Checker "official"
Version: 4.29.0 · 📄 Declaration · 🔗 Source
The official Lean 4 kernel checker implementation.
This is the reference implementation from the Lean 4 repository, wrapped in a program that reads the exported proofs and replays them in the kernel.
96/96
44/44
1
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: 292 ms · instructions: 302.3 M · max rss memory: 65.1 MB
stderr:
uncaught exception: (kernel) declaration type mismatch, 'thm' has type True but it is expected to have type @Eq Nat 0 1
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: 👍 accepted · exit code 0 · wall time: 2.1 m · instructions: 841.9 G · max rss memory: 1.2 GB
stdout:
Accepted 120026 declarations.
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: 💥 error · exit code 139 · wall time: 129 ms · instructions: 205.2 M · max rss memory: 64.6 MB
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: 👍 accepted · exit code 0 · wall time: 3.7 m · instructions: 1.5 T · max rss memory: 2.1 GB
stdout:
Accepted 262980 declarations.
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: 1.0 m · instructions: 441.6 G · max rss memory: 549.9 MB
stdout:
Accepted 54472 declarations.
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: 265 ms · instructions: 2.4 G · max rss memory: 72.6 MB
stdout:
Accepted 2056 declarations.
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: 39 ms · instructions: 200.6 M · max rss memory: 65.6 MB
stderr:
uncaught exception: (kernel) declaration type mismatch, 'down' has type Type (imax u v) → Type (imax u v) but it is expected to have type Type (imax u v) → Sort (imax u v)
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: 39 ms · instructions: 201.2 M · max rss memory: 65.6 MB
stderr:
uncaught exception: (kernel) declaration type mismatch, 'down' has type Type (imax 0 v) → Type (imax 0 v) but it is expected to have type Type (imax 0 v) → Sort (imax 0 v)
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: 👍 accepted · exit code 0 · wall time: 37.4 m · instructions: 11.8 T · max rss memory: 9.1 GB
stdout:
Accepted 670627 declarations.
Test "mlir"
Expected: 👍 accept · Size: 28.8 MB · Lines: 576.3 k · lean4export: 3.1.0 · Lean: 4.27.0-nightly-2025-12-01 · 📄 Declaration · 🔗 Source
The main theorems from lean-mlir.
Test result: 👍 accepted · exit code 0 · wall time: 3.7 s · instructions: 29.8 G · max rss memory: 114.6 MB
stdout:
Accepted 4966 declarations.
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: 43 ms · instructions: 214.2 M · max rss memory: 66.0 MB
stderr:
uncaught exception: (kernel) application type mismatch
@Nat.rec (fun n => @Bool.rec (fun x => Prop) False True (Nat.beq n 0)) True.intro fun n ih => True.intro
argument has type
(n : Nat) → (@fun n => @Bool.rec (fun x => Prop) False True (Nat.beq n 0)) n → True
but function has type
((n : Nat) →
(@fun n => @Bool.rec (fun x => Prop) False True (Nat.beq n 0)) n →
(@fun n => @Bool.rec (fun x => Prop) False True (Nat.beq n 0)) (Nat.succ n)) →
(t : Nat) → (@fun n => @Bool.rec (fun x => Prop) False True (Nat.beq n 0)) t
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: 4.4 s · instructions: 32.3 G · max rss memory: 1.4 GB
stdout:
Accepted 34 declarations.
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: 1.8 s · instructions: 14.6 G · max rss memory: 230.8 MB
stdout:
Accepted 2429 declarations.
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: 53 ms · instructions: 322.9 M · max rss memory: 66.7 MB
stdout:
Accepted 10 declarations.
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: 👍 accepted · exit code 0 · wall time: 1.8 m · instructions: 746.4 G · max rss memory: 1007.4 MB
stdout:
Accepted 93046 declarations.
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: 43 ms · instructions: 196.9 M · max rss memory: 64.5 MB
stdout:
Accepted 1 declarations.
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: 41 ms · instructions: 197.7 M · max rss memory: 65.3 MB
stderr:
uncaught exception: (kernel) declaration type mismatch, 'badDef' has type Type 1 but it is expected to have type Prop
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: 64 ms · instructions: 197.0 M · max rss memory: 64.4 MB
stdout:
Accepted 1 declarations.
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: 58 ms · instructions: 196.8 M · max rss memory: 64.5 MB
stdout:
Accepted 1 declarations.
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: 38 ms · instructions: 197.0 M · max rss memory: 64.5 MB
stdout:
Accepted 1 declarations.
