Ejemplo n.º 1
0
        public DisjunctiveExamplesSpec WitnessFilter_ColorParam(GrammarRule rule, AbstractImageSpec spec)
        {
            var result = new Dictionary <State, IEnumerable <object> >();

            foreach (KeyValuePair <State, object> example in spec.AbstractImageExamples)
            {
                State inputState = example.Key;
                var   output     = example.Value as AbstractImage;
                // None values are meaningless, so we don't consider them
                if (output.ContainsNoneValue())
                {
                    Program.DEBUG("Returning null from WitnessFilter_ColorParam --> output contained NONE value");
                    return(null);
                }
                ISet <int> candidateSet = new HashSet <int>(new[] { 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 });

                for (int i = 0; i < output.abstract_data.Length; i++)
                {
                    ISet <int> colorSet = output.abstract_data[i].ToSet();
                    if (!colorSet.Contains(0))
                    {
                        candidateSet.IntersectWith(colorSet);
                    }
                }
                result[inputState] = candidateSet.ToList().Cast <object>();
            }
            return(new DisjunctiveExamplesSpec(result));
        }
Ejemplo n.º 2
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        public AbstractImageSpec WitnessRecolor_SingleParam(GrammarRule rule, AbstractImageSpec spec, ExampleSpec colorSpec)
        {
            var result = new Dictionary <State, object>();

            foreach (var example in spec.AbstractImageExamples)
            {
                State inputState = example.Key;
                var   output     = example.Value as AbstractImage;
                int   color      = (int)colorSpec.Examples[inputState];
                // create blank preimage
                AbstractImage preimage = new AbstractImage(output.x, output.y, output.w, output.h);
                // loop through all pixels of output image
                for (int i = 0; i < output.abstract_data.Length; i++)
                {
                    ISet <int> colorSet = output.abstract_data[i].ToSet();

                    if (colorSet.Contains(0))
                    {
                        preimage.abstract_data[i].UnionWith(new AbstractValue(new List <int> {
                            0
                        }));
                    }
                    if (colorSet.Contains(color))
                    {
                        preimage.abstract_data[i].UnionWith(new AbstractValue(AbstractConstants.NONZERO));
                    }
                    if (preimage.abstract_data[i].IsEmpty()) // empty set (output not 0 or color)
                    {
                        return(null);
                    }
                }
                result[inputState] = preimage;
            }
            return(new AbstractImageSpec(result));
        }
Ejemplo n.º 3
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        public AbstractImageSpec WitnessCompose_TopParam(GrammarRule rule, AbstractImageSpec spec)
        {
            Program.DEBUG("Entered WitnessCompose_TopParam");
            var result = new Dictionary <State, object>();

            foreach (var example in spec.AbstractImageExamples)
            {
                State inputState = example.Key;
                var   output     = example.Value as AbstractImage;
                // TODO: Determine if this is a problem
                if (output.isEmptySet())
                {
                    return(null);
                }

                AbstractImage preimage = new AbstractImage(output.x, output.y, output.w, output.h);
                for (int ay = preimage.y; ay < preimage.y + preimage.h; ay++)
                {
                    for (int ax = preimage.x; ax < preimage.x + preimage.w; ax++)
                    {
                        AbstractValue od = output.getAbstractValueAtPixel(ax, ay);
                        preimage.setAbstractValueAtPixel(ax, ay, new AbstractValue(od.d).UnionWith(new AbstractValue(AbstractConstants.ZERO)));
                    }
                }
                result[inputState] = preimage;
            }
            return(new AbstractImageSpec(result));
        }
Ejemplo n.º 4
0
        public AbstractImageSpec WitnessCompose_TopParam(GrammarRule rule, AbstractImageSpec spec)
        {
            Program.DEBUG("Entered WitnessCompose_TopParam");
            var result = new Dictionary <State, object>();

            foreach (var example in spec.AbstractImageExamples)
            {
                State inputState = example.Key;
                var   output     = example.Value as AbstractImage;
                // None values are meaningless, so we don't consider them
                if (output.ContainsNoneValue())
                {
                    Program.DEBUG("Returning null from WitnessCompose_TopParam --> output contained NONE value");
                    return(null);
                }

