Merge pull request 'feat: Add support for the `have`, `conv`, and `calc` tactics' (#59) from goal/have-conv-calc into dev

Reviewed-on: #59
This commit is contained in:
Leni Aniva 2024-04-11 15:36:19 -07:00
commit f20ee8dc87
9 changed files with 669 additions and 140 deletions

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@ -114,12 +114,22 @@ def execute (command: Protocol.Command): MainM Lean.Json := do
match state.goalStates.find? args.stateId with
| .none => return .error $ errorIndex s!"Invalid state index {args.stateId}"
| .some goalState => do
let nextGoalState?: Except _ GoalState ← match args.tactic?, args.expr? with
| .some tactic, .none => do
let nextGoalState?: Except _ GoalState ←
match args.tactic?, args.expr?, args.have?, args.calc?, args.conv? with
| .some tactic, .none, .none, .none, .none => do
pure ( Except.ok (← goalTactic goalState args.goalId tactic))
| .none, .some expr => do
pure ( Except.ok (← goalTryAssign goalState args.goalId expr))
| _, _ => pure (Except.error <| errorI "arguments" "Exactly one of {tactic, expr} must be supplied")
| .none, .some expr, .none, .none, .none => do
pure ( Except.ok (← goalAssign goalState args.goalId expr))
| .none, .none, .some type, .none, .none => do
let binderName := args.binderName?.getD ""
pure ( Except.ok (← goalHave goalState args.goalId binderName type))
| .none, .none, .none, .some pred, .none => do
pure ( Except.ok (← goalCalc goalState args.goalId pred))
| .none, .none, .none, .none, .some true => do
pure ( Except.ok (← goalConv goalState args.goalId))
| .none, .none, .none, .none, .some false => do
pure ( Except.ok (← goalConvExit goalState))
| _, _, _, _, _ => pure (Except.error <| errorI "arguments" "Exactly one of {tactic, expr, have} must be supplied")
match nextGoalState? with
| .error error => return .error error
| .ok (.success nextGoalState) =>
@ -137,6 +147,8 @@ def execute (command: Protocol.Command): MainM Lean.Json := do
return .ok { parseError? := .some message }
| .ok (.indexError goalId) =>
return .error $ errorIndex s!"Invalid goal id index {goalId}"
| .ok (.invalidAction message) =>
return .error $ errorI "invalid" message
| .ok (.failure messages) =>
return .ok { tacticErrors? := .some messages }
goal_continue (args: Protocol.GoalContinue): MainM (CR Protocol.GoalContinueResult) := do

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@ -1,3 +1,8 @@
/-
Functions for handling metavariables
All the functions starting with `try` resume their inner monadic state.
-/
import Pantograph.Protocol
import Lean
@ -10,6 +15,11 @@ def Lean.MessageLog.getErrorMessages (log : MessageLog) : MessageLog :=
namespace Pantograph
open Lean
def filename: String := "<pantograph>"
/--
Represents an interconnected set of metavariables, or a state in proof search
-/
structure GoalState where
savedState : Elab.Tactic.SavedState
@ -18,21 +28,22 @@ structure GoalState where
-- New metavariables acquired in this state
newMVars: SSet MVarId
-- The id of the goal in the parent
parentGoalId: Nat := 0
-- Parent state metavariable source
parentMVar: Option MVarId
parentMVar?: Option MVarId
abbrev M := Elab.TermElabM
-- Existence of this field shows that we are currently in `conv` mode.
convMVar?: Option (MVarId × MVarId) := .none
-- Previous RHS for calc, so we don't have to repeat it every time
-- WARNING: If using `state with` outside of `calc`, this must be set to `.none`
calcPrevRhs?: Option Expr := .none
protected def GoalState.create (expr: Expr): M GoalState := do
protected def GoalState.create (expr: Expr): Elab.TermElabM GoalState := do
-- May be necessary to immediately synthesise all metavariables if we need to leave the elaboration context.
-- See https://leanprover.zulipchat.com/#narrow/stream/270676-lean4/topic/Unknown.20universe.20metavariable/near/360130070
--Elab.Term.synthesizeSyntheticMVarsNoPostponing
--let expr ← instantiateMVars expr
let goal := (← Meta.mkFreshExprMVar expr (kind := MetavarKind.synthetic) (userName := .anonymous))
let goal ← Meta.mkFreshExprMVar expr (kind := MetavarKind.synthetic) (userName := .anonymous)
let savedStateMonad: Elab.Tactic.TacticM Elab.Tactic.SavedState := MonadBacktrack.saveState
let root := goal.mvarId!
