gapt.expr.util.replacementContext.scala Maven / Gradle / Ivy

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General Architecture for Proof Theory

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package gapt.expr.util

import gapt.expr.Abs
import gapt.expr.Expr
import gapt.expr.ReplacementContext
import gapt.expr.Var
import gapt.expr.containedNames
import gapt.expr.formula.hol.HOLPosition
import gapt.expr.ty.Ty

/**
 * Creates capture avoiding replacement contexts.
 */
object replacementContext {

  /**
   * Creates a replacement context.
   *
   * @param ty The type of the holes.
   * @param exp An expression φ for which a context is to be created.
   * @param positions A list of non-overlapping positions p_1, ..., p_n in φ.
   * @return An expression of the form λx.φ', where x is a fresh variable of
   * type `ty` and φ' = φ[p_1/x, ..., p_n/x].
   */
  def apply(ty: Ty, exp: Expr, positions: Iterable[LambdaPosition]): ReplacementContext = {
    val x = rename(Var("x", ty), containedNames(exp))
    Abs(x, positions.foldLeft(exp) { (acc, p) => acc.replace(p, x) })
  }

  /**
   * Creates a replacement context.
   *
   * @param ty The type of the holes.
   * @param exp An expression φ for which a context is to be created.
   * @param positions A list of non-overlapping positions p_1, ..., p_n in φ.
   * @return See `replacementContext.apply()`.
   */
  def apply(ty: Ty, exp: Expr, positions: Iterable[HOLPosition])(implicit d: DummyImplicit): ReplacementContext =
    apply(ty, exp, positions map { HOLPosition.toLambdaPosition(exp) })

  /**
   * Creates a replacement context.
   *
   * @param exp The expression φ for which a context is to be created.
   * @param t The term t to be replaced by holes.
   * @return An expression of the form λx.φ', where x is a fresh variable and
   * φ' = φ[t/x].
   */
  def abstractTerm(exp: Expr)(t: Expr): ReplacementContext =
    apply(t.ty, exp, exp.find(t))
}