                AbstractImage preimage = new AbstractImage(output.x, output.y, output.w, output.h);
                for (int ay = preimage.y; ay < preimage.y + preimage.h; ay++)
                {
                    for (int ax = preimage.x; ax < preimage.x + preimage.w; ax++)
                    {
                        AbstractValue output_ab_val = output.GetAbstractValueAtPixel(ax, ay);
                        preimage.SetAbstractValueAtPixel(ax, ay, output_ab_val.Clone().UnionWith(new AbstractValue(AbstractConstants.ZERO)));
                    }
                }
                result[inputState] = preimage;
            }
            return(new AbstractImageSpec(result));
        }
Ejemplo n.º 5
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        protected override bool EqualsOnInput(State state, Spec other)
        {
            AbstractImageSpec otherDIS = (AbstractImageSpec)other;
            AbstractImage     d0       = (AbstractImage)this.AbstractImageExamples[state];
            AbstractImage     d1       = (AbstractImage)otherDIS.AbstractImageExamples[state];

            return(d0.Equals(d1));
        }
Ejemplo n.º 6
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        public AbstractImageSpec WitnessIdentity(GrammarRule rule, AbstractImageSpec spec)
        {
            var result = new Dictionary <State, object>();

            foreach (KeyValuePair <State, object> example in spec.AbstractImageExamples)
            {
                State inputState = example.Key;
                // extract output image
                var output = example.Value as AbstractImage;
                if (output == null)
                {
                    return(null);
                }
                result[inputState] = new AbstractImage(output);
            }
            return(new AbstractImageSpec(result));
        }
Ejemplo n.º 7
0
        public DisjunctiveExamplesSpec WitnessFilter_ColorParam(GrammarRule rule, AbstractImageSpec spec)
        {
            var result = new Dictionary <State, IEnumerable <object> >();

            foreach (KeyValuePair <State, object> example in spec.AbstractImageExamples)
            {
                State      inputState   = example.Key;
                var        output       = example.Value as AbstractImage;
                ISet <int> candidateSet = new HashSet <int>(new[] { 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 });

                for (int i = 0; i < output.abstract_data.Length; i++)
                {
                    ISet <int> colorSet = output.abstract_data[i].ToSet();
                    if (!colorSet.Contains(0))
                    {
                        candidateSet.IntersectWith(colorSet);
                    }
                }
                result[inputState] = candidateSet.ToList().Cast <object>();
            }
            return(new DisjunctiveExamplesSpec(result));
        }
Ejemplo n.º 8
0
        public AbstractImageSpec WitnessFilter_SingleParam(GrammarRule rule, AbstractImageSpec spec, ExampleSpec colorSpec)
        {
            var result = new Dictionary <State, object>();

            foreach (var example in spec.AbstractImageExamples)
            {
                State inputState = example.Key;
                var   output     = example.Value as AbstractImage;
                // None values are meaningless, so we don't consider them
                if (output.ContainsNoneValue())
                {
                    Program.DEBUG("Returning null from WitnessFilter_SingleParam --> output contained NONE value");
                    return(null);
                }
                int color = (int)colorSpec.Examples[inputState];
                // create blank preimage
                AbstractImage preimage = new AbstractImage(output.x, output.y, output.w, output.h);
                // loop through all pixels of output image
                for (int i = 0; i < output.abstract_data.Length; i++)
                {
                    ISet <int> colorSet = output.abstract_data[i].ToSet();