let savedState ← savedStateMonad { elaborator := .anonymous } |>.run' { goals := [root]}
@ -40,28 +51,38 @@ protected def GoalState.create (expr: Expr): M GoalState := do
savedState,
root,
newMVars := SSet.insert .empty root,
parentMVar := .none,
parentMVar? := .none,
}
protected def GoalState.goals (state: GoalState): List MVarId := state.savedState.tactic.goals
protected def GoalState.runM {α: Type} (state: GoalState) (m: Elab.TermElabM α) : M α := do
state.savedState.term.restore
m
protected def GoalState.isConv (state: GoalState): Bool :=
state.convMVar?.isSome
protected def GoalState.goals (state: GoalState): List MVarId :=
state.savedState.tactic.goals
protected def GoalState.mctx (state: GoalState): MetavarContext :=
state.savedState.term.meta.meta.mctx
protected def GoalState.env (state: GoalState): Environment :=
state.savedState.term.meta.core.env
private def GoalState.mvars (state: GoalState): SSet MVarId :=
state.mctx.decls.foldl (init := .empty) fun acc k _ => acc.insert k
protected def GoalState.restoreMetaM (state: GoalState): MetaM Unit :=
state.savedState.term.meta.restore
private def GoalState.restoreElabM (state: GoalState): Elab.TermElabM Unit :=
state.savedState.term.restore
def GoalState.restoreMetaM (state: GoalState): MetaM Unit :=
state.savedState.term.meta.restore
private def GoalState.restoreTacticM (state: GoalState) (goal: MVarId): Elab.Tactic.TacticM Unit := do
state.savedState.restore
Elab.Tactic.setGoals [goal]
private def newMVarSet (mctxOld: @&MetavarContext) (mctxNew: @&MetavarContext): SSet MVarId :=
mctxNew.decls.foldl (fun acc mvarId mvarDecl =>
if let .some prevMVarDecl := mctxOld.decls.find? mvarId then
assert! prevMVarDecl.type == mvarDecl.type
acc
else
acc.insert mvarId
) SSet.empty
/-- Inner function for executing tactic on goal state -/
def executeTactic (state: Elab.Tactic.SavedState) (goal: MVarId) (tactic: Syntax) :
M (Except (Array String) Elab.Tactic.SavedState):= do
Elab.TermElabM (Except (Array String) Elab.Tactic.SavedState):= do
let tacticM (stx: Syntax): Elab.Tactic.TacticM (Except (Array String) Elab.Tactic.SavedState) := do
state.restore
Elab.Tactic.setGoals [goal]
@ -87,19 +108,22 @@ inductive TacticResult where
| parseError (message: String)
-- The goal index is out of bounds
| indexError (goalId: Nat)
-- The given action cannot be executed in the state
| invalidAction (message: String)
/-- Execute tactic on given state -/
protected def GoalState.execute (state: GoalState) (goalId: Nat) (tactic: String):
M TacticResult := do
protected def GoalState.tryTactic (state: GoalState) (goalId: Nat) (tactic: String):
Elab.TermElabM TacticResult := do
state.restoreElabM
let goal ← match state.savedState.tactic.goals.get? goalId with
| .some goal => pure $ goal
| .none => return .indexError goalId
goal.checkNotAssigned `GoalState.tryTactic
let tactic ← match Parser.runParserCategory
(env := ← MonadEnv.getEnv)
(catName := `tactic)
(catName := if state.isConv then `conv else `tactic)
(input := tactic)
(fileName := "<stdin>") with
(fileName := filename) with
| .ok stx => pure $ stx
| .error error => return .parseError error
match (← executeTactic (state := state.savedState) (goal := goal) (tactic := tactic)) with
@ -108,25 +132,59 @@ protected def GoalState.execute (state: GoalState) (goalId: Nat) (tactic: String
| .ok nextSavedState =>
-- Assert that the definition of metavariables are the same
let nextMCtx := nextSavedState.term.meta.meta.mctx
let prevMCtx := state.savedState.term.meta.meta.mctx
let prevMCtx := state.mctx
-- Generate a list of mvarIds that exist in the parent state; Also test the
-- assertion that the types have not changed on any mvars.
let newMVars ← nextMCtx.decls.foldlM (fun acc mvarId mvarDecl => do
if let .some prevMVarDecl := prevMCtx.decls.find? mvarId then
assert! prevMVarDecl.type == mvarDecl.type
return acc
else
return acc.insert mvarId
) SSet.empty
return .success {
root := state.root,
state with
savedState := nextSavedState
newMVars,
parentGoalId := goalId,
parentMVar := .some goal,
newMVars := newMVarSet prevMCtx nextMCtx,
parentMVar? := .some goal,
calcPrevRhs? := .none,
}
protected def GoalState.tryAssign (state: GoalState) (goalId: Nat) (expr: String): M TacticResult := do
/-- Assumes elabM has already been restored. Assumes expr has already typechecked -/
protected def GoalState.assign (state: GoalState) (goal: MVarId) (expr: Expr):
Elab.TermElabM TacticResult := do
let goalType ← goal.getType
try
-- For some reason this is needed. One of the unit tests will fail if this isn't here
let error?: Option String ← goal.withContext (do
let exprType ← Meta.inferType expr
if ← Meta.isDefEq goalType exprType then
pure .none
else do
return .some s!"{← Meta.ppExpr expr} : {← Meta.ppExpr exprType} != {← Meta.ppExpr goalType}"
)
if let .some error := error? then
return .parseError error
goal.checkNotAssigned `GoalState.assign
goal.assign expr
if (← getThe Core.State).messages.hasErrors then
let messages := (← getThe Core.State).messages.getErrorMessages |>.toList.toArray
let errors ← (messages.map Message.data).mapM fun md => md.toString
return .failure errors
else
let prevMCtx := state.savedState.term.meta.meta.mctx
let nextMCtx ← getMCtx
-- Generate a list of mvarIds that exist in the parent state; Also test the
-- assertion that the types have not changed on any mvars.
let newMVars := newMVarSet prevMCtx nextMCtx
let nextGoals ← newMVars.toList.filterM (λ mvar => do pure !(← mvar.isAssigned))
return .success {
root := state.root,
savedState := {
term := ← MonadBacktrack.saveState,
tactic := { goals := nextGoals }
},
newMVars,
parentMVar? := .some goal,
}
catch exception =>
return .failure #[← exception.toMessageData.toString]
protected def GoalState.tryAssign (state: GoalState) (goalId: Nat) (expr: String):
Elab.TermElabM TacticResult := do
state.restoreElabM
let goal ← match state.savedState.tactic.goals.get? goalId with
| .some goal => pure goal
@ -135,50 +193,221 @@ protected def GoalState.tryAssign (state: GoalState) (goalId: Nat) (expr: String
(env := state.env)
(catName := `term)
(input := expr)
(fileName := "<stdin>") with
(fileName := filename) with
| .ok syn => pure syn
| .error error => return .parseError error
let tacticM: Elab.Tactic.TacticM TacticResult := do
let goalType ← goal.getType
try
let expr ← goal.withContext $
Elab.Term.elabTermAndSynthesize (stx := expr) (expectedType? := .some goalType)
state.assign goal expr
catch exception =>
return .failure #[← exception.toMessageData.toString]
-- Specialized Tactics
protected def GoalState.tryHave (state: GoalState) (goalId: Nat) (binderName: String) (type: String):
Elab.TermElabM TacticResult := do
state.restoreElabM
let goal ← match state.savedState.tactic.goals.get? goalId with
| .some goal => pure goal
| .none => return .indexError goalId
let type ← match Parser.runParserCategory
(env := state.env)
(catName := `term)
(input := type)
(fileName := filename) with
| .ok syn => pure syn
| .error error => return .parseError error
let binderName := binderName.toName
try
-- Implemented similarly to the intro tactic
let nextGoals: List MVarId ← goal.withContext $ (do
let type ← Elab.Term.elabType (stx := type)
let lctx ← MonadLCtx.getLCtx
-- The branch goal inherits the same context, but with a different type
let mvarBranch ← Meta.mkFreshExprMVarAt lctx (← Meta.getLocalInstances) type
-- Create the context for the `upstream` goal
let fvarId ← mkFreshFVarId
let lctxUpstream := lctx.mkLocalDecl fvarId binderName type
let fvar := mkFVar fvarId
let mvarUpstream ←
withTheReader Meta.Context (fun ctx => { ctx with lctx := lctxUpstream }) do
Meta.withNewLocalInstances #[fvar] 0 (do
let mvarUpstream ← Meta.mkFreshExprMVarAt (← getLCtx) (← Meta.getLocalInstances)
(← goal.getType) (kind := MetavarKind.synthetic) (userName := .anonymous)
let expr: Expr := .app (.lam binderName type mvarBranch .default) mvarUpstream
goal.assign expr
pure mvarUpstream)
pure [mvarBranch.mvarId!, mvarUpstream.mvarId!]
