesFact f2)
        => DependentFactsEquivalent(f1, f2);

    protected override Fact _ReInitializeMe(Dictionary<string, string> old_to_new, FactOrganizer organizer)
        => new EqualCirclesFact(old_to_new[this.Cid1], old_to_new[this.Cid2], organizer);
}

/// <summary>
/// A fact that describes, that two circles have not the same size and is comprised of two <see cref="CircleFact">CircleFacts</see> 
/// </summary>
public class UnEqualCirclesFact : FactWrappedCRTP<UnEqualCirclesFact>
{
    /// @{ <summary>
    /// two circles that are meant to be unequal in area
    /// </summary>
    public string Cid1, Cid2;
    /// @}

    [JsonIgnore]
    public CircleFact Circle1 { get => (CircleFact)FactOrganizer.AllFacts[Cid1]; }
    [JsonIgnore]
    public CircleFact Circle2 { get => (CircleFact)FactOrganizer.AllFacts[Cid2]; }

    /// <summary> \copydoc Fact.Fact </summary>
    public UnEqualCirclesFact() : base()
    {
        this.Cid1 = null;
        this.Cid2 = null;
    }

    /// <summary>
    /// Standard Constructor:
    /// Initiates members and creates MMT %Fact Server-Side
    /// </summary>
    /// <param name="cid1">sets <see cref="Cid1"/></param>
    /// <param name="cid2">sets <see cref="Cid2"/></param>
    /// <param name="organizer">sets <see cref="Fact._Facts"/></param>
    public UnEqualCirclesFact(string cid1, string cid2, FactOrganizer organizer) : base(organizer)
    {
        this.Cid1 = cid1;
        this.Cid2 = cid2;

        SendToMMT();
    }

    protected override void RecalculateTransform()
    {
        Position = Circle2.Position;
        Rotation = Circle2.Rotation;
    }

    /// <summary>
    /// Bypasses initialization of new MMT %Fact by using existend URI, _which is not checked for existence_.
    /// </summary>
    /// <param name="Cid1">sets <see cref="Cid1"/></param>
    /// <param name="Cid2">sets <see cref="Cid2"/></param>
    /// <param name="backendURI">MMT URI</param>
    /// <param name="organizer">sets <see cref="Fact._Facts"/></param>
    public UnEqualCirclesFact(string Cid1, string Cid2, string backendURI, FactOrganizer organizer) : base(organizer)
    {
        this.Cid1 = Cid1;
        this.Cid2 = Cid2;

        this._URI = backendURI;
        _ = this.Label;
    }

    /// \copydoc Fact.parseFact(ScrollFact)
    public new static UnEqualCirclesFact parseFact(MMTDeclaration fact)
    {
        if (((MMTSymbolDeclaration)fact).type is not OMA proof_OMA) // proof DED
            return null;

        OMA unequal_circles_OMA = (OMA)proof_OMA.arguments[0]; // unequal

        string circleAUri = ((OMS)unequal_circles_OMA.arguments[0]).uri;
        string circleBUri = ((OMS)unequal_circles_OMA.arguments[1]).uri;

        if (!FactOrganizer.AllFacts.ContainsKey(circleAUri)
         || !FactOrganizer.AllFacts.ContainsKey(circleBUri))
            return null;

        return new UnEqualCirclesFact(circleAUri, circleBUri, fact.@ref.uri, StageStatic.stage.factState);
    }

    /// \copydoc Fact.generateLabel
    protected override string generateLabel()
        => Circle1.Label + " = " + Circle2.Label;

    public override MMTDeclaration MakeMMTDeclaration()
    {
        SOMDoc tp = new OMA(
            new OMS(MMT_OMS_URI.Ded),
            new[] {
                new OMA(new OMS(MMT_OMS_URI.UnEqualityCircles),
                new[]  {
                    new OMS(Cid1),
                    new OMS(Cid2),
        }),});

