The result of simplifying some expression e
.
- expr : Lean.Expr
The simplified version of
e
A proof that
$e = $expr
, where the simplified expression is on the RHS. Ifnone
, the proof is assumed to berefl
.- cache : Bool
If
cache := true
the result is cached. Warning: we will remove this field in the future. It is currently used byarith := true
, but we can now refactor the code to avoid the hack.
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- Lean.Meta.Simp.instInhabitedResult = { default := { expr := default, proof? := default, cache := default } }
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- Lean.Meta.Simp.mkEqTransOptProofResult none true r = pure r
- Lean.Meta.Simp.mkEqTransOptProofResult none false r = pure { expr := r.expr, proof? := r.proof?, cache := false }
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- r₁.mkEqTrans r₂ = Lean.Meta.Simp.mkEqTransOptProofResult r₁.proof? r₁.cache r₂
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Flip the proof in a Simp.Result
.
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- config : Lean.Meta.Simp.Config
- maxDischargeDepth : UInt32
maxDischargeDepth
fromconfig
as anUInt32
. - simpTheorems : Lean.Meta.SimpTheoremsArray
- congrTheorems : Lean.Meta.SimpCongrTheorems
Stores the "parent" term for the term being simplified. If a simplification procedure result depends on this value, then it is its reponsability to set
Result.cache := false
.Motivation for this field: Suppose we have a simplification procedure for normalizing arithmetic terms. Then, given a term such as
t_1 + ... + t_n
, we don't want to apply the procedure to every subtermt_1 + ... + t_i
fori < n
for performance issues. The procedure can accomplish this by checking whether the parent term is also an arithmetical expression and do nothing if it is. However, it should setResult.cache := false
to ensure we don't miss simplification opportunities. For example, consider the following:example (x y : Nat) (h : y = 0) : id ((x + x) + y) = id (x + x) := by simp_arith only ...
If we don't set
Result.cache := false
for the firstx + x
, then we get the resulting state:... |- id (2*x + y) = id (x + x)
instead of
... |- id (2*x + y) = id (2*x)
as expected.
Remark: given an application
f a b c
the "parent" term forf
,a
,b
, andc
isf a b c
.- dischargeDepth : UInt32
- lctxInitIndices : Nat
Number of indices in the local context when starting
simp
. We use this information to decide which assumptions we can use without invalidating the cache. - inDSimp : Bool
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- ctx.isDeclToUnfold declName = ctx.simpTheorems.isDeclToUnfold declName
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- map : Lean.PHashMap Lean.Meta.Origin Nat
- size : Nat
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- Lean.Meta.Simp.instInhabitedUsedSimps = { default := { map := default, size := default } }
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- s.toArray = Array.map (fun (x : Lean.Meta.Origin × Nat) => x.fst) ((Lean.PersistentHashMap.toArray s.map).qsort fun (x1 x2 : Lean.Meta.Origin × Nat) => decide (x1.snd < x2.snd))
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- usedThmCounter : Lean.PHashMap Lean.Meta.Origin Nat
Number of times each simp theorem has been used/applied.
- triedThmCounter : Lean.PHashMap Lean.Meta.Origin Nat
Number of times each simp theorem has been tried.
- congrThmCounter : Lean.PHashMap Lake.Name Nat
Number of times each congr theorem has been tried.
- thmsWithBadKeys : Lean.PArray Lean.Meta.SimpTheorem
When using
Simp.Config.index := false
, andset_option diagnostics true
, for every theorem used bysimp
, we check whether the theorem would be also applied ifindex := true
, and we store it here if it would not have been tried.
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- Lean.Meta.Simp.instInhabitedDiagnostics = { default := { usedThmCounter := default, triedThmCounter := default, congrThmCounter := default, thmsWithBadKeys := default } }
- cache : Lean.Meta.Simp.Cache
- congrCache : Lean.Meta.Simp.CongrCache
- usedTheorems : Lean.Meta.Simp.UsedSimps
- numSteps : Nat
- diag : Lean.Meta.Simp.Diagnostics
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- usedTheorems : Lean.Meta.Simp.UsedSimps
- diag : Lean.Meta.Simp.Diagnostics
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- Lean.Meta.Simp.instInhabitedStats = { default := { usedTheorems := default, diag := default } }
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Result type for a simplification procedure. We have pre
and post
simplification procedures.
