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General Architecture for Proof Theory

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package gapt

import gapt.expr.VarOrConst
import gapt.expr.formula.fol.FOLConst
import gapt.expr.formula.fol.FOLVar
import gapt.expr.subst.FOLSubstitution
import gapt.expr.subst.Substitutable
import gapt.expr.subst.Substitution
import gapt.expr.util.ExpressionParseHelper
import gapt.formats.babel.BabelSignature
import gapt.utils.NameGenerator

package object expr {

  implicit def stringInterpolationForExpressions(
      sc: StringContext
  )(implicit file: sourcecode.File, line: sourcecode.Line, sig: BabelSignature): ExpressionParseHelper =
    new ExpressionParseHelper(sc, file, line, sig)

  // Type aliases that assert that a type `T` is closed under Substitution and FOLSubstitution, respectively.
  type ClosedUnderSub[T] = Substitutable[Substitution, T, T]
  type ClosedUnderFOLSub[T] = Substitutable[FOLSubstitution, T, T]

  type ClosedUnderReplacement[T] = Replaceable[T, T]

  implicit class ExprNameGenerator(private val nameGen: NameGenerator) extends AnyVal {
    def fresh(v: Var): Var = Var(nameGen.fresh(v.name), v.ty)
    def fresh(v: FOLVar): FOLVar = FOLVar(nameGen.fresh(v.name))
    def fresh(c: Const): Const = Const(nameGen.fresh(c.name), c.ty)
    def fresh(c: FOLConst): FOLConst = FOLConst(nameGen.fresh(c.name))
    def fresh(n: VarOrConst): VarOrConst = n match {
      case v: Var   => fresh(v)
      case c: Const => fresh(c)
    }
  }

  type ReplacementContext = Abs
}