object ReductiveCutElimination
This object implements a version of Gentzen's cut-elimination proof for our sequent calculus LK. For details, please refer to the documentation of the apply methods.
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def
apply(proof: LKProof, cleanStructRules: Boolean = true): LKProof
This methods implements a version of Gentzen's cut-elimination proof using the (known to be terminating) strategy of reducing a left-uppermost cut.
This methods implements a version of Gentzen's cut-elimination proof using the (known to be terminating) strategy of reducing a left-uppermost cut. The algorithm terminates when all cuts have been eliminated.
- proof
The proof to subject to cut-elimination or restructuring.
- cleanStructRules
Tells the algorithm whether or not to clean the structural rules default value is on, i.e. clean the structural rules
- returns
A proof.
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- def eliminateInduction(proof: LKProof, cleanStructRules: Boolean = true)(implicit ctx: Context): LKProof
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def
introOrCut(proof: LKProof, formula: Formula): Boolean
Checks if the last rule in proof is a leaf, a cut rule, or a weakening rule on the given formula.
Checks if the last rule in proof is a leaf, a cut rule, or a weakening rule on the given formula.
- proof
The proof we are checking.
- formula
The formula we are checking.
- returns
True is structure is correct or false if not.
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def
isACNF(proof: LKProof): Boolean
This method checks whether a proof is in ACNF
This method checks whether a proof is in ACNF
- proof
The proof to check for in ACNF.
- returns
True if proof is in ACNF, False otherwise.
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def
isACNFTop(proof: LKProof): Boolean
This method checks whether a proof is in ACNF top
This method checks whether a proof is in ACNF top
- proof
The proof to check for in ACNF top.
- returns
True if proof is in ACNF, False otherwise.
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def
isCutFree(proof: LKProof): Boolean
This method checks whether a proof is cut-free.
This method checks whether a proof is cut-free.
- proof
The proof to check for cut-freeness.
- returns
True if proof does not contain the cut rule, False otherwise.
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def
reduceToACNF(proof: LKProof, cleanStructRules: Boolean = true): LKProof
Reduces proof to ACNF using reductive cut elimination
Reduces proof to ACNF using reductive cut elimination
- proof
The proof to subject to cut-elimination or restructuring.
- cleanStructRules
Tells the algorithm whether or not to clean the structural rules default value is on, i.e. clean the structural rules
- returns
A proof.
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def
reduceToACNFTop(proof: LKProof, cleanStructRules: Boolean = true): LKProof
Reduces proof to ACNF top using reductive cut elimination
Reduces proof to ACNF top using reductive cut elimination
- proof
The proof to subject to cut-elimination or restructuring.
- cleanStructRules
Tells the algorithm whether or not to clean the structural rules default value is on, i.e. clean the structural rules
- returns
A proof.
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