253 lines
9.4 KiB
Plaintext
253 lines
9.4 KiB
Plaintext
import LSpec
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import Pantograph.Tactic
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import Pantograph.Serial
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namespace Pantograph.Test
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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 Commands.Options M)
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deriving instance DecidableEq, Repr for Commands.Expression
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deriving instance DecidableEq, Repr for Commands.Variable
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deriving instance DecidableEq, Repr for Commands.Goal
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def add_test (test: LSpec.TestSeq): TestM Unit := do
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set $ (← get) ++ test
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def start_proof (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? := str_to_name name |> env.find?
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add_test $ 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? := syntax_from_str env expr
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add_test $ 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? ← syntax_to_expr syn
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add_test $ 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 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},
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vars := (nameType.map fun x => ({
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name := 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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-- Like `build_goal` but allow certain variables to be elided.
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def build_goal_selective (nameType: List (String × Option String)) (target: String): Commands.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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name := 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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-- 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 proof_nat_add_comm: TestM Unit := do
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let goal? ← start_proof (.copy "Nat.add_comm")
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add_test $ LSpec.check "Start goal" goal?.isSome
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if let .some goal := goal? then
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if let .success #[(goal, sGoal)] ← goal.execute "intro n m" then
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let sGoal1e: Commands.Goal := build_goal [("n", "Nat"), ("m", "Nat")] "n + m = m + n"
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add_test $ LSpec.check "intro n m" (sGoal = sGoal1e)
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if let .failure #[message] ← goal.execute "assumption" then
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add_test $ LSpec.check "assumption" (message = "tactic 'assumption' failed\nn m : Nat\n⊢ n + m = m + n")
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else
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add_test $ assert_unreachable "assumption"
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if let .success #[] ← goal.execute "rw [Nat.add_comm]" then
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return ()
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else
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add_test $ assert_unreachable "rw [Nat.add_comm]"
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else
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add_test $ assert_unreachable "intro n m"
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def proof_nat_add_comm_manual: TestM Unit := do
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let goal? ← start_proof (.expr "∀ (a b: Nat), a + b = b + a")
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add_test $ LSpec.check "Start goal" goal?.isSome
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if let .some goal := goal? then
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if let .success #[(goal, sGoal)] ← goal.execute "intro n m" then
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let sGoal1e: Commands.Goal := build_goal [("n", "Nat"), ("m", "Nat")] "n + m = m + n"
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add_test $ LSpec.check "intro n m" (sGoal = sGoal1e)
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if let .failure #[message] ← goal.execute "assumption" then
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add_test $ LSpec.check "assumption" (message = "tactic 'assumption' failed\nn m : Nat\n⊢ n + m = m + n")
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else
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add_test $ assert_unreachable "assumption"
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if let .success #[] ← goal.execute "rw [Nat.add_comm]" then
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return ()
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else
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add_test $ assert_unreachable "rw [Nat.add_comm]"
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else
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add_test $ assert_unreachable "intro n m"
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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 proof_or_comm: TestM Unit := do
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let typeProp: Commands.Expression := { pp? := .some "Prop" }
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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 := #[
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{ name := "p", type? := .some typeProp, isInaccessible? := .some false },
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{ name := "q", type? := .some typeProp, isInaccessible? := .some false },
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{ name := "h✝", type? := .some { pp? := .some name }, isInaccessible? := .some true }
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]
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}
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let goal? ← start_proof (.expr "∀ (p q: Prop), p ∨ q → q ∨ p")
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add_test $ LSpec.check "Start goal" goal?.isSome
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if let .some goal := goal? then
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if let .success #[(goal, sGoal)] ← goal.execute "intro p q h" then
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let sGoal1e := build_goal [("p", "Prop"), ("q", "Prop"), ("h", "p ∨ q")] "q ∨ p"
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add_test $ LSpec.check "intro p q h" (sGoal = sGoal1e)
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if let .success #[(goal1, sGoal1), (goal2, sGoal2)] ← goal.execute "cases h" then
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add_test $ LSpec.check "cases h/1" (sGoal1 = branchGoal "inl" "p")
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if let .success #[(goal, _)] ← goal1.execute "apply Or.inr" then
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if let .success #[] ← goal.execute "assumption" then
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return ()
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else
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add_test $ assert_unreachable "assumption"
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else
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add_test $ assert_unreachable "apply Or.inr"
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add_test $ LSpec.check "cases h/2" (sGoal2 = branchGoal "inr" "q")
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if let .success #[(goal, _)] ← goal2.execute "apply Or.inl" then
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if let .success #[] ← goal.execute "assumption" then
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return ()
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else
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add_test $ assert_unreachable "assumption"
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else
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add_test $ assert_unreachable "apply Or.inl"
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else
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add_test $ assert_unreachable "cases h"
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else
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add_test $ assert_unreachable "intro p q h"
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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 proof_arith_1: TestM Unit := do
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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)")
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add_test $ LSpec.check "Start goal" goal?.isSome
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if let .some goal := goal? then
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if let .success #[(goal, _)] ← goal.execute "intros" then
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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
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if let .success #[] ← goal.execute "assumption" then
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return ()
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else
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add_test $ assert_unreachable "assumption"
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else
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add_test $ assert_unreachable "simp ..."
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else
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add_test $ assert_unreachable "intros"
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def proof_delta_variable: TestM Unit := withReader (fun _ => {proofVariableDelta := true}) do
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let goal? ← start_proof (.expr "∀ (a b: Nat), a + b = b + a")
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add_test $ LSpec.check "Start goal" goal?.isSome
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if let .some goal := goal? then
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if let .success #[(goal, sGoal)] ← goal.execute "intro n" then
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let sGoal1e: Commands.Goal := build_goal_selective [("n", .some "Nat")] "∀ (b : Nat), n + b = b + n"
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add_test $ LSpec.check "intro n" (sGoal = sGoal1e)
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if let .success #[(_, sGoal)] ← goal.execute "intro m" then
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let sGoal2e: Commands.Goal := build_goal_selective [("n", .none), ("m", .some "Nat")] "n + m = m + n"
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add_test $ LSpec.check "intro m" (sGoal = sGoal2e)
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else
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add_test $ assert_unreachable "intro m"
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else
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add_test $ assert_unreachable "intro n"
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def proof_runner (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 := {
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currNamespace := str_to_name "Aniva",
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openDecls := [], -- No 'open' directives needed
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fileName := "<Pantograph>",
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fileMap := { source := "", positions := #[0], lines := #[1] }
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}
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let metaM := termElabM.run' (ctx := {
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declName? := some "_pantograph",
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errToSorry := false
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})
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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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def test_proofs : IO LSpec.TestSeq := do
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let env: Lean.Environment ← Lean.importModules
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(imports := ["Init"].map (λ str => { module := str_to_name str, runtimeOnly := false }))
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(opts := {})
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(trustLevel := 1)
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let tests := [
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("Nat.add_comm", proof_nat_add_comm),
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("nat.add_comm manual", proof_nat_add_comm_manual),
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("Or.comm", proof_or_comm),
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("arithmetic 1", proof_arith_1),
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("delta variable", proof_delta_variable)
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]
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let tests ← tests.foldlM (fun acc tests => do
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let (name, tests) := tests
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let tests ← proof_runner env tests
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return acc ++ (LSpec.group name tests)) LSpec.TestSeq.done
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return LSpec.group "Proofs" tests
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end Pantograph.Test
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