Imperative

To complement the core Pure Scala language, Stainless proposes a few extensions to that core language.

On the technical side, these extensions do not have specific treatment in the back-end of Stainless. Instead, they are desugared into Pure Scala constructs during a preprocessing phase in the Stainless front-end.

These transformations are partly documented in the EPFL PhD thesis of Régis Blanc.

Imperative Code

Stainless lets you introduce local variables in functions, and use Scala assignments syntax.

def foo(x: Int): Int = {
  var a = x
  var b = 42
  a = a + b
  b = a
  b
}

The above example illustrates three new features introduced by imperative support:

  1. Declaring a variable in a local scope

  2. Blocks of expressions

  3. Assignments

You can use Scala variables with a few restrictions. The variables can only be declared and used locally, no variable declaration outside of a function body. There is also support for variables in case classes constructors. Imperative support introduces the possibility to use sequences of expressions (blocks) – a feature not available in Pure Scala, where your only option is a sequence of val which essentially introduce nested let declarations.

While loops

You can use the while keyword. While loops usually combine the ability to declare variables and make a sequence of assignments in order to compute something useful:

def foo(x: Int): Int = {
  var res = 0
  var i = 0
  while(i < 10) {
    res = res + i
    i = i + 1
  }
  res
}

Stainless will automatically generate a postcondition to the while loop, using the negation of the loop condition. It will automatically prove that verification condition and you should see an invariant postcondition marked as valid.

Stainless internally handles loops as a function with a postcondition. For the end-user, it means that Stainless is only going to rely on the postcondition of the loop to prove properties of code relying on loops. Usually that invariant is too weak to prove anything remotely useful and you will need to annotate the loop with a stronger invariant.

You can annotate a loop with an invariant as follows:

var res = 0
var i = 0
(while(i < 10) {
  res = res + i
  i = i + 1
}) invariant(i >= 0 && res >= i)

The strange syntax comes from some Scala magic in order to make the keyword invariant a valid keyword. Stainless is defining an implicit conversion from Unit to an InvariantFunction object that provides an invariant method. The invariant method takes a boolean expression as a parameter and its semantics is to hold at the following points during the execution of the loop:

  1. When first entering the loop: initialization.

  2. After each complete execution of the body.

  3. On exiting the loop.

Stainless will generate verification conditions invariant inductive and invariant postcondition to verify points (2) and (3) above. It will also generate a precondition corresponding to the line of the while loop. This verification condition is used to prove the invariant on initialization of the loop.

Arrays

PureScala supports functional arrays, that is, the operations apply and updated which do not modify an array but only returns some result. In particular, updated returns a new copy of the array.

def f(a: Array[Int]): Array[Int] = {
  a.updated(0, a(1))
}

However, using functional arrays is not the most natural way to work with arrays, and arrays are often used in imperative implementations of algorithms. We add the usual update operation on arrays:

val a = Array(1,2,3,4)
a(1) //2
a(1) = 10
a(1) //10

Stainless simply rewrite arrays using update operation as the assignment of function arrays using updated. This leverages the built-in algorithm for functional arrays and relies on the elimination procedure for assignments. Concretely, it would transform the above on the following equivalent implementation:

var a = Array(1,2,3,4)
a(1) //2
a = a.updated(1, 10)
a(1) //10

Stainless also has a swap operation in stainless.lang, which is equivalent to two updates.

def swap[@mutable T](a1: Array[T], i1: Int, a2: Array[T], i2: Int): Unit

Mutable Objects

A restricted form of mutable classes is supported via case classes with var arguments:

case class A(var x: Int)
def f(): Int = {
  val a = new A(10)
  a.x = 13
  a.x
}

Mutable case classes are behaving similarly to Array, and are handled with a rewriting, where each field updates becomes essentially a copy of the object with the modified parameter changed.

Aliasing

With mutable data structures comes the problem of aliasing. In Stainless, we maintain the invariant that in any scope, there is at most one pointer to some mutable structure. Stainless will issue an error if you try to create an alias to some mutable structure in the same scope:

val a = Array(1,2,3,4)
val b = a //error: illegal aliasing
b(0) = 10
assert(a(0) == 10)

However, Stainless correctly supports aliasing mutable structures when passing it as a parameter to a function (assuming its scope is not shared with the call site, i.e. not a nested function). Essentially you can do:

case class A(var x: Int)
def updateA(a: A): Unit = {
  a.x = 14
}
def f(): Unit = {
  val a = A(10)
  updateA(a)
  assert(a.x == 14)
}

The function updateA will have the side effect of updating its argument a and this will be visible at the call site.