)
return .success {
root := state.root,
savedState := {
term := ← MonadBacktrack.saveState,
tactic := { goals := nextGoals }
},
newMVars := nextGoals.toSSet,
parentMVar? := .some goal,
}
catch exception =>
return .failure #[← exception.toMessageData.toString]
/-- Enter conv tactic mode -/
protected def GoalState.conv (state: GoalState) (goalId: Nat):
Elab.TermElabM TacticResult := do
if state.convMVar?.isSome then
return .invalidAction "Already in conv state"
let goal ← match state.savedState.tactic.goals.get? goalId with
| .some goal => pure goal
| .none => return .indexError goalId
let tacticM : Elab.Tactic.TacticM (Elab.Tactic.SavedState × MVarId) := do
state.restoreTacticM goal
-- See Lean.Elab.Tactic.Conv.convTarget
let convMVar ← Elab.Tactic.withMainContext do
let (rhs, newGoal) ← Elab.Tactic.Conv.mkConvGoalFor (← Elab.Tactic.getMainTarget)
Elab.Tactic.setGoals [newGoal.mvarId!]
pure rhs.mvarId!
return (← MonadBacktrack.saveState, convMVar)
try
let (nextSavedState, convRhs) ← tacticM { elaborator := .anonymous } |>.run' state.savedState.tactic
let prevMCtx := state.mctx
let nextMCtx := nextSavedState.term.meta.meta.mctx
return .success {
root := state.root,
savedState := nextSavedState
newMVars := newMVarSet prevMCtx nextMCtx,
parentMVar? := .some goal,
convMVar? := .some (convRhs, goal),
}
catch exception =>
return .failure #[← exception.toMessageData.toString]
/-- Exit from `conv` mode. Resumes all goals before the mode starts and applys the conv -/
protected def GoalState.convExit (state: GoalState):
Elab.TermElabM TacticResult := do
let (convRhs, convGoal) ← match state.convMVar? with
| .some mvar => pure mvar
| .none => return .invalidAction "Not in conv state"
let tacticM : Elab.Tactic.TacticM Elab.Tactic.SavedState:= do
-- Vide `Lean.Elab.Tactic.Conv.convert`
state.savedState.restore
Elab.Tactic.setGoals [goal]
try
let expr ← Elab.Term.elabTerm (stx := expr) (expectedType? := .none)
-- Attempt to unify the expression
let goalType ← goal.getType
let exprType ← Meta.inferType expr
if !(← Meta.isDefEq goalType exprType) then
return .failure #["Type unification failed", toString (← Meta.ppExpr goalType), toString (← Meta.ppExpr exprType)]
goal.checkNotAssigned `GoalState.tryAssign
goal.assign expr
if (← getThe Core.State).messages.hasErrors then
let messages := (← getThe Core.State).messages.getErrorMessages |>.toList.toArray
let errors ← (messages.map Message.data).mapM fun md => md.toString
return .failure errors
-- Close all existing goals with `refl`
for mvarId in (← Elab.Tactic.getGoals) do
liftM <| mvarId.refl <|> mvarId.inferInstance <|> pure ()
Elab.Tactic.pruneSolvedGoals
unless (← Elab.Tactic.getGoals).isEmpty do
throwError "convert tactic failed, there are unsolved goals\n{Elab.goalsToMessageData (← Elab.Tactic.getGoals)}"
Elab.Tactic.setGoals [convGoal]
let targetNew ← instantiateMVars (.mvar convRhs)
let proof ← instantiateMVars (.mvar convGoal)
Elab.Tactic.liftMetaTactic1 fun mvarId => mvarId.replaceTargetEq targetNew proof
MonadBacktrack.saveState
try
let nextSavedState ← tacticM { elaborator := .anonymous } |>.run' state.savedState.tactic
let nextMCtx := nextSavedState.term.meta.meta.mctx
let prevMCtx := state.savedState.term.meta.meta.mctx
return .success {
root := state.root,
savedState := nextSavedState
newMVars := newMVarSet prevMCtx nextMCtx,
parentMVar? := .some convGoal,
convMVar? := .none
}
catch exception =>
return .failure #[← exception.toMessageData.toString]
protected def GoalState.tryCalc (state: GoalState) (goalId: Nat) (pred: String):
Elab.TermElabM TacticResult := do
state.restoreElabM
if state.convMVar?.isSome then
return .invalidAction "Cannot initiate `calc` while in `conv` state"
let goal ← match state.savedState.tactic.goals.get? goalId with
| .some goal => pure goal
| .none => return .indexError goalId
let `(term|$pred) ← match Parser.runParserCategory
(env := state.env)
(catName := `term)
(input := pred)
(fileName := filename) with
| .ok syn => pure syn
| .error error => return .parseError error
try
goal.withContext do
let target ← instantiateMVars (← goal.getDecl).type
let tag := (← goal.getDecl).userName
let mut step ← Elab.Term.elabType <| ← do
if let some prevRhs := state.calcPrevRhs? then
Elab.Term.annotateFirstHoleWithType pred (← Meta.inferType prevRhs)
else
let prevMCtx := state.savedState.term.meta.meta.mctx
let nextMCtx ← getMCtx
-- Generate a list of mvarIds that exist in the parent state; Also test the
-- assertion that the types have not changed on any mvars.
