Merge pull request 'Simplify goal bookkeeping mechanism' (#10) from tactic/book into dev

Reviewed-on: #10
This commit is contained in:
Leni Aniva 2023-08-30 19:18:36 -07:00
commit c4a97d8a76
7 changed files with 435 additions and 260 deletions

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@ -2,6 +2,7 @@ import Pantograph.Commands
import Pantograph.Serial
import Pantograph.Symbols
import Pantograph.Tactic
import Pantograph.SemihashMap
namespace Pantograph
@ -11,8 +12,7 @@ structure Context where
/-- Stores state of the REPL -/
structure State where
options: Commands.Options := {}
--environments: Array Lean.Environment := #[]
proofTrees: Array ProofTree := #[]
goalStates: SemihashMap GoalState := SemihashMap.empty
-- State monad
abbrev MainM := ReaderT Context (StateT State Lean.Elab.TermElabM)
@ -30,14 +30,15 @@ def execute (command: Commands.Command): MainM Lean.Json := do
| .error error => return Lean.toJson $ errorCommand s!"Unable to parse json: {error}"
match command.cmd with
| "reset" => run reset
| "stat" => run stat
| "expr.echo" => run expr_echo
| "lib.catalog" => run lib_catalog
| "lib.inspect" => run lib_inspect
| "options.set" => run options_set
| "options.print" => run options_print
| "proof.start" => run proof_start
| "proof.tactic" => run proof_tactic
| "proof.printTree" => run proof_print_tree
| "goal.start" => run goal_start
| "goal.tactic" => run goal_tactic
| "goal.delete" => run goal_delete
| cmd =>
let error: Commands.InteractionError :=
errorCommand s!"Unknown command {cmd}"
@ -47,11 +48,15 @@ def execute (command: Commands.Command): MainM Lean.Json := do
errorCommand := errorI "command"
errorIndex := errorI "index"
-- Command Functions
reset (_: Commands.Reset): MainM (CR Commands.ResetResult) := do
reset (_: Commands.Reset): MainM (CR Commands.StatResult) := do
let state ← get
let nTrees := state.proofTrees.size
set { state with proofTrees := #[] }
return .ok { nTrees := nTrees }
let nGoals := state.goalStates.size
set { state with goalStates := SemihashMap.empty }
return .ok { nGoals }
stat (_: Commands.Stat): MainM (CR Commands.StatResult) := do
let state ← get
let nGoals := state.goalStates.size
return .ok { nGoals }
lib_catalog (_: Commands.LibCatalog): MainM (CR Commands.LibCatalogResult) := do
let env ← Lean.MonadEnv.getEnv
let names := env.constants.fold (init := #[]) (λ acc name info =>
@ -113,7 +118,7 @@ def execute (command: Commands.Command): MainM Lean.Json := do
return .ok { }
options_print (_: Commands.OptionsPrint): MainM (CR Commands.OptionsPrintResult) := do
return .ok (← get).options
proof_start (args: Commands.ProofStart): MainM (CR Commands.ProofStartResult) := do
goal_start (args: Commands.GoalStart): MainM (CR Commands.GoalStartResult) := do
let state ← get
let env ← Lean.MonadEnv.getEnv
let expr?: Except _ Lean.Expr ← (match args.expr, args.copyFrom with
@ -134,32 +139,36 @@ def execute (command: Commands.Command): MainM Lean.Json := do
match expr? with
| .error error => return .error error
| .ok expr =>
let tree ← ProofTree.create expr
-- Put the new tree in the environment
let nextTreeId := state.proofTrees.size
set { state with proofTrees := state.proofTrees.push tree }
return .ok { treeId := nextTreeId }
proof_tactic (args: Commands.ProofTactic): MainM (CR Commands.ProofTacticResult) := do
let goalState ← GoalState.create expr
let (goalStates, goalId) := state.goalStates.insert goalState
