Lean Kernel Arena / rpylean

Checker "rpylean"

Version: v2026.6.4 · 📄 Declaration · 🔗 Source

rpylean - A Lean type checker written in (R)Python.

Completeness (rightfully accepted tests)

96/102

Soundness (rightfully rejected tests)

49/49

Declined tests

0

Test Expected Result ⏱️ 🧠
bogus1 4 ms 7.6 MB
cedar 👍 43.1 s 2.4 GB
constlevels 2 ms 7.9 MB
cslib 👍 1.5 h 14.2 GB
init 👍 👍 3.2 m (+159%) 4.7 GB (+771%)
init-prelude 👍 👍 219 ms (-46%) 114.5 MB
large-elim-param 2 ms 7.1 MB
level-imax-leq 2 ms 7.5 MB
level-imax-normalization 2 ms 7.5 MB
level-index-out-of-order 👍 2 ms 7.0 MB
mathlib 👍 17.7 m 14.2 GB
nat-rec-rules 4 ms 7.6 MB
perf/app-lam 👍 👍 192 ms (-96%) 120.9 MB (-92%)
perf/grind-ring-5 👍 👍 7.4 s (+204%) 1.2 GB (+436%)
perf/shift-cascade 👍 👍 9 ms (-83%) 17.0 MB
proj-of-prop 2 ms 7.4 MB
sparse-name-index 👍 2 ms 7.0 MB
std 👍 3.8 m 14.2 GB
tutorial/001_basicDef 👍 👍 3 ms 7.2 MB
tutorial/002_badDef 2 ms 7.4 MB
tutorial/003_arrowType 👍 👍 2 ms 7.4 MB
tutorial/004_dependentType 👍 👍 2 ms 7.4 MB
tutorial/005_constType 👍 👍 2 ms 7.4 MB
tutorial/006_betaReduction 👍 👍 2 ms 7.4 MB
tutorial/007_betaReduction2 👍 👍 2 ms 7.4 MB
tutorial/008_forallSortWhnf 👍 👍 2 ms 7.4 MB
tutorial/009_forallSortBad 2 ms 7.4 MB
tutorial/010_nonTypeType 2 ms 7.4 MB
tutorial/011_nonPropThm 2 ms 7.4 MB
tutorial/012_levelComp1 👍 👍 2 ms 7.4 MB
tutorial/013_levelComp2 👍 👍 2 ms 7.4 MB
tutorial/014_levelComp3 👍 👍 2 ms 7.4 MB
tutorial/015_levelParams 👍 👍 2 ms 7.4 MB
tutorial/016_tut06_bad01 2 ms 7.2 MB
tutorial/017_levelComp4 👍 👍 2 ms 7.4 MB
tutorial/018_levelComp5 👍 👍 2 ms 7.4 MB
tutorial/019_imax1 👍 👍 2 ms 7.4 MB
tutorial/020_imax2 👍 👍 2 ms 7.4 MB
tutorial/021_levelMaxComm 👍 👍 2 ms 7.4 MB
tutorial/022_levelMaxAssoc 👍 👍 2 ms 7.4 MB
tutorial/023_levelMaxIdem 👍 👍 2 ms 7.4 MB
tutorial/024_levelMaxAbsorb 👍 👍 2 ms 7.4 MB
tutorial/025_inferVar 👍 👍 2 ms 7.4 MB
tutorial/026_defEqLambda 👍 👍 2 ms 7.4 MB
tutorial/027_peano1 👍 👍 2 ms 7.5 MB
tutorial/028_peano2 👍 👍 2 ms 7.5 MB
tutorial/029_peano3 👍 👍 2 ms 7.6 MB
tutorial/030_letType 👍 👍 2 ms 7.4 MB
tutorial/031_letTypeDep 👍 👍 2 ms 7.4 MB
tutorial/032_letRed 👍 👍 2 ms 7.4 MB
tutorial/033_empty 👍 👍 2 ms 7.4 MB
tutorial/034_boolType 👍 👍 2 ms 7.4 MB
tutorial/035_twoBool 👍 👍 2 ms 7.4 MB
tutorial/036_andType 👍 👍 2 ms 7.4 MB
tutorial/037_prodType 👍 👍 2 ms 7.4 MB
tutorial/038_pprodType 👍 👍 2 ms 7.4 MB
tutorial/039_pUnitType 👍 👍 2 ms 7.4 MB
tutorial/040_eqType 👍 👍 2 ms 7.4 MB
tutorial/041_natDef 👍 👍 2 ms 7.4 MB
tutorial/042_rbTreeDef 👍 👍 2 ms 7.6 MB
tutorial/043_inductBadNonSort 2 ms 7.4 MB
tutorial/044_inductBadNonSort2 2 ms 7.4 MB
tutorial/045_inductLevelParam 2 ms 7.2 MB
tutorial/046_inductTooFewParams 2 ms 7.4 MB
tutorial/047_inductWrongCtorParams 2 ms 7.4 MB
tutorial/048_inductWrongCtorResParams 2 ms 7.4 MB
tutorial/049_inductWrongCtorResLevel 2 ms 7.4 MB
tutorial/050_inductInIndex 2 ms 7.4 MB
tutorial/051_indNeg 2 ms 7.4 MB
tutorial/052_reduceCtorParam.mk 👍 👍 2 ms 7.5 MB
tutorial/053_reduceCtorType.mk 2 ms 7.4 MB
tutorial/054_indNegReducible 2 ms 7.4 MB
tutorial/055_predWithTypeField 👍 👍 2 ms 7.4 MB
tutorial/056_typeWithTypeField 👍 👍 2 ms 7.4 MB
tutorial/057_typeWithTypeFieldPoly 👍 👍 2 ms 7.4 MB
tutorial/058_typeWithTooHighTypeField.mk 2 ms 7.4 MB
tutorial/059_emptyRec 👍 👍 2 ms 7.4 MB
tutorial/060_boolRec 👍 👍 2 ms 7.4 MB
tutorial/061_twoBoolRec 👍 👍 2 ms 7.5 MB
tutorial/062_andRec 👍 👍 2 ms 7.5 MB
tutorial/063_prodRec 👍 👍 2 ms 7.5 MB
tutorial/064_pprodRec 👍 👍 2 ms 7.5 MB
tutorial/065_punitRec 👍 👍 2 ms 7.4 MB
tutorial/066_eqRec 👍 👍 2 ms 7.5 MB
tutorial/067_nRec 👍 👍 2 ms 7.4 MB
tutorial/068_rbTreeRef 👍 👍 2 ms 7.9 MB
tutorial/069_boolPropRec 👍 👍 2 ms 7.4 MB
tutorial/070_existsRec 👍 👍 2 ms 7.5 MB
tutorial/071_sortElimPropRec 👍 👍 2 ms 7.5 MB
tutorial/072_sortElimProp2Rec 👍 👍 2 ms 7.5 MB
tutorial/073_boolRecEqns 👍 👍 2 ms 7.8 MB
tutorial/074_prodRecEqns 👍 👍 2 ms 7.9 MB
tutorial/075_nRecReduction 👍 👍 2 ms 7.8 MB
tutorial/076_listRecReduction 👍 👍 3 ms 8.2 MB
tutorial/077_RBTree.id_spec 👍 👍 5 ms 11.2 MB
tutorial/078_And.right 👍 👍 2 ms 7.5 MB
tutorial/079_Prod.snd 👍 👍 2 ms 7.5 MB
tutorial/080_PProd.snd 👍 👍 2 ms 7.5 MB
tutorial/081_PSigma.snd 👍 👍 2 ms 7.5 MB
tutorial/082_projOutOfRange 2 ms 7.5 MB
tutorial/083_projNotStruct 2 ms 7.4 MB
tutorial/084_projProp1 👍 👍 2 ms 7.5 MB
tutorial/085_projProp2 2 ms 7.5 MB
tutorial/086_projProp3 👍 👍 2 ms 7.5 MB
tutorial/087_projProp4 2 ms 7.5 MB
tutorial/088_projProp5 2 ms 7.5 MB
tutorial/089_projProp6 2 ms 7.5 MB
tutorial/090_projDataIndexRec 👍 👍 2 ms 7.5 MB
tutorial/091_projIndexData 2 ms 7.5 MB
tutorial/092_projIndexData2 2 ms 7.5 MB
tutorial/093_projRed 👍 👍 2 ms 7.6 MB
tutorial/094_ruleK 👍 👍 2 ms 7.5 MB
tutorial/095_ruleKbad 2 ms 7.6 MB
tutorial/096_ruleKAcc 2 ms 8.1 MB
tutorial/097_aNatLit 👍 👍 2 ms 7.4 MB
tutorial/098_natLitEq 👍 👍 2 ms 7.5 MB
tutorial/099_proofIrrelevance 👍 👍 2 ms 7.5 MB
tutorial/100_proofIrrelevanceBad 2 ms 7.5 MB
tutorial/101_proofIrrelevanceWhnf 👍 👍 2 ms 7.5 MB
tutorial/102_unitEta1 👍 👍 2 ms 7.5 MB
tutorial/103_unitEta2 👍 👍 2 ms 7.5 MB
tutorial/104_unitEta3 👍 👍 2 ms 7.5 MB
tutorial/105_structEta 👍 👍 2 ms 7.9 MB
tutorial/106_funEta 👍 👍 2 ms 7.5 MB
tutorial/107_funEtaDep 👍 👍 2 ms 7.5 MB
tutorial/108_funEtaBad 2 ms 7.6 MB
tutorial/109_etaRuleK 2 ms 7.6 MB
tutorial/110_etaCtor 2 ms 7.5 MB
tutorial/111_reflOccLeft 2 ms 7.4 MB
tutorial/112_reflOccInIndex 2 ms 7.5 MB
tutorial/113_reduceCtorParamRefl.mk 👍 👍 2 ms 7.5 MB
tutorial/114_reduceCtorParamRefl2.mk 👍 👍 2 ms 7.5 MB
tutorial/115_rTreeRec 👍 👍 2 ms 7.5 MB
tutorial/116_rtreeRecReduction 👍 👍 2 ms 7.6 MB
tutorial/117_accRecType 👍 👍 2 ms 7.5 MB
tutorial/118_accRecReduction 👍 👍 3 ms 8.2 MB
tutorial/119_accRecNoEta 2 ms 8.1 MB
tutorial/120_quotMkType 👍 👍 2 ms 7.5 MB
tutorial/121_quotIndType 👍 👍 2 ms 7.5 MB
tutorial/122_quotLiftType 👍 👍 2 ms 7.5 MB
tutorial/123_quotSoundType 👍 👍 2 ms 7.5 MB
tutorial/124_quotLiftReduction 👍 👍 2 ms 7.9 MB
tutorial/125_quotIndReduction 👍 👍 2 ms 7.8 MB
tutorial/126_dup_defs 2 ms 7.4 MB
tutorial/127_dup_ind_def 2 ms 7.4 MB
tutorial/128_dup_ctor_def 2 ms 7.4 MB
tutorial/129_dup_rec_def 2 ms 7.4 MB
tutorial/130_misnamed_rec 2 ms 7.0 MB
tutorial/131_dup_rec_def2 2 ms 7.4 MB
tutorial/132_dup_ctor_rec 2 ms 7.0 MB
tutorial/133_DupConCon 2 ms 7.0 MB

Detailed results

Test "bogus1"

Expected: ✋ reject · Size: 11.4 KB · Lines: 198 · lean4export: 3.1.0 · Lean: 4.29.0 · 📄 Declaration · 🔗 Source

A clearly bogus proof. Also serves as an example for how to write simple cases.

