Function Repository Resource:

# FindStringProof

Try to find a proof of equivalence between strings in a given multiway system

Contributed by: Jonathan Gorard
 ResourceFunction["FindStringProof"][thm,axms] tries to find a proof of the string equivalence theorem thm using the multiway system axioms axms.

## Details and Options

If ResourceFunction["FindStringProof"][thm,axms] succeeds in deriving the theorem thm from the axioms axms, then it returns a ProofObject expression. If it succeeds in showing that the theorem cannot be derived from the axioms, it returns a Failure object. Otherwise, it may not terminate unless time constrained.
ResourceFunction["FindStringProof"] accepts both individual axioms and lists of axioms, and likewise for theorems.
ResourceFunction["FindStringProof"] has the following option:
 TimeConstraint Infinity how much time to allow
If ResourceFunction["FindStringProof"] exceeds the specified time constraint, it returns a Failure object.
ResourceFunction["FindStringProof"][thms,axms] uses the Knuth–Bendix completion to prove that the theorem thm follows from the axioms axms.

## Examples

### Basic Examples (2)

Prove an elementary theorem regarding the equivalence of two strings in a simple multiway system:

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Show the abstract proof network, with tooltips showing the intermediate expressions:

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Show the complete list of proof steps as a Dataset object:

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Typeset a natural language argument:

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Prove a more sophisticated theorem involving multiple rules and hypotheses:

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Show the abstract proof network:

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### Scope (2)

Show that a string equivalence proposition cannot be derived from a given set of multiway system axioms:

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#### Rules and Initial Conditions (2)

FindStringProof accepts both individual axioms and lists of axioms:

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Likewise for theorems:

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### Options (2)

#### TimeConstraint (2)

Use to limit the computation time to t seconds:

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By default, FindStringProof looks for a proof indefinitely:

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### Properties and Relations (1)

FindStringProof will return a proof object for a particular theorem if and only if the associated path exists in the corresponding multiway system:

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Jonathan Gorard

## Version History

• 1.0.0 – 03 August 2020