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General Architecture for Proof Theory

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package gapt.provers.viper

import gapt.expr.{Const, Expr}
import gapt.expr.formula.{Formula, Neg}
import gapt.expr.ty.{TArr, Ty}
import gapt.proofs.Sequent
import gapt.proofs.context.Context

package object spin {

  // Replaces x with e in f.
  def replaceExpr(f: Formula, x: Expr, e: Expr): Formula =
    f.find(x).foldLeft(f)((f, pos) => f.replace(pos, e))

  def negate(f: Formula): Formula = f match {
    case Neg(g) => g
    case _      => Neg(f)
  }

  def resType(ty: Ty): Ty =
    ty match {
      case TArr(_, t) => resType(t)
      case _          => ty
    }

  // Is c a constructor
  def isConstructor(c: Const)(implicit ctx: Context): Boolean =
    ctx.getConstructors(resType(c.ty)) match {
      case None          => false
      case Some(constrs) => constrs.contains(c)
    }

  def lambdaType(t: String): Boolean = t.matches("fun[0-9]+")

  private[spin] implicit def labeledSequentToHOLSequent(sequent: Sequent[(String, Formula)]): Sequent[Formula] =
    sequent map { case (_, f) => f }
}