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: 53 ms · instructions: 197.2 M · max rss memory: 64.5 MB
stdout:
Accepted 2 declarations.
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: 38 ms · instructions: 197.6 M · max rss memory: 64.5 MB
stdout:
Accepted 2 declarations.
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: 38 ms · instructions: 197.1 M · max rss memory: 64.5 MB
stdout:
Accepted 2 declarations.
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: 53 ms · instructions: 197.9 M · max rss memory: 65.8 MB
stderr:
uncaught exception: (kernel) type expected x
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: 39 ms · instructions: 198.1 M · max rss memory: 65.7 MB
stderr:
uncaught exception: (kernel) type expected constType
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: 38 ms · instructions: 197.2 M · max rss memory: 65.5 MB
stderr:
uncaught exception: (kernel) type of theorem 'nonPropThm' is not a proposition Prop
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: 51 ms · instructions: 196.8 M · max rss memory: 64.5 MB
stdout:
Accepted 1 declarations.
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: 47 ms · instructions: 197.1 M · max rss memory: 64.5 MB
stdout:
Accepted 1 declarations.
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: 55 ms · instructions: 196.9 M · max rss memory: 64.5 MB
stdout:
Accepted 1 declarations.
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: 44 ms · instructions: 197.2 M · max rss memory: 64.5 MB
stdout:
Accepted 2 declarations.
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: 38 ms · instructions: 197.0 M · max rss memory: 65.0 MB
stderr:
uncaught exception: (kernel) failed to add declaration to environment, duplicate universe level parameter: 'u'
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: 51 ms · instructions: 196.9 M · max rss memory: 64.5 MB
stdout:
Accepted 1 declarations.
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: 48 ms · instructions: 197.1 M · max rss memory: 64.5 MB
stdout:
Accepted 1 declarations.
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: 38 ms · instructions: 197.1 M · max rss memory: 64.5 MB
stdout:
Accepted 1 declarations.
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: 35 ms · instructions: 197.0 M · max rss memory: 64.5 MB
stdout:
Accepted 1 declarations.
Test "tutorial/021_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: 32 ms · instructions: 196.8 M · max rss memory: 64.5 MB
stdout:
Accepted 1 declarations.
Test "tutorial/022_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: 37 ms · instructions: 197.2 M · max rss memory: 64.5 MB
stdout:
Accepted 1 declarations.
Test "tutorial/023_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: 52 ms · instructions: 198.6 M · max rss memory: 64.5 MB
stdout:
Accepted 7 declarations.
Test "tutorial/024_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: 38 ms · instructions: 199.2 M · max rss memory: 64.5 MB
stdout:
Accepted 8 declarations.
Test "tutorial/025_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: 46 ms · instructions: 199.6 M · max rss memory: 64.5 MB
stdout:
Accepted 10 declarations.
Test "tutorial/026_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: 64 ms · instructions: 197.2 M · max rss memory: 64.5 MB
stdout:
Accepted 1 declarations.
Test "tutorial/027_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: 38 ms · instructions: 197.2 M · max rss memory: 64.6 MB
stdout:
Accepted 3 declarations.
Test "tutorial/028_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: 56 ms · instructions: 196.9 M · max rss memory: 64.6 MB
stdout:
Accepted 2 declarations.
Test "tutorial/029_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: 39 ms · instructions: 197.4 M · max rss memory: 64.6 MB
stdout:
Accepted 3 declarations.
Test "tutorial/030_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: 38 ms · instructions: 197.7 M · max rss memory: 64.6 MB
stdout:
Accepted 5 declarations.
Test "tutorial/031_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: 46 ms · instructions: 198.6 M · max rss memory: 64.6 MB
stdout:
Accepted 8 declarations.
Test "tutorial/032_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: 39 ms · instructions: 198.3 M · max rss memory: 64.6 MB
stdout:
Accepted 4 declarations.
Test "tutorial/033_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: 38 ms · instructions: 198.9 M · max rss memory: 64.6 MB
stdout:
Accepted 4 declarations.
Test "tutorial/034_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: 39 ms · instructions: 198.7 M · max rss memory: 64.6 MB
stdout:
Accepted 4 declarations.
Test "tutorial/035_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: 38 ms · instructions: 197.4 M · max rss memory: 64.6 MB
stdout:
Accepted 4 declarations.
Test "tutorial/036_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: 39 ms · instructions: 198.6 M · max rss memory: 64.6 MB
stdout:
Accepted 4 declarations.
