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Add explicit heads
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‎Documentation/Generators/GenerateMultihistory.md‎

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@@ -23,4 +23,6 @@ In[] := #["ExpressionsEventsGraph", VertexLabels -> Placed[Automatic, After]] &
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<img src="/Documentation/Images/GenerateMultihistoryExample.png"
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width="478.2"
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alt="Out[] = ... {1, 2} -> {3 (* token 5 *)}, {2, 1} -> {3 (* token 6 *)}, {1, 3 (* init *)} -> {4}, <<7>> ...">
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alt="Out[] = Graph[...
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{1, 2} -> {3 (* token 5 *)}, {2, 1} -> {3 (* token 6 *)}, {1, 3 (* init *)} -> {4}, <<7>>
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...]">

‎Documentation/Generators/GenerateSingleHistory.md‎

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@@ -22,13 +22,13 @@ In[] := #["ExpressionsEventsGraph", VertexLabels -> Placed[Automatic, After]] &
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<img src="/Documentation/Images/GenerateSingleHistoryExample.png"
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width="478.2"
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alt="Out[] = ...
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alt="Out[] = Graph[...
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token-event graph where all tokens have out degrees less or equal than 1:
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{1, 2 (* init *)} -> {3, -1, 2 (* gen 1 *)},
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{3, -1} -> {2 (* gen 2 *), 4 (* gen 2 *), -3},
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{2 (* gen 1 *), 2 (* gen 2 *)} -> {4 (* gen 3 sum *), 0, 4 (* gen 3 product *)},
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<<7>>
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...">
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...]">
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Note that there is a distinction between single-history and single-path systems. Single-path systems are defined as ones
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where there is only one event possible from every state. A Turing machine would be an example of a single-path system.

‎Documentation/Generators/MaxDestroyerEvents.md‎

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@@ -12,7 +12,7 @@ In[] := #["ExpressionsEventsGraph", VertexLabels -> Placed[Automatic, After]] &
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<img src="/Documentation/Images/MaxDestroyerEvents1.png"
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width="322.2"
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alt="Out[] = ... {1, 2} -> {3 (* gen 1 *)}, {3 (* init *), 3 (* gen 1 *)} -> 6 ...">
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alt="Out[] = Graph[... {1, 2} -> {3 (* gen 1 *)}, {3 (* init *), 3 (* gen 1 *)} -> 6 ...]">
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If unset (which defaults to [`Infinity`](https://reference.wolfram.com/language/ref/Infinity.html)), it will generate a
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full multihistory object subject to other selection and stopping parameters:
@@ -26,7 +26,7 @@ In[] := #["ExpressionsEventsGraph", VertexLabels -> Placed[Automatic, After]] &
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<img src="/Documentation/Images/MaxDestroyerEventsInfinity.png"
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width="478.2"
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alt="Out[] = ... {1, 2} -> {3 (* 1 + 2 *)}, {2, 1} -> {3 (* 2 + 1 *)}, {1, 3 (* init *)} -> {4}, <<3>> ...">
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alt="Out[] = Graph[... {1, 2} -> {3 (* 1 + 2 *)}, {2, 1} -> {3 (* 2 + 1 *)}, {1, 3 (* init *)} -> {4}, <<3>> ...]">
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If set to a finite number, it will generate a partial multihistory:
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@@ -38,6 +38,6 @@ In[] := #["ExpressionsEventsGraph", VertexLabels -> Placed[Automatic, After]] &
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<img src="/Documentation/Images/MaxDestroyerEvents5.png"
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width="478.2"
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alt="Out[] = ... token-event graph containing tokens with out degrees up to 5 ...">
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alt="Out[] = Graph[... token-event graph containing tokens with out degrees up to 5 ...]">
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Note that results generally depend on the event order in this case, similar to single histories.

