SampleableExt Class

This class permits the creation samples of a given type controlling the size of those values using the Gen monad.

Shrinkable Class

This class helps minimize examples by creating smaller versions of given values.

When testing a proposition like ∀ n : Nat, Prime n → n ≤ 100, Plausible requires that Nat have an instance of SampleableExt and for Prime n to be decidable. Plausible will then use the instance of SampleableExt to generate small examples of Nat and progressively increase in size. For each example n, Prime n is tested. If it is false, the example will be rejected (not a test success nor a failure) and Plausible will move on to other examples. If Prime n is true, n ≤ 100 will be tested. If it is false, n is a counter-example of ∀ n : Nat, Prime n → n ≤ 100 and the test fails. If n ≤ 100 is true, the test passes and Plausible moves on to trying more examples.

Main definitions

• SampleableExt class
• Shrinkable class

SampleableExt

SampleableExt can be used in two ways. The first (and most common) is to simply generate values of a type directly using the Gen monad, if this is what you want to do then the way to go is to declare an Arbitrary instance, and rely on the default selfContained instance.

Furthermore it makes it possible to express generators for types that do not lend themselves to introspection, such as Nat → Nat. If we test a quantification over functions the counter-examples cannot be shrunken or printed meaningfully. For that purpose, SampleableExt provides a proxy representation proxy that can be printed and shrunken as well as interpreted (using interp) as an object of the right type. If you are using it in the first way, this proxy type will simply be the type itself and the interp function id.

Shrinkable

Given an example x : α, Shrinkable α gives us a way to shrink it and suggest simpler examples.

Shrinking

Shrinking happens when Plausible finds a counter-example to a property. It is likely that the example will be more complicated than necessary so Plausible proceeds to shrink it as much as possible. Although equally valid, a smaller counter-example is easier for a user to understand and use.

The Shrinkable class, , has a shrink function so that we can use specialized knowledge while shrinking a value. It is not responsible for the whole shrinking process however. It only has to take one step in the shrinking process. Plausible will repeatedly call shrink until no more steps can be taken. Because shrink guarantees that the size of the candidates it produces is strictly smaller than the argument, we know that Plausible is guaranteed to terminate.

Tags

random testing

References

• https://hackage.haskell.org/package/QuickCheck

class Plausible.Shrinkable (α : Type u) : Type u

Given an example x : α, Shrinkable α gives us a way to shrink it and suggest simpler examples.

• shrink (x : α) : List α

class Plausible.SampleableExt (α : Sort u) : Sort (max u (v + 2))

SampleableExt can be used in two ways. The first (and most common) is to simply generate values of a type directly using the Gen monad, if this is what you want to do then declaring an Arbitrary instance is the way to go.

Furthermore it makes it possible to express generators for types that do not lend themselves to introspection, such as Nat → Nat. If we test a quantification over functions the counter-examples cannot be shrunken or printed meaningfully. For that purpose, SampleableExt provides a proxy representation proxy that can be printed and shrunken as well as interpreted (using interp) as an object of the right type.

• proxy : Type v
• proxyRepr : Repr (proxy α)
• shrink : Shrinkable (proxy α)
• sample : Arbitrary (proxy α)
• interp : proxy α → α

@[defaultInstance 1000]

instance Plausible.SampleableExt.selfContained {α : Type u_1} [Repr α] [Shrinkable α] [Arbitrary α] : SampleableExt α

Default instance whose purpose is to simply generate values of a type directly using the Arbitrary instance

Equations

• Plausible.SampleableExt.selfContained = { proxy := α, proxyRepr := inferInstance, shrink := inferInstance, sample := inferInstance, interp := id }

def Plausible.SampleableExt.mkSelfContained {α : Type u_1} [Repr α] [Shrinkable α] (g : Gen α) : SampleableExt α

This is kept for backwards compatibility

Equations

• Plausible.SampleableExt.mkSelfContained g = inferInstance

def Plausible.SampleableExt.interpSample (α : Type u) [SampleableExt α] : Gen α

First samples a proxy value and interprets it. Especially useful if the proxy and target type are the same.

Equations

• Plausible.SampleableExt.interpSample α = Plausible.SampleableExt.interp <$> Plausible.Arbitrary.arbitrary

instance Plausible.instShrinkableSum {α : Type u_1} {β : Type u_2} [Shrinkable α] [Shrinkable β] : Shrinkable (α ⊕ β)

Equations

• One or more equations did not get rendered due to their size.

instance Plausible.Unit.shrinkable : Shrinkable Unit

Equations

• Plausible.Unit.shrinkable = { }

@[irreducible]

def Plausible.Nat.shrink (n : Nat) : List Nat

Nat.shrink' n creates a list of smaller natural numbers by successively dividing n by 2 . For example, Nat.shrink 5 = [2, 1, 0].