Test "tutorial/037_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: 38 ms · instructions: 198.3 M · max rss memory: 64.6 MB
stdout:
Accepted 5 declarations.
Test "tutorial/038_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: 38 ms · instructions: 205.1 M · max rss memory: 64.6 MB
stdout:
Accepted 14 declarations.
Test "tutorial/039_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: 38 ms · instructions: 198.1 M · max rss memory: 65.6 MB
stderr:
uncaught exception: (kernel) type expected fun x y => x
Test "tutorial/040_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: 38 ms · instructions: 198.0 M · max rss memory: 65.8 MB
stderr:
uncaught exception: (kernel) type expected aType
Test "tutorial/041_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: 38 ms · instructions: 197.1 M · max rss memory: 65.0 MB
stderr:
uncaught exception: (kernel) failed to add declaration to environment, duplicate universe level parameter: 'u'
Test "tutorial/042_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: 38 ms · instructions: 197.2 M · max rss memory: 65.0 MB
stderr:
uncaught exception: (kernel) invalid inductive datatype declaration, incorrect number of parameters
Test "tutorial/043_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: 38 ms · instructions: 197.4 M · max rss memory: 65.1 MB
stderr:
uncaught exception: (kernel) arg #1 of 'inductWrongCtorParams.mk' does not match inductive datatypes parameters'
Test "tutorial/044_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: 57 ms · instructions: 197.6 M · max rss memory: 65.0 MB
stderr:
uncaught exception: (kernel) invalid return type for 'inductWrongCtorResParams.mk'
Test "tutorial/045_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: 41 ms · instructions: 197.6 M · max rss memory: 65.0 MB
stderr:
uncaught exception: (kernel) invalid return type for 'inductWrongCtorResLevel.mk'
Test "tutorial/046_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: 39 ms · instructions: 197.4 M · max rss memory: 65.1 MB
stderr:
uncaught exception: (kernel) invalid return type for 'inductInIndex.mk'
Test "tutorial/047_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: 39 ms · instructions: 197.8 M · max rss memory: 65.1 MB
stderr:
uncaught exception: (kernel) arg #1 of 'indNeg.mk' has a non positive occurrence of the datatypes being declared
Test "tutorial/048_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: 38 ms · instructions: 198.6 M · max rss memory: 64.6 MB
stdout:
Accepted 5 declarations.
Test "tutorial/049_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: 51 ms · instructions: 197.7 M · max rss memory: 65.1 MB
stderr:
uncaught exception: (kernel) invalid return type for 'reduceCtorType.mk'
Test "tutorial/050_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: 56 ms · instructions: 197.9 M · max rss memory: 65.1 MB
stderr:
uncaught exception: (kernel) arg #1 of 'indNegReducible.mk' has a non positive occurrence of the datatypes being declared
Test "tutorial/051_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: 38 ms · instructions: 197.5 M · max rss memory: 64.6 MB
stdout:
Accepted 4 declarations.
Test "tutorial/052_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: 39 ms · instructions: 198.0 M · max rss memory: 64.6 MB
stdout:
Accepted 4 declarations.
Test "tutorial/053_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: 60 ms · instructions: 197.6 M · max rss memory: 64.6 MB
stdout:
Accepted 4 declarations.
Test "tutorial/054_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: 36 ms · instructions: 197.2 M · max rss memory: 65.1 MB
stderr:
uncaught exception: (kernel) universe level of type_of(arg #1) of 'typeWithTooHighTypeField.mk' is too big for the corresponding inductive datatype
Test "tutorial/055_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: 49 ms · instructions: 197.2 M · max rss memory: 64.6 MB
stdout:
Accepted 3 declarations.
Test "tutorial/056_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: 38 ms · instructions: 198.1 M · max rss memory: 64.6 MB
stdout:
Accepted 5 declarations.
Test "tutorial/057_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: 50 ms · instructions: 199.0 M · max rss memory: 64.6 MB
stdout:
Accepted 8 declarations.
Test "tutorial/058_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: 37 ms · instructions: 198.4 M · max rss memory: 64.6 MB
stdout:
Accepted 4 declarations.
Test "tutorial/059_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: 39 ms · instructions: 198.7 M · max rss memory: 64.6 MB
stdout:
Accepted 4 declarations.
Test "tutorial/060_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: 56 ms · instructions: 198.8 M · max rss memory: 64.6 MB
stdout:
Accepted 4 declarations.
