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 : ℕ, prime n → n ≤ 100, SlimCheck requires that ℕ have an instance of SampleableExt and for prime n to be decidable. SlimCheck will then use the instance of SampleableExt to generate small examples of ℕ 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 SlimCheck 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 : ℕ, prime n → n ≤ 100 and the test fails. If n ≤ 100 is true, the test passes and SlimCheck moves on to trying more examples.

This is a port of the Haskell QuickCheck library.

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 SampleableExt.mkSelfContained is the way to go.

Furthermore it makes it possible to express generators for types that do not lend themselves to introspection, such as ℕ → ℕ. 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 SlimCheck find a counter-example to a property. It is likely that the example will be more complicated than necessary so SlimCheck 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. SlimCheck 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 SlimCheck is guaranteed to terminate.

Tags

random testing

References

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

class SlimCheck.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 : α → List α

class SlimCheck.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 SampleableExt.mkSelfContained is the way to go.

Furthermore it makes it possible to express generators for types that do not lend themselves to introspection, such as ℕ → ℕ. 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 (SlimCheck.SampleableExt.proxy α)
• shrink : SlimCheck.Shrinkable (SlimCheck.SampleableExt.proxy α)
• sample : SlimCheck.Gen (SlimCheck.SampleableExt.proxy α)
• interp : SlimCheck.SampleableExt.proxy α → α

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

Use to generate instance whose purpose is to simply generate values of a type directly using the Gen monad

Equations

• SlimCheck.SampleableExt.mkSelfContained sample = SlimCheck.SampleableExt.mk α sample id

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

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

Equations

• SlimCheck.SampleableExt.interpSample α = SlimCheck.SampleableExt.interp <$> SlimCheck.SampleableExt.sample

def SlimCheck.Nat.shrink (n : ℕ) : List ℕ

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

• SlimCheck.Nat.shrink n = if h : 0 < n then let m := n / 2; let_fun this := ⋯; m :: SlimCheck.Nat.shrink m else []

instance SlimCheck.Nat.shrinkable : SlimCheck.Shrinkable ℕ

Equations

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

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

Equations

• SlimCheck.Fin.shrinkable = { shrink := fun (m : Fin (Nat.succ n)) => do let a ← SlimCheck.Nat.shrink ↑m pure ↑a }

instance SlimCheck.Int.shrinkable : SlimCheck.Shrinkable ℤ

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

Equations

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instance SlimCheck.Rat.shrinkable : SlimCheck.Shrinkable Rat

Equations

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

instance SlimCheck.Bool.shrinkable : SlimCheck.Shrinkable Bool

Equations

• SlimCheck.Bool.shrinkable = { shrink := fun (x : Bool) => [] }

instance SlimCheck.Char.shrinkable : SlimCheck.Shrinkable Char

Equations

• SlimCheck.Char.shrinkable = { shrink := fun (x : Char) => [] }

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

Equations

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

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

Equations

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

instance SlimCheck.List.shrinkable {α : Type u_1} [SlimCheck.Shrinkable α] : SlimCheck.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 SlimCheck.Nat.sampleableExt : SlimCheck.SampleableExt ℕ

Equations

• SlimCheck.Nat.sampleableExt = SlimCheck.SampleableExt.mkSelfContained do let __do_lift ← SlimCheck.Gen.getSize let a ← SlimCheck.Gen.choose ℕ 0 __do_lift ⋯ pure ↑a

instance SlimCheck.Fin.sampleableExt {n : ℕ} : SlimCheck.SampleableExt (Fin (Nat.succ n))

Equations

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instance SlimCheck.Int.sampleableExt : SlimCheck.SampleableExt ℤ

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instance SlimCheck.Rat.sampleableExt : SlimCheck.SampleableExt Rat

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

instance SlimCheck.Bool.sampleableExt : SlimCheck.SampleableExt Bool

Equations

• SlimCheck.Bool.sampleableExt = SlimCheck.SampleableExt.mkSelfContained (SlimCheck.Gen.chooseAny Bool)

def SlimCheck.Char.sampleable (length : ℕ) (chars : List Char) (pos : 0 < List.length chars) : SlimCheck.SampleableExt Char

This can be specialized into customized SampleableExt Char instances. The resulting instance has 1 / length chances of making an unrestricted choice of characters and it otherwise chooses a character from chars with uniform probabilities.

Equations

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

instance SlimCheck.Char.sampleableDefault : SlimCheck.SampleableExt Char

Equations

• SlimCheck.Char.sampleableDefault = SlimCheck.Char.sampleable 3 (String.toList " 0123abcABC:,;`\\/") SlimCheck.Char.sampleableDefault.proof_1

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

Equations

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

instance SlimCheck.Prop.sampleableExt : SlimCheck.SampleableExt Prop

Equations

• SlimCheck.Prop.sampleableExt = SlimCheck.SampleableExt.mk Bool (SlimCheck.SampleableExt.interpSample Bool) Coe.coe

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

Equations

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

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

An annotation for values that should never get shrinked.

Equations

• SlimCheck.NoShrink α = α

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

Equations

• SlimCheck.NoShrink.mk x = x

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

Equations

• SlimCheck.NoShrink.get x = x

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

Equations

• SlimCheck.NoShrink.inhabited = inst

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

Equations

• SlimCheck.NoShrink.repr = inst

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

Equations

• SlimCheck.NoShrink.shrinkable = { shrink := fun (x : SlimCheck.NoShrink α) => [] }

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

Equations

• SlimCheck.NoShrink.sampleableExt = SlimCheck.SampleableExt.mkSelfContained ((SlimCheck.NoShrink.mk ∘ SlimCheck.SampleableExt.interp) <$> SlimCheck.SampleableExt.sample)

def SlimCheck.printSamples {t : Type} [Repr t] (g : SlimCheck.Gen t) : IO PUnit.{1}

Print (at most) 10 samples of a given type to stdout for debugging.

Equations

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

def SlimCheck.mkGenerator (e : Lean.Expr) : Lean.MetaM ((u : Lean.Level) × (α : let u := u; Q(Type u)) × Q(Repr «$α») × Q(SlimCheck.Gen «$α»))

Create a Gen α expression from the argument of #sample

def SlimCheck.«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

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