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@@ -2259,42 +2259,6 @@ with grind
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```
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This is more convenient than the equivalent `· by rename_i _ acc _; exact I1 acc`.
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### Witnesses
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When a specification has a parameter whose type is tagged with `@[mvcgen_witness_type]`, `mvcgen`
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classifies the corresponding goal as a *witness* rather than a verification condition.
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Witnesses are concrete values that the user must provide (inspired by zero-knowledge proofs),
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as opposed to invariants (predicates maintained across loop iterations) or verification conditions
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(propositions to prove).
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Witness goals are labelled `witness1`, `witness2`, etc. and can be provided in a `witnesses` section
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that appears before the `invariants` section:
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```
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mvcgen [...] witnesses
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· W1
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· W2
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invariants
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· I1
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with grind
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```
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Like invariants, witnesses support case label syntax:
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```
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mvcgen [...] witnesses
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| witness1 => W1
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```
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See the `@[mvcgen_witness_type]` attribute for how to register custom witness types.
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### Invariant and witness type attributes
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The `@[mvcgen_invariant_type]` and `@[mvcgen_witness_type]` tag attributes control how `mvcgen`
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classifies subgoals:
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* A goal whose type is an application of a type tagged with `@[mvcgen_invariant_type]` is classified
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as an invariant (`inv<n>`).
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* A goal whose type is an application of a type tagged with `@[mvcgen_witness_type]` is classified
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as a witness (`witness<n>`).
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* All other goals are classified as verification conditions (`vc<n>`).
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### Invariant suggestions
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`mvcgen` will suggest invariants for you if you use the `invariants?` keyword.
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@@ -10,6 +10,7 @@ public import Lean.Compiler.IR.Format
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public import Lean.Compiler.ExportAttr
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public import Lean.Compiler.LCNF.PublicDeclsExt
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import Lean.Compiler.InitAttr
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import all Lean.Compiler.ModPkgExt
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import Init.Data.Format.Macro
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import Lean.Compiler.LCNF.Basic
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@@ -129,8 +130,14 @@ private def exportIREntries (env : Environment) : Array (Name × Array EnvExtens
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-- safety: cast to erased type
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let initDecls : Array EnvExtensionEntry := unsafe unsafeCast initDecls
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-- needed during initialization via interpreter
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let modPkg : Array (Option PkgId) := modPkgExt.exportEntriesFn env (modPkgExt.getState env) .private
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-- safety: cast to erased type
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let modPkg : Array EnvExtensionEntry := unsafe unsafeCast modPkg
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#[(declMapExt.name, irEntries),
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(Lean.regularInitAttr.ext.name, initDecls)]
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(Lean.regularInitAttr.ext.name, initDecls),
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(modPkgExt.name, modPkg)]
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def findEnvDecl (env : Environment) (declName : Name) : Option Decl :=
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Compiler.LCNF.findExtEntry? env declMapExt declName findAtSorted? (·.2.find?)
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@@ -268,24 +268,3 @@ def isMVCGenInvariantType (env : Environment) (ty : Expr) : Bool :=
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mvcgenInvariantAttr.hasTag env name
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else
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false
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/--
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Marks a type as a witness type for the `mvcgen` tactic.
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Goals whose type is an application of a tagged type will be classified
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as witnesses rather than verification conditions.
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In the spirit of zero-knowledge proofs, witnesses are concrete values that the user
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must provide, as opposed to invariants (predicates maintained across iterations)
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or verification conditions (propositions to prove).
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-/
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builtin_initialize mvcgenWitnessTypeAttr : TagAttribute ←
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registerTagAttribute `mvcgen_witness_type
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"marks a type as a witness type for the `mvcgen` tactic"
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/--
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Returns `true` if `ty` is an application of a type tagged with `@[mvcgen_witness_type]`.
