471 lines
18 KiB
Plaintext
471 lines
18 KiB
Plaintext
/-
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Tests pertaining to goals with no interdependencies
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-/
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import LSpec
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import Pantograph.Goal
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import Pantograph.Serial
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import Test.Common
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namespace Pantograph.Test.Proofs
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open Pantograph
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open Lean
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inductive Start where
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| copy (name: String) -- Start from some name in the environment
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| expr (expr: String) -- Start from some expression
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abbrev TestM := StateRefT LSpec.TestSeq (ReaderT Protocol.Options Elab.TermElabM)
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def addTest (test: LSpec.TestSeq): TestM Unit := do
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set $ (← get) ++ test
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def startProof (start: Start): TestM (Option GoalState) := do
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let env ← Lean.MonadEnv.getEnv
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match start with
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| .copy name =>
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let cInfo? := name.toName |> env.find?
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addTest $ LSpec.check s!"Symbol exists {name}" cInfo?.isSome
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match cInfo? with
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| .some cInfo =>
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let goal ← GoalState.create (expr := cInfo.type)
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return Option.some goal
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| .none =>
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return Option.none
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| .expr expr =>
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let syn? := parseTerm env expr
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addTest $ LSpec.check s!"Parsing {expr}" (syn?.isOk)
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match syn? with
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| .error error =>
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IO.println error
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return Option.none
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| .ok syn =>
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let expr? ← elabType syn
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addTest $ LSpec.check s!"Elaborating" expr?.isOk
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match expr? with
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| .error error =>
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IO.println error
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return Option.none
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| .ok expr =>
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let goal ← GoalState.create (expr := expr)
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return Option.some goal
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def buildGoal (nameType: List (String × String)) (target: String) (userName?: Option String := .none): Protocol.Goal :=
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{
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userName?,
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target := { pp? := .some target},
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vars := (nameType.map fun x => ({
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userName := x.fst,
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type? := .some { pp? := .some x.snd },
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isInaccessible? := .some false
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})).toArray
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}
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def proofRunner (env: Lean.Environment) (tests: TestM Unit): IO LSpec.TestSeq := do
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let termElabM := tests.run LSpec.TestSeq.done |>.run {} -- with default options
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let coreContext: Lean.Core.Context ← createCoreContext #[]
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let metaM := termElabM.run' (ctx := defaultTermElabMContext)
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let coreM := metaM.run'
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match ← (coreM.run' coreContext { env := env }).toBaseIO with
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| .error exception =>
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return LSpec.test "Exception" (s!"internal exception #{← exception.toMessageData.toString}" = "")
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| .ok (_, a) =>
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return a
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-- Individual test cases
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example: ∀ (a b: Nat), a + b = b + a := by
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intro n m
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rw [Nat.add_comm]
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def test_nat_add_comm (manual: Bool): TestM Unit := do
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let state? ← startProof <| match manual with
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| false => .copy "Nat.add_comm"
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| true => .expr "∀ (a b: Nat), a + b = b + a"
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addTest $ LSpec.check "Start goal" state?.isSome
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let state0 ← match state? with
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| .some state => pure state
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| .none => do
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addTest $ assertUnreachable "Goal could not parse"
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return ()
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let state1 ← match ← state0.tryTactic (goalId := 0) (tactic := "intro n m") with
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| .success state => pure state
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| other => do
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addTest $ assertUnreachable $ other.toString
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return ()
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addTest $ LSpec.check "intro n m" ((← state1.serializeGoals (options := ← read)).map (·.devolatilize) =
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#[buildGoal [("n", "Nat"), ("m", "Nat")] "n + m = m + n"])
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match ← state1.tryTactic (goalId := 0) (tactic := "assumption") with
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| .failure #[message] =>
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addTest $ LSpec.check "assumption" (message = "tactic 'assumption' failed\nn m : Nat\n⊢ n + m = m + n")
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| other => do
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addTest $ assertUnreachable $ other.toString
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let state2 ← match ← state1.tryTactic (goalId := 0) (tactic := "rw [Nat.add_comm]") with
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| .success state => pure state
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| other => do
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addTest $ assertUnreachable $ other.toString
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return ()
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addTest $ LSpec.test "rw [Nat.add_comm]" state2.goals.isEmpty
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return ()
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def test_delta_variable: TestM Unit := do
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let options: Protocol.Options := { noRepeat := true }
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let state? ← startProof <| .expr "∀ (a b: Nat), a + b = b + a"
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addTest $ LSpec.check "Start goal" state?.isSome
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let state0 ← match state? with
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| .some state => pure state
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| .none => do
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addTest $ assertUnreachable "Goal could not parse"
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return ()
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let state1 ← match ← state0.tryTactic (goalId := 0) (tactic := "intro n") with
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| .success state => pure state
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| other => do
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addTest $ assertUnreachable $ other.toString
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return ()
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addTest $ LSpec.check "intro n" ((← state1.serializeGoals (parent := state0) options).map (·.devolatilize) =
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#[buildGoalSelective [("n", .some "Nat")] "∀ (b : Nat), n + b = b + n"])
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let state2 ← match ← state1.tryTactic (goalId := 0) (tactic := "intro m") with
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| .success state => pure state
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| other => do
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addTest $ assertUnreachable $ other.toString
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return ()
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addTest $ LSpec.check "intro m" ((← state2.serializeGoals (parent := state1) options).map (·.devolatilize) =
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#[buildGoalSelective [("n", .none), ("m", .some "Nat")] "n + m = m + n"])
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return ()
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where
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-- Like `buildGoal` but allow certain variables to be elided.