                    if (colorSet.Contains(0))
                    {
                        preimage.abstract_data[i].UnionWith(new AbstractValue(new List <int> {
                            color
                        }).Complement());
                    }
                    if (colorSet.Contains(color))
                    {
                        preimage.abstract_data[i].UnionWith(new AbstractValue(new List <int> {
                            color
                        }));
                    }
                }
                result[inputState] = preimage;
            }
            return(new AbstractImageSpec(result));
        }
Ejemplo n.º 9
0
        public AbstractImageSpec WitnessIdentity(GrammarRule rule, AbstractImageSpec spec)
        {
            var result = new Dictionary <State, object>();

            foreach (KeyValuePair <State, object> example in spec.AbstractImageExamples)
            {
                State inputState = example.Key;
                // extract output image
                var output = example.Value as AbstractImage;
                // None values are meaningless, so we don't consider them
                if (output.ContainsNoneValue())
                {
                    Program.DEBUG("Returning null from WitnessIdentity --> output contained NONE value");
                    return(null);
                }
                if (output == null)
                {
                    return(null);
                }
                result[inputState] = new AbstractImage(output);
            }
            return(new AbstractImageSpec(result));
        }
Ejemplo n.º 10
0
        public AbstractImageSpec WitnessRecolor_SingleParam(GrammarRule rule, AbstractImageSpec spec, ExampleSpec colorSpec)
        {
            Program.DEBUG("Entering WitnessRecolor_SingleParam");
            var result = new Dictionary <State, object>();

            foreach (var example in spec.AbstractImageExamples)
            {
                State inputState = example.Key;
                var   output     = example.Value as AbstractImage;
                // None values are meaningless, so we don't consider them
                if (output.ContainsNoneValue())
                {
                    Program.DEBUG("Returning null from WitnessRecolor_SingleParam --> output contained NONE value");
                    return(null);
                }
                int color = (int)colorSpec.Examples[inputState];
                // create blank preimage
                AbstractImage preimage = new AbstractImage(output.x, output.y, output.w, output.h);
                // loop through all pixels of output image
                for (int i = 0; i < output.abstract_data.Length; i++)
                {
                    // TODO:
                    if (output.abstract_data[i].AllowsColor(0))
                    {
                        // TODO: change this back to normal
                        preimage.abstract_data[i] = preimage.abstract_data[i].UnionWith(new AbstractValue(AbstractConstants.ZERO));
                    }
                    if (output.abstract_data[i].AllowsColor(color))
                    {
                        preimage.abstract_data[i] = preimage.abstract_data[i].UnionWith(new AbstractValue(AbstractConstants.NONZERO));
                    }
                }
                result[inputState] = preimage;
            }
            return(new AbstractImageSpec(result));
        }
Ejemplo n.º 11
0
        private static void LearnFromNewExample()
        {
            Task task;

            while (true)
            {
                try
                {
                    Console.Out.Write("Enter a task name: ");
                    _taskName = Console.ReadLine().Trim();
                    task      = TaskLoader.LoadTask("tasks/" + _taskName + ".json");
                    break;
                }
                catch (FileNotFoundException)
                {
                    Console.Out.WriteLine("Could not find task " + _taskName + ".json. Try again.");
                }
                catch (DirectoryNotFoundException)
                {
                    Console.Out.WriteLine("Could not find task " + _taskName + ".json. Try again.");
                }
                catch (Exception)
                {
                    Console.Out.WriteLine("Unable to parse " + _taskName + ".json. Try again.");
                }
            }

            Console.Out.WriteLine(@"List the functions that this task is invariant under (i.e. g such that F(x)=y => F(g(x))=g(y)
c    Color mapping
r    Rotation
f    Reflection
t    Translation");

            List <Invariant> invariants = new List <Invariant>();

            while (true)
            {
                string invInput = Console.ReadLine().Trim();
                foreach (char c in invInput)
                {
                    switch (c)
                    {
                    case 'c':
                        invariants.Add(new ColormapInvariant());
                        break;

                    case 'r':
                        invariants.Add(new RotationInvariant());
                        break;

                    case 'f':
                        invariants.Add(new ReflectionInvariant());
                        break;

                    case 't':
                        invariants.Add(new TranslationInvariant());
                        break;

                    default:
                        Console.Out.WriteLine("Unknown invariant " + c);
                        continue;
                    }
                }
                break;
            }