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-/
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def isMVCGenWitnessType (env : Environment) (ty : Expr) : Bool :=
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if let .const name .. := ty.getAppFn then
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mvcgenWitnessTypeAttr.hasTag env name
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else
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false
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@@ -35,7 +35,6 @@ namespace VCGen
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structure Result where
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invariants : Array MVarId
|
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witnesses : Array MVarId
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vcs : Array MVarId
|
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partial def genVCs (goal : MVarId) (ctx : Context) (fuel : Fuel) : MetaM Result := do
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@@ -46,13 +45,10 @@ partial def genVCs (goal : MVarId) (ctx : Context) (fuel : Fuel) : MetaM Result
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for h : idx in *...state.invariants.size do
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let mv := state.invariants[idx]
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mv.setTag (Name.mkSimple ("inv" ++ toString (idx + 1)))
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for h : idx in *...state.witnesses.size do
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let mv := state.witnesses[idx]
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mv.setTag (Name.mkSimple ("witness" ++ toString (idx + 1)))
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for h : idx in *...state.vcs.size do
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let mv := state.vcs[idx]
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mv.setTag (Name.mkSimple ("vc" ++ toString (idx + 1)) ++ (← mv.getTag).eraseMacroScopes)
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return { invariants := state.invariants, witnesses := state.witnesses, vcs := state.vcs }
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return { invariants := state.invariants, vcs := state.vcs }
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where
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onFail (goal : MGoal) (name : Name) : VCGenM Expr := do
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-- trace[Elab.Tactic.Do.vcgen] "fail {goal.toExpr}"
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@@ -356,70 +352,53 @@ where
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end VCGen
|
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/-- Shared implementation for elaborating goal sections (invariants, witnesses).
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`tagPrefix` is `"inv"` or `"witness"`, used to parse labels like `inv1` or `witness2`.
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`label` is `"invariant"` or `"witness"`, used in error messages.
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When `requireAll` is true, an error is thrown if fewer alts are provided than goals. -/
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private def elabGoalSection (goals : Array MVarId) (alts : Array Syntax)
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(tagPrefix : String) (label : String) (requireAll := true) : TacticM Unit := do
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let goals ← goals.filterM (not <$> ·.isAssigned)
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let mut dotOrCase := LBool.undef -- .true => dot
|
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for h : n in 0...alts.size do
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let alt := alts[n]
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match alt with
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| `(goalDotAlt| · $rhs) =>
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if dotOrCase matches .false then
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logErrorAt alt m!"Alternation between labelled and bulleted {label}s is not supported."
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break
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dotOrCase := .true
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let some mv := goals[n]? | do
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logErrorAt alt m!"More {label}s have been defined ({alts.size}) than there were unassigned {label} goals `{tagPrefix}<n>` ({goals.size})."
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continue
|
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withRef rhs do
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discard <| evalTacticAt (← `(tactic| exact $rhs)) mv
|
||||
| `(goalCaseAlt| | $tag $args* => $rhs) =>
|
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if dotOrCase matches .true then
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logErrorAt alt m!"Alternation between labelled and bulleted {label}s is not supported."
|
||||
break
|
||||
dotOrCase := .false
|
||||
let n? : Option Nat := do
|
||||
let `(binderIdent| $tag:ident) := tag | some n -- fall back to ordinal
|
||||
let .str .anonymous s := tag.getId | none
|
||||
s.dropPrefix? tagPrefix >>= String.Slice.toNat?
|
||||
let some mv := do goals[(← n?) - 1]? | do
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logErrorAt alt m!"No {label} with label {tag} {repr tag}."
|
||||
continue
|
||||
if ← mv.isAssigned then
|
||||
logErrorAt alt m!"{label} {n?.get!} is already assigned."