Equations

• Plausible.Nat.shrink n = if h : 0 < n then have m := n / 2; m :: Plausible.Nat.shrink m else []

instance Plausible.Nat.shrinkable : Shrinkable Nat

Equations

• Plausible.Nat.shrinkable = { shrink := Plausible.Nat.shrink }

instance Plausible.Fin.shrinkable {n : Nat} : Shrinkable (Fin n.succ)

Equations

• Plausible.Fin.shrinkable = { shrink := fun (m : Fin n.succ) => List.map (Fin.ofNat n.succ) (Plausible.Nat.shrink ↑m) }

instance Plausible.BitVec.shrinkable {n : Nat} : Shrinkable (BitVec n)

Equations

• Plausible.BitVec.shrinkable = { shrink := fun (m : BitVec n) => List.map (BitVec.ofNat n) (Plausible.Nat.shrink m.toNat) }

instance Plausible.UInt8.shrinkable : Shrinkable UInt8

Equations

• Plausible.UInt8.shrinkable = { shrink := fun (m : UInt8) => List.map UInt8.ofNat (Plausible.Nat.shrink m.toNat) }

instance Plausible.UInt16.shrinkable : Shrinkable UInt16

Equations

• Plausible.UInt16.shrinkable = { shrink := fun (m : UInt16) => List.map UInt16.ofNat (Plausible.Nat.shrink m.toNat) }

instance Plausible.UInt32.shrinkable : Shrinkable UInt32

Equations

• Plausible.UInt32.shrinkable = { shrink := fun (m : UInt32) => List.map UInt32.ofNat (Plausible.Nat.shrink m.toNat) }

instance Plausible.UInt64.shrinkable : Shrinkable UInt64

Equations

• Plausible.UInt64.shrinkable = { shrink := fun (m : UInt64) => List.map UInt64.ofNat (Plausible.Nat.shrink m.toNat) }

instance Plausible.USize.shrinkable : Shrinkable USize

Equations

• Plausible.USize.shrinkable = { shrink := fun (m : USize) => List.map USize.ofNat (Plausible.Nat.shrink m.toNat) }

instance Plausible.Int.shrinkable : Shrinkable Int

Int.shrinkable operates like Nat.shrinkable but also includes the negative variants.

Equations

• One or more equations did not get rendered due to their size.

instance Plausible.Bool.shrinkable : Shrinkable Bool

Equations

• Plausible.Bool.shrinkable = { }

instance Plausible.Char.shrinkable : Shrinkable Char

Equations

• Plausible.Char.shrinkable = { }

instance Plausible.Option.shrinkable {α : Type u_1} [Shrinkable α] : Shrinkable (Option α)

Equations

• Plausible.Option.shrinkable = { shrink := fun (o : Option α) => match o with | some x => List.map some (Plausible.Shrinkable.shrink x) | none => [] }

instance Plausible.Prod.shrinkable {α : Type u_1} {β : Type u_2} [shrA : Shrinkable α] [shrB : Shrinkable β] : Shrinkable (α × β)

Equations

• One or more equations did not get rendered due to their size.

instance Plausible.Sigma.shrinkable {α : Type u_1} {β : Type u_2} [shrA : Shrinkable α] [shrB : Shrinkable β] : Shrinkable ((_ : α) × β)

Equations

• One or more equations did not get rendered due to their size.

instance Plausible.List.shrinkable {α : Type u_1} [Shrinkable α] : Shrinkable (List α)

Shrink a list of a shrinkable type, either by discarding an element or shrinking an element.

Equations

• One or more equations did not get rendered due to their size.

instance Plausible.ULift.shrinkable {α : Type u_1} [Shrinkable α] : Shrinkable (ULift α)

Equations

• Plausible.ULift.shrinkable = { shrink := fun (u : ULift α) => List.map ULift.up (Plausible.Shrinkable.shrink u.down) }

instance Plausible.String.shrinkable : Shrinkable String

Equations

• Plausible.String.shrinkable = { shrink := fun (s : String) => List.map String.mk (Plausible.Shrinkable.shrink s.toList) }

instance Plausible.Array.shrinkable {α : Type u_1} [Shrinkable α] : Shrinkable (Array α)