set { state with goalStates }
return .ok { goalId }
goal_tactic (args: Commands.GoalTactic): MainM (CR Commands.GoalTacticResult) := do
let state ← get
match state.proofTrees.get? args.treeId with
| .none => return .error $ errorIndex "Invalid tree index {args.treeId}"
| .some tree =>
let (result, nextTree) ← ProofTree.execute
(stateId := args.stateId)
(goalId := args.goalId.getD 0)
(tactic := args.tactic) |>.run state.options |>.run tree
match state.goalStates.get? args.goalId with
| .none => return .error $ errorIndex s!"Invalid goal index {args.goalId}"
| .some goalState =>
let result ← GoalState.execute goalState args.tactic |>.run state.options
match result with
| .invalid message => return .error $ errorIndex message
| .success nextId? goals =>
set { state with proofTrees := state.proofTrees.set! args.treeId nextTree }
return .ok { nextId? := nextId?, goals? := .some goals }
| .success goals =>
if goals.isEmpty then
return .ok {}
else
-- Append all goals
let (goalStates, goalIds, sGoals) := Array.foldl (λ acc itr =>
let (map, indices, serializedGoals) := acc
let (goalState, sGoal) := itr
let (map, index) := map.insert goalState
(map, index :: indices, sGoal :: serializedGoals)
) (state.goalStates, [], []) goals
set { state with goalStates }
return .ok { goals? := .some sGoals.reverse.toArray, goalIds? := .some goalIds.reverse.toArray }
| .failure messages =>
return .ok { tacticErrors? := .some messages }
proof_print_tree (args: Commands.ProofPrintTree): MainM (CR Commands.ProofPrintTreeResult) := do
goal_delete (args: Commands.GoalDelete): MainM (CR Commands.GoalDeleteResult) := do
let state ← get
match state.proofTrees.get? args.treeId with
| .none => return .error $ errorIndex "Invalid tree index {args.treeId}"
| .some tree =>
return .ok { parents := tree.structure_array }
let goalStates := args.goalIds.foldl (λ map id => map.remove id) state.goalStates
set { state with goalStates }
return .ok {}
end Pantograph

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@ -80,8 +80,11 @@ structure InteractionError where
structure Reset where
deriving Lean.FromJson
structure ResetResult where
nTrees: Nat
structure Stat where
deriving Lean.FromJson
structure StatResult where
-- Number of goals states
nGoals: Nat
deriving Lean.ToJson
-- Return the type of an expression
@ -127,35 +130,34 @@ structure OptionsPrint where
deriving Lean.FromJson
abbrev OptionsPrintResult := Options
structure ProofStart where
structure GoalStart where
-- Only one of the fields below may be populated.
expr: Option String -- Proof expression
copyFrom: Option String -- Theorem name
deriving Lean.FromJson
structure ProofStartResult where
treeId: Nat := 0 -- Proof tree id
structure GoalStartResult where
goalId: Nat := 0 -- Proof tree id
deriving Lean.ToJson
structure ProofTactic where
structure GoalTactic where
-- Identifiers for tree, state, and goal
treeId: Nat
stateId: Nat
goalId: Option Nat -- Defaults to 0
goalId: Nat
tactic: String
deriving Lean.FromJson
structure ProofTacticResult where
structure GoalTacticResult where
-- Existence of this field shows success
goals?: Option (Array Goal) := .none
-- Next proof state id, if successful
nextId?: Option Nat := .none
goalIds?: Option (Array Nat) := .none
-- Existence of this field shows failure
tacticErrors?: Option (Array String) := .none
deriving Lean.ToJson
structure ProofPrintTree where
treeId: Nat
-- Remove a bunch of goals.
