Pantograph/Test/Proofs.lean

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