Annotations for Imperative Programming

We introduce the special function old that can be used in postconditions to talk about the value of a variable before the execution of the block. When you refer to a variable or mutable structure in a post-condition, Stainless will always consider the current value of the object, so that in the case of a post-condition this would refer to the final value of the object. Using old, you can refer to the original value of the variable and check some properties:

 case class A(var x: Int)
 def inc(a: A): Unit = {
   a.x = a.x + 1
}.ensuring(_ => a.x == old(a).x + 1)

old can be wrapped around any identifier that is affected by the body. You can also use old for variables in scope, in the case of nested functions:

def f(): Int = {
  var x = 0
  def inc(): Unit = {
    x = x + 1
 }.ensuring(_ => x == old(x) + 1)

  inc(); inc();
  assert(x == 2)
}

Another useful and similar construct is snapshot that semantically makes a deep copy of a mutable object. Contrarily to old, snapshot allows to refer to the state of an object prior to its mutation within the body of the function, as long as it is used in a ghost context.

For instance:

def updateArray(a: Array[BigInt], i: Int, x: BigInt): Unit = {
  require(0 <= i && i < a.length - 1)
  require(a(i) == 0 && a(i + 1) == 0)
  @ghost val a0 = snapshot(a)
  a(i) = x
  // a0 is unaffected by the update of a
  // Note: using StaticChecks assert, which introduces a ghost context
  assert(a0(i) == 0 && a(i) == x)
  @ghost val a1 = snapshot(a)
  a(i + 1) = 2 * x
  assert(a1(i + 1) == 0 && a(i + 1) == 2 * x)
}

Extern functions and abstract methods

@extern functions and abstract methods of non-sealed trait taking mutable objects as parameters are treated as-if they were applying arbitrary modifications to them. For instance, the assertions in the following snippet are invalid:

@extern
def triple(mc: MutableClass): BigInt = ???

trait UnsealedTrait {
  def quadruple(mc: MutableClass): BigInt
}

def test1(mc: MutableClass): Unit = {
  val i = mc.i
  triple(mc)
  assert(i == mc.i) // Invalid, mc.i could be anything
}

def test2(ut: UnsealedTrait, mc: MutableClass): Unit = {
  val i = mc.i
  ut.quadruple(mc)
  assert(i == mc.i) // Invalid as well
}

Annotating such methods or functions with @pure tells Stainless to assume the parameters are not mutated:

case class MutableClass(var i: BigInt)

@pure @extern
def triple(mc: MutableClass): BigInt = ???

trait UnsealedTrait {
  @pure
  def quadruple(mc: MutableClass): BigInt
}

def test1(mc: MutableClass): Unit = {
  val i = mc.i
  triple(mc)
  assert(i == mc.i) // Ok
}

def test2(ut: UnsealedTrait, mc: MutableClass): Unit = {
  val i = mc.i
  ut.quadruple(mc)
  assert(i == mc.i) // Ok
}

Note that Stainless will enforce purity for visible implementations of quadruple.

Sometimes, a method or @extern function may mutate some parameters but not all of them. In such cases, the untouched parameters can be annotated with @pure:

case class MutableClass(var i: BigInt)

@extern
def sum(@pure mc1: MutableClass, mc2: MutableClass): BigInt = ???

trait UnsealedTrait {
  def doubleSum(@pure mc1: MutableClass, mc2: MutableClass): BigInt
}

def test1(mc1: MutableClass, mc2: MutableClass): Unit = {
  val i1 = mc1.i
  val i2 = mc2.i
  sum(mc1, mc2)
  assert(i1 == mc1.i) // Ok
  assert(i2 == mc2.i) // Invalid, mc2.i may have any value
}

def test2(ut: UnsealedTrait, mc1: MutableClass, mc2: MutableClass): Unit = {
  val i1 = mc1.i
  val i2 = mc2.i
  ut.doubleSum(mc1, mc2)
  assert(i1 == mc1.i) // Ok
  assert(i2 == mc2.i) // Invalid
}

Trait Variables

Traits are allowed to declare variables, with the restriction that these cannot be assigned a default value.

trait MutableBox[A] {
  var value: A
}

Such abstract variables must be overridden at some point by either:

  1. a mutable field of a case class

case class Box[A](var value: A) extends MutableBox[A]

  1. a pair of getter/setter

case class WriteOnceBox[A](
  var underlying: A,
  var written: Boolean = false
) extends MutableBox[A] {

  def value: A = underlying

  def value_=(newValue: A): Unit = {
    if (!written) {
      underlying = newValue
      written = true
    }
  }
}

