223 lines
8.4 KiB
Plaintext
223 lines
8.4 KiB
Plaintext
import LSpec
|
||
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 := ReaderT Commands.Options StateRefT ProofTree M
|
||
|
||
def start_proof (start: Start): M (LSpec.TestSeq × Option ProofTree) := do
|
||
let env ← Lean.MonadEnv.getEnv
|
||
let mut testSeq := LSpec.TestSeq.done
|
||
match start with
|
||
| .copy name =>
|
||
let cInfo? := str_to_name name |> env.find?
|
||
testSeq := testSeq ++ LSpec.check s!"Symbol exists {name}" cInfo?.isSome
|
||
match cInfo? with
|
||
| .some cInfo =>
|
||
let state ← ProofTree.create
|
||
(name := str_to_name "TestExample")
|
||
(expr := cInfo.type)
|
||
return (testSeq, Option.some state)
|
||
| .none =>
|
||
return (testSeq, Option.none)
|
||
| .expr expr =>
|
||
let syn? := syntax_from_str env expr
|
||
testSeq := testSeq ++ LSpec.check s!"Parsing {expr}" (syn?.isOk)
|
||
match syn? with
|
||
| .error error =>
|
||
IO.println error
|
||
return (testSeq, Option.none)
|
||
| .ok syn =>
|
||
let expr? ← syntax_to_expr syn
|
||
testSeq := testSeq ++ LSpec.check s!"Elaborating" expr?.isOk
|
||
match expr? with
|
||
| .error error =>
|
||
IO.println error
|
||
return (testSeq, Option.none)
|
||
| .ok expr =>
|
||
let state ← ProofTree.create
|
||
(name := str_to_name "TestExample")
|
||
(expr := expr)
|
||
return (testSeq, Option.some state)
|
||
|
||
deriving instance DecidableEq, Repr for Commands.Expression
|
||
deriving instance DecidableEq, Repr for Commands.Variable
|
||
deriving instance DecidableEq, Repr for Commands.Goal
|
||
deriving instance DecidableEq, Repr for TacticResult
|
||
|
||
/-- Check the output of each proof step -/
|
||
def proof_step (stateId: Nat) (goalId: Nat) (tactic: String)
|
||
(expected: TacticResult) : TestM LSpec.TestSeq := do
|
||
let options ← read
|
||
let result: TacticResult ← ProofTree.execute stateId goalId tactic |>.run options
|
||
match expected, result with
|
||
| .success (.some i) #[], .success (.some _) goals =>
|
||
-- If the goals are omitted but the next state is specified, we imply that
|
||
-- the tactic succeeded.
|
||
let expected := .success (.some i) goals
|
||
return LSpec.test s!"{stateId}.{goalId} {tactic}" (result = expected)
|
||
| _, _ =>
|
||
return LSpec.test s!"{stateId}.{goalId} {tactic}" (result = expected)
|
||
|
||
/-- Check that the tree structure is correct -/
|
||
def proof_inspect (expected: Array String) : TestM LSpec.TestSeq := do
|
||
let result := (← get).structure_array
|
||
return LSpec.test s!"tree structure" (result = expected)
|
||
|
||
def proof_runner (env: Lean.Environment) (options: Commands.Options) (start: Start) (steps: List (TestM LSpec.TestSeq)): IO LSpec.TestSeq := do
|
||
let termElabM := do
|
||
let (testSeq, state?) ← start_proof start
|
||
match state? with
|
||
| .none => return testSeq
|
||
| .some state => steps.foldlM (fun tests m => do pure $ tests ++ (← m)) testSeq |>.run options |>.run' state
|
||
|
||
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 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
|
||
}
|
||
|
||
example: ∀ (a b: Nat), a + b = b + a := by
|
||
intro n m
|
||
rw [Nat.add_comm]
|
||
def proof_nat_add_comm (env: Lean.Environment): IO LSpec.TestSeq := do
|
||
let goal1: Commands.Goal := build_goal [("n", "Nat"), ("m", "Nat")] "n + m = m + n"