let newMVars ← nextMCtx.decls.foldlM (fun acc mvarId mvarDecl => do
if let .some prevMVarDecl := prevMCtx.decls.find? mvarId then
assert! prevMVarDecl.type == mvarDecl.type
return acc
else
return mvarId :: acc
) []
-- The new goals are the newMVars that lack an assignment
Elab.Tactic.setGoals (← newMVars.filterM (λ mvar => do pure !(← mvar.isAssigned)))
let nextSavedState ← MonadBacktrack.saveState
return .success {
root := state.root,
savedState := nextSavedState,
newMVars := newMVars.toSSet,
parentGoalId := goalId,
parentMVar := .some goal,
}
catch exception =>
return .failure #[← exception.toMessageData.toString]
tacticM { elaborator := .anonymous } |>.run' state.savedState.tactic
pure pred
let some (_, lhs, rhs) ← Elab.Term.getCalcRelation? step |
throwErrorAt pred "invalid 'calc' step, relation expected{indentExpr step}"
if let some prevRhs := state.calcPrevRhs? then
unless (← Meta.isDefEqGuarded lhs prevRhs) do
throwErrorAt pred "invalid 'calc' step, left-hand-side is{indentD m!"{lhs} : {← Meta.inferType lhs}"}\nprevious right-hand-side is{indentD m!"{prevRhs} : {← Meta.inferType prevRhs}"}" -- "
-- Creates a mvar to represent the proof that the calc tactic solves the
-- current branch
-- In the Lean `calc` tactic this is gobbled up by
-- `withCollectingNewGoalsFrom`
let mut proof ← Meta.mkFreshExprMVarAt (← getLCtx) (← Meta.getLocalInstances) step
(userName := tag ++ `calc)
let mvarBranch := proof.mvarId!
let calcPrevRhs? := Option.some rhs
let mut proofType ← Meta.inferType proof
let mut remainder := Option.none
-- The calc tactic either solves the main goal or leaves another relation.
-- Replace the main goal, and save the new goal if necessary
if ¬(← Meta.isDefEq proofType target) then
let rec throwFailed :=
throwError "'calc' tactic failed, has type{indentExpr proofType}\nbut it is expected to have type{indentExpr target}"
let some (_, _, rhs) ← Elab.Term.getCalcRelation? proofType | throwFailed
let some (r, _, rhs') ← Elab.Term.getCalcRelation? target | throwFailed
let lastStep := mkApp2 r rhs rhs'
let lastStepGoal ← Meta.mkFreshExprSyntheticOpaqueMVar lastStep tag
(proof, proofType) ← Elab.Term.mkCalcTrans proof proofType lastStepGoal lastStep
unless (← Meta.isDefEq proofType target) do throwFailed
remainder := .some lastStepGoal.mvarId!
goal.assign proof
let goals := [ mvarBranch ] ++ remainder.toList
return .success {
root := state.root,
savedState := {
term := ← MonadBacktrack.saveState,
tactic := { goals },
},
newMVars := goals.toSSet,
parentMVar? := .some goal,
calcPrevRhs?
}
catch exception =>
return .failure #[← exception.toMessageData.toString]
protected def GoalState.focus (state: GoalState) (goalId: Nat): Option GoalState := do
let goal ← state.savedState.tactic.goals.get? goalId
return {
state with
savedState := {
state.savedState with
tactic := { goals := [goal] },
},
calcPrevRhs? := .none,
}
/--
Brings into scope a list of goals
@ -197,8 +426,8 @@ protected def GoalState.resume (state: GoalState) (goals: List MVarId): Except S
term := state.savedState.term,
tactic := { goals := unassigned },
},
calcPrevRhs? := .none,
}
/--
Brings into scope all goals from `branch`
-/
@ -221,7 +450,7 @@ protected def GoalState.rootExpr? (goalState: GoalState): Option Expr := do
assert! goalState.goals.isEmpty
return expr
protected def GoalState.parentExpr? (goalState: GoalState): Option Expr := do
let parent ← goalState.parentMVar
let parent ← goalState.parentMVar?
let expr := goalState.mctx.eAssignment.find! parent
let (expr, _) := instantiateMVarsCore (mctx := goalState.mctx) (e := expr)
return expr

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@ -136,8 +136,8 @@ def parseElabExpr (expr: String) (expectedType?: Option String := .none): Lean.E
@[export pantograph_expr_echo_m]
def exprEcho (expr: String) (expectedType?: Option String := .none) (options: @&Protocol.Options):
Lean.CoreM (Protocol.CR Protocol.ExprEchoResult) := do
let termElabM: Lean.Elab.TermElabM _ := do
Lean.CoreM (Protocol.CR Protocol.ExprEchoResult) :=
runTermElabM do
let expr ← match ← parseElabExpr expr expectedType? with
| .error e => return .error e
| .ok expr => pure expr
@ -149,40 +149,58 @@ def exprEcho (expr: String) (expectedType?: Option String := .none) (options: @&
}
catch exception =>
return .error $ errorI "typing" (← exception.toMessageData.toString)
runTermElabM termElabM
@[export pantograph_goal_start_expr_m]
def goalStartExpr (expr: String): Lean.CoreM (Protocol.CR GoalState) :=
let termElabM: Lean.Elab.TermElabM _ := do
runTermElabM do
let expr ← match ← parseElabType expr with
| .error e => return .error e
| .ok expr => pure $ expr
return .ok $ ← GoalState.create expr
runTermElabM termElabM
@[export pantograph_goal_tactic_m]