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buildGoalSelective (nameType: List (String × Option String)) (target: String): Protocol.Goal :=
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{
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target := { pp? := .some target},
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vars := (nameType.map fun x => ({
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userName := x.fst,
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type? := x.snd.map (λ type => { pp? := type }),
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isInaccessible? := x.snd.map (λ _ => false)
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})).toArray
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}
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example (w x y z : Nat) (p : Nat → Prop)
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(h : p (x * y + z * w * x)) : p (x * w * z + y * x) := by
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simp [Nat.add_assoc, Nat.add_comm, Nat.add_left_comm, Nat.mul_comm, Nat.mul_assoc, Nat.mul_left_comm] at *
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assumption
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def test_arith: TestM Unit := do
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let state? ← startProof (.expr "∀ (w x y z : Nat) (p : Nat → Prop) (h : p (x * y + z * w * x)), p (x * w * z + y * x)")
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let state0 ← match state? with
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| .some state => pure state
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| .none => do
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addTest $ assertUnreachable "Goal could not parse"
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return ()
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let tactic := "intros"
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let state1 ← match ← state0.tryTactic (goalId := 0) (tactic := tactic) with
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| .success state => pure state
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| other => do
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addTest $ assertUnreachable $ other.toString
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return ()
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addTest $ LSpec.check tactic (state1.goals.length = 1)
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addTest $ LSpec.test "(1 root)" state1.rootExpr?.isNone
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let state2 ← match ← state1.tryTactic (goalId := 0) (tactic := "simp [Nat.add_assoc, Nat.add_comm, Nat.add_left_comm, Nat.mul_comm, Nat.mul_assoc, Nat.mul_left_comm] at *") with
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| .success state => pure state
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| other => do
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addTest $ assertUnreachable $ other.toString
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return ()
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addTest $ LSpec.check "simp ..." (state2.goals.length = 1)
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addTest $ LSpec.check "(2 root)" state2.rootExpr?.isNone
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let tactic := "assumption"
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let state3 ← match ← state2.tryTactic (goalId := 0) (tactic := tactic) with
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| .success state => pure state
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| other => do
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addTest $ assertUnreachable $ other.toString
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return ()
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addTest $ LSpec.test tactic state3.goals.isEmpty
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addTest $ LSpec.check "(3 root)" state3.rootExpr?.isSome
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return ()
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-- Two ways to write the same theorem
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example: ∀ (p q: Prop), p ∨ q → q ∨ p := by
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intro p q h
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cases h
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apply Or.inr
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assumption
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apply Or.inl
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assumption
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example: ∀ (p q: Prop), p ∨ q → q ∨ p := by
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intro p q h
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cases h
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. apply Or.inr
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assumption
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. apply Or.inl
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assumption
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def test_or_comm: TestM Unit := do
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let state? ← startProof (.expr "∀ (p q: Prop), p ∨ q → q ∨ p")
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let state0 ← match state? with
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| .some state => pure state
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| .none => do
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addTest $ assertUnreachable "Goal could not parse"
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return ()
