Documentation

Lean.Meta.Basic

This module provides four (mutually dependent) goodies that are needed for building the elaborator and tactic frameworks. 1- Weak head normal form computation with support for metavariables and transparency modes. 2- Definitionally equality checking with support for metavariables (aka unification modulo definitional equality). 3- Type inference. 4- Type class resolution.

They are packed into the MetaM monad.

opaque Lean.Meta.isDefEqStuckExceptionId :

InternalExceptionId

def Lean.Meta.TransparencyMode.toUInt64 :

TransparencyMode → UInt64

Equations

def Lean.Meta.EtaStructMode.toUInt64 :

EtaStructMode → UInt64

Equations

inductive Lean.Meta.ProjReductionKind :

Configuration for projection reduction. See whnfCore.

no : ProjReductionKind
Projections s.i are not reduced at whnfCore.
yes : ProjReductionKind
Projections s.i are reduced at whnfCore, and whnfCore is used at s during the process. Recall that whnfCore does not perform delta reduction (i.e., it will not unfold constant declarations).
yesWithDelta : ProjReductionKind
Projections s.i are reduced at whnfCore, and whnf is used at s during the process. Recall that whnfCore does not perform delta reduction (i.e., it will not unfold constant declarations), but whnf does.
yesWithDeltaI : ProjReductionKind
Projections s.i are reduced at whnfCore, and whnfAtMostI is used at s during the process. Recall that whnfAtMostI is like whnf but uses transparency at most instances. This option is stronger than yes, but weaker than yesWithDelta. We use this option to ensure we reduce projections to prevent expensive defeq checks when unifying TC operations. When unifying e.g. (@Field.toNeg α inst1).1 =?= (@Field.toNeg α inst2).1, we only want to unify negation (and not all other field operations as well). Unifying the field instances slowed down unification: https://github.com/leanprover/lean4/issues/1986

Instances For

instance Lean.Meta.instDecidableEqProjReductionKind :

DecidableEq ProjReductionKind

Equations

Lean.Meta.instDecidableEqProjReductionKind x✝ y✝ = if h : x✝.toCtorIdx = y✝.toCtorIdx then isTrue ⋯ else isFalse ⋯

instance Lean.Meta.instInhabitedProjReductionKind :

Inhabited ProjReductionKind

Equations

Lean.Meta.instInhabitedProjReductionKind = { default := Lean.Meta.ProjReductionKind.no }

instance Lean.Meta.instReprProjReductionKind :

Repr ProjReductionKind

Equations

Lean.Meta.instReprProjReductionKind = { reprPrec := Lean.Meta.reprProjReductionKind✝ }

def Lean.Meta.ProjReductionKind.toUInt64 :

ProjReductionKind → UInt64

Equations

structure Lean.Meta.Config :

Configuration flags for the MetaM monad. Many of them are used to control the isDefEq function that checks whether two terms are definitionally equal or not. Recall that when isDefEq is trying to check whether ?m@C a₁ ... aₙ and t are definitionally equal (?m@C a₁ ... aₙ =?= t), where ?m@C as a shorthand for C |- ?m : t where t is the type of ?m. We solve it using the assignment ?m := fun a₁ ... aₙ => t if

a₁ ... aₙ are pairwise distinct free variables that are not let-variables.
a₁ ... aₙ are not in C
t only contains free variables in C and/or {a₁, ..., aₙ}
For every metavariable ?m'@C' occurring in t, C' is a subprefix of C
?m does not occur in t

foApprox : Bool

If foApprox is set to true, and some aᵢ is not a free variable, then we use first-order unification