‎Documentation/Generators/MaxEvents.md‎

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@@ -11,6 +11,6 @@ In[] := #["ExpressionsEventsGraph"] & @
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<img src="/Documentation/Images/MaxEventsExample.png"
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width="478.2"
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alt="Out[] = ... token-event graph with 9 events ...">
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alt="Out[] = Graph[... token-event graph with 9 events ...]">
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Compare to [`MaxGeneration`](MaxGeneration.md), which controls the depth of the evaluation instead.

‎Documentation/Generators/MaxGeneration.md‎

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@@ -21,7 +21,9 @@ In[] := #["ExpressionsEventsGraph",
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<img src="/Documentation/Images/TokenEventGraphGenerations.png"
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width="444.6"
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alt="Out[] = ... token-event graph with 9 tokens arranged in 3 layers, and 3 events in 2 layers in between ...">
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alt="Out[] = Graph[...
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token-event graph with 9 tokens arranged in 3 layers, and 3 events in 2 layers in between
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...]">
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Restricting the number of generations to one will prevent the last two events from occurring. Note, however, that
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another event is created instead:
@@ -34,7 +36,7 @@ In[] := #["ExpressionsEventsGraph"] & @ SetReplaceTypeConvert[WolframModelEvolut
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<img src="/Documentation/Images/MaxGeneration.png"
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width="478.2"
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alt="Out[] = ... token-event graph with 2 layers of tokens and a single layer of events ...">
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alt="Out[] = Graph[... token-event graph with 2 layers of tokens and a single layer of events ...]">
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`MaxGeneration` is an event selection parameter, not a stopping condition. That is, the evolution of the system won't
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stop if a match (tentative event) with a generation greater than the constraint is encountered. Instead, it will ignore

‎Documentation/Generators/MinEventInputs.md‎

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@@ -14,7 +14,9 @@ In[] := #["ExpressionsEventsGraph", VertexLabels -> Placed[Automatic, After]] &
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<img src="/Documentation/Images/MinEventInputs0.png"
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width="367.8"
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alt="Out[] = ... {} -> {0}, {1 (* init *)} -> {1 (* gen 1 *)}, {2 (* init *)} -> {2 (* gen 1 *)}, <<7>> ...">
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alt="Out[] = Graph[...
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{} -> {0}, {1 (* init *)} -> {1 (* gen 1 *)}, {2 (* init *)} -> {2 (* gen 1 *)}, <<7>>
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...]">
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and `MinEventInputs -> 2`:
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@@ -27,4 +29,4 @@ In[] := #["ExpressionsEventsGraph", VertexLabels -> Placed[Automatic, After]] &
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<img src="/Documentation/Images/MinEventInputs2.png"
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width="478.2"
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alt="Out[] = ... {1, 2} -> {3 (* 1 + 2 *)}, {2, 1} -> {3 (* 2 + 1 *)}, {1, 3 (* init *)} -> {4}, <<7>> ...">
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alt="Out[] = Graph[... {1, 2} -> {3 (* 1 + 2 *)}, {2, 1} -> {3 (* 2 + 1 *)}, {1, 3 (* init *)} -> {4}, <<7>> ...]">

‎Documentation/Generators/README.md‎

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@@ -28,7 +28,7 @@ In[] := #["ExpressionsEventsGraph", VertexLabels -> Placed[Automatic, After]] &
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<img src="/Documentation/Images/MultisetSubstitutionSystemExample.png"
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width="444.6"
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alt="Out[] = ... {1, 2} -> {3 (* gen 1 *)}, {3 (* init *), 4} -> {7}, {3 (* gen 1 *), 7} -> {10} ...">
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alt="Out[] = Graph[... {1, 2} -> {3 (* gen 1 *)}, {3 (* init *), 4} -> {7}, {3 (* gen 1 *), 7} -> {10} ...]">
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We can also use a more general [`GenerateMultihistory`](GenerateMultihistory.md) and specify
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[`MaxDestroyerEvents`](MaxDestroyerEvents.md) manually.
@@ -42,13 +42,13 @@ In[] := #["ExpressionsEventsGraph", VertexLabels -> Placed[Automatic, After]] &
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<img src="/Documentation/Images/MultisetSubstitutionSystemPartialMultihistory.png"
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width="478.2"
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alt="Out[] = ...
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alt="Out[] = Graph[...
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{1, 2} -> {3 (* gen 1 *)},
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{1, 3 (* init *)} -> {4 (* gen 1 *)},
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{2, 3 (* init *)} -> {5},
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{3 (* gen 1 *), 4 (* init *)} -> {7},
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{4 (* init *), 5} -> {9}
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...">
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...]">
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The same generators support multiple systems. In addition to
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[`MultisetSubstitutionSystem`](/Documentation/Systems/MultisetSubstitutionSystem.md), other examples include