            Console.Out.WriteLine(@"List the functions that this task is equivalent under (i.e. g such that F(x)=y => F(g(x))=y
c    Color mapping
r    Rotation
f    Reflection
t    Translation");
            List <Invariant> equivalences = new List <Invariant>();

            while (true)
            {
                string invInput = Console.ReadLine().Trim();
                foreach (char c in invInput)
                {
                    switch (c)
                    {
                    case 'c':
                        equivalences.Add(new ColormapInvariant());
                        break;

                    case 'r':
                        equivalences.Add(new RotationInvariant());
                        break;

                    case 'f':
                        equivalences.Add(new ReflectionInvariant());
                        break;

                    case 't':
                        equivalences.Add(new TranslationInvariant());
                        break;

                    default:
                        Console.Out.WriteLine("Unknown equivalence " + c);
                        continue;
                    }
                }
                break;
            }

            Example[] train = task.train;
            Console.Out.WriteLine("Learning a program for input examples:\n");
            Examples.Clear();
            foreach (Example example in train)
            {
                example.Print();
                Console.Out.WriteLine();
                State inputState = State.CreateForExecution(Grammar.InputSymbol, new Image(example.input));
                Examples.Add(inputState, new AbstractImage(new Image(example.output)));
            }

            if (equivalences.Count() > 0 || invariants.Count() > 0)
            {
                Console.Out.WriteLine("and generated examples:\n");
                foreach (Invariant inv in invariants)
                {
                    inv.reseed();
                    foreach (Example example in train)
                    {
                        Image   newIn      = inv.generate(new Image(example.input));
                        Image   newOut     = inv.generate(new Image(example.output));
                        Example newExample = Example.FromImages(newIn, newOut);
                        newExample.Print();
                        Console.Out.WriteLine();
                        State newInState = State.CreateForExecution(Grammar.InputSymbol, newIn);
                        Examples.Add(newInState, new AbstractImage(newOut));
                    }
                }
                foreach (Invariant eq in equivalences)
                {
                    eq.reseed();
                    foreach (Example example in train)
                    {
                        Image   newIn      = eq.generate(new Image(example.input));
                        Image   newOut     = new Image(example.output);
                        Example newExample = Example.FromImages(newIn, newOut);
                        newExample.Print();
                        Console.Out.WriteLine();
                        State newInState = State.CreateForExecution(Grammar.InputSymbol, newIn);
                        Examples.Add(newInState, new AbstractImage(newOut));
                    }
                }
            }

            //var spec = new ExampleSpec(Examples);
            var spec = new AbstractImageSpec(Examples);

            var        scoreFeature = new RankingScore(Grammar);
            int        K            = 4;
            ProgramSet topPrograms  = _prose.LearnGrammarTopK(spec, scoreFeature, K, null);

            if (topPrograms.IsEmpty)
            {
                Console.Out.WriteLine("No program was found for this specification.");
            }
            else
            {
                _topProgram = topPrograms.RealizedPrograms.First();
                Console.Out.WriteLine("Top " + K + " learned programs:");
                var counter = 1;
                foreach (ProgramNode program in topPrograms.RealizedPrograms)
                {
                    if (counter > 4)
                    {
                        break;
                    }
                    Console.Out.WriteLine("==========================");
                    Console.Out.WriteLine("Program {0}: ", counter);
                    Console.Out.WriteLine(program.PrintAST(ASTSerializationFormat.HumanReadable));
                    counter++;
                }
                Console.Out.WriteLine("==========================");
            }
        }
Ejemplo n.º 12
0
        public AbstractImageSpec WitnessOrthogonal_SingleParam(GrammarRule rule, AbstractImageSpec spec, ExampleSpec orthOptionSpec)
        {
            var result = new Dictionary <State, object>();
            int Y_AXIS = 0;
            int X_AXIS = 1;
            int ROT_90 = 2;