Test "tutorial/061_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: 36 ms · instructions: 197.6 M · max rss memory: 64.6 MB
stdout:
Accepted 4 declarations.
Test "tutorial/062_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: 38 ms · instructions: 198.3 M · max rss memory: 64.6 MB
stdout:
Accepted 4 declarations.
Test "tutorial/063_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: 38 ms · instructions: 198.2 M · max rss memory: 64.4 MB
stdout:
Accepted 5 declarations.
Test "tutorial/064_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: 39 ms · instructions: 205.9 M · max rss memory: 64.6 MB
stdout:
Accepted 14 declarations.
Test "tutorial/065_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: 38 ms · instructions: 197.7 M · max rss memory: 64.5 MB
stdout:
Accepted 5 declarations.
Test "tutorial/066_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: 39 ms · instructions: 198.7 M · max rss memory: 64.6 MB
stdout:
Accepted 4 declarations.
Test "tutorial/067_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: 39 ms · instructions: 199.9 M · max rss memory: 64.6 MB
stdout:
Accepted 8 declarations.
Test "tutorial/068_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: 39 ms · instructions: 200.0 M · max rss memory: 64.6 MB
stdout:
Accepted 9 declarations.
Test "tutorial/069_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: 39 ms · instructions: 202.7 M · max rss memory: 64.6 MB
stdout:
Accepted 11 declarations.
Test "tutorial/070_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: 57 ms · instructions: 202.4 M · max rss memory: 64.6 MB
stdout:
Accepted 7 declarations.
Test "tutorial/071_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: 40 ms · instructions: 203.4 M · max rss memory: 64.6 MB
stdout:
Accepted 13 declarations.
Test "tutorial/072_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: 39 ms · instructions: 206.9 M · max rss memory: 64.6 MB
stdout:
Accepted 14 declarations.
Test "tutorial/073_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: 41 ms · instructions: 226.4 M · max rss memory: 64.5 MB
stdout:
Accepted 19 declarations.
Test "tutorial/074_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: 38 ms · instructions: 198.8 M · max rss memory: 64.6 MB
stdout:
Accepted 5 declarations.
Test "tutorial/075_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: 53 ms · instructions: 199.0 M · max rss memory: 64.6 MB
stdout:
Accepted 5 declarations.
Test "tutorial/076_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: 56 ms · instructions: 198.9 M · max rss memory: 64.6 MB
stdout:
Accepted 5 declarations.
Test "tutorial/077_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: 49 ms · instructions: 199.5 M · max rss memory: 64.6 MB
stdout:
Accepted 5 declarations.
Test "tutorial/078_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: 39 ms · instructions: 199.5 M · max rss memory: 65.8 MB
stderr:
uncaught exception: (kernel) invalid projection z.3
Test "tutorial/079_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: 39 ms · instructions: 199.0 M · max rss memory: 65.8 MB
stderr:
uncaught exception: (kernel) invalid projection x.1
Test "tutorial/080_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: 38 ms · instructions: 200.6 M · max rss memory: 64.6 MB
stdout:
Accepted 10 declarations.
Test "tutorial/081_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: 39 ms · instructions: 201.6 M · max rss memory: 65.8 MB
stderr:
uncaught exception: (kernel) invalid projection x.2
Test "tutorial/082_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: 38 ms · instructions: 200.7 M · max rss memory: 64.6 MB
stdout:
Accepted 10 declarations.
Test "tutorial/083_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: 39 ms · instructions: 201.5 M · max rss memory: 65.8 MB
stderr:
uncaught exception: (kernel) invalid projection x.4
Test "tutorial/084_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: 63 ms · instructions: 201.6 M · max rss memory: 65.8 MB
stderr:
uncaught exception: (kernel) invalid projection x.4
Test "tutorial/085_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: 39 ms · instructions: 201.4 M · max rss memory: 65.8 MB
stderr:
uncaught exception: (kernel) invalid projection x.6
Test "tutorial/086_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: 39 ms · instructions: 199.9 M · max rss memory: 64.6 MB
stdout:
Accepted 11 declarations.
Test "tutorial/087_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: 39 ms · instructions: 200.6 M · max rss memory: 65.8 MB
stderr:
uncaught exception: (kernel) invalid projection x.1
Test "tutorial/088_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: 39 ms · instructions: 201.0 M · max rss memory: 65.8 MB
stderr:
uncaught exception: (kernel) invalid projection x.2
Test "tutorial/089_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: 51 ms · instructions: 201.6 M · max rss memory: 64.6 MB
stdout:
Accepted 13 declarations.