‎Documentation/Systems/AtomicStateSystem.md‎

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@@ -11,7 +11,7 @@ In[] := #["ExpressionsEventsGraph", VertexLabels -> Placed[Automatic, After]] &
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<img src="/Documentation/Images/AtomicStateSystemExample.png"
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width="858.6"
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alt="Out[] = ... 0 -> Rule 1 -> 1, 0 -> Rule 2 -> -1, 1 -> Rule 1 -> 2, <<26>>, -3 -> Rule 2 -> -4 ...">
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alt="Out[] = Graph[... 0 -> Rule 1 -> 1, 0 -> Rule 2 -> -1, 1 -> Rule 1 -> 2, <<26>>, -3 -> Rule 2 -> -4 ...]">
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Note that spacelike separation is not possible in the `AtomicStateSystem`. As a result, branching due to overlaps of
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different subsets of input tokens cannot occur. And, since events cannot produce branchlike-separated outputs and there

‎Documentation/Systems/MultisetSubstitutionSystem.md‎

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@@ -24,7 +24,7 @@ In[] := #["ExpressionsEventsGraph", VertexLabels -> Placed[Automatic, After]] &
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<img src="/Documentation/Images/MultisetSubstitutionSystemExample.png"
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width="444.6"
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alt="Out[] = ... {1, 2} -> {3 (* gen 1 *)}, {3 (* init *), 4} -> {7}, {3 (* gen 1 *), 7} -> {10} ...">
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alt="Out[] = Graph[... {1, 2} -> {3 (* gen 1 *)}, {3 (* init *), 4} -> {7}, {3 (* gen 1 *), 7} -> {10} ...]">
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Arbitrary Wolfram Language patterns are supported including
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[conditions](https://reference.wolfram.com/language/ref/Condition.html) such as `{a_ /; a > 0, b_}` and
@@ -42,10 +42,10 @@ In[] := #["ExpressionsEventsGraph", VertexLabels -> Placed[Automatic, After]] &
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<img src="/Documentation/Images/MultisetSubstitutionSystemConditionsAndSequences.png"
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width="478.2"
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alt="Out[] = ...
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alt="Out[] = Graph[...
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generation 1: {1, 2} -> {3}, {1, 4} -> {5}, {2, 3} -> {5}, {3, 4} -> {7}, {1, 2, 4} -> {7},
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generation 2: {2, 5} -> {7}, {3 (* gen 1 *), 4} -> {7}
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...">
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...]">
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Note, however, that the system cannot recognize if the code on the right-hand side is nondeterministic, so only the
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first output will be used for each assignment of pattern variables.

‎Documentation/TypeSystem/$SetReplaceTypeGraph.md‎

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@@ -10,10 +10,10 @@ In[] := $SetReplaceTypeGraph
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<img src="/Documentation/Images/$SetReplaceTypeGraph.png"
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width="787.8"
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alt="Out[] = ...
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alt="Out[] = Graph[...
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AtomicStateSystem v0 -> MultisetSubstitutionSystem v0,
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MultisetSubstitutionSystem v0 -> WolframModelEvolutionObject v2
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...">
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...]">
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It is a [`Graph`](https://reference.wolfram.com/language/ref/Graph.html) representation of a directed hypergraph with
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types and properties as vertices and implementations of translations and properties as edges.

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