Note: a setter is not required to actually perform any mutation, and the following is a perfectly valid sub-class of MutableBox:

case class ImmutableBox[A](underlying: A) extends MutableBox[A] {
  def value: A = underlying
  def value_=(newValue: A): Unit = ()
}

Return keyword

Stainless partially supports the return keyword. For verification, an internal phase of Stainless (called ReturnElimination) injects a data-structure named ControlFlow to simulate the control flow of programs with returns.

sealed abstract class ControlFlow[Ret, Cur]
case class Return[Ret, Cur](value: Ret)  extends ControlFlow[Ret, Cur]
case class Proceed[Ret, Cur](value: Cur) extends ControlFlow[Ret, Cur]

Here is a function taken from ControlFlow2.scala:

def foo(x: Option[BigInt], a: Boolean, b: Boolean): BigInt = {
  if (a && b) {
    return 1
  }

  val y = x match {
    case None()       => return 0
    case Some(x) if a => return x + 1
    case Some(x) if b => return x + 2
    case Some(x)      => x
  };

  -y
}

The program transformation can be inspected by running:

stainless ControlFlow2.scala --batched --debug=trees --debug-objects=foo --debug-phases=ReturnElimination

We get the following output (with cf identifiers renamed for clarity; you can use the --print-ids option so that Stainless expressions get displayed with unique identifiers, at the cost of readability):

def foo(x: Option[BigInt], a: Boolean, b: Boolean): BigInt = {
  val cf0: ControlFlow[BigInt, Unit] = if (a && b) {
    Return[BigInt, Unit](1)
  } else {
    Proceed[BigInt, Unit](())
  }
  cf0 match {
    case Return(retValue) =>
      retValue
    case Proceed(proceedValue) =>
      val cf1: ControlFlow[BigInt, BigInt] = x match {
        case None()       => Return[BigInt, BigInt](0)
        case Some(x) if a => Return[BigInt, BigInt](x + 1)
        case Some(x) if b => Return[BigInt, BigInt](x + 2)
        case Some(x)      => Proceed[BigInt, BigInt](x)
      }
      cf1 match {
        case Return(retValue) =>
          retValue
        case Proceed(proceedValue) =>
          -proceedValue
      }
  }
}

Stainless also supports return in while loops, and transforms them to local functions, also in the ReturnElimination phase. Here is a function taken from ReturnInWhile.scala.

 def returnN(n: Int): Int = {
   require(n >= 0)
   var i = 0
   (while (true) {
     decreases(n - i)
     if (i == n) return i
     i += 1
   }).invariant(0 <= i && i <= n)

   assert(false, "unreachable code")
   0
}.ensuring((res: Int) => res == n)

After transformation, we get a recursive (local) function named returnWhile that returns a control flow element to indicate whether the loop terminated normally or returned. We check that the invariant clause of the while loop is indeed an invariant by adding it to the pre and postconditions of the generated returnWhile function. When the while loop returns, we check in addition that the postcondition of the top-level holds (see comment).

 def returnN(n: Int): Int = {
   require(n >= 0)

   var i: Int = 0
   val cf0: ControlFlow[Int, Unit] = {
     def returnNWhile: ControlFlow[Int, Unit] = {
       require(0 <= i && i <= n)
       decreases(n - i)
       {
         val cf1: ControlFlow[Int, Unit] = if (i == n) {
           Return[Int, Unit](i)
         } else {
           Proceed[Int, Unit](())
         }
         cf1 match {
           case Return(retValue) => Return[Int, Unit](retValue)
           case Proceed(proceedValue) =>
             Proceed[Int, Unit]({
               i = (i + 1)
               ()
             })
         }
       } match {
         case Return(retValue) =>
           Return[Int, Unit](retValue)
         case Proceed(proceedValue) =>
           if (true) {
             returnNWhile
           } else {
             Proceed[Int, Unit](())
           }
       }
    }.ensuring {
       (cfWhile: ControlFlow[Int, Unit]) => cfWhile match {
         case Return(retValue) =>
           // we check the postcondition `retValue == n` of the top-level function
           retValue == n &&
           0 <= i && i <= n
         case Proceed(proceedValue) =>
           ¬true && 0 <= i && i <= n
       }
     }
     if (true) {
       returnNWhile
     } else {
       Proceed[Int, Unit](())
     }
   }
   cf0 match {
     case Return(retValue) => retValue
     case Proceed(proceedValue) =>
       assert(false, "unreachable code")
       0
   }
}.ensuring {
   (res: Int) => res == n
 }

Finally, return is also supported for local function definitions, with the same transformation. It is however not supported for anonymous functions.