structure GoalDelete where
goalIds: List Nat
deriving Lean.FromJson
structure ProofPrintTreeResult where
-- "" if no parents, otherwise "parentId.goalId"
parents: Array String
structure GoalDeleteResult where
deriving Lean.ToJson
end Pantograph.Commands

149
Pantograph/SemihashMap.lean Normal file
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@ -0,0 +1,149 @@
namespace Pantograph.SemihashMap
structure Imp (β: Type u) where
data: Array (Option β)
-- Number of elements currently in use
size: Nat
-- Next index that has never been touched
allocFront: Nat
-- Deallocated indices
deallocs: Array Nat
-- Number of valid entries in `deallocs` array
lastDealloc: Nat
namespace Imp
structure WF (m: Imp β): Prop where
capacity: m.data.size = m.deallocs.size
front_dealloc: ∀ i: Fin m.deallocs.size, (i < m.allocFront) → (m.deallocs.get i) < m.allocFront
front_data: ∀ i: Fin m.data.size, (i ≥ m.allocFront) → (m.data.get i).isNone
def empty (capacity := 16): Imp β :=
{
data := mkArray capacity .none,
size := 0,
allocFront := 0,
deallocs := mkArray capacity 0,
lastDealloc := 0,
}
private theorem list_get_replicate (x: α) (i: Fin (List.replicate n x).length):
List.get (List.replicate n x) i = x := by
sorry
theorem empty_wf : WF (empty n: Imp β) := by
unfold empty
apply WF.mk
case capacity =>
conv =>
lhs
congr
simp
conv =>
rhs
congr
simp
simp
case front_dealloc =>
simp_all
intro i
intro a
contradiction
case front_data =>
simp_all
intro i
unfold Imp.data at i
simp at i
conv =>
lhs
unfold Array.get
unfold mkArray
simp [List.replicate]
rewrite [list_get_replicate]
-- FIXME: Merge this with the well-formed versions below so proof and code can
-- mesh seamlessly.
@[inline] def insert (map: Imp β) (v: β): (Imp β × Nat) :=
match map.lastDealloc with
| 0 => -- Capacity is full, buffer expansion is required
if map.size == map.data.size then
let nextIndex := map.data.size
let extendCapacity := map.size
let result: Imp β := {
data := (map.data.append #[Option.some v]).append (mkArray extendCapacity .none),
size := map.size + 1,
allocFront := map.size + 1,
deallocs := mkArray (map.data.size + 1 + extendCapacity) 0,
lastDealloc := 0,
}
(result, nextIndex)
else
let nextIndex := map.size
let result: Imp β := {
map
with
data := map.data.set ⟨nextIndex, sorry⟩ (Option.some v),
size := map.size + 1,
allocFront := map.allocFront + 1,
}
(result, nextIndex)
| (.succ k) => -- Allocation list has space
let nextIndex := map.deallocs.get! k
let result: Imp β := {
map with
data := map.data.set ⟨nextIndex, sorry⟩ (Option.some v),
size := map.size + 1,
lastDealloc := map.lastDealloc - 1
}
(result, nextIndex)
@[inline] def remove (map: Imp β) (index: Fin (map.size)): Imp β :=
have h: index.val < map.data.size := by sorry
match map.data.get ⟨index.val, h⟩ with
| .none => map
| .some _ =>
{
map with
data := map.data.set ⟨index, sorry⟩ .none,
size := map.size - 1,
deallocs := map.deallocs.set ⟨map.lastDealloc, sorry⟩ index,
lastDealloc := map.lastDealloc + 1,
}
/-- Retrieval is efficient -/
@[inline] def get? (map: Imp β) (index: Fin (map.size)): Option β :=
have h: index.val < map.data.size := by sorry
map.data.get ⟨index.val, h⟩
@[inline] def capacity (map: Imp β): Nat := map.data.size
end Imp
/--
This is like a hashmap but you cannot control the keys.
-/
def _root_.Pantograph.SemihashMap β := {m: Imp β // m.WF}
@[inline] def empty (capacity := 16): SemihashMap β :=
⟨ Imp.empty capacity, Imp.empty_wf ⟩
@[inline] def insert (map: SemihashMap β) (v: β): (SemihashMap β × Nat) :=
let ⟨imp, pre⟩ := map
let ⟨result, id⟩ := imp.insert v
( ⟨ result, sorry ⟩, id)
@[inline] def remove (map: SemihashMap β) (index: Nat): SemihashMap β :=
let ⟨imp, pre⟩ := map
let result := imp.remove ⟨index, sorry⟩
⟨ result, sorry ⟩
@[inline] def get? (map: SemihashMap β) (index: Nat): Option β :=
let ⟨imp, _⟩ := map
imp.get? ⟨index, sorry⟩
@[inline] def size (map: SemihashMap β): Nat :=
let ⟨imp, _⟩ := map
imp.size
end Pantograph.SemihashMap

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@ -24,35 +24,22 @@ def Lean.MessageLog.getErrorMessages (log : MessageLog) : MessageLog :=
namespace Pantograph
open Lean
structure ProofState where
goals : List MVarId
structure GoalState where
mvarId: MVarId
savedState : Elab.Tactic.SavedState
parent : Option Nat := none
parentGoalId : Nat := 0
structure ProofTree where
-- Set of proof states
states : Array ProofState := #[]
abbrev M := Elab.TermElabM
def ProofTree.create (expr: Expr): M ProofTree := do
def GoalState.create (expr: Expr): M GoalState := do
let expr ← instantiateMVars expr
let goal := (← Meta.mkFreshExprMVar expr (kind := MetavarKind.synthetic))
let savedStateMonad: Elab.Tactic.TacticM Elab.Tactic.SavedState := MonadBacktrack.saveState
let savedState ← savedStateMonad { elaborator := .anonymous } |>.run' { goals := [goal.mvarId!]}
return {
states := #[{
savedState := savedState,
goals := [goal.mvarId!]