            foreach (KeyValuePair <State, object> example in spec.AbstractImageExamples)
            {
                State         inputState = example.Key;
                var           output     = example.Value as AbstractImage;
                int           orthOption = (int)orthOptionSpec.Examples[inputState];
                AbstractImage preimage   = null;
                // TODO: We want to handle changes in x and y
                if (orthOption == Y_AXIS || orthOption == X_AXIS)
                {
                    preimage = new AbstractImage(output.x, output.y, output.w, output.h);
                }
                else if (orthOption == ROT_90)
                {
                    preimage = new AbstractImage(output.x, output.y, output.h, output.w);
                }
                else
                {
                    throw new NotSupportedException("We don't support that option for Orthogonal yet");
                }

                if (orthOption == Y_AXIS)
                {
                    for (int i = 0; i < output.h; i++)
                    {
                        for (int j = 0; j < output.w; j++)
                        {
                            preimage.abstract_data[i * preimage.w + j] = output.abstract_data[i * output.w + (output.w - j - 1)];
                        }
                    }
                }
                else if (orthOption == X_AXIS)
                {
                    for (int i = 0; i < output.h; i++)
                    {
                        for (int j = 0; j < output.w; j++)
                        {
                            preimage.abstract_data[i * preimage.w + j] = output.abstract_data[(output.h - i - 1) * output.w + j];
                        }
                    }
                }
                else if (orthOption == ROT_90)
                {
                    // TODO: Verify this
                    for (int i = 0; i < preimage.h; i++)     // n = preimage.h
                    {
                        for (int j = 0; j < preimage.w; j++) // m = preimage.w
                        {
                            // preimage[i,j] = output[j,n-1-i];
                            preimage.abstract_data[i * preimage.w + j] = output.abstract_data[j * output.w + (output.w - 1 - i)];
                        }
                    }
                }
                else
                {
                    throw new NotSupportedException("We don't support that option for Orthogonal yet");
                }
                result[inputState] = preimage;
            }
            return(new AbstractImageSpec(result));
        }
Ejemplo n.º 13
0
        public DisjunctiveExamplesSpec WitnessOrthogonal_OrthOptionParam(GrammarRule rule, AbstractImageSpec spec)
        {
            var result = new Dictionary <State, IEnumerable <object> >();
            int Y_AXIS = 0;
            int X_AXIS = 1;
            int ROT_90 = 2;

            foreach (KeyValuePair <State, object> example in spec.AbstractImageExamples)
            {
                State inputState = example.Key;

                var occurrences = new List <int>();
                occurrences.Add(Y_AXIS);
                occurrences.Add(X_AXIS);
                occurrences.Add(ROT_90);
                result[inputState] = occurrences.Cast <object>();
            }
            return(new DisjunctiveExamplesSpec(result));
        }
Ejemplo n.º 14
0
        public AbstractImageSpec WitnessCompose_BottomParam(GrammarRule rule, AbstractImageSpec spec, AbstractImageSpec topSpec)
        {
            Program.DEBUG("Entered WitnessCompose_BottomParam");
            var result = new Dictionary <State, object>();

