Object

at.logic.gapt.proofs.lkOld

EquationLeftRule

Related Doc: package lkOld

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object EquationLeftRule extends EquationRuleLogger

This macro rule unifies EquationLeft1Rule and EquationLeft2Rule by automatically choosing the appropriate rule.

Source
macroRules.scala
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  1. EquationLeftRule
  2. EquationRuleLogger
  3. Logger
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Value Members

  1. final def !=(arg0: Any): Boolean

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  2. final def ##(): Int

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  3. final def ==(arg0: Any): Boolean

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  4. def apply(s1: LKProof, term1oc: FormulaOccurrence, eq: HOLFormula, main: HOLFormula): BinaryTree[OccSequent] with base.BinaryLKProof with AuxiliaryFormulas with PrincipalFormulas

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    This version creates an axiom for the equation.

  5. def apply(s1: LKProof, s2: LKProof, term1: HOLFormula, term2: HOLFormula, main: HOLFormula): BinaryTree[OccSequent] with base.BinaryLKProof with AuxiliaryFormulas with PrincipalFormulas

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    This version of the rule operates on formulas instead of occurrences.

    This version of the rule operates on formulas instead of occurrences. It will attempt to find appropriate occurrences in the premises.

    s1

    A proof ending with term1oc in the succedent.

    s2

    A proof ending with term2oc in the antecedent.

    term1

    An equation s = t.

    term2

    A formula A.

    main

    A formula A' such that A' is obtained by replacing one occurrence of s in A by t or vice versa.

    returns

    A proof ending with either an EquationLeft1Rule or an EquationLeft2Rule according to which one leads from A to A'.

  6. def apply(s1: OccSequent, s2: OccSequent, term1oc: FormulaOccurrence, term2oc: FormulaOccurrence, pos: Seq[HOLPosition]): OccSequent

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    s1

    A sequent with term1oc in the succedent.

    s2

    A sequent with term2oc in the antecedent.

    term1oc

    An equation s = t.

    term2oc

    A formula A.

    pos

    A position such that A(pos) = s or A(pos) = t

    returns

    A proof ending with either an EquationLeft1Rule or an EquationLeft2Rule according to which replacement is sensible.

  7. def apply(s1: OccSequent, s2: OccSequent, term1oc: FormulaOccurrence, term2oc: FormulaOccurrence, main: HOLFormula): OccSequent

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    s1

    A sequent with term1oc in the succedent.

    s2

    A sequent with term2oc in the antecedent.

    term1oc

    An equation s = t.

    term2oc

    A formula A.

    main

    A formula A' such that A' is obtained by replacing one occurrence of s in A by t or vice versa.

    returns

    A proof ending with either an EquationLeft1Rule or an EquationLeft2Rule according to which one leads from A to A'.

  8. def apply(s1: LKProof, s2: LKProof, term1oc: FormulaOccurrence, term2oc: FormulaOccurrence, main: HOLFormula): BinaryTree[OccSequent] with base.BinaryLKProof with AuxiliaryFormulas with PrincipalFormulas with TermPositions

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    s1

    A proof ending with term1oc in the succedent.

    s2

    A proof ending with term2oc in the antecedent.

    term1oc

    An equation s = t.

    term2oc

    A formula A.

    main

    A formula A' such that A' is obtained by replacing one occurrence of s in A by t or vice versa.

    returns

    A proof ending with either an EquationLeft1Rule or an EquationLeft2Rule according to which one leads from A to A'.

  9. def apply(s1: LKProof, s2: LKProof, term1oc: FormulaOccurrence, term2oc: FormulaOccurrence, pos: Seq[HOLPosition]): BinaryTree[OccSequent] with base.BinaryLKProof with AuxiliaryFormulas with PrincipalFormulas with TermPositions

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    s1

    A proof ending with term1oc in the succedent.

    s2

    A proof ending with term2oc in the antecedent.

    term1oc

    An equation s = t.

    term2oc

    A formula A.

    pos

    A position such that A(pos) = s or A(pos) = t

    returns

    A proof ending with either an EquationLeft1Rule or an EquationLeft2Rule according to which replacement is sensible.

  10. final def asInstanceOf[T0]: T0

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  11. def clone(): AnyRef

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    protected[java.lang]
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    @throws( ... )
  12. def debug(msg: ⇒ String): Unit

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    Logger
  13. final def eq(arg0: AnyRef): Boolean

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  14. def equals(arg0: Any): Boolean

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  15. def error(msg: ⇒ String, e: Throwable): Nothing

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  16. def error(msg: ⇒ String): Unit

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  17. def finalize(): Unit

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    protected[java.lang]
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    @throws( classOf[java.lang.Throwable] )
  18. final def getClass(): Class[_]

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  19. def hashCode(): Int

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  20. def info(msg: ⇒ String): Unit

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    protected
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    Logger
  21. final def isInstanceOf[T0]: Boolean

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  22. val log: Logger

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    protected
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    Logger
  23. def loggerName: String

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    Definition Classes
    EquationRuleLoggerLogger
  24. final def ne(arg0: AnyRef): Boolean

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  25. final def notify(): Unit

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  26. final def notifyAll(): Unit

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  27. final def synchronized[T0](arg0: ⇒ T0): T0

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  28. def toString(): String

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  29. def trace(msg: ⇒ String): Unit

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  30. final def wait(): Unit

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    @throws( ... )
  31. final def wait(arg0: Long, arg1: Int): Unit

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  32. final def wait(arg0: Long): Unit

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    @throws( ... )
  33. def warn(msg: ⇒ String, e: Throwable): Unit

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    protected
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  34. def warn(msg: ⇒ String): Unit

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    protected
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Inherited from EquationRuleLogger

Inherited from Logger

Inherited from AnyRef

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