}]
mvarId := goal.mvarId!
}
-- Print the tree structures in readable form
def ProofTree.structure_array (tree: ProofTree): Array String :=
tree.states.map λ state => match state.parent with
| .none => ""
| .some parent => s!"{parent}.{state.parentGoalId}"
def execute_tactic (state: Elab.Tactic.SavedState) (goal: MVarId) (tactic: String) :
M (Except (Array String) (Elab.Tactic.SavedState × List MVarId)):= do
let tacticM (stx: Syntax): Elab.Tactic.TacticM (Except (Array String) (Elab.Tactic.SavedState × List MVarId)) := do
@ -78,44 +65,38 @@ def execute_tactic (state: Elab.Tactic.SavedState) (goal: MVarId) (tactic: Strin
/-- Response for executing a tactic -/
inductive TacticResult where
-- Invalid id
| invalid (message: String): TacticResult
-- Goes to next state
| success (nextId?: Option Nat) (goals: Array Commands.Goal)
| success (goals: Array (GoalState × Commands.Goal))
-- Fails with messages
| failure (messages: Array String)
namespace TacticResult
def is_success: TacticResult → Bool
| .success _ => true
| .failure _ => false
end TacticResult
/-- Execute tactic on given state -/
def ProofTree.execute (stateId: Nat) (goalId: Nat) (tactic: String):
Commands.OptionsT StateRefT ProofTree M TacticResult := do
def GoalState.execute (goal: GoalState) (tactic: String):
Commands.OptionsT M TacticResult := do
let options ← read
let tree ← get
match tree.states.get? stateId with
| .none => return .invalid s!"Invalid state id {stateId}"
| .some state =>
match state.goals.get? goalId with
| .none => return .invalid s!"Invalid goal id {goalId}"
| .some goal =>
match (← execute_tactic (state := state.savedState) (goal := goal) (tactic := tactic)) with
match (← execute_tactic (state := goal.savedState) (goal := goal.mvarId) (tactic := tactic)) with
| .error errors =>
return .failure errors
| .ok (nextState, nextGoals) =>
let nextId := tree.states.size
if nextGoals.isEmpty then
return .success .none #[]
return .success #[]
else
let proofState: ProofState := {
savedState := nextState,
goals := nextGoals,
parent := stateId,
parentGoalId := goalId
}
modify fun s => { s with states := s.states.push proofState }
let parentDecl? := (← MonadMCtx.getMCtx).findDecl? goal
let goals ← nextGoals.mapM fun mvarId => do
match (← MonadMCtx.getMCtx).findDecl? mvarId with
| .some mvarDecl => serialize_goal options mvarDecl (parentDecl? := parentDecl?)
| .none => throwError mvarId
return .success (.some nextId) goals.toArray
let nextGoals: List GoalState := nextGoals.map fun mvarId => { mvarId, savedState := nextState }
let parentDecl? := (← MonadMCtx.getMCtx).findDecl? goal.mvarId
let goals ← nextGoals.mapM fun nextGoal => do
match (← MonadMCtx.getMCtx).findDecl? nextGoal.mvarId with
| .some mvarDecl =>
let serializedGoal ← serialize_goal options mvarDecl (parentDecl? := parentDecl?)