            foreach (var example in spec.AbstractImageExamples)
            {
                State inputState = example.Key;
                var   output     = example.Value as AbstractImage;
                if (output.isEmptySet())
                {
                    Program.DEBUG("null from WitnessCompose_BottomParam --> output.isEmptySet()");
                    return(null);
                }
                AbstractImage top_image = (AbstractImage)topSpec.AbstractImageExamples[inputState];
                // TODO: Handle different dimensions for bottom_preimage, currently we assume output is proper dimension
                AbstractImage bottom_preimage = new AbstractImage(output.x, output.y, output.w, output.h);
                for (int ay = bottom_preimage.y; ay < bottom_preimage.y + bottom_preimage.h; ay++)
                {
                    for (int ax = bottom_preimage.x; ax < bottom_preimage.x + bottom_preimage.w; ax++)
                    {
                        AbstractValue output_ab_val = output.getAbstractValueAtPixel(ax, ay);
                        if (top_image.InBounds(ax, ay)) // Checking that the x and y coords are in the bounds for top_image
                        {
                            AbstractValue top_image_ab_val = output.getAbstractValueAtPixel(ax, ay);
                            // If either the top_image or the output images allowed no values (not even 0), then return null
                            // as we've entered an invalid state
                            if (top_image_ab_val.IsEmpty() || output_ab_val.IsEmpty())
                            {
                                Program.DEBUG("null from WitnessCompose_BottomParam --> top or output contained no valid values");
                                return(null);
                            }
                            // Check if we ONLY allow 0 on output (HammingWeight is the # of 1 bits in our inner representation)
                            if (output_ab_val.Allows(0) && output_ab_val.HammingWeight() == 1)
                            {
                                // If the top_image doesn't allow 0, this is impossible. Return null
                                if (!top_image_ab_val.Allows(0))
                                {
                                    Program.DEBUG("null from WitnessCompose_BottomParam --> top image didn't allow 0");
                                    return(null);
                                }
                                // if it allows 0 and no other values, that's good, just return 0 for bottom
                                else if (top_image_ab_val.HammingWeight() >= 1)
                                {
                                    bottom_preimage.setAbstractValueAtPixel(ax, ay,
                                                                            new AbstractValue(AbstractConstants.ZERO));
                                }
                                else
                                {
                                    throw new Exception("WitnessCompose_BottomParam --> This shouldn't happen");
                                }
                            }
                            // output is ONLY nonzeros
                            else if (!output_ab_val.Allows(0) && output_ab_val.HammingWeight() >= 1)
                            {
                                // If the top_image doesn't allow 0, that's cool.
                                // It means that our bottom_preimage can contain literally anything
                                // since its contents will be completely ignored
                                if (!top_image_ab_val.Allows(0))
                                {
                                    bottom_preimage.setAbstractValueAtPixel(ax, ay,
                                                                            new AbstractValue(AbstractConstants.ANY));
                                }
                                // otherwise, if top image does allow 0, our bottom preimage
                                // can take on the union of top_image's nonzero values and
                                // the values in output
                                // Example:
                                // output: [1,2,3]
                                // top: [0,1]
                                // bottom: [1,2,3]
                                else
                                {
                                    // First, sanity check! Ensure the nonzero elements of top
                                    // are contained within output, otherwise that's bad and we return null