|
||
proof_runner env {} (.copy "Nat.add_comm") [
|
||
proof_step 0 0 "intro n m"
|
||
(.success (.some 1) #[goal1]),
|
||
proof_step 1 0 "assumption"
|
||
(.failure #[s!"tactic 'assumption' failed\nn m : Nat\n⊢ n + m = m + n"]),
|
||
proof_step 1 0 "rw [Nat.add_comm]"
|
||
(.success .none #[])
|
||
]
|
||
def proof_nat_add_comm_manual (env: Lean.Environment): IO LSpec.TestSeq := do
|
||
let goal1: Commands.Goal := build_goal [("n", "Nat"), ("m", "Nat")] "n + m = m + n"
|
||
proof_runner env {} (.expr "∀ (a b: Nat), a + b = b + a") [
|
||
proof_step 0 0 "intro n m"
|
||
(.success (.some 1) #[goal1]),
|
||
proof_step 1 0 "assumption"
|
||
(.failure #[s!"tactic 'assumption' failed\nn m : Nat\n⊢ n + m = m + n"]),
|
||
proof_step 1 0 "rw [Nat.add_comm]"
|
||
(.success .none #[])
|
||
]
|
||
|
||
-- 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 (env: Lean.Environment): IO LSpec.TestSeq := 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 }
|
||
]
|
||
}
|
||
proof_runner env {} (.expr "∀ (p q: Prop), p ∨ q → q ∨ p") [
|
||
proof_step 0 0 "intro p q h"
|
||
(.success (.some 1) #[build_goal [("p", "Prop"), ("q", "Prop"), ("h", "p ∨ q")] "q ∨ p"]),
|
||
proof_step 1 0 "cases h"
|
||
(.success (.some 2) #[branchGoal "inl" "p", branchGoal "inr" "q"]),
|
||
proof_inspect #["", "0.0", "1.0"],
|
||
proof_step 2 0 "apply Or.inr"
|
||
(.success (.some 3) #[]),
|
||
proof_inspect #["", "0.0", "1.0", "2.0"],
|
||
proof_step 3 0 "assumption"
|
||
(.success .none #[]),
|
||
proof_step 2 1 "apply Or.inl"
|
||
(.success (.some 4) #[]),
|
||
proof_step 4 0 "assumption"
|
||
(.success .none #[]),
|
||
proof_inspect #["", "0.0", "1.0", "2.0", "2.1"]
|
||
]
|
||
|
||
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 (env: Lean.Environment): IO LSpec.TestSeq := do
|
||
proof_runner env {} (.expr "∀ (w x y z : Nat) (p : Nat → Prop) (h : p (x * y + z * w * x)), p (x * w * z + y * x)") [
|
||
proof_step 0 0 "intros"
|
||
(.success (.some 1) #[]),
|
||
proof_step 1 0 "simp [Nat.add_assoc, Nat.add_comm, Nat.add_left_comm, Nat.mul_comm, Nat.mul_assoc, Nat.mul_left_comm] at *"
|
||
(.success (.some 2) #[]),
|
||
proof_step 2 0 "assumption"
|
||
(.success .none #[])
|
||
]
|
||
|
||
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
|
||
}
|
||
def proof_delta_variable (env: Lean.Environment): IO LSpec.TestSeq := do
|
||
let goal1: Commands.Goal := build_goal_selective [("n", .some "Nat")] "∀ (b : Nat), n + b = b + n"
|
||
let goal2: Commands.Goal := build_goal_selective [("n", .none), ("m", .some "Nat")] "n + m = m + n"
|
||
proof_runner env { proofVariableDelta := true } (.expr "∀ (a b: Nat), a + b = b + a") [
|
||
proof_step 0 0 "intro n"
|
||
(.success (.some 1) #[goal1]),
|
||
proof_step 1 0 "intro m"
|
||
(.success (.some 2) #[goal2])
|
||
]
|
||
|
||
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)
|
||
|
||
return LSpec.group "Proofs" $
|
||
(LSpec.group "Nat.add_comm" $ (← proof_nat_add_comm env)) ++
|
||
(LSpec.group "Nat.add_comm manual" $ (← proof_nat_add_comm_manual env)) ++
|
||
(LSpec.group "Or.comm" $ (← proof_or_comm env)) ++
|
||
(LSpec.group "Arithmetic 1" $ (← proof_arith_1 env)) ++
|
||
(LSpec.group "Delta variable" $ (← proof_delta_variable env))
|
||
|
||
end Pantograph.Test
|
||
|