Test result: ✋ rejected · exit code 1 · wall time: 14 ms · instructions: 21.9 M · max rss memory: 7.6 MB

stderr:
theorem thm : Eq (OfNat.ofNat 0) (OfNat.ofNat 1) := True.intro
                                                    ^^^^^^^^^^
                                                    has type
                                                      True
                                                    but is expected to have type
                                                      Eq (OfNat.ofNat 0) (OfNat.ofNat 1)
summary: 16/16 decls checked, peak 32 MB, allocated 0 MB, heartbeats 0
checked in 0.002532s

Test "cedar"

Expected: 👍 accept · Size: 728.6 MB · Lines: 13.4 M · lean4export: 3.1.0 · Lean: 4.26.0 · 📄 Declaration · 🔗 Source

Lean formalization of, and proofs about, Cedar.

Auto-generated documentation is available at https://cedar-policy.github.io/cedar-spec/docs/.

This test case exports the whole Cedar module and as such contains even unused parts Init and Batteries.

Test result: ✋ rejected · exit code 1 · wall time: 46.5 s · instructions: 258.8 G · max rss memory: 2.4 GB

stderr:
theorem Cedar.Spec.Value._sizeOf_5_eq : ∀ (x : List.{0} (Prod.{0, 0} Cedar.Spec.Attr Cedar.Spec.Value)), Eq (Cedar.Spec.Value._sizeOf_5 x) (SizeOf.sizeOf x) := fun x ↦ List.rec (Eq.refl (SizeOf.sizeOf (List.nil))) (fun head tail tail_ih ↦ Eq.trans (congrArg (Nat.add (HAdd.hAdd (OfNat.ofNat 1) (SizeOf.sizeOf head))) tail_ih) (Eq.symm (List.cons.sizeOf_spec head tail))) x
                                                                                                                                                                                                                       ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
                                                                                                                                                                                                                       has type
                                                                                                                                                                                                                         ∀ (head : Prod.{0, 0} Cedar.Spec.Attr Cedar.Spec.Value), ∀ (tail : List.{0} (Prod.{0, 0} Cedar.Spec.Attr Cedar.Spec.Value)), Eq (Cedar.Spec.Value._sizeOf_5 tail) (SizeOf.sizeOf tail) → Eq (Nat.add (HAdd.hAdd (OfNat.ofNat 1) (SizeOf.sizeOf head)) (Cedar.Spec.Value._sizeOf_5 tail)) (SizeOf.sizeOf (List.cons head tail))
                                                                                                                                                                                                                       but is expected to have type
                                                                                                                                                                                                                         (head : Prod.{0, 0} Cedar.Spec.Attr Cedar.Spec.Value) → (tail : List.{0} (Prod.{0, 0} Cedar.Spec.Attr Cedar.Spec.Value)) → (fun t ↦ Eq (Cedar.Spec.Value._sizeOf_5 t) (SizeOf.sizeOf t)) tail → (fun t ↦ Eq (Cedar.Spec.Value._sizeOf_5 t) (SizeOf.sizeOf t)) (List.cons head tail)
theorem Cedar.SymCC.Term._sizeOf_5_eq : ∀ (x : List.{0} (Prod.{0, 0} Cedar.Spec.Attr Cedar.SymCC.Term)), Eq (Cedar.SymCC.Term._sizeOf_5 x) (SizeOf.sizeOf x) := fun x ↦ List.rec (Eq.refl (SizeOf.sizeOf (List.nil))) (fun head tail tail_ih ↦ Eq.trans (congrArg (Nat.add (HAdd.hAdd (OfNat.ofNat 1) (SizeOf.sizeOf head))) tail_ih) (Eq.symm (List.cons.sizeOf_spec head tail))) x
                                                                                                                                                                                                                       ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
                                                                                                                                                                                                                       has type
                                                                                                                                                                                                                         ∀ (head : Prod.{0, 0} Cedar.Spec.Attr Cedar.SymCC.Term), ∀ (tail : List.{0} (Prod.{0, 0} Cedar.Spec.Attr Cedar.SymCC.Term)), Eq (Cedar.SymCC.Term._sizeOf_5 tail) (SizeOf.sizeOf tail) → Eq (Nat.add (HAdd.hAdd (OfNat.ofNat 1) (SizeOf.sizeOf head)) (Cedar.SymCC.Term._sizeOf_5 tail)) (SizeOf.sizeOf (List.cons head tail))
                                                                                                                                                                                                                       but is expected to have type
                                                                                                                                                                                                                         (head : Prod.{0, 0} Cedar.Spec.Attr Cedar.SymCC.Term) → (tail : List.{0} (Prod.{0, 0} Cedar.Spec.Attr Cedar.SymCC.Term)) → (fun t ↦ Eq (Cedar.SymCC.Term._sizeOf_5 t) (SizeOf.sizeOf t)) tail → (fun t ↦ Eq (Cedar.SymCC.Term._sizeOf_5 t) (SizeOf.sizeOf t)) (List.cons head tail)
theorem Cedar.SymCC.TermType._sizeOf_3_eq : ∀ (x : List.{0} (Prod.{0, 0} Cedar.Spec.Attr Cedar.SymCC.TermType)), Eq (Cedar.SymCC.TermType._sizeOf_3 x) (SizeOf.sizeOf x) := fun x ↦ List.rec (Eq.refl (SizeOf.sizeOf (List.nil))) (fun head tail tail_ih ↦ Eq.trans (congrArg (Nat.add (HAdd.hAdd (OfNat.ofNat 1) (SizeOf.sizeOf head))) tail_ih) (Eq.symm (List.cons.sizeOf_spec head tail))) x
                                                                                                                                                                                                                                   ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
                                                                                                                                                                                                                                   has type
                                                                                                                                                                                                                                     ∀ (head : Prod.{0, 0} Cedar.Spec.Attr Cedar.SymCC.TermType), ∀ (tail : List.{0} (Prod.{0, 0} Cedar.Spec.Attr Cedar.SymCC.TermType)), Eq (Cedar.SymCC.TermType._sizeOf_3 tail) (SizeOf.sizeOf tail) → Eq (Nat.add (HAdd.hAdd (OfNat.ofNat 1) (SizeOf.sizeOf head)) (Cedar.SymCC.TermType._sizeOf_3 tail)) (SizeOf.sizeOf (List.cons head tail))
                                                                                                                                                                                                                                   but is expected to have type
                                                                                                                                                                                                                                     (head : Prod.{0, 0} Cedar.Spec.Attr Cedar.SymCC.TermType) → (tail : List.{0} (Prod.{0, 0} Cedar.Spec.Attr Cedar.SymCC.TermType)) → (fun t ↦ Eq (Cedar.SymCC.TermType._sizeOf_3 t) (SizeOf.sizeOf t)) tail → (fun t ↦ Eq (Cedar.SymCC.TermType._sizeOf_3 t) (SizeOf.sizeOf t)) (List.cons head tail)
RPython traceback:
  File "rpylean_objects_1.c", line 59348, in W_Declaration_type_check
  File "rpylean_objects.c", line 24875, in W_Definition_type_check
  File "rpylean_objects.c", line 49559, in _iter_infer
  File "rpylean_objects.c", line 11051, in W_Proj_infer
Fatal RPython error: AssertionError

Test "constlevels"

Expected: ✋ reject · Size: 15.3 KB · Lines: 283 · lean4export: 3.1.0 · Lean: 4.29.0-rc2 · 📄 Declaration

Regression test for undefined behavior in lazy_delta_reduction_step in the official kernel

In the function lazy_delta_reduction_step, the official kernel expects unfold_definition to always succeed. However, if the constant has an incorrect number of level parameters, it actually fails, which leads to memory corruption in lazy_delta_reduction_step.

This test is to check that the official kernel and also other kernels that closely follow the logic of the official kernel correctly handle this unfolding failure.

The issue in the official kernel was originally reported as https://github.com/leanprover/lean4/issues/10577.

Test result: ✋ rejected · exit code 1 · wall time: 7 ms · instructions: 14.2 M · max rss memory: 7.9 MB

stderr:
theorem _test : let x : Nat := Nat
                        ^^^
                        has type
                          Type
                        but is expected to have type
                          Nat
summary: 20/20 decls checked, peak 32 MB, allocated 0 MB, heartbeats 0
checked in 0.001139s

Test "cslib"

Expected: 👍 accept · Size: 1.2 GB · Lines: 22.8 M · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

The Lean Computer Science Library (CSLib).

Test result: ✋ rejected · exit code 1 · wall time: 30.4 m · instructions: 31.7 T · max rss memory: 14.2 GB

Test "init"

Expected: 👍 accept · Size: 309.5 MB · Lines: 6.1 M · lean4export: 3.1.0 · Lean: 4.29.0 · 📄 Declaration · 🔗 Source

The Init module export from Lean 4 core.

This test contains the fundamental building blocks of Lean 4, including:

  • Basic data types (Nat, List, Array, String, etc.)
  • Core tactics and syntax
  • Foundational mathematical structures
  • Essential metaprogramming infrastructure

This is one of the smallest meaningful test cases, making it ideal for initial checker validation and debugging.

Test result: 👍 accepted · exit code 0 · wall time: 3.3 m · instructions: 1.1 T · max rss memory: 4.7 GB

stderr:
summary: 54475/54475 decls checked, peak 4801 MB, allocated 3714 MB, heartbeats 0
checked in 196.441556s

Test "init-prelude"

Expected: 👍 accept · Size: 3.5 MB · Lines: 63.7 k · lean4export: 3.1.0 · Lean: 4.29.0 · 📄 Declaration · 🔗 Source

The Init.Prelude module export.

Test result: 👍 accepted · exit code 0 · wall time: 241 ms · instructions: 1.3 G · max rss memory: 114.5 MB

stderr:
summary: 2059/2059 decls checked, peak 102 MB, allocated 72 MB, heartbeats 0
checked in 0.225803s

Test "large-elim-param"

Expected: ✋ reject · Size: 3.1 KB · Lines: 48 · 📄 Declaration

Proof of False via incorrect large elimination restriction.

If the check for whether a level is surely not zero is implemented wrong, in particular if it incorrectly returns true for params, we can create a universe-polymorphic

inductive MyBool.{u} : Sort u | tt | ff

where the recursor MyBool.rec.{1,0} can do large elimination of a Prop. Because of proof irrelevance we have tt = ff, so we can derive a contradiction.

Found by Anthony Wang using Aristotle.

Test result: ✋ rejected · exit code 1 · wall time: 6 ms · instructions: 11.6 M · max rss memory: 7.1 MB

stderr:
expected level index 2, got 3

summary: 0/0 decls checked, peak 32 MB, allocated 0 MB, heartbeats 0
checked in 0.000389s

Test "level-imax-leq"

Expected: ✋ reject · Size: 5.6 KB · Lines: 93 · lean4export: 3.1.0 · Lean: 4.29.0-rc1 · 📄 Declaration

Proof of False via incorrect universe level comparison for imax.

A correct kernel must reject leq(imax(u,v)+1, imax(u,v)), since at u=0, v=0 this becomes leq(1, 0) which is false. However, a checker that only compares the imax arguments structurally (without accounting for an accumulated successor offset) will incorrectly accept it.

This allows defining a universe-collapsing identity function down.{u,v} : Sort (succ (imax u v)) → Sort (imax u v), which is used to cast between True and False via Bool.rec at Sort (imax 0 0) = Prop.

Nanoda incorrectly accepted this proof until it was fixed.

Test result: ✋ rejected · exit code 1 · wall time: 6 ms · instructions: 12.3 M · max rss memory: 7.5 MB

stderr:
def down.{u, v} : Type (imax u v) → Sort (imax u v) :=
  fun x ↦ x
  ^^^^^^^^^
  has type
    Type (imax u v) → Type (imax u v)
  but is expected to have type
    Type (imax u v) → Sort (imax u v)
summary: 11/11 decls checked, peak 32 MB, allocated 0 MB, heartbeats 0
checked in 0.000615s

Test "level-imax-normalization"

Expected: ✋ reject · Size: 5.8 KB · Lines: 96 · lean4export: 3.1.0 · Lean: 4.26.0 · 📄 Declaration

Proof of False via incorrect universe level normalization for imax.

