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WOLFRAM NOTEBOOK
Non-Identical Results
Non-Identical Results
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Clear[f]
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f[f[x_]]:=x
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f[x_]:=x+1
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?f
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MultiEvaluate[f[f[0]],5,"Graph","EvaluatePattern"->_Plus]
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Are pure _ pattern matching rules always confluent (i.e. without evaluation of other functions)?
Even in S, K combinators ... in the hypergraph case ... confluence is different
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Clear[f]
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f[f[x_]]:=x
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f[x_]:=g[x]
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MultiEvaluate[f[f[0]],5,"Graph"]
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MultiEvaluate[f[f[0]],5,"EvolutionCausalGraph"]
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If it’s always the same rule that self overlaps, it’ll be confluent [ ?? ]
Cf. x1, x2
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MultiEvaluate[x,3,"Graph","ExplicitRules"->{x->1,x->2}]
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Side effects are a different way to get distinct results
Side effects are a different way to get distinct results
The only reason is because we’re not seeing the whole symbol table / state of the kernel
Some information is not seen.
Some information is not seen.
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Clear[f]
Confluent vs. Non-Confluent Rules
Confluent vs. Non-Confluent Rules
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ResourceFunction["EnumerateSubstitutionSystemRules"][{2->2},2]
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{{AAAA},{AAAB},{AABB},{ABAA},{ABAB},{ABBA}}
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ResourceFunction["TotalCausalInvariantQ"][{"AA"->"AB","B"->"BA"},4]
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True
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ResourceFunction["MultiwaySystem"][{"AA"->"AB","B"->"BA"},"AA",8,"StatesGraph"]
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Clear[f]
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f[x_][y_]:=x[x[x]]
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MultiEvaluate[f[f[f[f]]][f],10,"Graph",GraphLayout->"LayeredDigraphEmbedding"]
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Non-Terminating Rules
Non-Terminating Rules
Infinities
Infinities
Combinators
Combinators
Side Effects
Side Effects
Treelike Separation
Treelike Separation