Equality For All!

Equality For All!
Scala by the Bay, 2014
BillVenners
Artima, Inc.
Escalate Software
Saturday, August 9, 2014

Equality: An equivalence relation with
one element per equivalence class
42 4341
42 = 4241 = 41 43 = 43
reﬂexive: x = x
symmetric: x = y iff y = x
transitive: if x = y and y = z then x = z

How do I say forty two in code?
Let me count the ways...
42
42L
42.0
42.0F
42.toShort
'*'
42.toByte BigInt(42)
BigDecimal(42)
new java.lang.Integer(42)
new java.lang.Long(42L)
new java.lang.Double(42.0)
new java.lang.Float(42.0F) new java.lang.Short(42.toShort)
new java.lang.Character(42)
new java.lang.Byte(42.toByte)
new java.math.BigInteger("42")
new java.math.BigDecimal(42) Complex(42.0, 0.0)
DigitString("42") DigitString("042")

The equals method implements an equivalence relation on non-null object references:
• It is reflexive: for any non-null reference value x, x.equals(x) should return true.
• It is symmetric: for any non-null reference values x and y, x.equals(y) should return true
if and only if y.equals(x) returns true.
• It is transitive: for any non-null reference values x, y, and z, if x.equals(y) returns true
and y.equals(z) returns true, then x.equals(z) should return true.
• It is consistent: for any non-null reference values x and y, multiple invocations of
x.equals(y) consistently return true or consistently return false, provided no
information used in equals comparisons on the objects is modified.
• For any non-null reference value x, x.equals(null) should return false.
Java's equals contract
public boolean equals(Object obj)
final def == (other:Any): Boolean

scala> 42 == 42L
res0: Boolean = true
scala> BigDecimal(42) == '*'
scala> 42.0F == BigInt(42)
scala> new java.lang.Float(42.0F) == 42.toShort
Co-operative Equality Between Types

scala> import scala.collection.mutable
import scala.collection.mutable
scala> Set(BigInt(4), BigInt(2)) == mutable.Set(4.toByte,
2.toByte)
scala> Vector(Left(4), Right(2)) == List(Left(4L), Right(2L))
scala> List(mutable.Set(Map(Some(4L) -> BigInt(2)))) ==
Vector(Set(mutable.Map(Some(4.0) -> new java.lang.Long(2L))))
Co-operative Equality Between Types

scala> Array(4, 2) == Array(4, 2)
res7: Boolean = false
scala> <forty><two></two></forty> == <forty> <two></two> </forty>
scala> new java.math.BigDecimal("42.0") ==
new java.math.BigDecimal("42.00")
scala> 42.0 == 41.9999999999
scala> "case" == "CASE"
Wanted: Alternate equalities

scala> "forty two" == 42
scala> List(mutable.Set(Map(Some(4L) -> BigInt(2)))) ==
Vector(Set(mutable.Map(Some("4.0") -> new java.lang.Long(2L))))
Wanted: Type errors
But how to decide which comparisons compile?

scala> "forty two" == 42
<console>:20: error: types String and Int do not adhere to the
type constraint selected for the === and !== operators; the
missing implicit parameter is of type
org.scalactic.EqualityConstraint[String,Int]
"forty two" === 42
^
scala> BigInt(42) === BigDecimal(42)
Fail to compile if L can never equal R.

scala> Vector.empty === List.empty
<console>:20: error: ambiguous implicit values:
both method conflictingEmptySeqConstraint1 in object EqualityConstraint of type [LSEQ[e] <:
scala.collection.GenSeq[e], RSEQ[e] <: scala.collection.GenSeq[e]]=>
org.scalactic.EqualityConstraint[LSEQ[Nothing],RSEQ[Nothing]]
and method conflictingEmptySeqConstraint2 in object EqualityConstraint of type [LSEQ[e] <:
scala.collection.GenSeq[e], RSEQ[e] <: scala.collection.GenSeq[e]]=>
org.scalactic.EqualityConstraint[LSEQ[Nothing],RSEQ[Nothing]]
match expected type
org.scalactic.EqualityConstraint[scala.collection.immutable.Vector[A],List[Nothing]]
Vector.empty === List.empty
^
scala> Vector.empty === List.empty[Int]
scala> Vector.empty[String] === List.empty
Fail to compile if L will always equal R.

Candidate rule:
To compile, an equality comparison
must be interesting: values of types L
and R can be either equal or unequal.

scala> case class Complex(real: Double, imaginary: Double)
defined class Complex
scala> implicit def convertIntToComplex(i: Int): Complex = Complex(i, 0.0)
convertIntToComplex: (i: Int)Complex
scala> 42 === Complex(42, 0)
<console>:24: error: types Int and Complex do not adhere to the type constraint selected for the
=== and !== operators; the missing implicit parameter is of type
org.scalactic.EqualityConstraint[Int,Complex]
42 === Complex(42, 0)
^
scala> Complex(42, 0) === 42
<console>:24: error: types Complex and Int do not adhere to the type constraint selected for the
=== and !== operators; the missing implicit parameter is of type
org.scalactic.EqualityConstraint[Complex,Int]
Complex(42, 0) === 42
^
What about implicit conversions?

scala> implicit val enabler = EqualityEnabledBetween[Int, Complex]
enabler: org.scalactic.EqualityEnabledBetween[Int,Complex] =
org.scalactic.EqualityEnabledBetween@e5d2d9b
scala> 42 === Complex(42, 0)
scala> Complex(42, 0) === 42
scala> new AnyShouldWrapper(1) === 1 // Probably shouldn't enable...
Intuition: enable some but not all
But what would the rule be?

