Pantograph/Test/Proofs.lean

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import LSpec
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import Pantograph.Tactic
import Pantograph.Serial
namespace Pantograph.Test
open Pantograph
open Lean
inductive Start where
| copy (name: String) -- Start from some name in the environment
| expr (expr: String) -- Start from some expression
abbrev TestM := StateRefT LSpec.TestSeq (ReaderT Commands.Options M)
deriving instance DecidableEq, Repr for Commands.Expression
deriving instance DecidableEq, Repr for Commands.Variable
deriving instance DecidableEq, Repr for Commands.Goal
def add_test (test: LSpec.TestSeq): TestM Unit := do
set $ (← get) ++ test
def start_proof (start: Start): TestM (Option GoalState) := do
let env ← Lean.MonadEnv.getEnv
match start with
| .copy name =>
let cInfo? := str_to_name name |> env.find?
add_test $ LSpec.check s!"Symbol exists {name}" cInfo?.isSome
match cInfo? with
| .some cInfo =>
let goal ← GoalState.create (expr := cInfo.type)
return Option.some goal
| .none =>
return Option.none
| .expr expr =>
let syn? := syntax_from_str env expr
add_test $ LSpec.check s!"Parsing {expr}" (syn?.isOk)
match syn? with
| .error error =>
IO.println error
return Option.none
| .ok syn =>
let expr? ← syntax_to_expr syn
add_test $ LSpec.check s!"Elaborating" expr?.isOk
match expr? with
| .error error =>
IO.println error
return Option.none
| .ok expr =>
let goal ← GoalState.create (expr := expr)
return Option.some goal
def assert_unreachable (message: String): LSpec.TestSeq := LSpec.check message false
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def build_goal (nameType: List (String × String)) (target: String): Commands.Goal :=
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{
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target := { pp? := .some target},
vars := (nameType.map fun x => ({
name := x.fst,
type? := .some { pp? := .some x.snd },
isInaccessible? := .some false
})).toArray
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}
-- Like `build_goal` but allow certain variables to be elided.
def build_goal_selective (nameType: List (String × Option String)) (target: String): Commands.Goal :=
{
target := { pp? := .some target},
vars := (nameType.map fun x => ({
name := x.fst,
type? := x.snd.map (λ type => { pp? := type }),
isInaccessible? := x.snd.map (λ _ => false)
})).toArray
}
-- Individual test cases
example: ∀ (a b: Nat), a + b = b + a := by
intro n m
rw [Nat.add_comm]
def proof_nat_add_comm: TestM Unit := do
let goal? ← start_proof (.copy "Nat.add_comm")
add_test $ LSpec.check "Start goal" goal?.isSome
if let .some goal := goal? then
if let .success #[(goal, sGoal)] ← goal.execute "intro n m" then
let sGoal1e: Commands.Goal := build_goal [("n", "Nat"), ("m", "Nat")] "n + m = m + n"
add_test $ LSpec.check "intro n m" (sGoal = sGoal1e)
if let .failure #[message] ← goal.execute "assumption" then
add_test $ LSpec.check "assumption" (message = "tactic 'assumption' failed\nn m : Nat\n⊢ n + m = m + n")
else
add_test $ assert_unreachable "assumption"
if let .success #[] ← goal.execute "rw [Nat.add_comm]" then
return ()
else
add_test $ assert_unreachable "rw [Nat.add_comm]"
else
add_test $ assert_unreachable "intro n m"
def proof_nat_add_comm_manual: TestM Unit := do
let goal? ← start_proof (.expr "∀ (a b: Nat), a + b = b + a")
add_test $ LSpec.check "Start goal" goal?.isSome
if let .some goal := goal? then
if let .success #[(goal, sGoal)] ← goal.execute "intro n m" then
let sGoal1e: Commands.Goal := build_goal [("n", "Nat"), ("m", "Nat")] "n + m = m + n"
add_test $ LSpec.check "intro n m" (sGoal = sGoal1e)
if let .failure #[message] ← goal.execute "assumption" then
add_test $ LSpec.check "assumption" (message = "tactic 'assumption' failed\nn m : Nat\n⊢ n + m = m + n")
else
add_test $ assert_unreachable "assumption"
if let .success #[] ← goal.execute "rw [Nat.add_comm]" then
return ()
else
add_test $ assert_unreachable "rw [Nat.add_comm]"
else
add_test $ assert_unreachable "intro n m"
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-- Two ways to write the same theorem
example: ∀ (p q: Prop), p q → q p := by
intro p q h
cases h
apply Or.inr
assumption
apply Or.inl
assumption
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example: ∀ (p q: Prop), p q → q p := by
intro p q h
cases h
. apply Or.inr
assumption
. apply Or.inl
assumption
def proof_or_comm: TestM Unit := do
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let typeProp: Commands.Expression := { pp? := .some "Prop" }
let branchGoal (caseName name: String): Commands.Goal := {