def goalTactic (state: GoalState) (goalId: Nat) (tactic: String): Lean.CoreM TacticResult :=
runTermElabM <| GoalState.execute state goalId tactic
runTermElabM <| state.tryTactic goalId tactic
@[export pantograph_goal_try_assign_m]
def goalTryAssign (state: GoalState) (goalId: Nat) (expr: String): Lean.CoreM TacticResult :=
runTermElabM <| GoalState.tryAssign state goalId expr
@[export pantograph_goal_assign_m]
def goalAssign (state: GoalState) (goalId: Nat) (expr: String): Lean.CoreM TacticResult :=
runTermElabM <| state.tryAssign goalId expr
@[export pantograph_goal_continue]
def goalContinue (target: GoalState) (branch: GoalState): Except String GoalState :=
target.continue branch
@[export pantograph_goal_have_m]
def goalHave (state: GoalState) (goalId: Nat) (binderName: String) (type: String): Lean.CoreM TacticResult :=
runTermElabM <| state.tryHave goalId binderName type
@[export pantograph_goal_conv_m]
def goalConv (state: GoalState) (goalId: Nat): Lean.CoreM TacticResult :=
runTermElabM <| state.conv goalId
@[export pantograph_goal_conv_exit_m]
def goalConvExit (state: GoalState): Lean.CoreM TacticResult :=
runTermElabM <| state.convExit
@[export pantograph_goal_calc_m]
def goalCalc (state: GoalState) (goalId: Nat) (pred: String): Lean.CoreM TacticResult :=
runTermElabM <| state.tryCalc goalId pred
@[export pantograph_goal_focus]
def goalFocus (state: GoalState) (goalId: Nat): Option GoalState :=
state.focus goalId
@[export pantograph_goal_resume]
def goalResume (target: GoalState) (goals: Array String): Except String GoalState :=
target.resume (goals.map (λ n => { name := n.toName }) |>.toList)
@[export pantograph_goal_continue]
def goalContinue (target: GoalState) (branch: GoalState): Except String GoalState :=
target.continue branch
@[export pantograph_goal_serialize_m]
def goalSerialize (state: GoalState) (options: @&Protocol.Options): Lean.CoreM (Array Protocol.Goal) :=
runMetaM <| state.serializeGoals (parent := .none) options
@[export pantograph_goal_print_m]
def goalPrint (state: GoalState) (options: @&Protocol.Options): Lean.CoreM Protocol.GoalPrintResult := do
let metaM := do
def goalPrint (state: GoalState) (options: @&Protocol.Options): Lean.CoreM Protocol.GoalPrintResult :=
runMetaM do
state.restoreMetaM
return {
root? := ← state.rootExpr?.mapM (λ expr => do
@ -190,7 +208,6 @@ def goalPrint (state: GoalState) (options: @&Protocol.Options): Lean.CoreM Proto
parent? := ← state.parentExpr?.mapM (λ expr => do
serialize_expression options (← unfoldAuxLemmas expr)),
}
runMetaM metaM
end Pantograph

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@ -209,6 +209,14 @@ structure GoalTactic where
-- One of the fields here must be filled
tactic?: Option String := .none
expr?: Option String := .none
have?: Option String := .none
calc?: Option String := .none
-- true to enter `conv`, `false` to exit. In case of exit the `goalId` is ignored.
conv?: Option Bool := .none
-- In case of the `have` tactic, the new free variable name is provided here
binderName?: Option String := .none
deriving Lean.FromJson
structure GoalTacticResult where
-- The next goal state id. Existence of this field shows success

View File

@ -254,9 +254,7 @@ protected def GoalState.serializeGoals
MetaM (Array Protocol.Goal):= do
state.restoreMetaM
let goals := state.goals.toArray
let parentDecl? := parent.bind (λ parentState =>
let parentGoal := parentState.goals.get! state.parentGoalId
parentState.mctx.findDecl? parentGoal)
let parentDecl? := parent.bind (λ parentState => parentState.mctx.findDecl? state.parentMVar?.get!)
goals.mapM fun goal => do
match state.mctx.findDecl? goal with
| .some mvarDecl =>

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@ -81,7 +81,12 @@ See `Pantograph/Protocol.lean` for a description of the parameters and return va
have to be set via command line arguments.), for options, see `Pantograph/Protocol.lean`
- `options.print`: Display the current set of options
- `goal.start {["name": <name>], ["expr": <expr>], ["copyFrom": <symbol>]}`: Start a new goal from a given expression or symbol
- `goal.tactic {"stateId": <id>, "goalId": <id>, ["tactic": <tactic>], ["expr": <expr>]}`: Execute a tactic string on a given goal
- `goal.tactic {"stateId": <id>, "goalId": <id>, ["tactic": <tactic>], ["expr":
<expr>]}`: Execute a tactic string on a given goal. `tactic` executes an
ordinary tactic, `expr` assigns an expression to the current goal, `have`
executes the have tactic, ``calc` (of the form `lhs op rhs`) executes one step
of `calc`, and `"conv": true`/`"conv": false` enters/exits conversion tactic
mode.
- `goal.continue {"stateId": <id>, ["branch": <id>], ["goals": <names>]}`: Continue from a proof state
- `goal.remove {"stateIds": [<id>]}"`: Remove a bunch of stored goals.