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addTest $ LSpec.check "(0 parent)" state0.parentExpr?.isNone
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addTest $ LSpec.check "(0 root)" state0.rootExpr?.isNone
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let tactic := "intro p q h"
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let state1 ← match ← state0.tryTactic (goalId := 0) (tactic := tactic) with
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| .success state => pure state
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| other => do
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addTest $ assertUnreachable $ other.toString
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return ()
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addTest $ LSpec.check tactic ((← state1.serializeGoals (options := ← read)).map (·.devolatilize) =
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#[buildGoal [("p", "Prop"), ("q", "Prop"), ("h", "p ∨ q")] "q ∨ p"])
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addTest $ LSpec.check "(1 parent)" state1.parentExpr?.isSome
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addTest $ LSpec.check "(1 root)" state1.rootExpr?.isNone
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let tactic := "cases h"
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let state2 ← match ← state1.tryTactic (goalId := 0) (tactic := tactic) with
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| .success state => pure state
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| other => do
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addTest $ assertUnreachable $ other.toString
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return ()
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addTest $ LSpec.check tactic ((← state2.serializeGoals (options := ← read)).map (·.devolatilize) =
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#[branchGoal "inl" "p", branchGoal "inr" "q"])
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addTest $ LSpec.check "(2 parent)" state2.parentExpr?.isSome
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addTest $ LSpec.check "(2 root)" state2.rootExpr?.isNone
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let state2parent ← serialize_expression_ast state2.parentExpr?.get! (sanitize := false)
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-- This is due to delayed assignment
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addTest $ LSpec.test "(2 parent)" (state2parent ==
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"((:mv _uniq.43) (:fv _uniq.16) ((:c Eq.refl) ((:c Or) (:fv _uniq.10) (:fv _uniq.13)) (:fv _uniq.16)))")
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let state3_1 ← match ← state2.tryTactic (goalId := 0) (tactic := "apply Or.inr") with
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| .success state => pure state
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| other => do
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addTest $ assertUnreachable $ other.toString
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return ()
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let state3_1parent ← serialize_expression_ast state3_1.parentExpr?.get! (sanitize := false)
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addTest $ LSpec.test "(3_1 parent)" (state3_1parent == "((:c Or.inr) (:fv _uniq.13) (:fv _uniq.10) (:mv _uniq.78))")
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addTest $ LSpec.check "· apply Or.inr" (state3_1.goals.length = 1)
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let state4_1 ← match ← state3_1.tryTactic (goalId := 0) (tactic := "assumption") with
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| .success state => pure state
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| other => do
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addTest $ assertUnreachable $ other.toString
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return ()
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addTest $ LSpec.check " assumption" state4_1.goals.isEmpty
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let state4_1parent ← serialize_expression_ast state4_1.parentExpr?.get! (sanitize := false)
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addTest $ LSpec.test "(4_1 parent)" (state4_1parent == "(:fv _uniq.47)")
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addTest $ LSpec.check "(4_1 root)" state4_1.rootExpr?.isNone
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let state3_2 ← match ← state2.tryTactic (goalId := 1) (tactic := "apply Or.inl") with
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| .success state => pure state
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| other => do
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addTest $ assertUnreachable $ other.toString
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return ()
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addTest $ LSpec.check "· apply Or.inl" (state3_2.goals.length = 1)
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let state4_2 ← match ← state3_2.tryTactic (goalId := 0) (tactic := "assumption") with
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| .success state => pure state
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| other => do
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addTest $ assertUnreachable $ other.toString
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return ()
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addTest $ LSpec.check " assumption" state4_2.goals.isEmpty
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addTest $ LSpec.check "(4_2 root)" state4_2.rootExpr?.isNone
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-- Ensure the proof can continue from `state4_2`.