- done: Lean.Meta.Simp.Result → Lean.Meta.Simp.Step
- visit: Lean.Meta.Simp.Result → Lean.Meta.Simp.Step
- continue: optParam (Option Lean.Meta.Simp.Result) none → Lean.Meta.Simp.Step
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- Lean.Meta.Simp.instInhabitedStep = { default := Lean.Meta.Simp.Step.done default }
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Similar to Simproc
, but resulting expression should be definitionally equal to the input one.
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- (Lean.TransformStep.done e).toStep = Lean.Meta.Simp.Step.done { expr := e, proof? := none, cache := true }
- (Lean.TransformStep.visit e).toStep = Lean.Meta.Simp.Step.visit { expr := e, proof? := none, cache := true }
- (Lean.TransformStep.continue (some e)).toStep = Lean.Meta.Simp.Step.continue (some { expr := e, proof? := none, cache := true })
- Lean.TransformStep.continue.toStep = Lean.Meta.Simp.Step.continue
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- Lean.Meta.Simp.mkEqTransResultStep r (Lean.Meta.Simp.Step.done r') = do let __do_lift ← Lean.Meta.Simp.mkEqTransOptProofResult r.proof? r.cache r' pure (Lean.Meta.Simp.Step.done __do_lift)
- Lean.Meta.Simp.mkEqTransResultStep r (Lean.Meta.Simp.Step.visit r') = do let __do_lift ← Lean.Meta.Simp.mkEqTransOptProofResult r.proof? r.cache r' pure (Lean.Meta.Simp.Step.visit __do_lift)
- Lean.Meta.Simp.mkEqTransResultStep r Lean.Meta.Simp.Step.continue = pure (Lean.Meta.Simp.Step.continue (some r))
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"Compose" the two given simplification procedures. We use the following semantics.
- If
f
producesdone
orvisit
, then returnf
's result. - If
f
producescontinue
, then applyg
to new expression returned byf
.
See Simp.Step
type.
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- Lean.Meta.Simp.instAndThenSimproc = { andThen := fun (s₁ : Lean.Meta.Simp.Simproc) (s₂ : Unit → Lean.Meta.Simp.Simproc) => Lean.Meta.Simp.andThen s₁ (s₂ ()) }
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- Lean.Meta.Simp.instAndThenDSimproc = { andThen := fun (s₁ : Lean.Meta.Simp.DSimproc) (s₂ : Unit → Lean.Meta.Simp.DSimproc) => Lean.Meta.Simp.dandThen s₁ (s₂ ()) }
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- Lean.Meta.Simp.instInhabitedSimprocOLeanEntry = { default := { declName := default, post := default, keys := default } }
Simproc
entry. It is the .olean entry plus the actual function.
- declName : Lake.Name
- post : Bool
- keys : Array Lean.Meta.SimpTheoremKey
Recall that we cannot store
Simproc
into .olean files because it is a closure. GivenSimprocOLeanEntry.declName
, we convert it into aSimproc
by using the unsafe functionevalConstCheck
.
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- post : Lean.Meta.Simp.SimprocTree
- simprocNames : Lean.PHashSet Lake.Name
- erased : Lean.PHashSet Lake.Name
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- Lean.Meta.Simp.instInhabitedSimprocs = { default := { pre := default, post := default, simprocNames := default, erased := default } }
- pre : Lean.Meta.Simp.Simproc
- post : Lean.Meta.Simp.Simproc
- dpre : Lean.Meta.Simp.DSimproc
- dpost : Lean.Meta.Simp.DSimproc
- discharge? : Lean.Expr → Lean.Meta.SimpM (Option Lean.Expr)
- wellBehavedDischarge : Bool
wellBehavedDischarge
must not be set totrue
IFdischarge?
access local declarations with index >=Context.lctxInitIndices
whencontextual := false
. Reason: it would prevent us from aggressively cachingsimp
results.