- `goal.print {"stateId": <id>}"`: Print a goal state

View File

@ -37,6 +37,7 @@ def TacticResult.toString : TacticResult → String
s!".failure {messages}"
| .parseError error => s!".parseError {error}"
| .indexError index => s!".indexError {index}"
| .invalidAction error => s!".invalidAction {error}"
namespace Test

View File

@ -8,7 +8,7 @@ namespace Pantograph.Test.Metavar
open Pantograph
open Lean
abbrev TestM := StateRefT LSpec.TestSeq (ReaderT Protocol.Options M)
abbrev TestM := StateRefT LSpec.TestSeq (ReaderT Protocol.Options Elab.TermElabM)
def addTest (test: LSpec.TestSeq): TestM Unit := do
set $ (← get) ++ test
@ -84,7 +84,7 @@ def test_m_couple: TestM Unit := do
addTest $ assertUnreachable "Goal could not parse"
return ()
let state1 ← match ← state0.execute (goalId := 0) (tactic := "apply Nat.le_trans") with
let state1 ← match ← state0.tryTactic (goalId := 0) (tactic := "apply Nat.le_trans") with
| .success state => pure state
| other => do
addTest $ assertUnreachable $ other.toString
@ -93,7 +93,7 @@ def test_m_couple: TestM Unit := do
#[.some "2 ≤ ?m", .some "?m ≤ 5", .some "Nat"])
addTest $ LSpec.test "(1 root)" state1.rootExpr?.isNone
-- Set m to 3
let state2 ← match ← state1.execute (goalId := 2) (tactic := "exact 3") with
let state2 ← match ← state1.tryTactic (goalId := 2) (tactic := "exact 3") with
| .success state => pure state
| other => do
addTest $ assertUnreachable $ other.toString
@ -116,14 +116,14 @@ def test_m_couple_simp: TestM Unit := do
addTest $ assertUnreachable "Goal could not parse"
return ()
let state1 ← match ← state0.execute (goalId := 0) (tactic := "apply Nat.le_trans") with
let state1 ← match ← state0.tryTactic (goalId := 0) (tactic := "apply Nat.le_trans") with
| .success state => pure state
| other => do
addTest $ assertUnreachable $ other.toString
return ()
addTest $ LSpec.check "apply Nat.le_trans" ((← state1.serializeGoals (options := ← read)).map (·.target.pp?) =
#[.some "2 ≤ ?m", .some "?m ≤ 5", .some "Nat"])
let state2 ← match ← state1.execute (goalId := 2) (tactic := "exact 2") with
let state2 ← match ← state1.tryTactic (goalId := 2) (tactic := "exact 2") with
| .success state => pure state
| other => do
addTest $ assertUnreachable $ other.toString
@ -137,7 +137,7 @@ def test_m_couple_simp: TestM Unit := do
addTest $ LSpec.check "exact 2" ((← state1b.serializeGoals (options := ← read)).map (·.target.pp?) =
#[.some "2 ≤ 2", .some "2 ≤ 5"])
addTest $ LSpec.test "(2 root)" state1b.rootExpr?.isNone
let state3 ← match ← state1b.execute (goalId := 0) (tactic := "simp") with
let state3 ← match ← state1b.tryTactic (goalId := 0) (tactic := "simp") with
| .success state => pure state
| other => do
addTest $ assertUnreachable $ other.toString
@ -147,7 +147,7 @@ def test_m_couple_simp: TestM Unit := do
addTest $ assertUnreachable $ msg
return ()
| .ok state => pure state
let state5 ← match ← state4.execute (goalId := 0) (tactic := "simp") with
let state5 ← match ← state4.tryTactic (goalId := 0) (tactic := "simp") with
| .success state => pure state
| other => do
addTest $ assertUnreachable $ other.toString
@ -174,7 +174,7 @@ def test_proposition_generation: TestM Unit := do
addTest $ assertUnreachable "Goal could not parse"
return ()
let state1 ← match ← state0.execute (goalId := 0) (tactic := "apply PSigma.mk") with
let state1 ← match ← state0.tryTactic (goalId := 0) (tactic := "apply PSigma.mk") with
| .success state => pure state
| other => do
addTest $ assertUnreachable $ other.toString
@ -216,7 +216,7 @@ def test_partial_continuation: TestM Unit := do
addTest $ assertUnreachable "Goal could not parse"
return ()
let state1 ← match ← state0.execute (goalId := 0) (tactic := "apply Nat.le_trans") with
let state1 ← match ← state0.tryTactic (goalId := 0) (tactic := "apply Nat.le_trans") with
| .success state => pure state
| other => do
addTest $ assertUnreachable $ other.toString
@ -224,7 +224,7 @@ def test_partial_continuation: TestM Unit := do
addTest $ LSpec.check "apply Nat.le_trans" ((← state1.serializeGoals (options := ← read)).map (·.target.pp?) =
#[.some "2 ≤ ?m", .some "?m ≤ 5", .some "Nat"])
let state2 ← match ← state1.execute (goalId := 2) (tactic := "apply Nat.succ") with
let state2 ← match ← state1.tryTactic (goalId := 2) (tactic := "apply Nat.succ") with
| .success state => pure state
| other => do
addTest $ assertUnreachable $ other.toString

View File

@ -14,7 +14,7 @@ inductive Start where
| copy (name: String) -- Start from some name in the environment
| expr (expr: String) -- Start from some expression
abbrev TestM := StateRefT LSpec.TestSeq (ReaderT Protocol.Options M)
abbrev TestM := StateRefT LSpec.TestSeq (ReaderT Protocol.Options Elab.TermElabM)
def addTest (test: LSpec.TestSeq): TestM Unit := do
set $ (← get) ++ test
@ -75,7 +75,7 @@ def proofRunner (env: Lean.Environment) (tests: TestM Unit): IO LSpec.TestSeq :=
example: ∀ (a b: Nat), a + b = b + a := by
intro n m
rw [Nat.add_comm]
def proof_nat_add_comm (manual: Bool): TestM Unit := do
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"
@ -86,7 +86,7 @@ def proof_nat_add_comm (manual: Bool): TestM Unit := do
addTest $ assertUnreachable "Goal could not parse"
return ()
let state1 ← match ← state0.execute (goalId := 0) (tactic := "intro n m") with
let state1 ← match ← state0.tryTactic (goalId := 0) (tactic := "intro n m") with
| .success state => pure state
| other => do
addTest $ assertUnreachable $ other.toString
@ -94,13 +94,13 @@ def proof_nat_add_comm (manual: Bool): TestM Unit := do
addTest $ LSpec.check "intro n m" ((← state1.serializeGoals (options := ← read)).map (·.devolatilize) =
#[buildGoal [("n", "Nat"), ("m", "Nat")] "n + m = m + n"])
match ← state1.execute (goalId := 0) (tactic := "assumption") with
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.execute (goalId := 0) (tactic := "rw [Nat.add_comm]") with
let state2 ← match ← state1.tryTactic (goalId := 0) (tactic := "rw [Nat.add_comm]") with
| .success state => pure state
| other => do
addTest $ assertUnreachable $ other.toString
@ -108,7 +108,7 @@ def proof_nat_add_comm (manual: Bool): TestM Unit := do
