gapt.proofs.epsilon.ExpansionProofToEpsilon.scala Maven / Gradle / Ivy

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General Architecture for Proof Theory

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package gapt.proofs.epsilon

import gapt.expr._
import gapt.expr.formula.All
import gapt.expr.formula.Ex
import gapt.expr.formula.Formula
import gapt.expr.formula.Quant
import gapt.expr.formula.hol.instantiate
import gapt.expr.util.rename
import gapt.logic.hol.SkolemFunctions
import gapt.proofs.context.Context
import gapt.proofs.context.facet.skolemFunsFacet
import gapt.proofs.expansion._

object ExpansionProofToEpsilon {

  def apply(e: ExpansionProof)(implicit ctx: Context): EpsilonProof = {
    val skolemToEpsilonMap = ctx.get[SkolemFunctions].skolemDefs.map {
      case (sk, Abs.Block(vs, q @ Quant(x, _, isForall))) =>
        val x_ = rename(x, vs)
        (sk: Expr) -> Abs.Block(
          vs,
          Epsilon(
            x_,
            epsilonize(
              if (isForall) -instantiate(q, x_) else instantiate(q, x_)
            )
          )
        )
    }
    def replaceSkolemByEpsilon(t: Expr) =
      BetaReduction.betaNormalize(TermReplacement(t, skolemToEpsilonMap))

    val criticalFormulas = e.subProofs flatMap {
      case ETWeakQuantifier(sh, insts) =>
        val ex = sh match {
          case All(x, f) => Ex(x, -epsilonize(replaceSkolemByEpsilon(f).asInstanceOf[Formula]))
          case Ex(x, f)  => Ex(x, epsilonize(replaceSkolemByEpsilon(f).asInstanceOf[Formula]))
        }
        for ((term, _) <- insts) yield CriticalFormula(ex, replaceSkolemByEpsilon(term))
      case ETStrongQuantifier(_, _, _) =>
        throw new IllegalArgumentException
      case _ => Set()
    }

    EpsilonProof(criticalFormulas.toSeq, e.shallow)
  }

}