  ?m a_1 ... a_i a_{i+1} ... a_{i+k} =?= f b_1 ... b_k

reduces to

  ?m a_1 ... a_i =?= f
  a_{i+1}        =?= b_1
  ...
  a_{i+k}        =?= b_k

ctxApprox : Bool
When ctxApprox is set to true, we relax condition 4, by creating an auxiliary metavariable ?n' with a smaller context than ?m'.
quasiPatternApprox : Bool
When quasiPatternApprox is set to true, we ignore condition 2.
constApprox : Bool
When constApprox is set to true, we solve ?m t =?= c using ?m := fun _ => c when ?m t is not a higher-order pattern and c is not an application as
isDefEqStuckEx : Bool
When the following flag is set, isDefEq throws the exception Exception.isDefEqStuck whenever it encounters a constraint ?m ... =?= t where ?m is read only. This feature is useful for type class resolution where we may want to notify the caller that the TC problem may be solvable later after it assigns ?m.
unificationHints : Bool
Enable/disable the unification hints feature.
proofIrrelevance : Bool
Enables proof irrelevance at isDefEq
assignSyntheticOpaque : Bool
By default synthetic opaque metavariables are not assigned by isDefEq. Motivation: we want to make sure typing constraints resolved during elaboration should not "fill" holes that are supposed to be filled using tactics. However, this restriction is too restrictive for tactics such as exact t. When elaborating t, we dot not fill named holes when solving typing constraints or TC resolution. But, we ignore the restriction when we try to unify the type of t with the goal target type. We claim this is not a hack and is defensible behavior because this last unification step is not really part of the term elaboration.
offsetCnstrs : Bool
Enable/Disable support for offset constraints such as ?x + 1 =?= e
transparency : TransparencyMode
Controls which definitions and theorems can be unfolded by isDefEq and whnf.
etaStruct : EtaStructMode
Eta for structures configuration mode.
univApprox : Bool
When univApprox is set to true, we use approximations when solving postponed universe constraints. Examples:
- max u ?v =?= u is solved with ?v := u and ignoring the solution ?v := 0.
- max u w =?= mav u ?v is solved with ?v := w ignoring the solution ?v := max u w
iota : Bool
If true, reduce recursor/matcher applications, e.g., Nat.rec true (fun _ _ => false) Nat.zero reduces to true
beta : Bool
If true, reduce terms such as (fun x => t[x]) a into t[a]
proj : ProjReductionKind
Control projection reduction at whnfCore.
zeta : Bool
Zeta reduction: let x := v; e[x] reduces to e[v]. We say a let-declaration let x := v; e is non dependent if it is equivalent to (fun x => e) v. Recall that
```
fun x : BitVec 5 => let n := 5; fun y : BitVec n => x = y
```
is type correct, but
```
fun x : BitVec 5 => (fun n => fun y : BitVec n => x = y) 5
```
is not.
zetaDelta : Bool
Zeta-delta reduction: given a local context containing entry x : t := e, free variable x reduces to e.
zetaUnused : Bool
Zeta reduction for unused let-declarations: let x := v; e reduces to e when x does not occur in e.

Instances For

instance Lean.Meta.instInhabitedConfig :

Inhabited Config

Equations

One or more equations did not get rendered due to their size.

instance Lean.Meta.instReprConfig_2 :

Equations

Lean.Meta.instReprConfig_2 = { reprPrec := Lean.Meta.reprConfig✝ }

structure Lean.Meta.ConfigWithKey :

Configuration with key produced by Config.toKey.

config : Config
key : UInt64

Instances For

Lean.Meta.instInhabitedConfigWithKey

instance Lean.Meta.instInhabitedConfigWithKey :

Inhabited ConfigWithKey

Equations

Lean.Meta.instInhabitedConfigWithKey = { default := { config := default, key := default } }

def Lean.Meta.Config.toConfigWithKey (c : Config) :

Equations

c.toConfigWithKey = { config := c, key := Lean.Meta.Config.toKey✝ c }

structure Lean.Meta.ParamInfo :

Function parameter information cache.

binderInfo : BinderInfo
The binder annotation for the parameter.
hasFwdDeps : Bool
hasFwdDeps is true if there is another parameter whose type depends on this one.
backDeps : Array Nat
backDeps contains the backwards dependencies. That is, the (0-indexed) position of previous parameters that this one depends on.
isProp : Bool
isProp is true if the parameter type is always a proposition.
isDecInst : Bool
isDecInst is true if the parameter's type is of the form Decidable .... This information affects the generation of congruence theorems.
higherOrderOutParam : Bool
higherOrderOutParam is true if this parameter is a higher-order output parameter of local instance. Example:
```
getElem :
  {cont : Type u_1} → {idx : Type u_2} → {elem : Type u_3} →
  {dom : cont → idx → Prop} → [self : GetElem cont idx elem dom] →
  (xs : cont) → (i : idx) → dom xs i → elem
```
This flag is true for the parameter dom because it is output parameter of [self : GetElem cont idx elem dom]
dependsOnHigherOrderOutParam : Bool
dependsOnHigherOrderOutParam is true if the type of this parameter depends on the higher-order output parameter of a previous local instance. Example:
```
getElem :
  {cont : Type u_1} → {idx : Type u_2} → {elem : Type u_3} →
  {dom : cont → idx → Prop} → [self : GetElem cont idx elem dom] →
  (xs : cont) → (i : idx) → dom xs i → elem
```
This flag is true for the parameter with type dom xs i since dom is an output parameter of the instance [self : GetElem cont idx elem dom]