OK if the conversion is an injection
scala> case class DigitString(digits: String) {
| val toInt: Int = digits.toInt
| }
defined class DigitString
scala> implicit def convert(d: DigitString): Int =
| d.digits.toInt
convertDigitStringToInt: (d: DigitString)Int
scala> DigitString("42") === DigitString("042")
scala> DigitString("42").toInt === DigitString("042").toInt
John C. Reynolds: Using category theory to design implicit conversions and generic operators.

How to decide:
1.To compile, an equality comparison must be
interesting: values of types L and R can be either
equal or unequal.
2.Allow select implicit conversions to be enabled,
and recommend that non-widening conversions
(non-injections) not be enabled.

scala> (Some(1): Option[Int]) === Some(1)
scala> Some(1) === (Some(1): Option[Int])
scala> Some(1) === Some(1)
What about the implicit conversion
from subtype to supertype (<:<)?

scala> def eqv[T](a: T, b: T): Boolean = a === b
eqv: [T](a: T, b: T)Boolean
scala> eqv(1, ())
scala> ((i: Int) => i + 1) === ((i: Int) => i + 1)
Even though <:< is an injection, is it
always desireable?

EqualityPolicy
UncheckedEquality CheckedEquality EnabledEquality

scala> import EnabledEquality._
import EnabledEquality._
scala> def eqv[T](a: T, b: T): Boolean = a === b
<console>:19: error: types T and T do not adhere to the type constraint selected for
the === and !== operators; the missing implicit parameter is of type
org.scalactic.EqualityConstraint[T,T]
def eqv[T](a: T, b: T): Boolean = a === b
^
scala> ((i: Int) => i + 1) === ((i: Int) => i + 1)
<console>:20: error: types Int => Int and Int => Int do not adhere to the type
constraint selected for the === and !== operators; the missing implicit parameter is
of type org.scalactic.EqualityConstraint[Int => Int,Int => Int]
((i: Int) => i + 1) === ((i: Int) => i + 1)
^
EnabledEquality beneﬁt

scala> case class Person(name: String)
defined class Person
scala> Person("Sue") === Person("Sue")
<console>:22: error: types Person and Person do not adhere to the type constraint
selected for the === and !== operators; the missing implicit parameter is of type
org.scalactic.EqualityConstraint[Person,Person]
Person("Sue") === Person("Sue")
^
scala> implicit val enabler = new EqualityEnabledFor[Person]
enabler: org.scalactic.EqualityEnabledFor[Person] =
org.scalactic.EqualityEnabledFor@1289d391
scala> Person("Sue") === Person("Sue")
EnabledEquality cost

scala> 1 should === ("one")
<console>:23: error: types Int and String do not adhere to the type constraint selected for the === and !==
operators; the missing implicit parameter is of type org.scalactic.Constraint[Int,String]
1 should === ("one")
^
scala> 1 should equal ("one")
<console>:23: error: could not find implicit value for parameter typeClass1:
org.scalactic.enablers.EvidenceThat[String]#CanEqual[Int]
1 should equal ("one")
^
scala> 1 should be ("one")
org.scalactic.enablers.EvidenceThat[String]#CanEqual[Int]
1 should be ("one")
^
scala> 1 should be_== ("one")
org.scalatest.exceptions.TestFailedException: 1 was not equal to "one"
ScalaTest's equal, be, and be_==

scala> List(1, 2, 3) should contain ("one")
org.scalactic.enablers.EvidenceThat[String]#CanBeContainedIn[List[Int]]
List(1, 2, 3) should contain ("one")
^
scala> List(1, 2, 3) should contain oneOf ("one", "two")
<console>:23: error: could not find implicit value for parameter evidence:
org.scalactic.enablers.EvidenceThat[String]#CanBeContainedIn[List[Int]]
List(1, 2, 3) should contain oneOf("one", "two")
^
scala> 1 isIn List(1, 2, 3)
scala> "one" isIn List(1, 2, 3)
<console>:23: error: Could not find evidence that String can be contained in List[Int]; the missing implicit
parameter is of type org.scalactic.enablers.ContainingConstraint[List[Int],String]
"one" isIn List(1, 2, 3)
^
ScalaTest's contain, Scalactic's isIn/isNotIn

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scala> 1L === 1
scala> 1 === 1L
<console>:14: error: could not find implicit value for parameter F0:
scalaz.Equal[Any]
1 === 1L
^
Scalaz or Spire
Scalactic
scala> 1L === 1
scala> 1 === 1L
Equal[T], Eq[T]
EqualityConstraint[L, R]
Equivalence[T]

Equality For All!

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