        SOMDoc df = null;

        return new MMTSymbolDeclaration(this.Label, tp, df);
    }

    /// \copydoc Fact.hasDependentFacts
    public override bool HasDependentFacts => true;

    /// \copydoc Fact.getDependentFactIds
    protected override string[] GetGetDependentFactIds()
        => new string[] { Cid1, Cid2 };

    /// \copydoc Fact.Equivalent(Fact, Fact)
    protected override bool EquivalentWrapped(UnEqualCirclesFact f1, UnEqualCirclesFact f2)
        => DependentFactsEquivalent(f1, f2);

    protected override Fact _ReInitializeMe(Dictionary<string, string> old_to_new, FactOrganizer organizer)
        => new UnEqualCirclesFact(old_to_new[this.Cid1], old_to_new[this.Cid2], organizer);
}

#pragma warning disable // Testing...

/// TEST FACT
/// use this if you need to test certain implementations of facts.

/// <summary>
/// just for testing purposes  
/// </summary>
public class TestFact : FactWrappedCRTP<TestFact>
{
    /// <summary> \copydoc Fact.Fact </summary>
    public TestFact() : base()
    {

    }

    /// <summary>
    /// Standard Constructor:
    /// Initiates members and creates MMT %Fact Server-Side
    /// </summary>
    /// <param name="pid1">sets <see cref="Pid1"/></param>
    /// <param name="pid2">sets <see cref="Pid2"/></param>
    /// <param name="radius">sets <see cref="radius"/></param>
    /// <param name="normal">sets <see cref="normal"/></param>
    /// <param name="organizer">sets <see cref="Fact._Facts"/></param>
    public TestFact(FactOrganizer organizer) : base(organizer)
    {
        SendToMMT();
    }

    protected override void RecalculateTransform() { }

    /// <summary>
    /// Bypasses initialization of new MMT %Fact by using existend URI, _which is not checked for existence_.
    /// </summary>
    /// <param name="Pid1">sets <see cref="Pid1"/></param>
    /// <param name="Pid2">sets <see cref="Pid2"/></param>
    /// <param name="radius">sets <see cref="radius"/></param>
    /// <param name="normal">sets <see cref="normal"/></param>
    /// <param name="backendURI">MMT URI</param>
    /// <param name="organizer">sets <see cref="Fact._Facts"/></param>
    public TestFact(string backendURI, FactOrganizer organizer) : base(organizer)
    {

        this._URI = backendURI;
        _ = this.Label;
    }

    /// <summary>
    /// parses the Circlefact response of the MMT-Server
    /// </summary>
    /// \copydoc Fact.parseFact(ScrollFact) 
    public new static TestFact parseFact(MMTDeclaration fact)
    {
        string uri = fact.@ref.uri;
        Debug.Log("TestFact Uri:" + uri);
        return new TestFact(uri, StageStatic.stage.factState);
    }

    /// \copydoc Fact.generateLabel
    protected override string generateLabel()
        => "test";

    /// \copydoc Fact.hasDependentFacts
    public override bool HasDependentFacts => false;

    /// \copydoc Fact.getDependentFactIds
    protected override string[] GetGetDependentFactIds()
        => new string[] { };

    /// \copydoc Fact.GetHashCode
    public override int GetHashCode()
        => base.GetHashCode();// this.Pid1.GetHashCode() ^ this.Pid2.GetHashCode();

    /// \copydoc Fact.Equivalent(Fact, Fact)
    protected override bool EquivalentWrapped(TestFact f1, TestFact f2)
    {
        return DependentFactsEquivalent(f1, f2);
    }

    protected override Fact _ReInitializeMe(Dictionary<string, string> old_to_new, FactOrganizer organizer)
        => new TestFact(organizer);

    public override MMTDeclaration MakeMMTDeclaration()
    {
        throw new NotImplementedException();
    }
}

#pragma warning restore // Testing over