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Multiple Typeclass Inheritance in Coq


Multiple Typeclass Inheritance in Coq

By : user44455
Date : November 19 2020, 12:41 AM
may help you . I don't know much about type classes myself, but doesn't B need to be variable? By separating it from foldr, you're making it fixed. I think it only makes sense to make C and A fixed.
code :
Class Foldable (C : Type -> Type) (A : Type)
  (foldr : forall B, (A -> B -> B) -> B -> C A -> B) : Type :=
{
  (* Foldable properties??? *)
}.

Class Collection C A insert empty foldr
  `{F : Foldable C A foldr}
  `{U : Unfoldable C A insert empty} :=
{
  collection_id : forall h, foldr (C A) insert empty h = h
}.
Class Collection C A insert empty foldr
  `{F : Foldable C A (C A) foldr}
  `{U : Unfoldable C A insert empty} :=
{
  collection_id : forall h, foldr insert empty h = h
}.
Axiom C : Type -> Type.
Axiom A : Type.
Axiom empty : C A.
Axiom insert : A -> C A -> C A.

Goal forall (x y : A) (h : C A), insert x h <> insert y h -> x <> y.
intros ? ? ? H1 H2.
apply H1.
rewrite H2.
apply eq_refl.
Qed.
Axiom C : Type -> Type.
Axiom A : Type.
Axiom B : Type.
Axiom insert : A -> C A -> C A.
Axiom empty : C A.
Axiom foldr : (A -> B -> B) -> B -> C A -> B.
(* Foldable properties??? *)
Axiom insert_neq : forall (x y : A) (h : C A), insert x h <> insert y h -> x <> y.
Axiom empty_insert_eq : forall x y : A, insert x empty = insert y empty <-> x = y.

Axiom collection_id : forall h : C A, foldr insert empty h = h.
Axiom C : Type -> Type.
Axiom A : Type.
Axiom insert : A -> C A -> C A.
Axiom empty : C A.
Axiom foldr : forall B : Type, (A -> B -> B) -> B -> C A -> B.
(* Foldable properties??? *)
Axiom insert_neq : forall (x y : A) (h : C A), insert x h <> insert y h -> x <> y.
Axiom empty_insert_eq : forall x y : A, insert x empty = insert y empty <-> x = y.

Axiom collection_id : forall h : C A, foldr (C A) insert empty h = h.
Axiom C : Type -> Type.
Axiom A : Type.
Axiom insert : A -> C A -> C A.
Axiom empty : C A.
Axiom foldr : (A -> C A -> C A) -> C A -> C A -> C A.
(* Foldable properties??? *)
Axiom insert_neq : forall (x y : A) (h : C A), insert x h <> insert y h -> x <> y.
Axiom empty_insert_eq : forall x y : A, insert x empty = insert y empty <-> x = y.

Axiom collection_id : forall h : C A, foldr insert empty h = h.


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Haskell typeclass inheritance and parametric typeclass

Haskell typeclass inheritance and parametric typeclass


By : user2132473
Date : March 29 2020, 07:55 AM
I hope this helps you . I suspect you can't do this directly. You can however cheat very effectively by adding a level of indirection. See John Hughes' Restricted Data Types in Haskell for how to do it: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.39.2816
This is the same technique used, e.g., to obtain open recursion in syb-with-class.
Declare all instances of a typeclass are in another typeclass without modifying the original class declarations

Declare all instances of a typeclass are in another typeclass without modifying the original class declarations