addTest $ LSpec.test "rw [Nat.add_comm]" state2.goals.isEmpty
return ()
def proof_delta_variable: TestM Unit := do
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
@ -118,14 +118,14 @@ def proof_delta_variable: TestM Unit := do
addTest $ assertUnreachable "Goal could not parse"
return ()
let state1 ← match ← state0.execute (goalId := 0) (tactic := "intro n") with
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.execute (goalId := 0) (tactic := "intro m") with
let state2 ← match ← state1.tryTactic (goalId := 0) (tactic := "intro m") with
| .success state => pure state
| other => do
addTest $ assertUnreachable $ other.toString
@ -149,7 +149,7 @@ 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: TestM Unit := do
def test_arith: TestM Unit := do
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
@ -157,26 +157,28 @@ def proof_arith: TestM Unit := do
addTest $ assertUnreachable "Goal could not parse"
return ()
let state1 ← match ← state0.execute (goalId := 0) (tactic := "intros") with
let tactic := "intros"
let state1 ← match ← state0.tryTactic (goalId := 0) (tactic := tactic) with
| .success state => pure state
| other => do
addTest $ assertUnreachable $ other.toString
return ()
addTest $ LSpec.check "intros" (state1.goals.length = 1)
addTest $ LSpec.check tactic (state1.goals.length = 1)
addTest $ LSpec.test "(1 root)" state1.rootExpr?.isNone
let state2 ← match ← state1.execute (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
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
| other => do
addTest $ assertUnreachable $ other.toString
return ()
addTest $ LSpec.check "simp ..." (state2.goals.length = 1)
addTest $ LSpec.check "(2 root)" state2.rootExpr?.isNone
let state3 ← match ← state2.execute (goalId := 0) (tactic := "assumption") with
let tactic := "assumption"
let state3 ← match ← state2.tryTactic (goalId := 0) (tactic := tactic) with
| .success state => pure state
| other => do
addTest $ assertUnreachable $ other.toString
return ()
addTest $ LSpec.test "assumption" state3.goals.isEmpty
addTest $ LSpec.test tactic state3.goals.isEmpty
addTest $ LSpec.check "(3 root)" state3.rootExpr?.isSome
return ()
@ -195,7 +197,7 @@ example: ∀ (p q: Prop), p q → q p := by
assumption
. apply Or.inl
assumption
def proof_or_comm: TestM Unit := do
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
@ -205,21 +207,24 @@ def proof_or_comm: TestM Unit := do
addTest $ LSpec.check "(0 parent)" state0.parentExpr?.isNone
addTest $ LSpec.check "(0 root)" state0.rootExpr?.isNone
let state1 ← match ← state0.execute (goalId := 0) (tactic := "intro p q h") with
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 ()
addTest $ LSpec.check "intro n m" ((← state1.serializeGoals (options := ← read)).map (·.devolatilize) =
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
let state2 ← match ← state1.execute (goalId := 0) (tactic := "cases h") with
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 ()
addTest $ LSpec.check "cases h" ((← state2.serializeGoals (options := ← read)).map (·.devolatilize) =
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
@ -229,7 +234,7 @@ def proof_or_comm: TestM Unit := do
addTest $ LSpec.test "(2 parent)" (state2parent ==
"((:mv _uniq.43) (:fv _uniq.16) ((:c Eq.refl) ((:c Or) (:fv _uniq.10) (:fv _uniq.13)) (:fv _uniq.16)))")
let state3_1 ← match ← state2.execute (goalId := 0) (tactic := "apply Or.inr") with
let state3_1 ← match ← state2.tryTactic (goalId := 0) (tactic := "apply Or.inr") with
| .success state => pure state
| other => do
addTest $ assertUnreachable $ other.toString
@ -237,7 +242,7 @@ def proof_or_comm: TestM Unit := do
let state3_1parent ← serialize_expression_ast state3_1.parentExpr?.get! (sanitize := false)
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.execute (goalId := 0) (tactic := "assumption") with
let state4_1 ← match ← state3_1.tryTactic (goalId := 0) (tactic := "assumption") with
| .success state => pure state
| other => do
addTest $ assertUnreachable $ other.toString
@ -246,13 +251,13 @@ def proof_or_comm: TestM Unit := do
let state4_1parent ← serialize_expression_ast state4_1.parentExpr?.get! (sanitize := false)
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.execute (goalId := 1) (tactic := "apply Or.inl") with
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.execute (goalId := 0) (tactic := "assumption") with
let state4_2 ← match ← state3_2.tryTactic (goalId := 0) (tactic := "assumption") with
| .success state => pure state
| other => do
addTest $ assertUnreachable $ other.toString
@ -266,13 +271,13 @@ def proof_or_comm: TestM Unit := do
return ()
| .ok state => pure state
addTest $ LSpec.test "(resume)" (state2b.goals == [state2.goals.get! 0])
let state3_1 ← match ← state2b.execute (goalId := 0) (tactic := "apply Or.inr") with
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.execute (goalId := 0) (tactic := "assumption") with
let state4_1 ← match ← state3_1.tryTactic (goalId := 0) (tactic := "assumption") with
| .success state => pure state
| other => do
addTest $ assertUnreachable $ other.toString
@ -293,14 +298,268 @@ def proof_or_comm: TestM Unit := do
]
}
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 ()
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 ()
addTest $ LSpec.check tactic ((← state1.serializeGoals (options := ← read)).map (·.devolatilize) =
#[buildGoal [("p", "Prop"), ("q", "Prop"), ("h", "p")] "(p q) p q"])
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 ()
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"
])
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 ()
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
example : ∀ (a b c1 c2: Nat), (b + a) + c1 = (b + a) + c2 → (a + b) + c1 = (b + a) + c2 := by
intro a b c1 c2 h
conv =>
lhs
congr
. rw [Nat.add_comm]
. rfl
exact h
def test_conv: TestM Unit := do
let state? ← startProof (.expr "∀ (a b c1 c2: Nat), (b + a) + c1 = (b + a) + c2 → (a + b) + c1 = (b + a) + c2")
let state0 ← match state? with
| .some state => pure state
| .none => do