A correct kernel must distinguish imax 0 v from succ(imax 0 v), since at v=0 these evaluate to 0 and 1 respectively. However, a level normalization algorithm that drops an accumulated successor offset when decomposing imax u (param v) will produce identical normal forms for both, causing the equivalence check to incorrectly return true.

This allows defining a universe-collapsing identity function down.{v} : Sort (succ (imax 0 v)) → Sort (imax 0 v), and then myProp : Prop := down.{0} Bool (a Prop that is computationally Bool). Proof irrelevance on myProp equates Bool.true and Bool.false, and Bool.rec maps this into False.

Test result: ✋ rejected · exit code 1 · wall time: 6 ms · instructions: 12.3 M · max rss memory: 7.5 MB

stderr:
def down.{v} : Type v → Sort v :=
  fun x ↦ x
  ^^^^^^^^^
  has type
    Type v → Type v
  but is expected to have type
    Type v → Sort v
summary: 12/12 decls checked, peak 32 MB, allocated 0 MB, heartbeats 0
checked in 0.000560s

Test "level-index-out-of-order"

Expected: 👍 accept · Size: 332 B · Lines: 6 · lean4export: 0.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration

Lean4export will create internalization-table references contiguously in order: in references for names, il references for levels, and ie references for expressions all work this way.

However, the spec merely requires that these are integers. It's reasonable for an implementation to assume these are approximately dense (and to treat them as array indices instead of hashtable entries), but a kernel should handle skipped indices or out-of-order indices.

This test checks that the kernel doesn't require internaliation-table references to be presented in ascending order. If the level referenes 2 and 1 were swapped, this would be the expected encoding of axiom foo : Sort 2. This encoding should be equivalent.

Test result: ✋ rejected · exit code 1 · wall time: 6 ms · instructions: 11.5 M · max rss memory: 7.0 MB

stderr:
expected level index 1, got 2

summary: 0/0 decls checked, peak 32 MB, allocated 0 MB, heartbeats 0
checked in 0.000277s

Test "mathlib"

Expected: 👍 accept · Size: 5.2 GB · Lines: 100.0 M · lean4export: 3.1.0 · Lean: 4.29.0 · 📄 Declaration · 🔗 Source

The complete Mathlib library export.

This test contains all the mathematical definitions, theorems, and proofs from Mathlib, representing the largest and most comprehensive test case in the Lean kernel arena.

Test result: ✋ rejected · exit code 1 · wall time: 13.1 m · instructions: 6.4 T · max rss memory: 14.2 GB

Test "nat-rec-rules"

Expected: ✋ reject · Size: 8.2 KB · Lines: 128 · lean4export: 3.1.0 · Lean: 4.29.0-rc1 · 📄 Declaration

Proof of False via incorrect recursor rule validation.

When processing an inductive type declaration, a correct kernel must verify that the generated recursor rules match the ones provided in the export data. A checker that accidentally compares the imported rules against themselves (instead of against independently constructed rules) will accept arbitrary recursor reduction behavior.

This test defines Nat with a wrong Nat.rec succ rule that always returns hzero (ignoring the induction hypothesis). Combined with a nat literal extension that hardcodes correct arithmetic for concrete nat literals but falls back to the wrong Nat.rec rules for symbolic arguments, this creates an inconsistency that yields a proof of False.

Nanoda incorrectly accepted this proof until it was fixed.

Test result: ✋ rejected · exit code 1 · wall time: 23 ms · instructions: 22.0 M · max rss memory: 7.6 MB

stderr:
recursor Nat.rec.{u_1} : {motive : Nat → Sort u_1} → motive Nat.zero → ((n : Nat) → motive n → motive (Nat.succ n)) → (t : Nat) → motive t
rule for Nat.succ rhs head is not the corresponding minor (expected bvar #1)
summary: 15/15 decls checked, peak 32 MB, allocated 0 MB, heartbeats 0
checked in 0.002508s

Test "perf/app-lam"

Expected: 👍 accept · Size: 1.2 MB · Lines: 28.6 k · lean4export: 3.1.0 · Lean: 4.29.0 · 📄 Declaration · 🔗 Source

A synthetically generated term with n levels of alternating applications and lambdas, with DAG sharing.

At each level, a constant is applied to two identical lambda arguments. The export format records these as a single shared expression (DAG). Each lambda body grows with the nesting depth, referencing all enclosing binders.

This tests two aspects of checker performance:

Infer cache: Since both arguments at each level are the same expression, a checker without an infer cache re-infers the type of each shared subterm, doubling work at every level — O(2ⁿ) total.

Substitution cost: Even with a cache, type-inferring each lambda requires substituting into its body (size O(n)) at each of the n levels, giving O(n²) total. Whether this cost arises depends on the checker's binder representation.

Test result: 👍 accepted · exit code 0 · wall time: 181 ms · instructions: 1.1 G · max rss memory: 120.9 MB

stderr:
summary: 34/34 decls checked, peak 112 MB, allocated 80 MB, heartbeats 0
checked in 0.166682s

Test "perf/grind-ring-5"

Expected: 👍 accept · Size: 9.7 MB · Lines: 199.2 k · lean4export: 3.1.0 · Lean: 4.29.0 · 📄 Declaration · 🔗 Source

A grind tactic test from the Lean 4 test suite.

This produces a theorem with a rather large proof term that needs fast reduction.

Test result: 👍 accepted · exit code 0 · wall time: 9.0 s · instructions: 44.3 G · max rss memory: 1.2 GB

stderr:
summary: 2432/2432 decls checked, peak 1178 MB, allocated 1023 MB, heartbeats 0
checked in 8.904406s

Test "perf/shift-cascade"

Expected: 👍 accept · Size: 256.3 KB · Lines: 5.1 k · lean4export: 3.1.0 · Lean: 4.29.0 · 📄 Declaration · 🔗 Source

Stress test for cascading substitution overhead in kernel let processing.

N nested let bindings inside a lambda, where each value references the outer lambda parameter and the previous binding:

fun (a : Nat → Nat) => let f₁ := fun x => a x let f₂ := fun x => a (f₁ x) ... let fₙ := fun x => a (fₙ₋₁ x) fₙ 0

The kernel processes each let by substituting the value into the body. Each value has a free bvar (references a), so substitution under inner binders creates shifted copies. In a de Bruijn kernel with deferred shifts, these Shift(val, offset) wrappers accumulate: step k must traverse through O(k) wrappers from previous steps, giving O(N²) total work.

A locally-nameless kernel substitutes fvars that need no shifting, giving O(N) total.

N=1000 in the Lean source. Increase to stress further.

Test result: 👍 accepted · exit code 0 · wall time: 14 ms · instructions: 52.4 M · max rss memory: 17.0 MB

stderr:
summary: 10/10 decls checked, peak 32 MB, allocated 0 MB, heartbeats 0
checked in 0.008010s

Test "proj-of-prop"

Expected: ✋ reject · Size: 3.9 KB · Lines: 56 · lean4export: 3.1.0 · Lean: 4.29.0 · 📄 Declaration · 🔗 Source

A proof of False via a projection from a Prop-typed structure whose constructor was applied to an ill-typed argument. The exported term is

badFalse : False := (Wrapper.mk True.intro).p

where Wrapper : Prop has a single field p : False, so Wrapper.mk expects a proof of False but is given True.intro : True.

A sound checker must reject this. A checker that types a projection by inferring (rather than checking) its structure argument — i.e. that trusts the structure to be well-typed instead of verifying the constructor's argument types against its binders — will accept it, because Wrapper.mk True.intro still formally inhabits Wrapper at the structural level, and the p projection is then read back out at the declared field type False.

Test result: ✋ rejected · exit code 1 · wall time: 6 ms · instructions: 11.9 M · max rss memory: 7.4 MB

stderr:
theorem badFalse : False := (Wrapper.mk True.intro).p
                                        ^^^^^^^^^^
                                        has type
                                          True
                                        but is expected to have type
                                          False
summary: 9/9 decls checked, peak 32 MB, allocated 0 MB, heartbeats 0
checked in 0.000493s

Test "sparse-name-index"

Expected: 👍 accept · Size: 296 B · Lines: 4 · lean4export: 0.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration

Lean4export will create internalization-table references contiguously in order: in references for names, il references for levels, and ie references for expressions all work this way.

However, the spec merely requires that these are integers. It's reasonable for an implementation to assume these are approximately dense (and to treat them as array indices instead of hashtable entries), but a kernel should handle skipped indices or out-of-order indices.

This test checks that a kernel doesn't require internalization-table references to be assigned sequentially starting from 1. If the "2" and "4" were replaced by "1" and "0", respectively, this would be the expected encoding of axiom foo : Prop. This encoding should be equivalent.

Test result: ✋ rejected · exit code 1 · wall time: 6 ms · instructions: 11.5 M · max rss memory: 7.0 MB

stderr:
expected name index 1, got 2

summary: 0/0 decls checked, peak 32 MB, allocated 0 MB, heartbeats 0
checked in 0.000322s

Test "std"

Expected: 👍 accept · Size: 526.1 MB · Lines: 10.0 M · lean4export: 3.1.0 · Lean: 4.29.0 · 📄 Declaration · 🔗 Source

The complete Std library export from Lean 4.

This test contains the standard library extensions beyond core Lean 4, including:

  • Enhanced data structures (HashMap, RBTree, etc.)
  • Additional mathematical operations
  • Extended list and array operations
  • Utility functions and theorems

This represents a medium-sized test case, larger than core modules but smaller than Mathlib, making it useful for performance testing.

Test result: ✋ rejected · exit code 1 · wall time: 3.7 m · instructions: 1.4 T · max rss memory: 14.2 GB

Test "tutorial/001_basicDef"

Expected: 👍 accept · Size: 371 B · Lines: 6 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Basic definition

Test result: 👍 accepted · exit code 0 · wall time: 21 ms · instructions: 20.7 M · max rss memory: 7.2 MB

stderr:
summary: 1/1 decls checked, peak 32 MB, allocated 0 MB, heartbeats 0
checked in 0.001920s

Test "tutorial/002_badDef"

Expected: ✋ reject · Size: 369 B · Lines: 6 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Mismatched types

Test result: ✋ rejected · exit code 1 · wall time: 6 ms · instructions: 11.7 M · max rss memory: 7.4 MB

stderr:
def badDef : Prop :=
  Type
  ^^^^
  has type
    Type 1
  but is expected to have type
    Prop
summary: 1/1 decls checked, peak 32 MB, allocated 0 MB, heartbeats 0
checked in 0.000356s

Test "tutorial/003_arrowType"

Expected: 👍 accept · Size: 626 B · Lines: 12 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Arrow type (function type)

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 11.6 M · max rss memory: 7.4 MB

stderr:
summary: 1/1 decls checked, peak 32 MB, allocated 0 MB, heartbeats 0
checked in 0.000300s

Test "tutorial/004_dependentType"

Expected: 👍 accept · Size: 464 B · Lines: 7 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Dependent type (forall)

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 11.6 M · max rss memory: 7.4 MB

stderr:
summary: 1/1 decls checked, peak 32 MB, allocated 0 MB, heartbeats 0
checked in 0.000302s

Test "tutorial/005_constType"

Expected: 👍 accept · Size: 901 B · Lines: 17 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Lambda expression

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 11.7 M · max rss memory: 7.4 MB

stderr:
summary: 1/1 decls checked, peak 32 MB, allocated 0 MB, heartbeats 0
checked in 0.000370s