                                    AbstractValue nonzero_top_image_ab_vals = AbstractValue.Intersect(
                                        new AbstractValue(AbstractConstants.NONZERO),
                                        top_image_ab_val
                                        );
                                    if (!output_ab_val.ContainsAllColors(nonzero_top_image_ab_vals))
                                    {
                                        Program.DEBUG("null from WitnessCompose_BottomParam --> output val wasn't superset of nonzero top vals");
                                        return(null);
                                    }
                                    // Now, easy-peasy, just set bottom_preimage to output
                                    bottom_preimage.setAbstractValueAtPixel(ax, ay, new AbstractValue(output_ab_val.d));
                                }
                            }
                            // output contains nonzero AND allows 0
                            else if (output_ab_val.Allows(0) && output_ab_val.HammingWeight() > 1)
                            {
                                // If the top_image doesn't allow 0, that's bad!
                                // means we can't get 0 on output, so return null
                                if (!top_image_ab_val.Allows(0))
                                {
                                    Program.DEBUG("null from WitnessCompose_BottomParam --> top image didn't allow 0, which is impossible given output accepts zero (and some other nonzeros)");
                                    return(null);
                                }
                                // otherwise, if top image does allow 0, our bottom preimage
                                // can take on the union of top_image's nonzero values and
                                // the nonzero values in output
                                // Example:
                                // output: [0,1,2,3]
                                // top: [0,1]
                                // bottom: [1,2,3]
                                else
                                {
                                    // First, sanity check! Ensure the nonzero elements of top
                                    // are contained within nonzero els of output, otherwise that's bad and we return null
                                    AbstractValue nonzero_top_image_ab_vals = AbstractValue.Intersect(
                                        new AbstractValue(AbstractConstants.NONZERO),
                                        top_image_ab_val
                                        );
                                    AbstractValue nonzero_output_ab_vals = AbstractValue.Intersect(
                                        new AbstractValue(AbstractConstants.NONZERO),
                                        output_ab_val
                                        );
                                    if (!nonzero_output_ab_vals.ContainsAllColors(nonzero_top_image_ab_vals))
                                    {
                                        Program.DEBUG("null from WitnessCompose_BottomParam --> nonzero output val wasn't superset of nonzero top vals");
                                        return(null);
                                    }
                                    // Now, easy-peasy, just set bottom_preimage to (nonzero elements) of output
                                    bottom_preimage.setAbstractValueAtPixel(ax, ay, new AbstractValue(nonzero_output_ab_vals.d));
                                }
                            }
                            else
                            {
                                throw new Exception("We should not have thrown this. Check WitnessCompose_BottomParam.");
                            }
                        }
                        else
                        {
                            // TODO: Determine if we want to support this?
                            bottom_preimage.setAbstractValueAtPixel(ax, ay, new AbstractValue(output_ab_val.d)); // clone out of fear and respect
                        }
                    }
                }
                result[inputState] = bottom_preimage;
            }
            return(new AbstractImageSpec(result));
        }
Ejemplo n.º 15
0
        public AbstractImageSpec WitnessCompose_BottomParam(GrammarRule rule, AbstractImageSpec spec, AbstractImageSpec topSpec)
        {
            Program.DEBUG("Entered WitnessCompose_BottomParam");
            var result = new Dictionary <State, object>();