|
||||
continue
|
||||
withRef rhs do
|
||||
discard <| evalTacticAt (← `(tactic| rename_i $args*; exact $rhs)) mv
|
||||
| _ => logErrorAt alt m!"Expected `goalDotAlt`, got {alt}"
|
||||
if requireAll && alts.size < goals.size then
|
||||
let missingTypes ← goals[alts.size:].toArray.mapM (·.getType)
|
||||
throwError "Lacking definitions for the following {label}s.\n{toMessageList missingTypes}"
|
||||
|
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def elabWitnesses (stx : Syntax) (witnesses : Array MVarId) : TacticM Unit := do
|
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let some stx := stx.getOptional? | return ()
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let stx : TSyntax ``witnessAlts := ⟨stx⟩
|
||||
withRef stx do
|
||||
match stx with
|
||||
| `(witnessAlts| witnesses $alts*) =>
|
||||
elabGoalSection witnesses alts "witness" "witness"
|
||||
| _ => logErrorAt stx m!"Expected witnessAlts, got {stx}"
|
||||
|
||||
def elabInvariants (stx : Syntax) (invariants : Array MVarId) (suggestInvariant : MVarId → TacticM Term) : TacticM Unit := do
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||||
let some stx := stx.getOptional? | return ()
|
||||
let stx : TSyntax ``invariantAlts := ⟨stx⟩
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||||
withRef stx do
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||||
match stx with
|
||||
| `(invariantAlts| $invariantsKW $alts*) =>
|
||||
let invariants ← invariants.filterM (not <$> ·.isAssigned)
|
||||
|
||||
let mut dotOrCase := LBool.undef -- .true => dot
|
||||
for h : n in 0...alts.size do
|
||||
let alt := alts[n]
|
||||
match alt with
|
||||
| `(goalDotAlt| · $rhs) =>
|
||||
if dotOrCase matches .false then
|
||||
logErrorAt alt m!"Alternation between labelled and bulleted invariants is not supported."
|
||||
break
|
||||
dotOrCase := .true
|
||||
let some mv := invariants[n]? | do
|
||||
logErrorAt alt m!"More invariants have been defined ({alts.size}) than there were unassigned invariants goals `inv<n>` ({invariants.size})."
|
||||
continue
|
||||
withRef rhs do
|
||||
discard <| evalTacticAt (← `(tactic| exact $rhs)) mv
|
||||
| `(goalCaseAlt| | $tag $args* => $rhs) =>
|
||||
if dotOrCase matches .true then
|
||||
logErrorAt alt m!"Alternation between labelled and bulleted invariants is not supported."
|
||||
break
|
||||
dotOrCase := .false
|
||||
let n? : Option Nat := do
|
||||
let `(binderIdent| $tag:ident) := tag | some n -- fall back to ordinal
|
||||
let .str .anonymous s := tag.getId | none
|
||||
s.dropPrefix? "inv" >>= String.Slice.toNat?
|
||||
let some mv := do invariants[(← n?) - 1]? | do
|
||||
logErrorAt alt m!"No invariant with label {tag} {repr tag}."
|
||||
continue
|
||||
if ← mv.isAssigned then
|
||||
logErrorAt alt m!"Invariant {n?.get!} is already assigned."
|
||||
continue
|
||||
withRef rhs do
|
||||
discard <| evalTacticAt (← `(tactic| rename_i $args*; exact $rhs)) mv
|
||||
| _ => logErrorAt alt m!"Expected `goalDotAlt`, got {alt}"
|
||||
|
||||
if let `(invariantsKW| invariants) := invariantsKW then
|
||||
elabGoalSection invariants alts "inv" "invariant"
|
||||
if alts.size < invariants.size then
|
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let missingTypes ← invariants[alts.size:].toArray.mapM (·.getType)
|
||||
throwErrorAt stx m!"Lacking definitions for the following invariants.\n{toMessageList missingTypes}"
|
||||
else
|
||||
-- We have `invariants?`. First elaborate any user-provided alts, then suggest the rest.
|
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elabGoalSection invariants alts "inv" "invariant" (requireAll := false)
|
||||
let invariants ← invariants.filterM (not <$> ·.isAssigned)
|
||||
-- Otherwise, we have `invariants?`. Suggest missing invariants.