Test "tutorial/006_betaReduction"

Expected: 👍 accept · Size: 1.3 KB · Lines: 27 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Lambda reduction

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 11.7 M · max rss memory: 7.4 MB

stderr:
summary: 2/2 decls checked, peak 32 MB, allocated 0 MB, heartbeats 0
checked in 0.000364s

Test "tutorial/007_betaReduction2"

Expected: 👍 accept · Size: 1.4 KB · Lines: 28 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Lambda reduction under binder

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 11.7 M · max rss memory: 7.4 MB

stderr:
summary: 2/2 decls checked, peak 32 MB, allocated 0 MB, heartbeats 0
checked in 0.000400s

Test "tutorial/008_forallSortWhnf"

Expected: 👍 accept · Size: 1.2 KB · Lines: 25 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

The binding domain of a forall may need to be reduce before it is a sort

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 11.7 M · max rss memory: 7.4 MB

stderr:
summary: 2/2 decls checked, peak 32 MB, allocated 0 MB, heartbeats 0
checked in 0.000343s

Test "tutorial/009_forallSortBad"

Expected: ✋ reject · Size: 1.2 KB · Lines: 26 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

The binding domain of a forall has to be a sort

Test result: ✋ rejected · exit code 1 · wall time: 6 ms · instructions: 11.8 M · max rss memory: 7.4 MB

stderr:
def forallSortBad : Prop :=
  ∀ (x : id Prop), ∀ (x : x), x → x
                          ^
                          has type
                            x
                          but is expected to be a Sort (Type or Prop)
summary: 2/2 decls checked, peak 32 MB, allocated 0 MB, heartbeats 0
checked in 0.000452s

Test "tutorial/010_nonTypeType"

Expected: ✋ reject · Size: 1.1 KB · Lines: 21 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

The type of a declaration has to be a type, not some other expression

Test result: ✋ rejected · exit code 1 · wall time: 6 ms · instructions: 11.7 M · max rss memory: 7.4 MB

stderr:
def nonTypeType : constType :=
                  ^^^^^^^^^
                  has type
                    Type → Type → Type
                  but is expected to be a Sort (Type or Prop)
summary: 2/2 decls checked, peak 32 MB, allocated 0 MB, heartbeats 0
checked in 0.000402s

Test "tutorial/011_nonPropThm"

Expected: ✋ reject · Size: 428 B · Lines: 7 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

The type of a theorem has to be a proposition

Test result: ✋ rejected · exit code 1 · wall time: 6 ms · instructions: 11.6 M · max rss memory: 7.4 MB

stderr:
theorem nonPropThm : Prop := ∀ (x : Prop), x
                     ^^^^
                     has sort
                       Type
                     but the type of a theorem must be a proposition (Prop)
summary: 1/1 decls checked, peak 32 MB, allocated 0 MB, heartbeats 0
checked in 0.000460s

Test "tutorial/012_levelComp1"

Expected: 👍 accept · Size: 395 B · Lines: 7 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Some level computation

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 11.6 M · max rss memory: 7.4 MB

stderr:
summary: 1/1 decls checked, peak 32 MB, allocated 0 MB, heartbeats 0
checked in 0.000337s

Test "tutorial/013_levelComp2"

Expected: 👍 accept · Size: 413 B · Lines: 8 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Some level computation

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 11.6 M · max rss memory: 7.4 MB

stderr:
summary: 1/1 decls checked, peak 32 MB, allocated 0 MB, heartbeats 0
checked in 0.000297s

Test "tutorial/014_levelComp3"

Expected: 👍 accept · Size: 431 B · Lines: 9 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Some level computation

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 11.6 M · max rss memory: 7.4 MB

stderr:
summary: 1/1 decls checked, peak 32 MB, allocated 0 MB, heartbeats 0
checked in 0.000268s

Test "tutorial/015_levelParams"

Expected: 👍 accept · Size: 1.4 KB · Lines: 29 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Level parameters

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 11.8 M · max rss memory: 7.4 MB

stderr:
summary: 2/2 decls checked, peak 32 MB, allocated 0 MB, heartbeats 0
checked in 0.000495s

Test "tutorial/016_tut06_bad01"

Expected: ✋ reject · Size: 431 B · Lines: 8 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Duplicate universe parameters

Test result: ✋ rejected · exit code 1 · wall time: 6 ms · instructions: 11.6 M · max rss memory: 7.2 MB

stderr:
Invalid declaration tut06_bad01.{u, u}: duplicate level parameter u

summary: 0/0 decls checked, peak 32 MB, allocated 0 MB, heartbeats 0
checked in 0.000271s

Test "tutorial/017_levelComp4"

Expected: 👍 accept · Size: 428 B · Lines: 8 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Some level computation

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 11.6 M · max rss memory: 7.4 MB

stderr:
summary: 1/1 decls checked, peak 32 MB, allocated 0 MB, heartbeats 0
checked in 0.000314s

Test "tutorial/018_levelComp5"

Expected: 👍 accept · Size: 428 B · Lines: 8 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Some level computation

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 11.6 M · max rss memory: 7.4 MB

stderr:
summary: 1/1 decls checked, peak 32 MB, allocated 0 MB, heartbeats 0
checked in 0.000351s

Test "tutorial/019_imax1"

Expected: 👍 accept · Size: 813 B · Lines: 16 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Type inference for forall using imax

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 11.7 M · max rss memory: 7.4 MB

stderr:
summary: 1/1 decls checked, peak 32 MB, allocated 0 MB, heartbeats 0
checked in 0.000355s

Test "tutorial/020_imax2"

Expected: 👍 accept · Size: 832 B · Lines: 17 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Type inference for forall using imax

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 11.7 M · max rss memory: 7.4 MB

stderr:
summary: 1/1 decls checked, peak 32 MB, allocated 0 MB, heartbeats 0
checked in 0.000414s

Test "tutorial/021_levelMaxComm"

Expected: 👍 accept · Size: 528 B · Lines: 12 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Level equality: max is commutative (max u v ≈ max v u).

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 11.6 M · max rss memory: 7.4 MB

stderr:
summary: 1/1 decls checked, peak 32 MB, allocated 0 MB, heartbeats 0
checked in 0.000354s

Test "tutorial/022_levelMaxAssoc"

Expected: 👍 accept · Size: 627 B · Lines: 16 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Level equality: max is associative (max (max u v) w ≈ max u (max v w)).

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 11.7 M · max rss memory: 7.4 MB

stderr:
summary: 1/1 decls checked, peak 32 MB, allocated 0 MB, heartbeats 0
checked in 0.000425s

Test "tutorial/023_levelMaxIdem"

Expected: 👍 accept · Size: 451 B · Lines: 9 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Level equality: max is idempotent (max u u ≈ u).

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 11.6 M · max rss memory: 7.4 MB

stderr:
summary: 1/1 decls checked, peak 32 MB, allocated 0 MB, heartbeats 0
checked in 0.000332s

Test "tutorial/024_levelMaxAbsorb"

Expected: 👍 accept · Size: 530 B · Lines: 12 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Level equality: max absorption (max u (max u v) ≈ max u v).

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 11.6 M · max rss memory: 7.4 MB

stderr:
summary: 1/1 decls checked, peak 32 MB, allocated 0 MB, heartbeats 0
checked in 0.000364s

Test "tutorial/025_inferVar"

Expected: 👍 accept · Size: 717 B · Lines: 12 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Type inference of local variables

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 11.7 M · max rss memory: 7.4 MB

stderr:
summary: 1/1 decls checked, peak 32 MB, allocated 0 MB, heartbeats 0
checked in 0.000394s

Test "tutorial/026_defEqLambda"

Expected: 👍 accept · Size: 1.4 KB · Lines: 26 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Definitional equality between lambdas

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 11.8 M · max rss memory: 7.4 MB

stderr:
summary: 1/1 decls checked, peak 32 MB, allocated 0 MB, heartbeats 0
checked in 0.000396s

Test "tutorial/027_peano1"

Expected: 👍 accept · Size: 3.6 KB · Lines: 73 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Peano arithmetic: 2 = 2

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 12.1 M · max rss memory: 7.5 MB

stderr:
summary: 7/7 decls checked, peak 32 MB, allocated 0 MB, heartbeats 0
checked in 0.000527s

Test "tutorial/028_peano2"

Expected: 👍 accept · Size: 4.5 KB · Lines: 90 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Peano arithmetic: 1 + 1 = 2

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 12.6 M · max rss memory: 7.5 MB

stderr:
summary: 8/8 decls checked, peak 32 MB, allocated 0 MB, heartbeats 0
checked in 0.000613s

Test "tutorial/029_peano3"

Expected: 👍 accept · Size: 4.9 KB · Lines: 98 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Peano arithmetic: 2 * 2 = 4

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 12.9 M · max rss memory: 7.6 MB

stderr:
summary: 10/10 decls checked, peak 32 MB, allocated 0 MB, heartbeats 0
checked in 0.000741s

Test "tutorial/030_letType"

Expected: 👍 accept · Size: 493 B · Lines: 9 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Type checking a non-dependent let

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 11.6 M · max rss memory: 7.4 MB

stderr:
summary: 1/1 decls checked, peak 32 MB, allocated 0 MB, heartbeats 0
checked in 0.000358s

Test "tutorial/031_letTypeDep"

Expected: 👍 accept · Size: 1.2 KB · Lines: 26 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Type checking a dependent let

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 11.7 M · max rss memory: 7.4 MB

stderr:
summary: 3/3 decls checked, peak 32 MB, allocated 0 MB, heartbeats 0
checked in 0.000396s

Test "tutorial/032_letRed"

Expected: 👍 accept · Size: 631 B · Lines: 12 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Reducing a let

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 11.7 M · max rss memory: 7.4 MB

stderr:
summary: 2/2 decls checked, peak 32 MB, allocated 0 MB, heartbeats 0
checked in 0.000330s

Test "tutorial/033_empty"

Expected: 👍 accept · Size: 1.2 KB · Lines: 20 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

A simple empty inductive type

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 11.8 M · max rss memory: 7.4 MB

stderr:
summary: 3/3 decls checked, peak 32 MB, allocated 0 MB, heartbeats 0
checked in 0.000422s

Test "tutorial/034_boolType"

Expected: 👍 accept · Size: 2.3 KB · Lines: 37 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

A simple enumeration inductive type

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 11.8 M · max rss memory: 7.4 MB

stderr:
summary: 5/5 decls checked, peak 32 MB, allocated 0 MB, heartbeats 0
checked in 0.000503s

Test "tutorial/035_twoBool"

Expected: 👍 accept · Size: 4.2 KB · Lines: 65 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

A simple product type

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 11.9 M · max rss memory: 7.4 MB

stderr:
summary: 8/8 decls checked, peak 32 MB, allocated 0 MB, heartbeats 0
checked in 0.000535s

Test "tutorial/036_andType"

Expected: 👍 accept · Size: 3.2 KB · Lines: 57 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

A parametrized product type (no level parameters)

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 11.8 M · max rss memory: 7.4 MB

stderr:
summary: 4/4 decls checked, peak 32 MB, allocated 0 MB, heartbeats 0
checked in 0.000430s

Test "tutorial/037_prodType"

Expected: 👍 accept · Size: 3.8 KB · Lines: 76 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

A parametrized product type (with level parameters)

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 11.9 M · max rss memory: 7.4 MB

stderr:
summary: 4/4 decls checked, peak 32 MB, allocated 0 MB, heartbeats 0
checked in 0.000438s

Test "tutorial/038_pprodType"

Expected: 👍 accept · Size: 3.8 KB · Lines: 75 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

A parametrized product type (with more general level parameters)

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 11.9 M · max rss memory: 7.4 MB

stderr:
summary: 4/4 decls checked, peak 32 MB, allocated 0 MB, heartbeats 0
checked in 0.000555s