Test "tutorial/090_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: 46 ms · instructions: 199.9 M · max rss memory: 64.6 MB
stdout:
Accepted 8 declarations.
Test "tutorial/091_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: 46 ms · instructions: 206.1 M · max rss memory: 65.8 MB
stderr:
uncaught exception: (kernel) declaration type mismatch, 'ruleKbad' has type
@Eq Bool Bool.true Bool.false → (a : Bool) → @Eq Bool a a
but it is expected to have type
(h : @Eq Bool Bool.true Bool.false) →
(a : Bool) → @Eq Bool (@Eq.rec Bool Bool.true (fun x x_1 => Bool) a Bool.false h) a
Test "tutorial/092_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: 40 ms · instructions: 211.9 M · max rss memory: 65.8 MB
stderr:
uncaught exception: (kernel) declaration type mismatch, 'ruleKAcc' has type
(α : Sort u) → (p : α → α → Prop) → (x : α) → @Acc α p x → (a : Bool) → @Eq Bool a a
but it is expected to have type
(α : Sort u) →
(p : α → α → Prop) →
(x : α) → (h : @Acc α p x) → (a : Bool) → @Eq Bool (@Acc.rec α p (fun x x_1 => Bool) (fun x x_1 x_2 => a) x h) a
Test "tutorial/093_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: 47 ms · instructions: 198.1 M · max rss memory: 64.6 MB
stdout:
Accepted 5 declarations.
Test "tutorial/094_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: 38 ms · instructions: 199.6 M · max rss memory: 64.6 MB
stdout:
Accepted 8 declarations.
Test "tutorial/095_proofIrrelevance"
Expected: 👍 accept · Size: 5.0 KB · Lines: 100 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source
Proof irrelevance
Test result: 👍 accepted · exit code 0 · wall time: 51 ms · instructions: 199.2 M · max rss memory: 64.6 MB
stdout:
Accepted 5 declarations.
Test "tutorial/096_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: 54 ms · instructions: 199.6 M · max rss memory: 64.6 MB
stdout:
Accepted 9 declarations.
Test "tutorial/097_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: 38 ms · instructions: 199.5 M · max rss memory: 64.6 MB
stdout:
Accepted 8 declarations.
Test "tutorial/098_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: 38 ms · instructions: 199.6 M · max rss memory: 64.6 MB
stdout:
Accepted 8 declarations.
Test "tutorial/099_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: 38 ms · instructions: 203.3 M · max rss memory: 64.6 MB
stdout:
Accepted 13 declarations.
Test "tutorial/100_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: 60 ms · instructions: 199.8 M · max rss memory: 64.6 MB
stdout:
Accepted 5 declarations.
Test "tutorial/101_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: 33 ms · instructions: 199.4 M · max rss memory: 64.6 MB
stdout:
Accepted 5 declarations.
Test "tutorial/102_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: 44 ms · instructions: 204.3 M · max rss memory: 65.8 MB
stderr:
uncaught exception: (kernel) declaration type mismatch, 'funEtaBad' has type (x x_1 : Type) → (x → x) → (f : x → x_1) → @Eq (x → x_1) f f but it is expected to have type (α β : Type) → (g : α → α) → (f : α → β) → @Eq (α → β) (fun x => f (g x)) f
Test "tutorial/103_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: 40 ms · instructions: 208.3 M · max rss memory: 65.8 MB
stderr:
uncaught exception: (kernel) declaration type mismatch, 'etaRuleK' has type
(a : @Eq Bool Bool.true Bool.true → Bool) → @Eq (@Eq Bool Bool.true Bool.true → Bool) a a
but it is expected to have type
(a : @Eq Bool Bool.true Bool.true → Bool) →
@Eq (@Eq Bool Bool.true Bool.true → Bool)
(@Eq.rec Bool Bool.true (fun x x_1 => Bool) (a (@Eq.refl Bool Bool.true)) Bool.true) a
Test "tutorial/104_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: 39 ms · instructions: 205.7 M · max rss memory: 66.0 MB
stderr:
uncaught exception: (kernel) declaration type mismatch, 'etaCtor' has type (x : True → T) → @Eq (True → T) x x but it is expected to have type (x : True → T) → @Eq (True → T) (T.mk (T.val (x True.intro))) x
Test "tutorial/105_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: 52 ms · instructions: 198.7 M · max rss memory: 65.1 MB
stderr:
uncaught exception: (kernel) arg #1 of 'reflOccLeft.mk' has a non positive occurrence of the datatypes being declared
Test "tutorial/106_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: 41 ms · instructions: 199.8 M · max rss memory: 65.8 MB
stderr:
uncaught exception: (kernel) application type mismatch reflOccInIndex x argument has type Nat but function has type Type → Type
Test "tutorial/107_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: 55 ms · instructions: 198.9 M · max rss memory: 64.6 MB
stdout:
Accepted 5 declarations.