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let state2b ← match state4_2.continue state2 with
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| .error msg => do
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addTest $ assertUnreachable $ msg
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return ()
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| .ok state => pure state
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addTest $ LSpec.test "(resume)" (state2b.goals == [state2.goals.get! 0])
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let state3_1 ← match ← state2b.tryTactic (goalId := 0) (tactic := "apply Or.inr") with
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| .success state => pure state
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| other => do
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addTest $ assertUnreachable $ other.toString
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return ()
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addTest $ LSpec.check "· apply Or.inr" (state3_1.goals.length = 1)
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let state4_1 ← match ← state3_1.tryTactic (goalId := 0) (tactic := "assumption") with
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| .success state => pure state
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| other => do
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addTest $ assertUnreachable $ other.toString
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return ()
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addTest $ LSpec.check " assumption" state4_1.goals.isEmpty
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addTest $ LSpec.check "(4_1 root)" state4_1.rootExpr?.isSome
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return ()
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where
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typeProp: Protocol.Expression := { pp? := .some "Prop" }
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branchGoal (caseName varName: String): Protocol.Goal := {
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userName? := .some caseName,
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target := { pp? := .some "q ∨ p" },
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vars := #[
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{ userName := "p", type? := .some typeProp, isInaccessible? := .some false },
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{ userName := "q", type? := .some typeProp, isInaccessible? := .some false },
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{ userName := "h✝", type? := .some { pp? := .some varName }, isInaccessible? := .some true }
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]
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}
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def test_have: TestM Unit := do
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let state? ← startProof (.expr "∀ (p q: Prop), p → ((p ∨ q) ∨ (p ∨ q))")
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let state0 ← match state? with
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| .some state => pure state
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| .none => do
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addTest $ assertUnreachable "Goal could not parse"
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return ()
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let tactic := "intro p q h"
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let state1 ← match ← state0.tryTactic (goalId := 0) (tactic := tactic) with
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| .success state => pure state
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| other => do
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addTest $ assertUnreachable $ other.toString
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return ()
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addTest $ LSpec.check tactic ((← state1.serializeGoals (options := ← read)).map (·.devolatilize) =
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#[buildGoal [("p", "Prop"), ("q", "Prop"), ("h", "p")] "(p ∨ q) ∨ p ∨ q"])
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let expr := "Or.inl (Or.inl h)"
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let state2 ← match ← state1.tryAssign (goalId := 0) (expr := expr) with
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| .success state => pure state
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| other => do
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addTest $ assertUnreachable $ other.toString
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return ()
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addTest $ LSpec.check s!":= {expr}" ((← state2.serializeGoals (options := ← read)).map (·.devolatilize) =
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#[])
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let haveBind := "y"
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let haveType := "p ∨ q"
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let state2 ← match ← state1.tryHave (goalId := 0) (binderName := haveBind) (type := haveType) with
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| .success state => pure state
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| other => do
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addTest $ assertUnreachable $ other.toString
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return ()
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addTest $ LSpec.check s!"have {haveBind}: {haveType}" ((← state2.serializeGoals (options := ← read)).map (·.devolatilize) =
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#[
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buildGoal [("p", "Prop"), ("q", "Prop"), ("h", "p")] "p ∨ q",
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buildGoal [("p", "Prop"), ("q", "Prop"), ("h", "p"), ("y", "p ∨ q")] "(p ∨ q) ∨ p ∨ q"
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])
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let expr := "Or.inl h"
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let state3 ← match ← state2.tryAssign (goalId := 0) (expr := expr) with
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| .success state => pure state
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| other => do
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addTest $ assertUnreachable $ other.toString
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return ()
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addTest $ LSpec.check s!":= {expr}" ((← state3.serializeGoals (options := ← read)).map (·.devolatilize) =
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#[])
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let state2b ← match state3.continue state2 with
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| .ok state => pure state
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| .error e => do
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addTest $ assertUnreachable e