Test "tutorial/039_pUnitType"

Expected: 👍 accept · Size: 1.8 KB · Lines: 31 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Level-polymorphic unit type

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 11.7 M · max rss memory: 7.4 MB

stderr:
summary: 4/4 decls checked, peak 32 MB, allocated 0 MB, heartbeats 0
checked in 0.000457s

Test "tutorial/040_eqType"

Expected: 👍 accept · Size: 3.2 KB · Lines: 62 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Equality, as an important indexed non-recursive data type

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 11.9 M · max rss memory: 7.4 MB

stderr:
summary: 4/4 decls checked, peak 32 MB, allocated 0 MB, heartbeats 0
checked in 0.000437s

Test "tutorial/041_natDef"

Expected: 👍 accept · Size: 3.3 KB · Lines: 61 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

A recursive inductive data type

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 11.8 M · max rss memory: 7.4 MB

stderr:
summary: 5/5 decls checked, peak 32 MB, allocated 0 MB, heartbeats 0
checked in 0.000402s

Test "tutorial/042_rbTreeDef"

Expected: 👍 accept · Size: 15.7 KB · Lines: 296 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

A recursive indexed data type

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 12.8 M · max rss memory: 7.6 MB

stderr:
summary: 14/14 decls checked, peak 32 MB, allocated 0 MB, heartbeats 0
checked in 0.000652s

Test "tutorial/043_inductBadNonSort"

Expected: ✋ reject · Size: 1.2 KB · Lines: 20 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

An inductive type with a non-sort type

Test result: ✋ rejected · exit code 1 · wall time: 6 ms · instructions: 11.7 M · max rss memory: 7.4 MB

stderr:
inductive inductBadNonSort : constType
                             ^^^^^^^^^
                             has type
                               Type → Type → Type
                             but is expected to be a Sort (Type or Prop)
summary: 2/2 decls checked, peak 32 MB, allocated 0 MB, heartbeats 0
checked in 0.000448s

Test "tutorial/044_inductBadNonSort2"

Expected: ✋ reject · Size: 602 B · Lines: 8 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Another inductive type with a non-sort type

Test result: ✋ rejected · exit code 1 · wall time: 6 ms · instructions: 11.7 M · max rss memory: 7.4 MB

stderr:
inductive inductBadNonSort2 : aType
                              ^^^^^
                              has type
                                Type
                              but is expected to be a Sort (Type or Prop)
summary: 2/2 decls checked, peak 32 MB, allocated 0 MB, heartbeats 0
checked in 0.000415s

Test "tutorial/045_inductLevelParam"

Expected: ✋ reject · Size: 519 B · Lines: 7 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

An inductive with duplicate level params

Test result: ✋ rejected · exit code 1 · wall time: 6 ms · instructions: 11.6 M · max rss memory: 7.2 MB

stderr:
Invalid declaration inductLevelParam.{u, u}: duplicate level parameter u

summary: 0/0 decls checked, peak 32 MB, allocated 0 MB, heartbeats 0
checked in 0.000270s

Test "tutorial/046_inductTooFewParams"

Expected: ✋ reject · Size: 552 B · Lines: 6 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

An inductive with too few parameters in the type

Test result: ✋ rejected · exit code 1 · wall time: 6 ms · instructions: 11.7 M · max rss memory: 7.4 MB

stderr:
inductive inductTooFewParams : Prop → Prop
                               ^^^^^^^^^^^
                               has type
                                 Prop
                               but is expected to be a Sort (Type or Prop)
summary: 1/1 decls checked, peak 32 MB, allocated 0 MB, heartbeats 0
checked in 0.000397s

Test "tutorial/047_inductWrongCtorParams"

Expected: ✋ reject · Size: 1.2 KB · Lines: 16 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

An inductive with a constructor with wrong parameters

Test result: ✋ rejected · exit code 1 · wall time: 6 ms · instructions: 11.7 M · max rss memory: 7.4 MB

stderr:
inductive inductWrongCtorParams : Prop → Type
| mk : Type → inductWrongCtorParams aProp
       ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
       invalid return type
summary: 4/4 decls checked, peak 32 MB, allocated 0 MB, heartbeats 0
checked in 0.000405s

Test "tutorial/048_inductWrongCtorResParams"

Expected: ✋ reject · Size: 1.3 KB · Lines: 19 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

An inductive with a constructor with wrong parameters in result (they are swapped)

Test result: ✋ rejected · exit code 1 · wall time: 6 ms · instructions: 11.8 M · max rss memory: 7.4 MB

stderr:
inductive inductWrongCtorResParams : Prop → Prop → Type
| mk : (x : Prop) → (y : Prop) → inductWrongCtorResParams y x
       ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
       invalid return type
summary: 3/3 decls checked, peak 32 MB, allocated 0 MB, heartbeats 0
checked in 0.000407s

Test "tutorial/049_inductWrongCtorResLevel"

Expected: ✋ reject · Size: 1.4 KB · Lines: 23 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

An inductive with a constructor with wrong level parameters in result (they are swapped)

Test result: ✋ rejected · exit code 1 · wall time: 6 ms · instructions: 11.8 M · max rss memory: 7.4 MB

stderr:
inductive inductWrongCtorResLevel.{u1, u2} : Prop → Prop → Type
| mk : (x : Prop) → (y : Prop) → inductWrongCtorResLevel.{u2, u1} x y
       ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
       invalid return type
summary: 3/3 decls checked, peak 32 MB, allocated 0 MB, heartbeats 0
checked in 0.000499s

Test "tutorial/050_inductInIndex"

Expected: ✋ reject · Size: 1.1 KB · Lines: 14 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

A constructor with an unexpected occurrence of the type in index position of a return type.

Test result: ✋ rejected · exit code 1 · wall time: 6 ms · instructions: 11.7 M · max rss memory: 7.4 MB

stderr:
inductive inductInIndex : Prop → Prop
| mk : inductInIndex (inductInIndex aProp)
       ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
       invalid return type
summary: 4/4 decls checked, peak 32 MB, allocated 0 MB, heartbeats 0
checked in 0.000459s

Test "tutorial/051_indNeg"

Expected: ✋ reject · Size: 1000 B · Lines: 12 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

The classic example of an inductive with negative recursive occurrence

Test result: ✋ rejected · exit code 1 · wall time: 6 ms · instructions: 11.7 M · max rss memory: 7.4 MB

stderr:
inductive indNeg : Type
| mk : (indNeg → indNeg) → indNeg
        ^^^^^^^^^^^^^^^
        arg #1 has a non-positive occurrence of the datatype being declared
summary: 3/3 decls checked, peak 32 MB, allocated 0 MB, heartbeats 0
checked in 0.000372s

Test "tutorial/052_reduceCtorParam.mk"

Expected: 👍 accept · Size: 4.1 KB · Lines: 80 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

When checking inductives, we expect the kernel to reduce the types of constructor arguments.

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 12.0 M · max rss memory: 7.5 MB

stderr:
summary: 5/5 decls checked, peak 32 MB, allocated 0 MB, heartbeats 0
checked in 0.000491s

Test "tutorial/053_reduceCtorType.mk"

Expected: ✋ reject · Size: 1.5 KB · Lines: 26 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

When checking inductives, we expect the kernel to not reduce the type of the constructor itself; that should be all manifest foralls

Test result: ✋ rejected · exit code 1 · wall time: 6 ms · instructions: 11.8 M · max rss memory: 7.4 MB

stderr:
inductive reduceCtorType : Type
| mk : id reduceCtorType
       ^^^^^^^^^^^^^^^^^
       invalid return type
summary: 4/4 decls checked, peak 32 MB, allocated 0 MB, heartbeats 0
checked in 0.000428s

Test "tutorial/054_indNegReducible"

Expected: ✋ reject · Size: 1.9 KB · Lines: 31 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

When checking inductives, we expect the kernel to not reduce the type of the constructor parameters further than head normal form. Recursive occurrences nested inside the head normal form are considered negative occurrences, even if they could be reduced to disappear.

Test result: ✋ rejected · exit code 1 · wall time: 6 ms · instructions: 11.8 M · max rss memory: 7.4 MB

stderr:
inductive indNegReducible : Type
| mk : (constType aType indNegReducible → indNegReducible) → indNegReducible
        ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
        arg #1 has a non-positive occurrence of the datatype being declared
summary: 5/5 decls checked, peak 32 MB, allocated 0 MB, heartbeats 0
checked in 0.000430s

Test "tutorial/055_predWithTypeField"

Expected: 👍 accept · Size: 2.0 KB · Lines: 32 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

An inductive proposition can have constructors with fields of arbitrary level.

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 11.7 M · max rss memory: 7.4 MB

stderr:
summary: 4/4 decls checked, peak 32 MB, allocated 0 MB, heartbeats 0
checked in 0.000422s

Test "tutorial/056_typeWithTypeField"

Expected: 👍 accept · Size: 2.1 KB · Lines: 36 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

An inductive type can have fields of level up to that of the inductive.

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 11.7 M · max rss memory: 7.4 MB

stderr:
summary: 4/4 decls checked, peak 32 MB, allocated 0 MB, heartbeats 0
checked in 0.000415s

Test "tutorial/057_typeWithTypeFieldPoly"

Expected: 👍 accept · Size: 2.1 KB · Lines: 38 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

An inductive type can have fields of level up to that of the inductive (polymorphic variant).

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 11.8 M · max rss memory: 7.4 MB

stderr:
summary: 4/4 decls checked, peak 32 MB, allocated 0 MB, heartbeats 0
checked in 0.000412s

Test "tutorial/058_typeWithTooHighTypeField.mk"

Expected: ✋ reject · Size: 947 B · Lines: 11 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

An inductive type can have fields of from higher universes.

Test result: ✋ rejected · exit code 1 · wall time: 6 ms · instructions: 11.7 M · max rss memory: 7.4 MB

stderr:
inductive typeWithTooHighTypeField : Type
| mk : Type → typeWithTooHighTypeField
       ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
       has field of type
         Type
       at universe level 2, but the inductive is at universe level 1
summary: 3/3 decls checked, peak 32 MB, allocated 0 MB, heartbeats 0
checked in 0.000363s

Test "tutorial/059_emptyRec"

Expected: 👍 accept · Size: 1.2 KB · Lines: 21 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Asserting the type of the generated recursor

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 11.7 M · max rss memory: 7.4 MB

stderr:
summary: 3/3 decls checked, peak 32 MB, allocated 0 MB, heartbeats 0
checked in 0.000364s

Test "tutorial/060_boolRec"

Expected: 👍 accept · Size: 3.0 KB · Lines: 53 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Asserting the type of the generated recursor

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 11.9 M · max rss memory: 7.4 MB

stderr:
summary: 5/5 decls checked, peak 32 MB, allocated 0 MB, heartbeats 0
checked in 0.000453s

Test "tutorial/061_twoBoolRec"

Expected: 👍 accept · Size: 4.8 KB · Lines: 78 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Asserting the type of the generated recursor

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 12.1 M · max rss memory: 7.5 MB

stderr:
summary: 8/8 decls checked, peak 32 MB, allocated 0 MB, heartbeats 0
checked in 0.000504s

Test "tutorial/062_andRec"

Expected: 👍 accept · Size: 3.2 KB · Lines: 58 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Asserting the type of the generated recursor

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 11.9 M · max rss memory: 7.5 MB

stderr:
summary: 4/4 decls checked, peak 32 MB, allocated 0 MB, heartbeats 0
checked in 0.000493s

Test "tutorial/063_prodRec"

Expected: 👍 accept · Size: 4.0 KB · Lines: 79 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Asserting the type of the generated recursor

