Combinatory calculi (2) 

MultiwayCombinator 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 combinatorial calculus, the following evaluation does not terminate at a normal form:

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Rules and initial conditions (2) 

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

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

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Event selection functions (2) 

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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State node rendering (3) 

By default, states are labeled by their contents:

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Use no labeling for states:

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"StatesGraphStructure" yields the same result:

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Use raw state names as node labels:

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Use a named shape as each state label:

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Event node rendering (2) 

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

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Use no labels for states or events:

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"EvolutionEventsGraphStructure" yields an equivalent result:

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Use raw event expressions as their labels:

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Initialization events (2) 

By default, "AllEventsList" does not include initialization events:

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The option "IncludeInitializationEvents" allows one to override this default:

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Initialization events have special default rendering:

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Graph layout options (2) 

Place arrows in the middle of edges:

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Generate an example of a multiway combinator evaluation:

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Force the initial state node to be at the top:

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Step numbers and state IDs (4) 

By default, equivalent states are merged across all time steps:

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Merging of equivalent states across different time steps can be prevented by including step numbers:

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List the states:

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Merging of equivalent states at the same time step can be prevented by also including state IDs:

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List the states:

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Step numbers and IDs also apply to events:

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See the events:

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Event instances (2) 

By default, multiple instances of equivalent updating events are merged in the states graph:

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Merging of equivalent events can be prevented by including event instances:

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State (path) weights (2) 

Vertices of a states graph can be weighted by their relative rate of occurrence at each time step:

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Vertices can also be weighted by the number of distinct evolution paths that lead to them:

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MaxItems (2) 

By default, "CausalGraphInstances" returns all possible causal graphs:

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The number of causal graphs returned can be limited using MaxItems:

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Predecessors and resolvents (2) 

By default, "BranchPairsList" returns only a list of branch pairs:

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Common predecessor states can be shown using "GivePredecessors":

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Similarly, "BranchPairResolutionsList" by default lists only resolved and unresolved branch pairs:

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Common resolvents of resolved branch pairs can be shown using "GiveResolvents":

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Show both common predecessors and common resolvents, where appropriate:

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Full branchial space (2) 

By default, non-branch pair states are not shown as part of the branchial graph:

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They can be shown by using "IncludeFullBranchialSpace":

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