equality for all!
DESCRIPTION
Bill Venners lightening talk about recent work on equality in Scalactic and ScalaTest from the Scala by the Bay 2014 conference.TRANSCRIPT
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
Saturday, August 9, 2014
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")
Saturday, August 9, 2014
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
Saturday, August 9, 2014
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
Saturday, August 9, 2014
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
Saturday, August 9, 2014
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
Saturday, August 9, 2014
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?
Saturday, August 9, 2014
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.
Saturday, August 9, 2014
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.
Saturday, August 9, 2014
Candidate rule:
To compile, an equality comparison must be interesting: values of types L
and R can be either equal or unequal.
Saturday, August 9, 2014
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?
Saturday, August 9, 2014
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.
Saturday, August 9, 2014
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.
Saturday, August 9, 2014
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 (<:<)?
Saturday, August 9, 2014
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?
Saturday, August 9, 2014
EqualityPolicy
UncheckedEquality CheckedEquality EnabledEquality
Saturday, August 9, 2014
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
Saturday, August 9, 2014
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
Saturday, August 9, 2014
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_==
Saturday, August 9, 2014
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
Saturday, August 9, 2014
if sufficientTimeRemains then (Q => A) else thanks
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Saturday, August 9, 2014
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]
Saturday, August 9, 2014