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 12.2 M · max rss memory: 7.5 MB

stderr:
summary: 4/4 decls checked, peak 32 MB, allocated 0 MB, heartbeats 0
checked in 0.000635s

Test "tutorial/064_pprodRec"

Expected: 👍 accept · Size: 4.0 KB · Lines: 78 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Asserting the type of the generated recursor

Test result: 👍 accepted · exit code 0 · wall time: 17 ms · instructions: 12.2 M · max rss memory: 7.5 MB

stderr:
summary: 4/4 decls checked, peak 32 MB, allocated 0 MB, heartbeats 0
checked in 0.000624s

Test "tutorial/065_punitRec"

Expected: 👍 accept · Size: 2.2 KB · Lines: 39 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Asserting the type of the generated recursor

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 11.8 M · max rss memory: 7.4 MB

stderr:
summary: 4/4 decls checked, peak 32 MB, allocated 0 MB, heartbeats 0
checked in 0.000375s

Test "tutorial/066_eqRec"

Expected: 👍 accept · Size: 3.3 KB · Lines: 63 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Asserting the type of the generated recursor

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 12.0 M · max rss memory: 7.5 MB

stderr:
summary: 4/4 decls checked, peak 32 MB, allocated 0 MB, heartbeats 0
checked in 0.000364s

Test "tutorial/067_nRec"

Expected: 👍 accept · Size: 3.3 KB · Lines: 61 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Asserting the type of the generated recursor

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 11.9 M · max rss memory: 7.4 MB

stderr:
summary: 5/5 decls checked, peak 32 MB, allocated 0 MB, heartbeats 0
checked in 0.000333s

Test "tutorial/068_rbTreeRef"

Expected: 👍 accept · Size: 16.2 KB · Lines: 303 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Asserting the type of the generated recursor

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 13.9 M · max rss memory: 7.9 MB

stderr:
summary: 14/14 decls checked, peak 32 MB, allocated 0 MB, heartbeats 0
checked in 0.000833s

Test "tutorial/069_boolPropRec"

Expected: 👍 accept · Size: 2.3 KB · Lines: 34 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Inductive predicates eliminate into Prop if they have more than one constructor.

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 11.8 M · max rss memory: 7.4 MB

stderr:
summary: 5/5 decls checked, peak 32 MB, allocated 0 MB, heartbeats 0
checked in 0.000317s

Test "tutorial/070_existsRec"

Expected: 👍 accept · Size: 3.6 KB · Lines: 66 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Inductive predicates eliminate into Prop if they have one constructors and it carries data.

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 12.0 M · max rss memory: 7.5 MB

stderr:
summary: 4/4 decls checked, peak 32 MB, allocated 0 MB, heartbeats 0
checked in 0.000384s

Test "tutorial/071_sortElimPropRec"

Expected: 👍 accept · Size: 5.6 KB · Lines: 97 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Inductive predicates eliminate into Sort if they have one constructors and it carries data, but the data is known from the type, e.g. a parameter or an index

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 12.2 M · max rss memory: 7.5 MB

stderr:
summary: 8/8 decls checked, peak 32 MB, allocated 0 MB, heartbeats 0
checked in 0.000427s

Test "tutorial/072_sortElimProp2Rec"

Expected: 👍 accept · Size: 6.6 KB · Lines: 114 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Inductive predicates eliminate into Sort if they have one constructors and it carries data, but the data is known from the type, e.g. a parameter or an index. However, it must occur directly in the result type, with no intervening reduction.

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 12.5 M · max rss memory: 7.5 MB

stderr:
summary: 9/9 decls checked, peak 32 MB, allocated 0 MB, heartbeats 0
checked in 0.000561s

Test "tutorial/073_boolRecEqns"

Expected: 👍 accept · Size: 10.8 KB · Lines: 199 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Reduction behavior of Bool.rec

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 13.2 M · max rss memory: 7.8 MB

stderr:
summary: 11/11 decls checked, peak 32 MB, allocated 0 MB, heartbeats 0
checked in 0.000729s

Test "tutorial/074_prodRecEqns"

Expected: 👍 accept · Size: 10.1 KB · Lines: 205 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Reduction behavior of Prod.rec

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 14.0 M · max rss memory: 7.9 MB

stderr:
summary: 7/7 decls checked, peak 32 MB, allocated 0 MB, heartbeats 0
checked in 0.000920s

Test "tutorial/075_nRecReduction"

Expected: 👍 accept · Size: 12.7 KB · Lines: 238 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

A proof relying on the reduction behavior of N.rec

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 13.5 M · max rss memory: 7.8 MB

stderr:
summary: 13/13 decls checked, peak 32 MB, allocated 0 MB, heartbeats 0
checked in 0.000818s

Test "tutorial/076_listRecReduction"

Expected: 👍 accept · Size: 17.5 KB · Lines: 335 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Reduction behavior of List.rec

Test result: 👍 accepted · exit code 0 · wall time: 7 ms · instructions: 16.0 M · max rss memory: 8.2 MB

stderr:
summary: 14/14 decls checked, peak 32 MB, allocated 0 MB, heartbeats 0
checked in 0.001391s

Test "tutorial/077_RBTree.id_spec"

Expected: 👍 accept · Size: 47.9 KB · Lines: 1.0 k · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Reduction behavior of RBTree.rec

Test result: 👍 accepted · exit code 0 · wall time: 10 ms · instructions: 28.7 M · max rss memory: 11.2 MB

stderr:
summary: 19/19 decls checked, peak 32 MB, allocated 0 MB, heartbeats 0
checked in 0.003924s

Test "tutorial/078_And.right"

Expected: 👍 accept · Size: 4.3 KB · Lines: 74 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Type-checking simple projection functions

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 12.1 M · max rss memory: 7.5 MB

stderr:
summary: 5/5 decls checked, peak 32 MB, allocated 0 MB, heartbeats 0
checked in 0.000532s

Test "tutorial/079_Prod.snd"

Expected: 👍 accept · Size: 4.5 KB · Lines: 83 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Type-checking projection functions with parameters

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 12.2 M · max rss memory: 7.5 MB

stderr:
summary: 5/5 decls checked, peak 32 MB, allocated 0 MB, heartbeats 0
checked in 0.000567s

Test "tutorial/080_PProd.snd"

Expected: 👍 accept · Size: 4.5 KB · Lines: 83 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Type-checking projection functions

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 12.2 M · max rss memory: 7.5 MB

stderr:
summary: 5/5 decls checked, peak 32 MB, allocated 0 MB, heartbeats 0
checked in 0.000518s

Test "tutorial/081_PSigma.snd"

Expected: 👍 accept · Size: 5.1 KB · Lines: 96 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Type-checking dependent projection functions

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 12.4 M · max rss memory: 7.5 MB

stderr:
summary: 5/5 decls checked, peak 32 MB, allocated 0 MB, heartbeats 0
checked in 0.000629s

Test "tutorial/082_projOutOfRange"

Expected: ✋ reject · Size: 3.8 KB · Lines: 67 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Out of range projection

Test result: ✋ rejected · exit code 1 · wall time: 6 ms · instructions: 12.1 M · max rss memory: 7.5 MB

stderr:
def projOutOfRange : ∀ (x : Prop), ∀ (x : Prop), And x x → x :=
  fun x y z ↦ z.2
  ^^^^^^^^^^^^^^^
  invalid projection And.2: And has only 2 fields
summary: 4/4 decls checked, peak 32 MB, allocated 0 MB, heartbeats 0
checked in 0.000493s

Test "tutorial/083_projNotStruct"

Expected: ✋ reject · Size: 3.5 KB · Lines: 64 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Projection out something that is not a structure

Test result: ✋ rejected · exit code 1 · wall time: 6 ms · instructions: 11.9 M · max rss memory: 7.4 MB

stderr:
def projNotStruct : N → N :=
  fun x ↦ x.0
          ^^^
          N is not a structure (it has 2 constructors)
summary: 5/5 decls checked, peak 32 MB, allocated 0 MB, heartbeats 0
checked in 0.000477s

Test "tutorial/084_projProp1"

Expected: 👍 accept · Size: 8.2 KB · Lines: 143 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Projecting out of a proposition

The lean kernel allows projections out of propositions if they precede all dependent data fields.

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 12.3 M · max rss memory: 7.5 MB

stderr:
summary: 10/10 decls checked, peak 32 MB, allocated 0 MB, heartbeats 0
checked in 0.000490s

Test "tutorial/085_projProp2"

Expected: ✋ reject · Size: 8.2 KB · Lines: 143 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Projecting out of a proposition

The lean kernel disallows data projections out of propositional structures.

Test result: ✋ rejected · exit code 1 · wall time: 6 ms · instructions: 12.4 M · max rss memory: 7.5 MB

stderr:
def projProp2 : PropStructure.{0, 1} → PUnit.{1} :=
  fun x ↦ x.someData
          ^^^^^^^^^^
          cannot project a non-propositional field from a propositional structure
summary: 10/10 decls checked, peak 32 MB, allocated 0 MB, heartbeats 0
checked in 0.000590s

Test "tutorial/086_projProp3"

Expected: 👍 accept · Size: 8.2 KB · Lines: 143 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Projecting out of a proposition

The lean kernel allows projections out of propositions if they precede all dependent data fields. Non-dependent data fields are not relevant.

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 12.3 M · max rss memory: 7.5 MB

stderr:
summary: 10/10 decls checked, peak 32 MB, allocated 0 MB, heartbeats 0
checked in 0.000603s

Test "tutorial/087_projProp4"

Expected: ✋ reject · Size: 8.2 KB · Lines: 143 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Projecting out of a proposition

The lean kernel disallows data projections out of propositional structures.

Test result: ✋ rejected · exit code 1 · wall time: 6 ms · instructions: 12.4 M · max rss memory: 7.5 MB

stderr:
def projProp4 : PropStructure.{0, 1} → PUnit.{1} :=
  fun x ↦ x.someMoreData
          ^^^^^^^^^^^^^^
          cannot project a non-propositional field from a propositional structure
summary: 10/10 decls checked, peak 32 MB, allocated 0 MB, heartbeats 0
checked in 0.000543s

Test "tutorial/088_projProp5"

Expected: ✋ reject · Size: 8.4 KB · Lines: 148 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Projecting out of a proposition

The lean kernel disallows proof projections out of propositional structures that depend on data.

Test result: ✋ rejected · exit code 1 · wall time: 6 ms · instructions: 12.4 M · max rss memory: 7.5 MB

stderr:
def projProp5 : ∀ (x : PropStructure.{0, 1}), Eq x.someMoreData x.someMoreData :=
                                                 ^^^^^^^^^^^^^^
                                                 cannot project a non-propositional field from a propositional structure
summary: 10/10 decls checked, peak 32 MB, allocated 0 MB, heartbeats 0
checked in 0.000603s

Test "tutorial/089_projProp6"

Expected: ✋ reject · Size: 8.2 KB · Lines: 143 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Projecting out of a proposition.

The lean kernel rejects any projections out of a proposition that come after a dependent data field, even if that is not used by the present projection.

Test result: ✋ rejected · exit code 1 · wall time: 6 ms · instructions: 12.3 M · max rss memory: 7.5 MB

stderr:
def projProp6 : PropStructure.{0, 1} → PUnit.{0} :=
  fun x ↦ x.aFinalProof
          ^^^^^^^^^^^^^
          cannot project a non-propositional field from a propositional structure
summary: 10/10 decls checked, peak 32 MB, allocated 0 MB, heartbeats 0
checked in 0.000549s

Test "tutorial/090_projDataIndexRec"

Expected: 👍 accept · Size: 6.8 KB · Lines: 111 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

The recursor for ProjDataIndex allows elimination into sort.