addTest $ assertUnreachable "Goal could not parse"
return ()
let tactic := "intro a b c1 c2 h"
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) =
#[interiorGoal [] "a + b + c1 = b + a + c2"])
let state2 ← match ← state1.conv (goalId := 0) with
| .success state => pure state
| other => do
addTest $ assertUnreachable $ other.toString
return ()
addTest $ LSpec.check "conv => ..." ((← state2.serializeGoals (options := ← read)).map (·.devolatilize) =
#[{ interiorGoal [] "a + b + c1 = b + a + c2" with isConversion := true }])
let convTactic := "rhs"
let state3R ← match ← state2.tryTactic (goalId := 0) convTactic with
| .success state => pure state
| other => do
addTest $ assertUnreachable $ other.toString
return ()
addTest $ LSpec.check s!" {convTactic} (discard)" ((← state3R.serializeGoals (options := ← read)).map (·.devolatilize) =
#[{ interiorGoal [] "b + a + c2" with isConversion := true }])
let convTactic := "lhs"
let state3L ← match ← state2.tryTactic (goalId := 0) convTactic with
| .success state => pure state
| other => do
addTest $ assertUnreachable $ other.toString
return ()
addTest $ LSpec.check s!" {convTactic}" ((← state3L.serializeGoals (options := ← read)).map (·.devolatilize) =
#[{ interiorGoal [] "a + b + c1" with isConversion := true }])
let convTactic := "congr"
let state4 ← match ← state3L.tryTactic (goalId := 0) convTactic with
| .success state => pure state
| other => do
addTest $ assertUnreachable $ other.toString
return ()
addTest $ LSpec.check s!" {convTactic}" ((← state4.serializeGoals (options := ← read)).map (·.devolatilize) =
#[
{ interiorGoal [] "a + b" with isConversion := true, userName? := .some "a" },
{ interiorGoal [] "c1" with isConversion := true, userName? := .some "a" }
])
let convTactic := "rw [Nat.add_comm]"
let state5_1 ← match ← state4.tryTactic (goalId := 0) convTactic with
| .success state => pure state
| other => do
addTest $ assertUnreachable $ other.toString
return ()
addTest $ LSpec.check s!" · {convTactic}" ((← state5_1.serializeGoals (options := ← read)).map (·.devolatilize) =
#[{ interiorGoal [] "b + a" with isConversion := true, userName? := .some "a" }])
let convTactic := "rfl"
let state6_1 ← match ← state5_1.tryTactic (goalId := 0) convTactic with
| .success state => pure state
| other => do
addTest $ assertUnreachable $ other.toString
return ()
addTest $ LSpec.check s!" {convTactic}" ((← state6_1.serializeGoals (options := ← read)).map (·.devolatilize) =
#[])
let state4_1 ← match state6_1.continue state4 with
| .ok state => pure state
| .error e => do
addTest $ expectationFailure "continue" e
return ()
let convTactic := "rfl"
let state6 ← match ← state4_1.tryTactic (goalId := 0) convTactic with
| .success state => pure state
| other => do
addTest $ assertUnreachable $ other.toString
return ()
addTest $ LSpec.check s!" · {convTactic}" ((← state6.serializeGoals (options := ← read)).map (·.devolatilize) =
#[])
let state1_1 ← match ← state6.convExit with
| .success state => pure state
| other => do
addTest $ assertUnreachable $ other.toString
return ()
let tactic := "exact h"
let stateF ← match ← state1_1.tryTactic (goalId := 0) (tactic := tactic) with
| .success state => pure state
| other => do
addTest $ assertUnreachable $ other.toString
return ()
addTest $ LSpec.check tactic ((← stateF.serializeGoals (options := ← read)).map (·.devolatilize) =
#[])
where
h := "b + a + c1 = b + a + c2"
interiorGoal (free: List (String × String)) (target: String) :=
let free := [("a", "Nat"), ("b", "Nat"), ("c1", "Nat"), ("c2", "Nat"), ("h", h)] ++ free
buildGoal free target
example : ∀ (a b c d: Nat), a + b = b + c → b + c = c + d → a + b = c + d := by
intro a b c d h1 h2
calc a + b = b + c := by apply h1
_ = c + d := by apply h2
def test_calc: TestM Unit := do
let state? ← startProof (.expr "∀ (a b c d: Nat), a + b = b + c → b + c = c + d → a + b = c + d")
let state0 ← match state? with
| .some state => pure state
| .none => do
addTest $ assertUnreachable "Goal could not parse"
return ()
let tactic := "intro a b c d h1 h2"
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) =
#[interiorGoal [] "a + b = c + d"])
let pred := "a + b = b + c"
let state2 ← match ← state1.tryCalc (goalId := 0) (pred := pred) with
| .success state => pure state
| other => do
addTest $ assertUnreachable $ other.toString
return ()
addTest $ LSpec.check s!"calc {pred} := _" ((← state2.serializeGoals (options := ← read)).map (·.devolatilize) =
#[
interiorGoal [] "a + b = b + c" (.some "calc"),
interiorGoal [] "b + c = c + d"
])
let tactic := "apply h1"
let state2m ← match ← state2.tryTactic (goalId := 0) (tactic := tactic) with
| .success state => pure state
| other => do
addTest $ assertUnreachable $ other.toString
return ()
let state3 ← match state2m.continue state2 with
| .ok state => pure state
| .error e => do
addTest $ expectationFailure "continue" e
return ()
let pred := "_ = c + d"
let state4 ← match ← state3.tryCalc (goalId := 0) (pred := pred) with
| .success state => pure state
| other => do
addTest $ assertUnreachable $ other.toString
return ()
addTest $ LSpec.check s!"calc {pred} := _" ((← state4.serializeGoals (options := ← read)).map (·.devolatilize) =
#[
interiorGoal [] "b + c = c + d" (.some "calc")
])
let tactic := "apply h2"
let state4m ← match ← state4.tryTactic (goalId := 0) (tactic := tactic) with
| .success state => pure state
| other => do
addTest $ assertUnreachable $ other.toString
return ()
addTest $ LSpec.test "(4m root)" state4m.rootExpr?.isSome
where
interiorGoal (free: List (String × String)) (target: String) (userName?: Option String := .none) :=
let free := [("a", "Nat"), ("b", "Nat"), ("c", "Nat"), ("d", "Nat"),
("h1", "a + b = b + c"), ("h2", "b + c = c + d")] ++ free
buildGoal free target userName?
def suite (env: Environment): List (String × IO LSpec.TestSeq) :=
let tests := [
("Nat.add_comm", proof_nat_add_comm false),
("Nat.add_comm manual", proof_nat_add_comm true),
("Nat.add_comm delta", proof_delta_variable),
("arithmetic", proof_arith),
("Or.comm", proof_or_comm)
("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