|
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let mut suggestions := #[]
|
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for i in 0...invariants.size do
|
||||
let mv := invariants[i]!
|
||||
@@ -478,8 +457,8 @@ def elabMVCGen : Tactic := fun stx => withMainContext do
|
||||
| none => .unlimited
|
||||
let goal ← getMainGoal
|
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let goal ← if ctx.config.elimLets then elimLets goal else pure goal
|
||||
let { invariants, witnesses, vcs } ← VCGen.genVCs goal ctx fuel
|
||||
trace[Elab.Tactic.Do.vcgen] "after genVCs {← (invariants ++ witnesses ++ vcs).mapM fun m => m.getTag}"
|
||||
let { invariants, vcs } ← VCGen.genVCs goal ctx fuel
|
||||
trace[Elab.Tactic.Do.vcgen] "after genVCs {← (invariants ++ vcs).mapM fun m => m.getTag}"
|
||||
let runOnVCs (tac : TSyntax `tactic) (extraMsg : MessageData) (vcs : Array MVarId) : TermElabM (Array MVarId) :=
|
||||
vcs.flatMapM fun vc =>
|
||||
tryCatchRuntimeEx
|
||||
@@ -488,13 +467,10 @@ def elabMVCGen : Tactic := fun stx => withMainContext do
|
||||
(fun ex => throwError "Error while running {tac} on {vc}Message: {indentD ex.toMessageData}\n{extraMsg}")
|
||||
let invariants ←
|
||||
if ctx.config.leave then runOnVCs (← `(tactic| try mleave)) "Try again with -leave." invariants else pure invariants
|
||||
trace[Elab.Tactic.Do.vcgen] "before elabWitnesses {← (invariants ++ witnesses ++ vcs).mapM fun m => m.getTag}"
|
||||
elabWitnesses stx[3] witnesses
|
||||
let witnesses ← witnesses.filterM (not <$> ·.isAssigned)
|
||||
trace[Elab.Tactic.Do.vcgen] "before elabInvariants {← (invariants ++ witnesses ++ vcs).mapM fun m => m.getTag}"
|
||||
elabInvariants stx[4] invariants (suggestInvariant vcs)
|
||||
trace[Elab.Tactic.Do.vcgen] "before elabInvariants {← (invariants ++ vcs).mapM fun m => m.getTag}"
|
||||
elabInvariants stx[3] invariants (suggestInvariant vcs)
|
||||
let invariants ← invariants.filterM (not <$> ·.isAssigned)
|
||||
trace[Elab.Tactic.Do.vcgen] "before trying trivial VCs {← (invariants ++ witnesses ++ vcs).mapM fun m => m.getTag}"
|
||||
trace[Elab.Tactic.Do.vcgen] "before trying trivial VCs {← (invariants ++ vcs).mapM fun m => m.getTag}"
|
||||
let vcs ← do
|
||||
let vcs ← if ctx.config.trivial then runOnVCs (← `(tactic| try mvcgen_trivial)) "Try again with -trivial." vcs else pure vcs
|
||||
let vcs ← if ctx.config.leave then runOnVCs (← `(tactic| try mleave)) "Try again with -leave." vcs else pure vcs
|
||||
@@ -502,17 +478,17 @@ def elabMVCGen : Tactic := fun stx => withMainContext do
|
||||
-- Eliminating lets here causes some metavariables in `mkFreshPair_triple` to become nonassignable
|
||||
-- so we don't do it. Presumably some weird delayed assignment thing is going on.