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 12.2 M · max rss memory: 7.5 MB

stderr:
summary: 11/11 decls checked, peak 32 MB, allocated 0 MB, heartbeats 0
checked in 0.000518s

Test "tutorial/091_projIndexData"

Expected: ✋ reject · Size: 6.8 KB · Lines: 111 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Projecting out data is not allowed, even if this data appears as an index and the recursor would allow it.

Test result: ✋ rejected · exit code 1 · wall time: 6 ms · instructions: 12.2 M · max rss memory: 7.5 MB

stderr:
def projIndexData : (x : N) → ProjDataIndex x → N :=
  fun x x ↦ x.0
  ^^^^^^^^^^^^^
  invalid projection PropStructure.0: unknown structure PropStructure
summary: 11/11 decls checked, peak 32 MB, allocated 0 MB, heartbeats 0
checked in 0.000507s

Test "tutorial/092_projIndexData2"

Expected: ✋ reject · Size: 6.8 KB · Lines: 111 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Projecting out data is not allowed, even if this data appears as an index and the recursor would allow it.

This also forbids projecting out proofs that follow such fields.

Test result: ✋ rejected · exit code 1 · wall time: 6 ms · instructions: 12.2 M · max rss memory: 7.5 MB

stderr:
def projIndexData2 : ∀ (x : N), ProjDataIndex x → True :=
  fun x x ↦ x.1
  ^^^^^^^^^^^^^
  invalid projection PropStructure.1: unknown structure PropStructure
summary: 11/11 decls checked, peak 32 MB, allocated 0 MB, heartbeats 0
checked in 0.000539s

Test "tutorial/093_projRed"

Expected: 👍 accept · Size: 9.9 KB · Lines: 177 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Projection reductions

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 12.7 M · max rss memory: 7.6 MB

stderr:
summary: 13/13 decls checked, peak 32 MB, allocated 0 MB, heartbeats 0
checked in 0.000679s

Test "tutorial/094_ruleK"

Expected: 👍 accept · Size: 6.5 KB · Lines: 121 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Rule k for Eq: The recursor reduces even if the major argument is not a constructor, as long replacing the major argument with a constructor is type correct.

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 12.4 M · max rss memory: 7.5 MB

stderr:
summary: 8/8 decls checked, peak 32 MB, allocated 0 MB, heartbeats 0
checked in 0.000551s

Test "tutorial/095_ruleKbad"

Expected: ✋ reject · Size: 6.5 KB · Lines: 121 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Rule k for Eq should not fire if the types of the major argument do not match that of the constructor.

Test result: ✋ rejected · exit code 1 · wall time: 6 ms · instructions: 12.6 M · max rss memory: 7.6 MB

stderr:
theorem ruleKbad : ∀ (h : Eq Bool.true Bool.false), ∀ (a : Bool), Eq (Eq.rec a h) a := fun x a ↦ Eq.refl a
                                                                                       ^^^^^^^^^^^^^^^^^^^
                                                                                       has type
                                                                                         Eq Bool.true Bool.false → ∀ (a : Bool), Eq a a
                                                                                       but is expected to have type
                                                                                         ∀ (h : Eq Bool.true Bool.false), ∀ (a : Bool), Eq (Eq.rec a h) a
summary: 8/8 decls checked, peak 32 MB, allocated 0 MB, heartbeats 0
checked in 0.000686s

Test "tutorial/096_ruleKAcc"

Expected: ✋ reject · Size: 12.8 KB · Lines: 238 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Rule k should not fire for Acc.

Test result: ✋ rejected · exit code 1 · wall time: 7 ms · instructions: 14.9 M · max rss memory: 8.1 MB

stderr:
theorem ruleKAcc.{u} : ∀ (α : Sort u), ∀ (p : ∀ (a : α), ∀ (a : α), Prop), ∀ (x : α), ∀ (h : Acc p x), ∀ (a : Bool), Eq (Acc.rec (fun x x x ↦ a) h) a := fun α p x h a ↦ Eq.refl a
                                                                                                                                                         ^^^^^^^^^^^^^^^^^^^^^^^^^
                                                                                                                                                         has type
                                                                                                                                                           ∀ (α : Sort u), ∀ (p : ∀ (a : α), ∀ (a : α), Prop), ∀ (x : α), Acc p x → ∀ (a : Bool), Eq a a
                                                                                                                                                         but is expected to have type
                                                                                                                                                           ∀ (α : Sort u), ∀ (p : ∀ (a : α), ∀ (a : α), Prop), ∀ (x : α), ∀ (h : Acc p x), ∀ (a : Bool), Eq (Acc.rec (fun x x x ↦ a) h) a
summary: 11/11 decls checked, peak 32 MB, allocated 0 MB, heartbeats 0
checked in 0.001166s

Test "tutorial/097_aNatLit"

Expected: 👍 accept · Size: 3.0 KB · Lines: 54 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Type checking Nat literals

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 11.8 M · max rss memory: 7.4 MB

stderr:
summary: 5/5 decls checked, peak 32 MB, allocated 0 MB, heartbeats 0
checked in 0.000393s

Test "tutorial/098_natLitEq"

Expected: 👍 accept · Size: 6.1 KB · Lines: 114 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Reducing Nat literals

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 12.1 M · max rss memory: 7.5 MB

stderr:
summary: 8/8 decls checked, peak 32 MB, allocated 0 MB, heartbeats 0
checked in 0.000512s

Test "tutorial/099_proofIrrelevance"

Expected: 👍 accept · Size: 5.0 KB · Lines: 100 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Proof irrelevance: every Prop is a subsingleton, if p : Prop then all elements of p are definitionally equal.

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 12.2 M · max rss memory: 7.5 MB

stderr:
summary: 5/5 decls checked, peak 32 MB, allocated 0 MB, heartbeats 0
checked in 0.000541s

Test "tutorial/100_proofIrrelevanceBad"

Expected: ✋ reject · Size: 4.7 KB · Lines: 93 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Proof irrelevance is limited to Prop: if p : Type, then all elements of p are not definitionally equal.

Test result: ✋ rejected · exit code 1 · wall time: 6 ms · instructions: 12.3 M · max rss memory: 7.5 MB

stderr:
def proofIrrelevanceBad : ∀ (p : Type), ∀ (h1 : p), ∀ (h2 : p), Eq h1 h2 :=
  fun p h1 h2 ↦ rfl
  ^^^^^^^^^^^^^^^^^
  has type
    ∀ (p : Type), ∀ (h1 : p), ∀ (h2 : p), Eq h1 h1
  but is expected to have type
    ∀ (p : Type), ∀ (h1 : p), ∀ (h2 : p), Eq h1 h2
summary: 5/5 decls checked, peak 32 MB, allocated 0 MB, heartbeats 0
checked in 0.000584s

Test "tutorial/101_proofIrrelevanceWhnf"

Expected: 👍 accept · Size: 5.6 KB · Lines: 112 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Proof irrelevance: if p : A and A is definitionally equal to Prop, then all elements of p are still definitionally equal. Just applying proof irrelevance at Sort 0 isn't sufficient.

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 12.3 M · max rss memory: 7.5 MB

stderr:
summary: 6/6 decls checked, peak 32 MB, allocated 0 MB, heartbeats 0
checked in 0.000565s

Test "tutorial/102_unitEta1"

Expected: 👍 accept · Size: 6.2 KB · Lines: 116 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Unit eta

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 12.2 M · max rss memory: 7.5 MB

stderr:
summary: 9/9 decls checked, peak 32 MB, allocated 0 MB, heartbeats 0
checked in 0.000554s

Test "tutorial/103_unitEta2"

Expected: 👍 accept · Size: 6.0 KB · Lines: 109 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Unit eta

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 12.2 M · max rss memory: 7.5 MB

stderr:
summary: 8/8 decls checked, peak 32 MB, allocated 0 MB, heartbeats 0
checked in 0.000635s

Test "tutorial/104_unitEta3"

Expected: 👍 accept · Size: 6.0 KB · Lines: 111 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Unit eta

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 12.3 M · max rss memory: 7.5 MB

stderr:
summary: 8/8 decls checked, peak 32 MB, allocated 0 MB, heartbeats 0
checked in 0.000525s

Test "tutorial/105_structEta"

Expected: 👍 accept · Size: 12.5 KB · Lines: 230 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Structure eta

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 13.8 M · max rss memory: 7.9 MB

stderr:
summary: 13/13 decls checked, peak 32 MB, allocated 0 MB, heartbeats 0
checked in 0.000867s

Test "tutorial/106_funEta"

Expected: 👍 accept · Size: 5.2 KB · Lines: 104 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Function eta for non-dependent functions.

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 12.4 M · max rss memory: 7.5 MB

stderr:
summary: 5/5 decls checked, peak 32 MB, allocated 0 MB, heartbeats 0
checked in 0.000590s

Test "tutorial/107_funEtaDep"

Expected: 👍 accept · Size: 5.3 KB · Lines: 106 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Function eta for dependent functions (pi types).

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 12.4 M · max rss memory: 7.5 MB

stderr:
summary: 5/5 decls checked, peak 32 MB, allocated 0 MB, heartbeats 0
checked in 0.000542s

Test "tutorial/108_funEtaBad"

Expected: ✋ reject · Size: 4.9 KB · Lines: 97 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Eta should not identify functions with different bodies.

Test result: ✋ rejected · exit code 1 · wall time: 6 ms · instructions: 12.6 M · max rss memory: 7.6 MB

stderr:
theorem funEtaBad : ∀ (α : Type), ∀ (β : Type), ∀ (g : α → α), ∀ (f : α → β), Eq (fun x ↦ f (g x)) f := fun x x x f ↦ Eq.refl f
                                                                                                        ^^^^^^^^^^^^^^^^^^^^^^^
                                                                                                        has type
                                                                                                          ∀ (x : Type), ∀ (x : Type), ∀ (x : x → x), ∀ (f : x → x), Eq f f
                                                                                                        but is expected to have type
                                                                                                          ∀ (α : Type), ∀ (β : Type), ∀ (g : α → α), ∀ (f : α → β), Eq (fun x ↦ f (g x)) f
summary: 4/4 decls checked, peak 32 MB, allocated 0 MB, heartbeats 0
checked in 0.000673s

Test "tutorial/109_etaRuleK"

Expected: ✋ reject · Size: 6.5 KB · Lines: 121 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Corner case for function eta: Does a defeq between a partially applied recursor with rule k and a free variable trigger eta expansion?

Taking the official kernel as the specification, the answer is no. See https://github.com/leanprover/lean4/issues/12520 for a discussion.

Test result: ✋ rejected · exit code 1 · wall time: 7 ms · instructions: 12.7 M · max rss memory: 7.6 MB

stderr:
def etaRuleK : ∀ (a : Eq Bool.true Bool.true → Bool), Eq (Eq.rec (a (Eq.refl Bool.true))) a :=
  fun a ↦ Eq.refl a
  ^^^^^^^^^^^^^^^^^
  has type
    ∀ (a : Eq Bool.true Bool.true → Bool), Eq a a
  but is expected to have type
    ∀ (a : Eq Bool.true Bool.true → Bool), Eq (Eq.rec (a (Eq.refl Bool.true))) a
summary: 8/8 decls checked, peak 32 MB, allocated 0 MB, heartbeats 0
checked in 0.000697s

Test "tutorial/110_etaCtor"

Expected: ✋ reject · Size: 9.0 KB · Lines: 148 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Corner case for function eta: Does a defeq between a partially applied constructor trigger eta expansion?

Taking the official kernel as the specification, the answer is no. See https://github.com/leanprover/lean4/issues/12520 for a discussion.