return (nextGoal, serializedGoal)
| .none => throwError nextGoal.mvarId
return .success goals.toArray
end Pantograph

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@ -1,5 +1,5 @@
namespace Pantograph
def version := "0.2.3"
def version := "0.2.4"
end Pantograph

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@ -50,15 +50,16 @@ Example with `mathlib4` (~90k symbols, may stack overflow, see troubleshooting)
$ lake env build/bin/Pantograph Mathlib.Analysis.Seminorm
lib.catalog
```
Example proving a theorem: (alternatively use `proof.start {"copyFrom": "Nat.add_comm"}`) to prime the proof
Example proving a theorem: (alternatively use `goal.start {"copyFrom": "Nat.add_comm"}`) to prime the proof
```
$ env build/bin/Pantograph Init
proof.start {"expr": "∀ (n m : Nat), n + m = m + n"}
proof.tactic {"treeId": 0, "stateId": 0, "goalId": 0, "tactic": "intro n m"}
proof.tactic {"treeId": 0, "stateId": 1, "goalId": 0, "tactic": "assumption"}
proof.printTree {"treeId": 0}
proof.tactic {"treeId": 0, "stateId": 1, "goalId": 0, "tactic": "rw [Nat.add_comm]"}
proof.printTree {"treeId": 0}
goal.start {"expr": "∀ (n m : Nat), n + m = m + n"}
goal.tactic {"goalId": 0, "tactic": "intro n m"}
goal.tactic {"goalId": 1, "tactic": "assumption"}
goal.delete {"goalIds": [0]}
stat {}
goal.tactic {"goalId": 1, "tactic": "rw [Nat.add_comm]"}
stat
```
where the application of `assumption` should lead to a failure.
@ -74,9 +75,10 @@ See `Pantograph/Commands.lean` for a description of the parameters and return va
- `options.set { key: value, ... }`: Set one or more options (not Lean options; those
have to be set via command line arguments.), for options, see `Pantograph/Commands.lean`
- `options.print`: Display the current set of options
- `proof.start {["name": <name>], ["expr": <expr>], ["copyFrom": <symbol>]}`: Start a new proof state from a given expression or symbol
- `proof.tactic {"treeId": <id>, "stateId": <id>, "goalId": <id>, "tactic": string}`: Execute a tactic on a given proof state
- `proof.printTree {"treeId": <id>}`: Print the topological structure of a proof tree
- `goal.start {["name": <name>], ["expr": <expr>], ["copyFrom": <symbol>]}`: Start a new goal from a given expression or symbol
- `goal.tactic {"goalId": <id>, "tactic": <tactic>}`: Execute a tactic string on a given goal
- `goal.remove {"goalIds": [<id>]}"`: Remove a bunch of stored goals.
- `stat`: Display resource usage
## Errors

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@ -10,87 +10,46 @@ 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
(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
(expr := expr)
return (testSeq, Option.some state)
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
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)
def add_test (test: LSpec.TestSeq): TestM Unit := do
set $ (← get) ++ test
/-- 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 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 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 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 assert_unreachable (message: String): LSpec.TestSeq := LSpec.check message false
def build_goal (nameType: List (String × String)) (target: String): Commands.Goal :=
{
@ -101,30 +60,61 @@ def build_goal (nameType: List (String × String)) (target: String): Commands.Go
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 (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 #[])
]
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
@ -141,7 +131,7 @@ example: ∀ (p q: Prop), p q → q p := by
assumption
. apply Or.inl
assumption
def proof_or_comm (env: Lean.Environment): IO LSpec.TestSeq := do
def proof_or_comm: TestM Unit := do
let typeProp: Commands.Expression := { pp? := .some "Prop" }
let branchGoal (caseName name: String): Commands.Goal := {
caseName? := .some caseName,
@ -152,69 +142,111 @@ def proof_or_comm (env: Lean.Environment): IO LSpec.TestSeq := do
{ 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"]
]
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 (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 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 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: 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 := str_to_name "Aniva",
openDecls := [], -- No 'open' directives needed
fileName := "<Pantograph>",
fileMap := { source := "", positions := #[0], lines := #[1] }
}
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])
]
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 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)
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" $
(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))
return LSpec.group "Proofs" tests
end Pantograph.Test