Instances For

Lean.Meta.instInhabitedParamInfo

instance Lean.Meta.instInhabitedParamInfo :

Inhabited ParamInfo

Equations

One or more equations did not get rendered due to their size.

def Lean.Meta.ParamInfo.isImplicit (p : ParamInfo) :

Equations

p.isImplicit = (p.binderInfo == Lean.BinderInfo.implicit)

def Lean.Meta.ParamInfo.isInstImplicit (p : ParamInfo) :

Equations

p.isInstImplicit = (p.binderInfo == Lean.BinderInfo.instImplicit)

def Lean.Meta.ParamInfo.isStrictImplicit (p : ParamInfo) :

Equations

p.isStrictImplicit = (p.binderInfo == Lean.BinderInfo.strictImplicit)

def Lean.Meta.ParamInfo.isExplicit (p : ParamInfo) :

Equations

p.isExplicit = (p.binderInfo == Lean.BinderInfo.default)

structure Lean.Meta.FunInfo :

Function information cache. See ParamInfo.

paramInfo : Array ParamInfo
Parameter information cache.
resultDeps : Array Nat
resultDeps contains the function result type backwards dependencies. That is, the (0-indexed) position of parameters that the result type depends on.

structure Lean.Meta.InfoCacheKey :

Key for the function information cache.

configKey : UInt64
key produced using Config.toKey.
expr : Expr
The function being cached information about. It is quite often an Expr.const.
nargs? : Option Nat
nargs? = some n if the cached information was computed assuming the function has arity n. If nargs? = none, then the cache information consumed the arrow type as much as possible using the current transparency setting. X

Instances For

instance Lean.Meta.instInhabitedInfoCacheKey :

Inhabited InfoCacheKey

Equations

Lean.Meta.instInhabitedInfoCacheKey = { default := { configKey := default, expr := default, nargs? := default } }

instance Lean.Meta.instBEqInfoCacheKey :

BEq InfoCacheKey

Equations

Lean.Meta.instBEqInfoCacheKey = { beq := Lean.Meta.beqInfoCacheKey✝ }

instance Lean.Meta.instHashableInfoCacheKey :

Hashable InfoCacheKey

Equations

One or more equations did not get rendered due to their size.

structure Lean.Meta.SynthInstanceCacheKey :

localInsts : LocalInstances
type : Expr
synthPendingDepth : Nat
Value of synthPendingDepth when instance was synthesized or failed to be synthesized. See issue #2522.

Instances For

instance Lean.Meta.instHashableSynthInstanceCacheKey :

Hashable SynthInstanceCacheKey

Equations

Lean.Meta.instHashableSynthInstanceCacheKey = { hash := Lean.Meta.hashSynthInstanceCacheKey✝ }

instance Lean.Meta.instBEqSynthInstanceCacheKey :

BEq SynthInstanceCacheKey

Equations

Lean.Meta.instBEqSynthInstanceCacheKey = { beq := Lean.Meta.beqSynthInstanceCacheKey✝ }

structure Lean.Meta.AbstractMVarsResult :

Resulting type for abstractMVars

paramNames : Array Name
numMVars : Nat
expr : Expr

Instances For

instance Lean.Meta.instInhabitedAbstractMVarsResult :

Inhabited AbstractMVarsResult

Equations

Lean.Meta.instInhabitedAbstractMVarsResult = { default := { paramNames := default, numMVars := default, expr := default } }

instance Lean.Meta.instBEqAbstractMVarsResult :

BEq AbstractMVarsResult

Equations

Lean.Meta.instBEqAbstractMVarsResult = { beq := Lean.Meta.beqAbstractMVarsResult✝ }

@[reducible, inline]

abbrev Lean.Meta.SynthInstanceCache :

Equations

Lean.Meta.SynthInstanceCache = Lean.PersistentHashMap Lean.Meta.SynthInstanceCacheKey (Option Lean.Meta.AbstractMVarsResult)

structure Lean.Meta.ExprConfigCacheKey :

expr : Expr
configKey : UInt64

Instances For

instance Lean.Meta.instInhabitedExprConfigCacheKey :

Inhabited ExprConfigCacheKey

Equations

Lean.Meta.instInhabitedExprConfigCacheKey = { default := { expr := default, configKey := default } }

instance Lean.Meta.instBEqExprConfigCacheKey :

BEq ExprConfigCacheKey

Equations

Lean.Meta.instBEqExprConfigCacheKey = { beq := fun (a b : Lean.Meta.ExprConfigCacheKey) => a.expr.equal b.expr && a.configKey == b.configKey }

instance Lean.Meta.instHashableExprConfigCacheKey :

Hashable ExprConfigCacheKey

Equations

One or more equations did not get rendered due to their size.