Test result: ✋ rejected · exit code 1 · wall time: 6 ms · instructions: 12.5 M · max rss memory: 7.5 MB

stderr:
def etaCtor : ∀ (x : True → T), Eq (T.mk (T.val (x True.intro))) x :=
  fun x ↦ Eq.refl x
  ^^^^^^^^^^^^^^^^^
  has type
    ∀ (x : True → T), Eq x x
  but is expected to have type
    ∀ (x : True → T), Eq (T.mk (T.val (x True.intro))) x
summary: 15/15 decls checked, peak 32 MB, allocated 0 MB, heartbeats 0
checked in 0.000630s

Test "tutorial/111_reflOccLeft"

Expected: ✋ reject · Size: 3.7 KB · Lines: 61 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Rejection: recursive occurrence on the left of an arrow, behind further arrows inside a constructor argument.

The constructor argument is a function type Nat → (I → Nat).

Test result: ✋ rejected · exit code 1 · wall time: 6 ms · instructions: 11.9 M · max rss memory: 7.4 MB

stderr:
inductive reflOccLeft : Type
| mk : (Nat → reflOccLeft → Nat) → reflOccLeft
        ^^^^^^^^^^^^^^^^^^^^^^^
        arg #1 has a non-positive occurrence of the datatype being declared
summary: 7/7 decls checked, peak 32 MB, allocated 0 MB, heartbeats 0
checked in 0.000455s

Test "tutorial/112_reflOccInIndex"

Expected: ✋ reject · Size: 4.0 KB · Lines: 66 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Rejection: recursive occurrence in index position, behind a further arrow.

We build an indexed inductive I : Type → Type with a constructor argument Nat → I (I α), so the recursive occurrence appears as an index argument.

Test result: ✋ rejected · exit code 1 · wall time: 6 ms · instructions: 12.0 M · max rss memory: 7.5 MB

stderr:
inductive reflOccInIndex : Type → Type
| mk : (α : Type) → ((x : Nat) → reflOccInIndex (reflOccInIndex x)) → reflOccInIndex α
       ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
       constructor declares 1 field but type has 2
summary: 7/7 decls checked, peak 32 MB, allocated 0 MB, heartbeats 0
checked in 0.000487s

Test "tutorial/113_reduceCtorParamRefl.mk"

Expected: 👍 accept · Size: 4.5 KB · Lines: 88 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

When checking inductives, we expect the kernel to reduce the types of constructor arguments in all positive positions.

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 12.0 M · max rss memory: 7.5 MB

stderr:
summary: 5/5 decls checked, peak 32 MB, allocated 0 MB, heartbeats 0
checked in 0.000527s

Test "tutorial/114_reduceCtorParamRefl2.mk"

Expected: 👍 accept · Size: 4.5 KB · Lines: 88 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

When checking inductives, we expect the kernel to reduce the types of constructor arguments in all positive positions.

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 12.0 M · max rss memory: 7.5 MB

stderr:
summary: 5/5 decls checked, peak 32 MB, allocated 0 MB, heartbeats 0
checked in 0.000561s

Test "tutorial/115_rTreeRec"

Expected: 👍 accept · Size: 5.5 KB · Lines: 91 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Asserting the type of the generated recursor.

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 12.1 M · max rss memory: 7.5 MB

stderr:
summary: 9/9 decls checked, peak 32 MB, allocated 0 MB, heartbeats 0
checked in 0.000479s

Test "tutorial/116_rtreeRecReduction"

Expected: 👍 accept · Size: 10.8 KB · Lines: 193 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Reduction behavior of RTree.rec on RTree.mk.

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 13.0 M · max rss memory: 7.6 MB

stderr:
summary: 14/14 decls checked, peak 32 MB, allocated 0 MB, heartbeats 0
checked in 0.000684s

Test "tutorial/117_accRecType"

Expected: 👍 accept · Size: 7.5 KB · Lines: 151 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Asserting the type of Acc.rec.

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 12.5 M · max rss memory: 7.5 MB

stderr:
summary: 4/4 decls checked, peak 32 MB, allocated 0 MB, heartbeats 0
checked in 0.000523s

Test "tutorial/118_accRecReduction"

Expected: 👍 accept · Size: 13.4 KB · Lines: 252 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Acc.rec reduces on Acc.intro.

Test result: 👍 accepted · exit code 0 · wall time: 7 ms · instructions: 15.7 M · max rss memory: 8.2 MB

stderr:
summary: 11/11 decls checked, peak 32 MB, allocated 0 MB, heartbeats 0
checked in 0.001198s

Test "tutorial/119_accRecNoEta"

Expected: ✋ reject · Size: 13.0 KB · Lines: 244 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Acc.rec does not have structure eta.

Test result: ✋ rejected · exit code 1 · wall time: 7 ms · instructions: 14.9 M · max rss memory: 8.1 MB

stderr:
theorem accRecNoEta : ∀ {α : Type}, ∀ (r : ∀ (a : α), ∀ (a : α), Prop), ∀ (a : α), ∀ (h : Acc r a), ∀ (p : Bool), Eq (Acc.rec (fun x x x ↦ p) h) p := fun α r a h p ↦ Eq.refl p
                                                                                                                                                      ^^^^^^^^^^^^^^^^^^^^^^^^^
                                                                                                                                                      has type
                                                                                                                                                        ∀ (α : Type), ∀ (r : ∀ (a : α), ∀ (a : α), Prop), ∀ (a : α), Acc r a → ∀ (p : Bool), Eq p p
                                                                                                                                                      but is expected to have type
                                                                                                                                                        ∀ {α : Type}, ∀ (r : ∀ (a : α), ∀ (a : α), Prop), ∀ (a : α), ∀ (h : Acc r a), ∀ (p : Bool), Eq (Acc.rec (fun x x x ↦ p) h) p
summary: 11/11 decls checked, peak 32 MB, allocated 0 MB, heartbeats 0
checked in 0.001093s

Test "tutorial/120_quotMkType"

Expected: 👍 accept · Size: 6.3 KB · Lines: 123 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Asserting the type of Quot.mk.

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 12.4 M · max rss memory: 7.5 MB

stderr:
summary: 8/8 decls checked, peak 32 MB, allocated 0 MB, heartbeats 0
checked in 0.000490s

Test "tutorial/121_quotIndType"

Expected: 👍 accept · Size: 6.3 KB · Lines: 124 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Asserting the type of Quot.ind.

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 12.4 M · max rss memory: 7.5 MB

stderr:
summary: 8/8 decls checked, peak 32 MB, allocated 0 MB, heartbeats 0
checked in 0.000525s

Test "tutorial/122_quotLiftType"

Expected: 👍 accept · Size: 6.3 KB · Lines: 124 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Asserting the type of Quot.lift.

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 12.5 M · max rss memory: 7.5 MB

stderr:
summary: 8/8 decls checked, peak 32 MB, allocated 0 MB, heartbeats 0
checked in 0.000546s

Test "tutorial/123_quotSoundType"

Expected: 👍 accept · Size: 7.2 KB · Lines: 141 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Asserting the type of Quot.sound.

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 12.6 M · max rss memory: 7.5 MB

stderr:
summary: 9/9 decls checked, peak 32 MB, allocated 0 MB, heartbeats 0
checked in 0.000613s

Test "tutorial/124_quotLiftReduction"

Expected: 👍 accept · Size: 7.8 KB · Lines: 153 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Reduction behavior of Quot.lift on Quot.mk.

Test result: 👍 accepted · exit code 0 · wall time: 7 ms · instructions: 13.6 M · max rss memory: 7.9 MB

stderr:
summary: 8/8 decls checked, peak 32 MB, allocated 0 MB, heartbeats 0
checked in 0.000826s

Test "tutorial/125_quotIndReduction"

Expected: 👍 accept · Size: 7.6 KB · Lines: 151 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Reduction behavior of Quot.ind on Quot.mk.

Test result: 👍 accepted · exit code 0 · wall time: 6 ms · instructions: 13.4 M · max rss memory: 7.8 MB

stderr:
summary: 8/8 decls checked, peak 32 MB, allocated 0 MB, heartbeats 0
checked in 0.000745s

Test "tutorial/126_dup_defs"

Expected: ✋ reject · Size: 479 B · Lines: 7 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Two definitions with the same name

Test result: ✋ rejected · exit code 1 · wall time: 6 ms · instructions: 11.6 M · max rss memory: 7.4 MB

stderr:
Invalid declaration dup_defs: already declared as def dup_defs : Type :=
  Prop

summary: 1/1 decls checked, peak 32 MB, allocated 0 MB, heartbeats 0
checked in 0.000303s

Test "tutorial/127_dup_ind_def"

Expected: ✋ reject · Size: 1.7 KB · Lines: 27 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

A definition and a constructor with the same name

Test result: ✋ rejected · exit code 1 · wall time: 6 ms · instructions: 11.7 M · max rss memory: 7.4 MB

stderr:
expected name index 4, got 8

summary: 1/1 decls checked, peak 32 MB, allocated 0 MB, heartbeats 0
checked in 0.000273s

Test "tutorial/128_dup_ctor_def"

Expected: ✋ reject · Size: 1.7 KB · Lines: 27 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

A definition and a constructor with the same name

Test result: ✋ rejected · exit code 1 · wall time: 6 ms · instructions: 11.6 M · max rss memory: 7.4 MB

stderr:
expected name index 4, got 8

summary: 1/1 decls checked, peak 32 MB, allocated 0 MB, heartbeats 0
checked in 0.000300s

Test "tutorial/129_dup_rec_def"

Expected: ✋ reject · Size: 1.7 KB · Lines: 27 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

A definition and a recursor with the same name

Test result: ✋ rejected · exit code 1 · wall time: 6 ms · instructions: 11.6 M · max rss memory: 7.4 MB

stderr:
expected name index 4, got 8

summary: 1/1 decls checked, peak 32 MB, allocated 0 MB, heartbeats 0
checked in 0.000310s

Test "tutorial/130_misnamed_rec"

Expected: ✋ reject · Size: 1.6 KB · Lines: 25 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

The name of the recursor for misnamed_rec must be misnamed_rec.rec: another name (like misnamed_rec.invalid_rec) should be rejected.

Test result: ✋ rejected · exit code 1 · wall time: 6 ms · instructions: 11.5 M · max rss memory: 7.0 MB

stderr:
expected name index 4, got 7

summary: 0/0 decls checked, peak 32 MB, allocated 0 MB, heartbeats 0
checked in 0.000310s

Test "tutorial/131_dup_rec_def2"

Expected: ✋ reject · Size: 1.7 KB · Lines: 28 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

Even if a kernel doesn't catch a recursor for dup_rec_def2 that is misnamed as dup_rec_def2.not_rec, it should catch some other constant being given the name dup_rec_def2.rec that is reserved for the recursor.

Test result: ✋ rejected · exit code 1 · wall time: 14 ms · instructions: 11.6 M · max rss memory: 7.4 MB

stderr:
expected name index 5, got 9

summary: 1/1 decls checked, peak 32 MB, allocated 0 MB, heartbeats 0
checked in 0.000417s

Test "tutorial/132_dup_ctor_rec"

Expected: ✋ reject · Size: 1.5 KB · Lines: 24 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

A constructor and a recursor with the same name

Test result: ✋ rejected · exit code 1 · wall time: 6 ms · instructions: 11.5 M · max rss memory: 7.0 MB

stderr:
expected name index 3, got 6

summary: 0/0 decls checked, peak 32 MB, allocated 0 MB, heartbeats 0
checked in 0.000322s

Test "tutorial/133_DupConCon"

Expected: ✋ reject · Size: 2.2 KB · Lines: 35 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source

An inductive with two constructors with the same name

Test result: ✋ rejected · exit code 1 · wall time: 6 ms · instructions: 11.5 M · max rss memory: 7.0 MB

stderr:
expected name index 4, got 7

summary: 0/0 decls checked, peak 32 MB, allocated 0 MB, heartbeats 0
checked in 0.000254s