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caseName? := .some caseName,
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target := { pp? := .some "q p" },
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vars := #[
{ name := "p", type? := .some typeProp, isInaccessible? := .some false },
{ name := "q", type? := .some typeProp, isInaccessible? := .some false },
{ name := "h✝", type? := .some { pp? := .some name }, isInaccessible? := .some true }
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]
}
let goal? ← start_proof (.expr "∀ (p q: Prop), p q → q p")
add_test $ LSpec.check "Start goal" goal?.isSome
if let .some goal := goal? then
if let .success #[(goal, sGoal)] ← goal.execute "intro p q h" then
let sGoal1e := build_goal [("p", "Prop"), ("q", "Prop"), ("h", "p q")] "q p"
add_test $ LSpec.check "intro p q h" (sGoal = sGoal1e)
if let .success #[(goal1, sGoal1), (goal2, sGoal2)] ← goal.execute "cases h" then
add_test $ LSpec.check "cases h/1" (sGoal1 = branchGoal "inl" "p")
if let .success #[(goal, _)] ← goal1.execute "apply Or.inr" then
if let .success #[] ← goal.execute "assumption" then
return ()
else
add_test $ assert_unreachable "assumption"
else
add_test $ assert_unreachable "apply Or.inr"
add_test $ LSpec.check "cases h/2" (sGoal2 = branchGoal "inr" "q")
if let .success #[(goal, _)] ← goal2.execute "apply Or.inl" then
if let .success #[] ← goal.execute "assumption" then
return ()
else
add_test $ assert_unreachable "assumption"
else
add_test $ assert_unreachable "apply Or.inl"
else
add_test $ assert_unreachable "cases h"
else
add_test $ assert_unreachable "intro p q h"
example (w x y z : Nat) (p : Nat → Prop)
(h : p (x * y + z * w * x)) : p (x * w * z + y * x) := by
simp [Nat.add_assoc, Nat.add_comm, Nat.add_left_comm, Nat.mul_comm, Nat.mul_assoc, Nat.mul_left_comm] at *
assumption
def proof_arith_1: TestM Unit := do
let goal? ← start_proof (.expr "∀ (w x y z : Nat) (p : Nat → Prop) (h : p (x * y + z * w * x)), p (x * w * z + y * x)")
add_test $ LSpec.check "Start goal" goal?.isSome
if let .some goal := goal? then
if let .success #[(goal, _)] ← goal.execute "intros" then
if let .success #[(goal, _)] ← goal.execute "simp [Nat.add_assoc, Nat.add_comm, Nat.add_left_comm, Nat.mul_comm, Nat.mul_assoc, Nat.mul_left_comm] at *" then
if let .success #[] ← goal.execute "assumption" then
return ()
else
add_test $ assert_unreachable "assumption"
else
add_test $ assert_unreachable "simp ..."
else
add_test $ assert_unreachable "intros"
def proof_delta_variable: TestM Unit := withReader (fun _ => {proofVariableDelta := true}) do
let goal? ← start_proof (.expr "∀ (a b: Nat), a + b = b + a")
add_test $ LSpec.check "Start goal" goal?.isSome
if let .some goal := goal? then
if let .success #[(goal, sGoal)] ← goal.execute "intro n" then
let sGoal1e: Commands.Goal := build_goal_selective [("n", .some "Nat")] "∀ (b : Nat), n + b = b + n"
add_test $ LSpec.check "intro n" (sGoal = sGoal1e)
if let .success #[(_, sGoal)] ← goal.execute "intro m" then
let sGoal2e: Commands.Goal := build_goal_selective [("n", .none), ("m", .some "Nat")] "n + m = m + n"
add_test $ LSpec.check "intro m" (sGoal = sGoal2e)
else
add_test $ assert_unreachable "intro m"
else
add_test $ assert_unreachable "intro n"
def proof_runner (env: Lean.Environment) (tests: TestM Unit): IO LSpec.TestSeq := do
let termElabM := tests.run LSpec.TestSeq.done |>.run {} -- with default options
let coreContext: Lean.Core.Context := {
currNamespace := str_to_name "Aniva",
openDecls := [], -- No 'open' directives needed
fileName := "<Pantograph>",
fileMap := { source := "", positions := #[0], lines := #[1] }
}
let metaM := termElabM.run' (ctx := {
declName? := some "_pantograph",
errToSorry := false
})
let coreM := metaM.run'
match ← (coreM.run' coreContext { env := env }).toBaseIO with
| .error exception =>
return LSpec.test "Exception" (s!"internal exception #{← exception.toMessageData.toString}" = "")
| .ok (_, a) =>
return a
def test_proofs : IO LSpec.TestSeq := do
let env: Lean.Environment ← Lean.importModules
(imports := ["Init"].map (λ str => { module := str_to_name str, runtimeOnly := false }))
(opts := {})
(trustLevel := 1)
let tests := [
("Nat.add_comm", proof_nat_add_comm),
("nat.add_comm manual", proof_nat_add_comm_manual),
("Or.comm", proof_or_comm),
("arithmetic 1", proof_arith_1),
("delta variable", proof_delta_variable)
]
let tests ← tests.foldlM (fun acc tests => do
let (name, tests) := tests
let tests ← proof_runner env tests
return acc ++ (LSpec.group name tests)) LSpec.TestSeq.done
return LSpec.group "Proofs" tests
end Pantograph.Test