import LSpec import Pantograph.Goal import Pantograph.Serial namespace Pantograph.Test.Proofs 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_type 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 def build_goal (nameType: List (String × String)) (target: String): Commands.Goal := { target := { pp? := .some target}, vars := (nameType.map fun x => ({ name := x.fst, type? := .some { pp? := .some x.snd }, isInaccessible? := .some false })).toArray } -- 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" -- 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 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 let typeProp: Commands.Expression := { pp? := .some "Prop" } let branchGoal (caseName name: String): Commands.Goal := { caseName? := .some caseName, target := { pp? := .some "q ∨ p" }, 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 } ] } 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 := Name.append .anonymous "Aniva", openDecls := [], -- No 'open' directives needed fileName := "", 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 /-- Tests the most basic form of proofs whose goals do not relate to each other -/ def suite: IO LSpec.TestSeq := do let env: Lean.Environment ← Lean.importModules (imports := #[{ module := Name.append .anonymous "Init", 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.Proofs