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|
{-# LANGUAGE NoImplicitPrelude #-}
{-# LANGUAGE PatternSynonyms #-}
module Test.Unit.Kernel (unitTests) where
import Base hiding (Empty)
import Checking.Core
import Checking.Foundation qualified as Foundation
import Checking.Kernel.Derivation
import Checking.Kernel.Semantics qualified as Semantics
import Checking.Kernel.SetLfp qualified as SetLfp
import Checking.Typed.Inductive qualified as Inductive
import Report.Location (pattern Nowhere)
import Syntax.Internal qualified as Internal
import Data.Set qualified as Set
import Data.Vector qualified as Vector
import Test.Tasty
import Test.Tasty.HUnit
data TestGlobal = TestGlobal
deriving (Show, Eq, Ord)
testGlobalType :: TestGlobal -> CoreType
testGlobalType _global = TySet
unitTests :: TestTree
unitTests =
testGroup "Kernel replay"
[ testCase
"replays equality reflexivity through kernel semantics"
replaysEqualityReflexivity
, testCase
"replays logical scopes and elimination"
replaysLogicalScopes
, testCase
"replays quantifier and equality structure"
replaysQuantifierAndEqualityStructure
, testCase
"records foundation and import leaves"
recordsAuthorityLeaves
, testCase
"checks and replays the exact set fixed-point rules"
checksSetLfpRules
, testCase
"replays direct inductive facts"
replaysDirectInductiveFacts
, testCase
"rejects altered set fixed-point applications"
rejectsAlteredSetLfpApplications
, testCase
"rejects invalid scoped replay"
rejectsInvalidScopedReplay
, testCase
"rejects a caller-supplied target mismatch"
rejectsTargetMismatch
]
replaysEqualityReflexivity :: Assertion
replaysEqualityReflexivity = do
foundation <-
expectRight Foundation.checkedFoundation
operand <-
expectRight
(checkCanonicalCore
absurd
(CIntrinsic Empty))
direct <-
expectRight
(Semantics.equalityReflexivity
absurd
(embedClosedCore [] operand))
directClosed <-
maybe
(assertFailure
"closed reflexivity result remained scoped")
pure
(closeScopedCore direct)
replayed <-
expectRight
(replayKernelDerivation
foundation
defaultKernelReplayLimits
absurd
Vector.empty
directClosed
(equalityReflexivityDerivation operand))
assertEqual
"replay agrees with direct semantics"
directClosed
(replayedKernelTarget replayed)
assertEqual
"one replayed inference"
1
(replayedKernelNodeCount replayed)
replaysLogicalScopes :: Assertion
replaysLogicalScopes = do
foundation <-
expectRight Foundation.checkedFoundation
proposition <-
checkedClosed
(CEq TySet
(CIntrinsic Empty)
(CIntrinsic Empty))
implication <-
checkedScoped []
(CImp
(frozenCoreTerm proposition)
(frozenCoreTerm proposition))
let propositionScoped =
embedClosedCore [] proposition
identity =
implicationIntroductionDerivation
propositionScoped
(localHypothesisDerivation
(hypothesisIx 0))
elimination =
implicationIntroductionDerivation
propositionScoped
(implicationIntroductionDerivation
implication
(implicationEliminationDerivation
(localHypothesisDerivation
(hypothesisIx 0))
(localHypothesisDerivation
(hypothesisIx 1))))
fromFalsum =
implicationIntroductionDerivation
falsum
(falsumEliminationDerivation
(localHypothesisDerivation
(hypothesisIx 0))
propositionScoped)
falsum =
unsafeScoped [] CFalsum
assertReplayTarget
foundation
(CImp
(frozenCoreTerm proposition)