By : feelsgoodman
Date : March 29 2020, 07:55 AM
wish helps you Crypto-API author here. Please don't do this - it's really a violation of the implicit properties of CryptoRandomGen.
That said, here's how I'd do it: Just make a newtype that wraps your RandomGen and make that newtype an instance of CryptoRandomGen.
code :
newtype AsCRG g = ACRG { unACRG :: g}

instance RandomGen g => CryptoRandomGen (AsCRG g) where
    newGen = -- This is not possible to implement with only a 'RandomGen' constraint.  Perhaps you want a 'Default' instance too?
    genSeedLength = -- This is also not possible from just 'RandomGen'
    genBytes nr g =
        let (g1,g2) = split g
            randInts :: [Word32]
            randInts = B.concat . map Data.Serialize.encode
                     . take ((nr + 3) `div` 4)
                     $ (randoms g1 :: [Word32])
        in (B.take nr randInts, g2)
    reseed _ _ = -- not possible w/o more constraints
    newGenIO = -- not possible w/o more constraints
Why can't Scala find my typeclass instance defined implicitly in the companion object, when the typeclass is not in a de

Why can't Scala find my typeclass instance defined implicitly in the companion object, when the typeclass is not in a de


By : Manuel Ramiro Moreta
Date : March 29 2020, 07:55 AM
I wish did fix the issue. There's a rule that implicit has to be defined earlier in the compilation unit.
So, move object Show to the top and it compiles.
code :
object Show {
  //implicit object StringShow extends Show[String] {
  implicit val x: Show[String] = new Show[String] {
    def show(s: String) = s"[String: $s]"
  }
}
Why prefer Typeclass over Inheritance?

Why prefer Typeclass over Inheritance?


By : user3721731
Date : March 29 2020, 07:55 AM
I wish this help you When using inheritance to achieve ad-hoc polymorphism we may need to heavily pollute the interface of our value objects.
Assume we want to implement a Real and a Complex number. Without any functionality, this is as simple as writing
code :
case class Real(value: Double)

case class Complex(real: Double, imaginary: Double)
trait AddableWithReal[A] {
  def add(other: Real): A
}

trait AddableWithComplex[A] {
  def add(other: Complex): A
}

case class Real(value: Double) extends AddableWithComplex[Complex] with AddableWithReal[Real] {
  override def add(other: Complex): Complex = Complex(value + other.real, other.imaginary)

  override def add(other: Real): Real = Real(value + other.value)
}

case class Complex(real: Double, imaginary: Double) extends AddableWithComplex[Complex] with AddableWithReal[Complex] {
  override def add(other: Complex): Complex = Complex(real + other.real, imaginary + other.imaginary)

  override def add(other: Real): Complex = Complex(other.value + real, imaginary)
}
trait CanAdd[A, B, C] {
  def add(a: A, b: B): C
}
object Implicits {
  def add[A, B, C](a: A, b: B)(implicit ev: CanAdd[A, B, C]): C = ev.add(a, b)
  implicit object CanAddRealReal extends CanAdd[Real, Real, Real] {
    override def add(a: Real, b: Real): Real = Real(a.value + b.value)
  }
  implicit object CanAddComplexComplex extends CanAdd[Complex, Complex, Complex] {
    override def add(a: Complex, b: Complex): Complex = Complex(a.real + b.real, a.imaginary + b.imaginary)
  }
  implicit object CanAddComplexReal extends CanAdd[Complex, Real, Complex] {
    override def add(a: Complex, b: Real): Complex = Complex(a.real + b.value, a.imaginary)
  }
  implicit object CanAddRealComplex extends CanAdd[Real, Complex, Complex] {
    override def add(a: Real, b: Complex): Complex = Complex(a.value + b.real, b.imaginary)
  }
}
implicit object CanAddIntInt extends CanAdd[Int, Int, Int] {
  override def add(a: Int, b: Int): Int = a + b
}
How to handle functions of a multi-parameter typeclass, who not need every type of the typeclass?

How to handle functions of a multi-parameter typeclass, who not need every type of the typeclass?


By : David Nowak
Date : March 29 2020, 07:55 AM
this will help This is impossible.
The underlying problem is that a multiparameter type class depends on every type parameter. If a particular definition in the class doesn't use every type parameter, the compiler will never be able to know what instance you mean, and you'll never even be able to specify it. Consider the following example:
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