Test "tutorial/108_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: 38 ms · instructions: 198.8 M · max rss memory: 64.6 MB
stdout:
Accepted 5 declarations.
Test "tutorial/109_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: 50 ms · instructions: 199.3 M · max rss memory: 64.6 MB
stdout:
Accepted 9 declarations.
Test "tutorial/110_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: 47 ms · instructions: 202.1 M · max rss memory: 64.6 MB
stdout:
Accepted 14 declarations.
Test "tutorial/111_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: 39 ms · instructions: 201.2 M · max rss memory: 64.5 MB
stdout:
Accepted 4 declarations.
Test "tutorial/112_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: 39 ms · instructions: 204.4 M · max rss memory: 64.6 MB
stdout:
Accepted 11 declarations.
Test "tutorial/113_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: 40 ms · instructions: 212.3 M · max rss memory: 65.8 MB
stderr:
uncaught exception: (kernel) declaration type mismatch, 'accRecNoEta' has type
(α : Type) → (r : α → α → Prop) → (a : α) → @Acc α r a → (p : Bool) → @Eq Bool p p
but it is expected to have type
{α : Type} →
(r : α → α → Prop) →
(a : α) → (h : @Acc α r a) → (p : Bool) → @Eq Bool (@Acc.rec α r (fun x x_1 => Bool) (fun x x_1 x_2 => p) a h) p
Test "tutorial/114_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: 39 ms · instructions: 199.5 M · max rss memory: 64.6 MB
stdout:
Accepted 5 declarations.
Test "tutorial/115_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: 50 ms · instructions: 199.7 M · max rss memory: 64.6 MB
stdout:
Accepted 5 declarations.
Test "tutorial/116_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: 39 ms · instructions: 199.6 M · max rss memory: 64.6 MB
stdout:
Accepted 5 declarations.
Test "tutorial/117_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: 38 ms · instructions: 200.0 M · max rss memory: 64.6 MB
stdout:
Accepted 6 declarations.
Test "tutorial/118_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: 38 ms · instructions: 200.7 M · max rss memory: 64.6 MB
stdout:
Accepted 5 declarations.
Test "tutorial/119_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: 39 ms · instructions: 201.1 M · max rss memory: 64.6 MB
stdout:
Accepted 5 declarations.
Test "tutorial/120_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: 53 ms · instructions: 195.5 M · max rss memory: 64.5 MB
stderr:
uncaught exception: Duplicate declaration: dup_defs
Test "tutorial/121_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: 49 ms · instructions: 195.9 M · max rss memory: 64.6 MB
stderr:
uncaught exception: Duplicate declaration: dup_ind_def
Test "tutorial/122_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: 37 ms · instructions: 195.9 M · max rss memory: 64.6 MB
stderr:
uncaught exception: Duplicate declaration: dup_ctor_def.mk
Test "tutorial/123_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: 38 ms · instructions: 196.3 M · max rss memory: 64.6 MB
stderr:
uncaught exception: Duplicate declaration: dup_rec_def.rec
Test "tutorial/124_dup_rec_def2"
Expected: ✋ reject · Size: 1.7 KB · Lines: 28 · lean4export: 3.1.0 · Lean: 4.27.0-rc1 · 📄 Declaration · 🔗 Source
A definition with the name of a recursor, and the recursor named differently. This would pass simple checks for duplicate definitions in the parser, but should still be rejected by the checker.
Test result: ✋ rejected · exit code 1 · wall time: 35 ms · instructions: 197.7 M · max rss memory: 65.5 MB
stderr:
uncaught exception: (kernel) constant has already been declared 'dup_rec_def2.rec'
Test "tutorial/125_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: 31 ms · instructions: 195.8 M · max rss memory: 64.6 MB
stderr:
uncaught exception: Duplicate declaration: dup_ctor_rec.rec
Test "tutorial/126_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: 37 ms · instructions: 196.0 M · max rss memory: 64.6 MB
stderr:
uncaught exception: Duplicate declaration: dup_ind_con_con.mk