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return ()
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let expr := "Or.inl y"
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let state4 ← match ← state2b.tryAssign (goalId := 0) (expr := expr) with
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| .success state => pure state
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| other => do
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addTest $ assertUnreachable $ other.toString
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return ()
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addTest $ LSpec.check s!":= {expr}" ((← state4.serializeGoals (options := ← read)).map (·.devolatilize) =
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#[])
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addTest $ LSpec.check "(4 root)" state4.rootExpr?.isSome
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example : ∀ (a b c: Nat), (a + b) + c = (b + a) + c := by
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intro a b c
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conv =>
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lhs
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congr
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rw [Nat.add_comm]
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rfl
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def test_conv: TestM Unit := do
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let state? ← startProof (.expr "∀ (a b c: Nat), (a + b) + c = (b + a) + c")
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let state0 ← match state? with
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| .some state => pure state
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| .none => do
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addTest $ assertUnreachable "Goal could not parse"
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return ()
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let tactic := "intro a b c"
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let state1 ← match ← state0.tryTactic (goalId := 0) (tactic := tactic) with
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| .success state => pure state
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| other => do
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addTest $ assertUnreachable $ other.toString
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return ()
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addTest $ LSpec.check tactic ((← state1.serializeGoals (options := ← read)).map (·.devolatilize) =
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#[buildGoal [("a", "Nat"), ("b", "Nat"), ("c", "Nat")] "a + b + c = b + a + c"])
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-- This solves the state in one-shot
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let tactic := "conv => { lhs; congr; rw [Nat.add_comm]; rfl }"
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let stateT ← match ← state1.tryTactic (goalId := 0) (tactic := tactic) with
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| .success state => pure state
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| other => do
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addTest $ assertUnreachable $ other.toString
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return ()
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addTest $ LSpec.check tactic ((← stateT.serializeGoals (options := ← read)).map (·.devolatilize) =
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#[])
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let state2 ← match ← state1.tryConv (goalId := 0) with
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| .success state => pure state
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| other => do
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addTest $ assertUnreachable $ other.toString
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return ()
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addTest $ LSpec.check "conv => ..." ((← state2.serializeGoals (options := ← read)).map (·.devolatilize) =
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#[{ buildGoal [("a", "Nat"), ("b", "Nat"), ("c", "Nat")] "a + b + c = b + a + c" with isConversion := true }])
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let convTactic := "lhs"
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let state3L ← match ← state2.tryConvTactic (goalId := 0) (convTactic := convTactic) with
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| .success state => pure state
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| other => do
|
||
addTest $ assertUnreachable $ other.toString
|
||
return ()
|
||
addTest $ LSpec.check s!" {convTactic}" ((← state3L.serializeGoals (options := ← read)).map (·.devolatilize) =
|
||
#[{ buildGoal [("a", "Nat"), ("b", "Nat"), ("c", "Nat")] "a + b + c" with isConversion := true }])
|
||
|
||
let convTactic := "rhs"
|
||
let state3R ← match ← state2.tryConvTactic (goalId := 0) (convTactic := convTactic) with
|
||
| .success state => pure state
|
||
| other => do
|
||
addTest $ assertUnreachable $ other.toString
|
||
return ()
|
||
addTest $ LSpec.check s!" {convTactic}" ((← state3R.serializeGoals (options := ← read)).map (·.devolatilize) =
|
||
#[{ buildGoal [("a", "Nat"), ("b", "Nat"), ("c", "Nat")] "b + a + c" with isConversion := true }])
|
||
|
||
example : ∀ (a: Nat), 1 + a + 1 = a + 2 := by
|
||
intro a
|
||
calc 1 + a + 1 = a + 1 + 1 := by conv =>
|
||
rhs
|
||
rw [Nat.add_comm]
|
||
_ = a + 2 := by rw [Nat.add_assoc]
|
||
|
||
def test_calc: TestM Unit := do
|
||
let state? ← startProof (.expr "∀ (a: Nat), 1 + a + 1 = a + 2")
|
||
let state0 ← match state? with
|
||
| .some state => pure state
|
||
| .none => do
|
||
addTest $ assertUnreachable "Goal could not parse"
|
||
return ()
|
||
let tactic := "intro a"
|
||
let state1 ← match ← state0.tryTactic (goalId := 0) (tactic := tactic) with
|
||
| .success state => pure state
|
||
| other => do
|
||
addTest $ assertUnreachable $ other.toString
|
||
return ()
|
||
addTest $ LSpec.check tactic ((← state1.serializeGoals (options := ← read)).map (·.devolatilize) =
|
||
#[buildGoal [("a", "Nat")] "1 + a + 1 = a + 2"])
|
||
let tactic := "calc"
|
||
let state2 ← match ← state1.tryTactic (goalId := 0) (tactic := tactic) with
|
||
| .success state => pure state
|
||
| other => do
|
||
addTest $ assertUnreachable $ other.toString
|
||
return ()
|
||
addTest $ LSpec.check tactic ((← state1.serializeGoals (options := ← read)).map (·.devolatilize) =
|
||
#[buildGoal [("a", "Nat")] "1 + a + 1 = a + 2"])
|
||
|
||
def suite (env: Environment): List (String × IO LSpec.TestSeq) :=
|
||
let tests := [
|
||
("Nat.add_comm", test_nat_add_comm false),
|
||
("Nat.add_comm manual", test_nat_add_comm true),
|
||
("Nat.add_comm delta", test_delta_variable),
|
||
("arithmetic", test_arith),
|
||
("Or.comm", test_or_comm),
|
||
("have", test_have),
|
||
("conv", test_conv),
|
||
("calc", test_calc),
|
||
]
|
||
tests.map (fun (name, test) => (name, proofRunner env test))
|
||
|
||
|
||
|
||
end Pantograph.Test.Proofs
|