|
||||
-- let vcs ← if ctx.config.elimLets then liftMetaM <| vcs.mapM elimLets else pure vcs
|
||||
trace[Elab.Tactic.Do.vcgen] "before elabVCs {← (invariants ++ witnesses ++ vcs).mapM fun m => m.getTag}"
|
||||
let vcs ← elabVCs stx[5] vcs
|
||||
trace[Elab.Tactic.Do.vcgen] "before replacing main goal {← (invariants ++ witnesses ++ vcs).mapM fun m => m.getTag}"
|
||||
replaceMainGoal (invariants ++ witnesses ++ vcs).toList
|
||||
trace[Elab.Tactic.Do.vcgen] "before elabVCs {← (invariants ++ vcs).mapM fun m => m.getTag}"
|
||||
let vcs ← elabVCs stx[4] vcs
|
||||
trace[Elab.Tactic.Do.vcgen] "before replacing main goal {← (invariants ++ vcs).mapM fun m => m.getTag}"
|
||||
replaceMainGoal (invariants ++ vcs).toList
|
||||
-- trace[Elab.Tactic.Do.vcgen] "replaced main goal, new: {← getGoals}"
|
||||
|
||||
@[builtin_tactic Lean.Parser.Tactic.mvcgenHint]
|
||||
def elabMVCGenHint : Tactic := fun stx => withMainContext do
|
||||
let stx' : TSyntax ``mvcgen := TSyntax.mk <| stx
|
||||
|>.setKind ``Lean.Parser.Tactic.mvcgen
|
||||
|>.modifyArgs (·.set! 0 (mkAtom "mvcgen") |>.push mkNullNode |>.push (mkNullNode #[← `(invariantAlts| invariants?)]) |>.push mkNullNode)
|
||||
|>.modifyArgs (·.set! 0 (mkAtom "mvcgen") |>.push (mkNullNode #[← `(invariantAlts| invariants?)]) |>.push mkNullNode)
|
||||
-- logInfo m!"{stx}\n{toString stx}\n{repr stx}"
|
||||
-- logInfo m!"{stx'}\n{toString stx'}\n{repr stx'}"
|
||||
Lean.Meta.Tactic.TryThis.addSuggestion stx stx'
|
||||
|
||||
@@ -73,10 +73,6 @@ structure State where
|
||||
-/
|
||||
invariants : Array MVarId := #[]
|
||||
/--
|
||||
Holes of witness type that have been generated so far.
|
||||
-/
|
||||
witnesses : Array MVarId := #[]
|
||||
/--
|
||||
The verification conditions that have been generated so far.
|
||||
-/
|
||||
vcs : Array MVarId := #[]
|
||||
@@ -108,11 +104,8 @@ def addSubGoalAsVC (goal : MVarId) : VCGenM PUnit := do
|
||||
-- VC to the user as-is, without abstracting any variables in the local context.
|
||||
-- This only makes sense for synthetic opaque metavariables.
|
||||
goal.setKind .syntheticOpaque
|
||||
let env ← getEnv
|
||||
if isMVCGenInvariantType env ty then
|
||||
if isMVCGenInvariantType (← getEnv) ty then
|
||||
modify fun s => { s with invariants := s.invariants.push goal }
|
||||
else if isMVCGenWitnessType env ty then
|
||||
modify fun s => { s with witnesses := s.witnesses.push goal }
|
||||
else
|
||||
modify fun s => { s with vcs := s.vcs.push goal }
|
||||
|
||||
|
||||
@@ -206,7 +206,7 @@ def handleApp : Simproc := fun e => do
|
||||
match fn with
|
||||
| .const constName _ =>
|
||||
if (← isCbvOpaque constName) then
|
||||
return (← tryCbvTheorems e).markAsDone
|
||||
return markAsDoneIfFailed <| ← tryCbvTheorems e
|
||||
let info ← getConstInfo constName
|
||||
tryCbvTheorems <|> (guardSimproc (fun _ => info.hasValue) handleConstApp) <|> reduceRecMatcher <| e
|
||||
| .lam .. => betaReduce e
|
||||
@@ -215,7 +215,7 @@ def handleApp : Simproc := fun e => do
|
||||
def handleOpaqueConst : Simproc := fun e => do
|
||||
let .const constName _ := e | return .rfl
|
||||
if (← isCbvOpaque constName) then
|
||||
return (← tryCbvTheorems e).markAsDone
|
||||
return markAsDoneIfFailed <| ← tryCbvTheorems e
|
||||
return .rfl
|
||||
|
||||
def foldLit : Simproc := fun e => do
|
||||
|
||||
@@ -108,4 +108,8 @@ public partial def getListLitElems (e : Expr) (acc : Array Expr := #[]) : Option
|
||||
| List.cons _ a as => getListLitElems as <| acc.push a
|
||||
| _ => none
|
||||
|
||||
public def markAsDoneIfFailed : Result → Result
|
||||
| .rfl _ cd => .rfl true cd
|
||||
| .step e h d cd => .step e h d cd
|
||||
|
||||
end Lean.Meta.Tactic.Cbv
|
||||
|
||||
@@ -364,30 +364,15 @@ macro "mvcgen_trivial" : tactic =>
|
||||
)
|
||||
|
||||
/--
|
||||
A goal section alternative of the form `· term`, one per goal.