            foreach (var example in spec.AbstractImageExamples)
            {
                State inputState = example.Key;
                var   output     = example.Value as AbstractImage;
                if (output.ContainsNoneValue())
                {
                    Program.DEBUG("null from WitnessCompose_BottomParam --> output contained NONE value");
                    return(null);
                }
                AbstractImage top_image = (AbstractImage)topSpec.AbstractImageExamples[inputState];
                // If either the top_image or output contain a pixel with "NONE" as output, then
                // it's an invalid candidate image
                if (top_image.ContainsNoneValue())
                {
                    Program.DEBUG("null from WitnessCompose_BottomParam --> top contained NONE value");
                    return(null);
                }


                // TODO: Handle different dimensions for bottom_preimage, currently we assume output is proper dimension
                // Future Idea: use NONE values or some sort of NEGATIVE value to indicate "out of bounds, but still a
                // viable candidate if a top image overwhelmed me. Could make all images arbitrarily sized, like 100x100 or something
                // to enable composition
                AbstractImage bottom_preimage = new AbstractImage(output.x, output.y, output.w, output.h);
                for (int ay = bottom_preimage.y; ay < bottom_preimage.y + bottom_preimage.h; ay++)
                {
                    for (int ax = bottom_preimage.x; ax < bottom_preimage.x + bottom_preimage.w; ax++)
                    {
                        AbstractValue output_ab_val = output.GetAbstractValueAtPixel(ax, ay);
                        if (top_image.InBounds(ax, ay)) // Checking that the x and y coords are in the bounds for top_image
                        {
                            AbstractValue top_image_ab_val = top_image.GetAbstractValueAtPixel(ax, ay);
                            // ONLY could allow 0 on output (thus top and bottom must both be 0)
                            if (output_ab_val.Equals(AbstractConstants.ZERO))
                            {
                                // If the top image isn't ONLY 0, then it's impossible to produce an output that is ONLY 0
                                if (!top_image_ab_val.Equals(AbstractConstants.ZERO))
                                {
                                    Program.DEBUG("null from WitnessCompose_BottomParam --> top image didn't allow 0");
                                    return(null);
                                }
                                // Top image IS only 0, so the only value must be 0 for the bottom preimage
                                else
                                {
                                    bottom_preimage.SetAbstractValueAtPixel(ax, ay,
                                                                            new AbstractValue(AbstractConstants.ZERO));
                                }
                            }
                            // Output is ONLY nonzeros
                            else if (!output_ab_val.AllowsColor(0))
                            {
                                // If the top_image doesn't allow 0, that's cool.
                                // It means that our bottom_preimage can contain literally anything
                                // since its contents will be completely ignored
                                if (!top_image_ab_val.AllowsColor(0))
                                {
                                    // But, the abstract domains must be equivalent between output and top in this case
                                    if (top_image_ab_val.Equals(output_ab_val))
                                    {
                                        bottom_preimage.SetAbstractValueAtPixel(ax, ay,
                                                                                new AbstractValue(AbstractConstants.ANY));
                                    }
                                    // Otherwise, no bottom preimage could be generated to satisfy this
                                    else
                                    {
                                        Program.DEBUG("null from WitnessCompose_BottomParam --> top != output");
                                        return(null);
                                    }
                                }
                                // otherwise, if top image does allow 0, our bottom preimage
                                // takes on the the nonzero values in output
                                // Example:
                                // output: [1,2,3]
                                // top: [0,1,2,3]
                                // bottom: [1,2,3]
                                else
                                {
                                    AbstractValue nonzero_top_image_ab_vals = AbstractValue.Intersect(
                                        new AbstractValue(AbstractConstants.NONZERO),
                                        top_image_ab_val
                                        );
                                    // First, sanity check! Ensure the nonzero elements of top
                                    // are contained within output, otherwise that's bad and we return null
                                    if (!output_ab_val.ContainsAllColors(nonzero_top_image_ab_vals))
                                    {
                                        Program.DEBUG("null from WitnessCompose_BottomParam --> output val wasn't superset of nonzero top vals");
                                        return(null);
                                    }
                                    // Now, easy-peasy, just set bottom_preimage to output
                                    bottom_preimage.SetAbstractValueAtPixel(ax, ay, output_ab_val.Clone());
                                }
                            }
                            // output contains nonzero AND allows 0
                            else if (output_ab_val.AllowsColor(0) && output_ab_val.HammingWeight() > 1)
                            {
                                // If the top_image doesn't allow 0, that's bad!
                                // means we can't get 0 on output, so return null
                                if (!top_image_ab_val.AllowsColor(0))
                                {
                                    Program.DEBUG("null from WitnessCompose_BottomParam --> top image didn't allow 0, which is impossible given output accepts zero (and some other nonzeros)");
                                    return(null);
                                }
                                // otherwise, if top image does allow 0, our bottom preimage is the values on output
                                // Example:
                                // output: [0,1,2,3]
                                // top: [0,1]
                                // bottom: [0,1,2,3]
                                else
                                {
                                    // First, sanity check! Ensure the elements of top
                                    // are contained within elementss of output, invalid
                                    if (!output_ab_val.ContainsAllColors(top_image_ab_val))
                                    {
                                        Program.DEBUG("null from WitnessCompose_BottomParam --> nonzero output val wasn't superset of nonzero top vals");
                                        return(null);
                                    }
                                    // Now, set to the values of output
                                    bottom_preimage.SetAbstractValueAtPixel(ax, ay, output_ab_val.Clone());
                                }
                            }
                            else
                            {
                                throw new Exception("We should not have thrown this. Check WitnessCompose_BottomParam.");
                            }
                        }
                        else
                        {
                            bottom_preimage.SetAbstractValueAtPixel(ax, ay, output_ab_val.Clone()); // clone out of fear and respect
                        }
                    }
                }
                result[inputState] = bottom_preimage;
            }
            return(new AbstractImageSpec(result));
        }