(frozenCoreTerm proposition))
identity
assertReplayTarget
foundation
(CImp
(frozenCoreTerm proposition)
(CImp
(scopedCoreTerm implication)
(frozenCoreTerm proposition)))
elimination
assertReplayTarget
foundation
(CImp
CFalsum
(frozenCoreTerm proposition))
fromFalsum
replaysQuantifierAndEqualityStructure :: Assertion
replaysQuantifierAndEqualityStructure = do
foundation <-
expectRight Foundation.checkedFoundation
boundSet <-
checkedScoped [TySet] (CBound 0)
emptySet <-
checkedScoped [] (CIntrinsic Empty)
unionFunction <-
checkedScoped [] (CIntrinsic FamilyUnion)
proposition <-
checkedClosed
(CEq TySet
(CIntrinsic Empty)
(CIntrinsic Empty))
convertedTarget <-
checkedScoped []
(CEq TySet
(CApp
(CLam TySet (CBound 0))
(CIntrinsic Empty))
(CIntrinsic Empty))
oneReduction <-
expectRight (conversionPlan 1)
let boundReflexivity =
scopedEqualityReflexivityDerivation boundSet
universalReflexivity =
forallIntroductionDerivation
TySet
boundReflexivity
specializedReflexivity =
forallEliminationDerivation
universalReflexivity
emptySet
applicationCongruence =
equalityCongruenceApplicationDerivation
(scopedEqualityReflexivityDerivation
unionFunction)
(scopedEqualityReflexivityDerivation
emptySet)
lambdaCongruence =
equalityCongruenceLambdaDerivation
TySet
boundReflexivity
equalityMp =
implicationIntroductionDerivation
(embedClosedCore [] proposition)
(equalityModusPonensDerivation
(scopedEqualityReflexivityDerivation
(embedClosedCore []
proposition))
(localHypothesisDerivation
(hypothesisIx 0)))
conversion =
convertJudgmentDerivation
(scopedEqualityReflexivityDerivation
emptySet)
convertedTarget
oneReduction
assertReplayTarget
foundation
(CForall TySet
(CEq TySet
(CBound 0)
(CBound 0)))
universalReflexivity
assertReplayTarget
foundation
(CEq TySet
(CIntrinsic Empty)
(CIntrinsic Empty))
specializedReflexivity
assertReplayTarget
foundation
(CEq TySet
(CApp
(CIntrinsic FamilyUnion)
(CIntrinsic Empty))
(CApp
(CIntrinsic FamilyUnion)
(CIntrinsic Empty)))
applicationCongruence
assertReplayTarget
foundation
(CEq
(TySet `TyArrow` TySet)
(CLam TySet (CBound 0))
(CLam TySet (CBound 0)))
lambdaCongruence
assertReplayTarget
foundation
(CImp
(frozenCoreTerm proposition)
(frozenCoreTerm proposition))
equalityMp
assertReplayTarget
foundation
(scopedCoreTerm convertedTarget)
conversion
recordsAuthorityLeaves :: Assertion
recordsAuthorityLeaves = do
foundation <-
expectRight Foundation.checkedFoundation
let foundationTag =
Foundation.EmptyCharacteristic
foundationTarget =
mapFrozenGlobals
absurd
(Foundation.foundationAxiomFrozen
foundation
foundationTag)
foundationReplay <-
expectRight
(replayKernelDerivation
foundation
defaultKernelReplayLimits
absurd
Vector.empty
foundationTarget
(foundationFactDerivation
foundationTag))
assertEqual
"exact foundation use"
(Set.singleton foundationTag)
(replayedKernelFoundationUses
foundationReplay)
importedStatement <-
checkedClosed
(CEq TySet
(CIntrinsic Empty)
(CIntrinsic Empty))
importedJudgment <-
expectRight
(derivationImportJudgment
importedStatement)
importedReplay <-
expectRight
(replayKernelDerivation
foundation
defaultKernelReplayLimits
absurd
(Vector.singleton importedJudgment)
importedStatement
(importedFactDerivation
(importIx 0)))
assertEqual
"exact import use"
(Set.singleton (importIx 0))
