Combinatory calculi (2) 

CombinatorGlocalMultiwaySystem supports all forms of combinatory calculi, including the single-variable fixed-point (Y) combinator:

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The two-variable fixed-point (Y) combinator:

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The S-K calculus:

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The S-K-I calculus:

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Schönfinkel's B and C combinators:

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Due to the undecidability of the S-K-I combinatory calculus, the following evaluation does not terminate at a normal form:

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Rules and initial conditions (2) 

CombinatorGlocalMultiwaySystem accepts both individual combinator rules and lists of combinator rules:

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CombinatorGlocalMultiwaySystem accepts both individual initial conditions and lists of initial conditions:

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Event selection functions (3) 

Apply only the first possible event at each step:

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Apply the first and last possible events at each step:

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Compare this to the full evolution causal graph (token event graph):

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Token deduplication (2) 

By default, equivalent tokens remain unmerged at each time step:

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Merging of equivalent tokens at each time step can be enforced using the option "DeduplicateTokens":

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Vertex rendering (2) 

By default, state/token vertices and event vertices use special rendering (inherited from the MultiwayCombinator resource function):

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This rendering can be disabled using the option "VertexRendering":

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State/Token vertex rendering (4) 

By default, states/tokens are labeled by their contents:

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Use no labeling for states/tokens:

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Use raw state/token names as vertex labels:

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Use a named shape as each state/token label:

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Event vertex rendering (5) 

By default, both states/tokens and events are labeled by their contents:

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Use no labeling for states/tokens:

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Also use no labeling for events:

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Disabling vertex rendering yields an equivalent result:

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Use raw event expressions as their labels:

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Initialization events (3) 

By default, combinator glocal multiway systems do not include initialization events:

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The option "IncludeInitializationEvents" allows one to override this default (note that initialization events have special default rendering):

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Disable vertex rendering:

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Graph layout options (3) 

Place arrows in the middle of edges:

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Generate an example of glocal multiway combinator evaluation:

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Force a layered digraph embedding (with the initial state/tokens at the top):

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