|
||||
Used by both `invariants` and `witnesses` sections.
|
||||
An invariant alternative of the form `· term`, one per invariant goal.
|
||||
-/
|
||||
syntax goalDotAlt := ppDedent(ppLine) cdotTk (colGe term)
|
||||
|
||||
/--
|
||||
A goal section alternative of the form `| label<n> a b c => term`, one per goal.
|
||||
Used by both `invariants` and `witnesses` sections.
|
||||
An invariant alternative of the form `| inv<n> a b c => term`, one per invariant goal.
|
||||
-/
|
||||
syntax goalCaseAlt := ppDedent(ppLine) "| " caseArg " => " (colGe term)
|
||||
|
||||
/--
|
||||
The contextual keyword ` witnesses `.
|
||||
-/
|
||||
syntax witnessesKW := &"witnesses "
|
||||
|
||||
/--
|
||||
After `mvcgen [...]`, there can be an optional `witnesses` followed by either
|
||||
* a bulleted list of witnesses `· term; · term`.
|
||||
* a labelled list of witnesses `| witness1 => term; witness2 a b c => term`, which is useful for
|
||||
naming inaccessibles.
|
||||
-/
|
||||
syntax witnessAlts := witnessesKW withPosition((colGe (goalDotAlt <|> goalCaseAlt))*)
|
||||
|
||||
/--
|
||||
Either the contextual keyword ` invariants ` or its tracing form ` invariants? ` which suggests
|
||||
skeletons for missing invariants as a hint.
|
||||
@@ -395,7 +380,7 @@ skeletons for missing invariants as a hint.
|
||||
syntax invariantsKW := &"invariants " <|> &"invariants? "
|
||||
|
||||
/--
|
||||
After `mvcgen [...] witnesses ...`, there can be an optional `invariants` followed by either
|
||||
After `mvcgen [...]`, there can be an optional `invariants` followed by either
|
||||
* a bulleted list of invariants `· term; · term`.
|
||||
* a labelled list of invariants `| inv1 => term; inv2 a b c => term`, which is useful for naming
|
||||
inaccessibles.
|
||||
@@ -419,7 +404,7 @@ syntax vcAlts := "with " (ppSpace colGt tactic)? withPosition((colGe vcAlt)*)
|
||||
@[tactic_alt Lean.Parser.Tactic.mvcgenMacro]
|
||||
syntax (name := mvcgen) "mvcgen" optConfig
|
||||
(" [" withoutPosition((simpStar <|> simpErase <|> simpLemma),*,?) "] ")?
|
||||
(witnessAlts)? (invariantAlts)? (vcAlts)? : tactic
|
||||
(invariantAlts)? (vcAlts)? : tactic
|
||||
|
||||
/--
|
||||
A hint tactic that expands to `mvcgen invariants?`.
|
||||
|
||||
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