Equations

• Plausible.Array.shrinkable = { shrink := fun (xs : Array α) => List.map Array.mk (Plausible.Shrinkable.shrink xs.toList) }

instance Plausible.Subtype.shrinkable {α : Type u} {β : α → Prop} [Shrinkable α] [(x : α) → Decidable (β x)] : Shrinkable { x : α // β x }

Equations

• One or more equations did not get rendered due to their size.

instance Plausible.arbitraryProxy {α : Type u_1} [SampleableExt α] : Arbitrary (SampleableExt.proxy α)

Equations

• Plausible.arbitraryProxy = Plausible.SampleableExt.sample

instance Plausible.Sum.SampleableExt {α : Type u_1} {β : Type u_2} [Plausible.SampleableExt α] [Plausible.SampleableExt β] : Plausible.SampleableExt (α ⊕ β)

Equations

• One or more equations did not get rendered due to their size.

instance Plausible.instSampleableExtSigma {α : Type u_1} {β : Type u_2} [SampleableExt α] [SampleableExt β] : SampleableExt ((_ : α) × β)

Equations

• One or more equations did not get rendered due to their size.

instance Plausible.Option.sampleableExt {α : Type u_1} [SampleableExt α] : SampleableExt (Option α)

Equations

• One or more equations did not get rendered due to their size.

instance Plausible.Prod.sampleableExt {α : Type u} {β : Type v} [SampleableExt α] [SampleableExt β] : SampleableExt (α × β)

Equations

• One or more equations did not get rendered due to their size.

instance Plausible.Prop.sampleableExt : SampleableExt Prop

Equations

• Plausible.Prop.sampleableExt = { proxy := Bool, proxyRepr := inferInstance, shrink := inferInstance, sample := inferInstance, interp := Coe.coe }

instance Plausible.List.sampleableExt {α : Type u_1} [SampleableExt α] : SampleableExt (List α)

Equations

• One or more equations did not get rendered due to their size.

instance Plausible.ULift.sampleableExt {α : Type u_1} [SampleableExt α] : SampleableExt (ULift α)

Equations

• One or more equations did not get rendered due to their size.

instance Plausible.Array.sampleableExt {α : Type u_1} [SampleableExt α] : SampleableExt (Array α)

Equations

• One or more equations did not get rendered due to their size.

def Plausible.NoShrink (α : Type u) : Type u

An annotation for values that should never get shrunk.

Equations

• Plausible.NoShrink α = α

def Plausible.NoShrink.mk {α : Type u_1} (x : α) : NoShrink α

Equations

• Plausible.NoShrink.mk x = x

def Plausible.NoShrink.get {α : Type u_1} (x : NoShrink α) : α

Equations

• x.get = x

instance Plausible.NoShrink.inhabited {α : Type u_1} [inst : Inhabited α] : Inhabited (NoShrink α)

Equations

• Plausible.NoShrink.inhabited = inst

instance Plausible.NoShrink.repr {α : Type u_1} [inst : Repr α] : Repr (NoShrink α)

Equations

• Plausible.NoShrink.repr = inst

instance Plausible.NoShrink.shrinkable {α : Type u_1} : Shrinkable (NoShrink α)

Equations

• Plausible.NoShrink.shrinkable = { }

instance Plausible.NoShrink.arbitrary {α : Type u_1} [arb : Arbitrary α] : Arbitrary (NoShrink α)

Equations

• Plausible.NoShrink.arbitrary = arb

instance Plausible.NoShrink.sampleableExt {α : Type u_1} [SampleableExt α] [Repr α] : SampleableExt (NoShrink α)

Equations

• One or more equations did not get rendered due to their size.

def Plausible.«command#sample_» : Lean.ParserDescr

#sample type, where type has an instance of SampleableExt, prints ten random values of type type using an increasing size parameter.

#sample Nat
-- prints
-- 0
-- 0
-- 2
-- 24
-- 64
-- 76
-- 5
-- 132
-- 8
-- 449
-- or some other sequence of numbers

#sample List Int
-- prints
-- []
-- [1, 1]
-- [-7, 9, -6]
-- [36]
-- [-500, 105, 260]
-- [-290]
-- [17, 156]
-- [-2364, -7599, 661, -2411, -3576, 5517, -3823, -968]
-- [-643]
-- [11892, 16329, -15095, -15461]
-- or whatever

Equations

• Plausible.«command#sample_» = Lean.ParserDescr.node `Plausible.«command#sample_» 1022 (Lean.ParserDescr.binary `andthen (Lean.ParserDescr.symbol "#sample ") (Lean.ParserDescr.cat `term 0))