(replayedKernelImportUses importedReplay)
checksSetLfpRules :: Assertion
checksSetLfpRules = do
foundation <-
expectRight Foundation.checkedFoundation
( domain
, operator
, predicate
, element
, fixedPoint
, closedPremise
, boundedPremise
, monotonePremise
, memberPremise
, closurePremise
) <-
setLfpFixture
bound <-
expectRight
(SetLfp.setLfpBound
foundation
absurd
domain
operator)
least <-
expectRight
(SetLfp.setLfpLeast
foundation
absurd
domain
operator
domain
closedPremise
boundedPremise)
fixed <-
expectRight
(SetLfp.setLfpFixed
foundation
absurd
domain
operator
monotonePremise)
inducted <-
expectRight
(SetLfp.setLfpInduct
foundation
absurd
domain
operator
predicate
element
monotonePremise
memberPremise
closurePremise)
expectedSubset <-
expectRight
(SetLfp.subsetProposition
absurd
fixedPoint
domain)
expectedFixed <-
checkedScoped []
(CEq TySet
(scopedCoreTerm fixedPoint)
(CApp
(scopedCoreTerm operator)
(scopedCoreTerm fixedPoint)))
expectedPredicate <-
checkedScoped []
(CApp
(scopedCoreTerm predicate)
(scopedCoreTerm element))
assertEqual "bound conclusion" expectedSubset bound
assertEqual "least conclusion" expectedSubset least
assertEqual "fixed conclusion" expectedFixed fixed
assertEqual "induction conclusion" expectedPredicate inducted
target <-
maybe
(assertFailure
"closed fixed-point bound remained scoped")
pure
(closeScopedCore bound)
replayed <-
expectRight
(replayKernelDerivation
foundation
defaultKernelReplayLimits
absurd
Vector.empty
target
(setLfpBoundDerivation
domain
operator))
assertEqual
"exact guarded-rule use"
(Set.singleton Foundation.SetLfpBound)
(replayedKernelRuleUses replayed)
replaysDirectInductiveFacts :: Assertion
replaysDirectInductiveFacts = do
foundation <-
expectRight Foundation.checkedFoundation
traverse_
(replayInductive foundation)
[ Inductive.DirectInductive
[]
(Internal.EmptySet Nowhere)
(Inductive.DirectInductiveClause
[]
[]
(Internal.EmptySet Nowhere)
:| [])
, let x = Internal.NamedVar "x"
in Inductive.DirectInductive
[]
(Internal.EmptySet Nowhere)
( Inductive.DirectInductiveClause
[]
[]
(Internal.EmptySet Nowhere)
:| [ Inductive.DirectInductiveClause
[x]
[Inductive.DirectRecursiveCondition
(Internal.TermVar x)]
(Internal.TermVar x)
]
)
]
where
replayInductive foundation inductive = do
prepared <-
expectRight
(Inductive.prepareTypedInductive
testGlobalType
foundation
(const Nothing)
(Internal.Marker "direct_inductive")
inductive)
imports <-
traverse
(expectRight . derivationImportJudgment)
(Inductive.typedInductiveGuardTargets
prepared)
traverse_
(\fact -> do
replayed <-
expectRight
(replayKernelDerivation
foundation
defaultKernelReplayLimits
(const Nothing)
imports
(Inductive.typedInductiveFactTarget
fact)
(Inductive.typedInductiveFactDerivation
fact))
assertEqual
"replay target"
(Inductive.typedInductiveFactTarget
fact)
(replayedKernelTarget replayed))
(Inductive.typedInductiveFacts
prepared)
rejectsAlteredSetLfpApplications :: Assertion
rejectsAlteredSetLfpApplications = do
foundation <-
expectRight Foundation.checkedFoundation
( domain
, operator
, predicate
, _element
, _fixedPoint
, _closedPremise
, boundedPremise
, _monotonePremise
, _memberPremise
, _closurePremise
) <-
setLfpFixture
falsum <-
checkedScoped [] CFalsum
assertEqual
"altered leastness premise"