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- Lean.Meta.Simp.instInhabitedMethods = { default := { pre := default, post := default, dpre := default, dpost := default, discharge? := default, wellBehavedDischarge := default } }
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- Lean.Meta.Simp.getMethods = do let __do_lift ← read pure (Lean.Meta.Simp.MethodsRef.toMethods __do_lift)
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- Lean.Meta.Simp.pre e = do let __do_lift ← Lean.Meta.Simp.getMethods __do_lift.pre e
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- Lean.Meta.Simp.post e = do let __do_lift ← Lean.Meta.Simp.getMethods __do_lift.post e
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- Lean.Meta.Simp.getConfig = do let __do_lift ← Lean.Meta.Simp.getContext pure __do_lift.config
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- Lean.Meta.Simp.getSimpTheorems = do let __do_lift ← readThe Lean.Meta.Simp.Context pure __do_lift.simpTheorems
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- Lean.Meta.Simp.getSimpCongrTheorems = do let __do_lift ← readThe Lean.Meta.Simp.Context pure __do_lift.congrTheorems
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Returns true
if simp
is in dsimp
mode.
That is, only transformations that preserve definitional equality should be applied.
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- Lean.Meta.Simp.inDSimp = do let __do_lift ← readThe Lean.Meta.Simp.Context pure __do_lift.inDSimp
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Save current cache, reset it, execute x
, and then restore original cache.
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- r.getProof = match r.proof? with | some p => pure p | none => Lean.Meta.mkEqRefl r.expr
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Similar to Result.getProof
, but adds a mkExpectedTypeHint
if proof?
is none
(i.e., result is definitionally equal to input), but we cannot establish that
source
and r.expr
are definitionally when using TransparencyMode.reducible
.
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Construct the Expr
cast h e
, from a Simp.Result
with proof h
.
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- r.mkCast e = do let __do_lift ← r.getProof Lean.Meta.mkAppM `cast #[__do_lift, e]
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- Lean.Meta.Simp.removeUnnecessaryCasts.isDummyEqRec e = ((e.isAppOfArity `Eq.rec 6 || e.isAppOfArity `Eq.ndrec 6) && e.appArg!.isAppOf `Eq.refl)
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Given a simplified function result r
and arguments args
, simplify arguments using simp
and dsimp
.
The resulting proof is built using congr
and congrFun
theorems.
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Try to use automatically generated congruence theorems. See mkCongrSimp?
.
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Return a WHNF configuration for retrieving [simp]
from the discrimination tree.
If user has disabled zeta
and/or beta
reduction in the simplifier, or enabled zetaDelta
,
we must also disable/enable them when retrieving lemmas from discrimination tree. See issues: #2669 and #2281
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- (Lean.Meta.Simp.Step.visit r).addExtraArgs extraArgs = do let __do_lift ← r.addExtraArgs extraArgs pure (Lean.Meta.Simp.Step.visit __do_lift)
- (Lean.Meta.Simp.Step.done r).addExtraArgs extraArgs = do let __do_lift ← r.addExtraArgs extraArgs pure (Lean.Meta.Simp.Step.done __do_lift)
- Lean.Meta.Simp.Step.continue.addExtraArgs extraArgs = pure Lean.Meta.Simp.Step.continue
- (Lean.Meta.Simp.Step.continue (some r)).addExtraArgs extraArgs = do let __do_lift ← r.addExtraArgs extraArgs pure (Lean.Meta.Simp.Step.continue (some __do_lift))
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- Lean.Meta.Simp.DStep.addExtraArgs (Lean.TransformStep.visit eNew) extraArgs = Lean.TransformStep.visit (Lean.mkAppN eNew extraArgs)
- Lean.Meta.Simp.DStep.addExtraArgs (Lean.TransformStep.done eNew) extraArgs = Lean.TransformStep.done (Lean.mkAppN eNew extraArgs)
- Lean.Meta.Simp.DStep.addExtraArgs Lean.TransformStep.continue extraArgs = Lean.TransformStep.continue
- Lean.Meta.Simp.DStep.addExtraArgs (Lean.TransformStep.continue (some eNew)) extraArgs = Lean.TransformStep.continue (some (Lean.mkAppN eNew extraArgs))
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Auxiliary method.
Given the current target
of mvarId
, apply r
which is a new target and proof that it is equal to the current one.
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