Equality For All!

Equality For All!Scala by the Bay, 2014

Bill VennersArtima, 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 == 42Lres0: Boolean = true

scala> BigDecimal(42) == '*'res1: Boolean = true

scala> 42.0F == BigInt(42)res2: Boolean = true

scala> new java.lang.Float(42.0F) == 42.toShortres3: Boolean = true

Co-operative Equality Between Types


scala> import scala.collection.mutableimport scala.collection.mutable

scala> Set(BigInt(4), BigInt(2)) == mutable.Set(4.toByte, 2.toByte)res4: Boolean = true

scala> Vector(Left(4), Right(2)) == List(Left(4L), Right(2L))res5: Boolean = true

scala> List(mutable.Set(Map(Some(4L) -> BigInt(2)))) == Vector(Set(mutable.Map(Some(4.0) -> new java.lang.Long(2L))))res6: Boolean = true

Co-operative Equality Between Types


scala> Array(4, 2) == Array(4, 2)res7: Boolean = false

scala> <forty><two></two></forty> == <forty> <two></two> </forty>res8: Boolean = false

scala> new java.math.BigDecimal("42.0") == new java.math.BigDecimal("42.00")res9: Boolean = false

scala> 42.0 == 41.9999999999res10: Boolean = false

scala> "case" == "CASE"res11: Boolean = false

Wanted: Alternate equalities


scala> "forty two" == 42res19: Boolean = false

scala> List(mutable.Set(Map(Some(4L) -> BigInt(2)))) == Vector(Set(mutable.Map(Some("4.0") -> new java.lang.Long(2L))))res23: Boolean = false

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)res1: Boolean = true

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]res3: Boolean = true

scala> Vector.empty[String] === List.emptyres4: Boolean = true

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)res2: Boolean = true

scala> Complex(42, 0) === 42res3: Boolean = true

scala> new AnyShouldWrapper(1) === 1 // Probably shouldn't enable...

Intuition: enable some but not all

But what would the rule be?Saturday, August 9, 2014

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.toIntconvertDigitStringToInt: (d: DigitString)Int

scala> DigitString("42") === DigitString("042")res0: Boolean = false

scala> DigitString("42").toInt === DigitString("042").toIntres1: Boolean = true

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)res0: Boolean = true

scala> Some(1) === (Some(1): Option[Int])res1: Boolean = true

scala> Some(1) === Some(1)res2: Boolean = true

What about the implicit conversion from subtype to supertype (<:<)?


scala> def eqv[T](a: T, b: T): Boolean = a === beqv: [T](a: T, b: T)Boolean

scala> eqv(1, ())res3: Boolean = false

scala> ((i: Int) => i + 1) === ((i: Int) => i + 1)res4: Boolean = false

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")res2: Boolean = true

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")<console>:23: error: could not find implicit value for parameter typeClass1: 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")<console>:23: error: could not find implicit value for parameter typeClass1: 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)res14: Boolean = true

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


if sufficientTimeRemains then (Q => A) else thanks

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scala> 1L === 1 res0: Boolean = true

scala> 1 === 1L<console>:14: error: could not find implicit value for parameter F0: scalaz.Equal[Any] 1 === 1L ^

Scalaz or Spire

Scalacticscala> 1L === 1res7: Boolean = true

scala> 1 === 1Lres8: Boolean = true

Equal[T], Eq[T]

EqualityConstraint[L, R]

Equivalence[T]


Equality For All!

Engineering

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