(Left
(SetLfp.SetLfpRulePremiseMismatch
Foundation.SetLfpLeast
0))
(SetLfp.setLfpLeast
foundation
absurd
domain
operator
domain
falsum
boundedPremise)
assertEqual
"operator type mismatch"
(Left
(SetLfp.SetLfpRuleArgumentTypeMismatch
Foundation.SetLfpBound
1
(TySet `TyArrow` TySet)
(TySet `TyArrow` TyProp)))
(SetLfp.setLfpBound
foundation
absurd
domain
predicate)
bound <-
expectRight
(SetLfp.setLfpBound
foundation
absurd
domain
operator)
wrongTarget <-
checkedClosed CFalsum
assertEqual
"altered replay target"
(Left KernelReplayTargetMismatch)
(replayedKernelTarget
<$> replayKernelDerivation
foundation
defaultKernelReplayLimits
absurd
Vector.empty
wrongTarget
(setLfpBoundDerivation
domain
operator))
assertEqual
"the direct bound remains well formed"
TyProp
(scopedCoreType bound)
setLfpFixture
:: IO
( ScopedCheckedCore Void
, ScopedCheckedCore Void
, ScopedCheckedCore Void
, ScopedCheckedCore Void
, ScopedCheckedCore Void
, ScopedCheckedCore Void
, ScopedCheckedCore Void
, ScopedCheckedCore Void
, ScopedCheckedCore Void
, ScopedCheckedCore Void
)
setLfpFixture = do
domain <-
checkedScoped [] (CIntrinsic Empty)
operator <-
checkedScoped []
(CLam TySet (CBound 0))
predicate <-
checkedScoped []
(CLam TySet
(CEq TySet
(CBound 0)
(CBound 0)))
element <-
checkedScoped [] (CIntrinsic Empty)
fixedPoint <-
expectRight
(SetLfp.setLfpTerm
absurd
domain
operator)
operatorDomain <-
checkedScoped []
(CApp
(scopedCoreTerm operator)
(scopedCoreTerm domain))
closedPremise <-
expectRight
(SetLfp.subsetProposition
absurd
operatorDomain
domain)
boundedPremise <-
expectRight
(SetLfp.subsetProposition
absurd
domain
domain)
monotonePremise <-
expectRight
(SetLfp.boundedMonoProposition
absurd
domain
operator)
memberPremise <-
expectRight
(SetLfp.memberProposition
absurd
element
fixedPoint)
closurePremise <-
expectRight
(SetLfp.inductionClosureProposition
absurd
domain
operator
predicate)
pure
( domain
, operator
, predicate
, element
, fixedPoint
, closedPremise
, boundedPremise
, monotonePremise
, memberPremise
, closurePremise
)
rejectsInvalidScopedReplay :: Assertion
rejectsInvalidScopedReplay = do
foundation <-
expectRight Foundation.checkedFoundation
proposition <-
checkedClosed
(CEq TySet
(CIntrinsic Empty)
(CIntrinsic Empty))
boundSet <-
checkedScoped [TySet] (CBound 0)
assertEqual
"missing local hypothesis"
(Left
(KernelReplayHypothesisOutOfBounds
(hypothesisIx 0)))
(replayedKernelTarget
<$> replayKernelDerivation
foundation
defaultKernelReplayLimits
absurd
Vector.empty
proposition
(localHypothesisDerivation
(hypothesisIx 0)))
assertEqual
"stored term from another lexical context"
(Left
(KernelReplayStoredContextMismatch
[]
[TySet]))
(replayedKernelTarget
<$> replayKernelDerivation
foundation
defaultKernelReplayLimits
absurd
Vector.empty
proposition
(scopedEqualityReflexivityDerivation
boundSet))
expanded <-
checkedScoped []
(CEq TySet
(CApp
(CLam TySet (CBound 0))
(CIntrinsic Empty))
(CIntrinsic Empty))
noReductions <-
expectRight (conversionPlan 0)
assertEqual
"conversion budget"
(Left
(KernelReplaySemanticsError
Semantics.KernelConversionBudgetExhausted))
(replayedKernelTarget
<$> replayKernelDerivation
foundation
defaultKernelReplayLimits
absurd
Vector.empty
(unsafeClosed
(scopedCoreTerm expanded))
