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gapt.proofs.nd

MRealizability

object MRealizability

Source
m-realizability.scala
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  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. final def asInstanceOf[T0]: T0
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  5. def clone(): AnyRef
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    protected[java.lang]
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    @throws(classOf[java.lang.CloneNotSupportedException]) @native()
  6. final def eq(arg0: AnyRef): Boolean
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  7. def equals(arg0: AnyRef): Boolean
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  8. def finalize(): Unit
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    @throws(classOf[java.lang.Throwable])
  9. def flat(formula: Formula)(implicit systemT: Context): Ty

    computes the type of a potential m-realizer for the formula

  10. final def getClass(): Class[_ <: AnyRef]
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    @native()
  11. def hashCode(): Int
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    @native()
  12. final def isInstanceOf[T0]: Boolean
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  13. def mrealize(proof: NDProof, re: Boolean = true)(implicit ctx: Context): (Map[SequentIndex, Var], Expr)

    Extracts an mrealizer for a theorem from its proof.

    Extracts an mrealizer for a theorem from its proof.

    proof

    proof from which the realizer is extracted

    re

    boolean whether or not the result should be normalized with respect to the empty program (default) or not

    ctx

    system T

    returns

    a term M of system T, and a map of sequentindices of the antecedent of the conclusion of the proof, to variables x1,...,xk, such that: if M1,...,Mk are m-realizers for the formulas in the antecedent, then M[M1/x1]...[Mk/xk] m-realizes the succedent of the conclusion

  14. final def ne(arg0: AnyRef): Boolean
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  15. final def notify(): Unit
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    @native()
  16. final def notifyAll(): Unit
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    @native()
  17. def recursor(indType: TBase, resultType: Ty)(implicit ctx: Context): Const

    Gives a recursor constant for an inductive type.

    Gives a recursor constant for an inductive type.

    indType

    the inductive type that the recursor is for

    resultType

    type of the result of applying terms to the recursor

    ctx

    context that the inductive type is defined in

    returns

    recursor constant

  18. def remEmpProg(term: Expr)(implicit systemT: Context): Expr

    removes all occurences of the empty program i : 1 from term, or is i : 1 itself, except for match and inl and inr term: sometimes not possible to remove all occurences.

  19. def remEmpProgType(typee: Ty)(implicit systemT: Context): Ty

    removes all occurences of the empty program type 1 from term, or is 1 itself, except for the sum type.

  20. def remEmpProgTypes(types: List[Ty])(implicit systemT: Context): List[Ty]
  21. final def synchronized[T0](arg0: => T0): T0
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  22. def systemT(ctx: Context): Context

    Transforms a context into system T.

    Transforms a context into system T.

    ctx

    original context

    returns

    original context with recursors for inductive types, pair and sum types and terms, and the empty program

  23. def toString(): String
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  24. final def wait(): Unit
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    @throws(classOf[java.lang.InterruptedException])
  25. final def wait(arg0: Long, arg1: Int): Unit
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    @throws(classOf[java.lang.InterruptedException])
  26. final def wait(arg0: Long): Unit
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    @throws(classOf[java.lang.InterruptedException]) @native()

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