(convertJudgmentDerivation
(equalityReflexivityDerivation
(unsafeClosed
(CIntrinsic Empty)))
expanded
noReductions))
let checkedAsSet _global =
Just TySet
replayedAsProposition _global =
Just TyProp
globalTarget <-
expectRight
(checkCanonicalCore
checkedAsSet
(CEq TySet
(CGlobal TestGlobal)
(CGlobal TestGlobal)))
assertEqual
"stored global types are rechecked"
(Left
(KernelReplayStoredTermIllTyped
(EqualityOperandTypeMismatch
TySet
TyProp)))
(replayedKernelTarget
<$> replayKernelDerivation
foundation
defaultKernelReplayLimits
replayedAsProposition
Vector.empty
globalTarget
(equalityReflexivityDerivation
(unsafeGlobalOperand
checkedAsSet)))
oneNode <-
expectRight (kernelReplayLimits 1 10)
let propositionScoped =
embedClosedCore [] proposition
identityTarget =
unsafeClosed
(CImp
(frozenCoreTerm proposition)
(frozenCoreTerm proposition))
assertEqual
"replay node limit"
(Left
(KernelReplayNodeLimitExceeded 1))
(replayedKernelTarget
<$> replayKernelDerivation
foundation
oneNode
absurd
Vector.empty
identityTarget
(implicationIntroductionDerivation
propositionScoped
(localHypothesisDerivation
(hypothesisIx 0))))
rejectsTargetMismatch :: Assertion
rejectsTargetMismatch = do
foundation <-
expectRight Foundation.checkedFoundation
operand <-
expectRight
(checkCanonicalCore
absurd
(CIntrinsic Empty))
wrongTarget <-
expectRight
(checkCanonicalCore
absurd
(CImp CFalsum CFalsum))
assertEqual
"the expected target is comparison input, not evidence"
(Left KernelReplayTargetMismatch)
(replayedKernelTarget
<$> replayKernelDerivation
foundation
defaultKernelReplayLimits
absurd
Vector.empty
wrongTarget
(equalityReflexivityDerivation operand))
assertReplayTarget
:: Foundation.CheckedFoundation
-> CanonicalTerm Void
-> KernelDerivation Void
-> Assertion
assertReplayTarget foundation expectedTerm derivation = do
expected <-
checkedClosed expectedTerm
replayed <-
expectRight
(replayKernelDerivation
foundation
defaultKernelReplayLimits
absurd
Vector.empty
expected
derivation)
assertEqual
"replayed exact target"
expected
(replayedKernelTarget replayed)
checkedClosed
:: CanonicalTerm Void
-> IO (FrozenCheckedCore Void)
checkedClosed =
expectRight . checkCanonicalCore absurd
checkedScoped
:: [CoreType]
-> CanonicalTerm Void
-> IO (ScopedCheckedCore Void)
checkedScoped context =
expectRight
. checkScopedCanonicalCore absurd context
unsafeScoped
:: [CoreType]
-> CanonicalTerm Void
-> ScopedCheckedCore Void
unsafeScoped context term =
case checkScopedCanonicalCore absurd context term of
Left coreError ->
impossible
("invalid static kernel fixture: "
<> show coreError)
Right checked ->
checked
unsafeClosed
:: CanonicalTerm Void
-> FrozenCheckedCore Void
unsafeClosed term =
case checkCanonicalCore absurd term of
Left coreError ->
impossible
("invalid static closed kernel fixture: "
<> show coreError)
Right checked ->
checked
unsafeGlobalOperand
:: (TestGlobal -> Maybe CoreType)
-> FrozenCheckedCore TestGlobal
unsafeGlobalOperand globalType =
case checkCanonicalCore
globalType
(CGlobal TestGlobal) of
Left coreError ->
impossible
("invalid static global kernel fixture: "
<> show coreError)
Right checked ->
checked
expectRight
:: Show error
=> Either error value
-> IO value
expectRight =
either
(assertFailure . show)
pure
|