@[reducible, inline]

abbrev Lean.Meta.InferTypeCache :

Equations

Lean.Meta.InferTypeCache = Lean.PersistentHashMap Lean.Meta.ExprConfigCacheKey Lean.Expr

@[reducible, inline]

abbrev Lean.Meta.FunInfoCache :

Equations

Lean.Meta.FunInfoCache = Lean.PersistentHashMap Lean.Meta.InfoCacheKey Lean.Meta.FunInfo

@[reducible, inline]

abbrev Lean.Meta.WhnfCache :

Equations

Lean.Meta.WhnfCache = Lean.PersistentHashMap Lean.Meta.ExprConfigCacheKey Lean.Expr

structure Lean.Meta.DefEqCacheKey :

lhs : Expr
rhs : Expr
configKey : UInt64

Instances For

instance Lean.Meta.instInhabitedDefEqCacheKey :

Inhabited DefEqCacheKey

Equations

Lean.Meta.instInhabitedDefEqCacheKey = { default := { lhs := default, rhs := default, configKey := default } }

instance Lean.Meta.instBEqDefEqCacheKey :

BEq DefEqCacheKey

Equations

Lean.Meta.instBEqDefEqCacheKey = { beq := Lean.Meta.beqDefEqCacheKey✝ }

instance Lean.Meta.instHashableDefEqCacheKey :

Hashable DefEqCacheKey

Equations

One or more equations did not get rendered due to their size.

@[reducible, inline]

abbrev Lean.Meta.DefEqCache :

A mapping (s, t) ↦ isDefEq s t. TODO: consider more efficient representations (e.g., a proper set) and caching policies (e.g., imperfect cache). We should also investigate the impact on memory consumption.

Equations

Lean.Meta.DefEqCache = Lean.PersistentHashMap Lean.Meta.DefEqCacheKey Bool

structure Lean.Meta.Cache :

Cache datastructures for type inference, type class resolution, whnf, and definitional equality.

inferType : InferTypeCache
funInfo : FunInfoCache
synthInstance : SynthInstanceCache
whnf : WhnfCache
defEqTrans : DefEqCache
defEqPerm : DefEqCache

Instances For

Lean.Meta.instInhabitedCache

instance Lean.Meta.instInhabitedCache :

Inhabited Cache

Equations

Lean.Meta.instInhabitedCache = { default := { inferType := default, funInfo := default, synthInstance := default, whnf := default, defEqTrans := default, defEqPerm := default } }

structure Lean.Meta.DefEqContext :

"Context" for a postponed universe constraint. lhs and rhs are the surrounding isDefEq call when the postponed constraint was created.

lhs : Expr
rhs : Expr
lctx : LocalContext
localInstances : LocalInstances

structure Lean.Meta.PostponedEntry :

Auxiliary structure for representing postponed universe constraints. Remark: the fields ref and rootDefEq? are used for error message generation only. Remark: we may consider improving the error message generation in the future.

ref : Syntax
We save the ref at entry creation time. This is used for reporting errors back to the user.
lhs : Level
rhs : Level
ctx? : Option DefEqContext
Context for the surrounding isDefEq call when the entry was created.

Instances For

Lean.Meta.instInhabitedPostponedEntry

instance Lean.Meta.instInhabitedPostponedEntry :

Inhabited PostponedEntry

Equations

Lean.Meta.instInhabitedPostponedEntry = { default := { ref := default, lhs := default, rhs := default, ctx? := default } }

structure Lean.Meta.Diagnostics :

unfoldCounter : PHashMap Name Nat
Number of times each declaration has been unfolded
heuristicCounter : PHashMap Name Nat
Number of times f a =?= f b heuristic has been used per function f.
instanceCounter : PHashMap Name Nat
Number of times a TC instance is used.
synthPendingFailures : PHashMap Expr MessageData
Pending instances that were not synthesized because maxSynthPendingDepth has been reached.

Instances For

Lean.Meta.instInhabitedDiagnostics

instance Lean.Meta.instInhabitedDiagnostics :

Inhabited Diagnostics

Equations

Lean.Meta.instInhabitedDiagnostics = { default := { unfoldCounter := default, heuristicCounter := default, instanceCounter := default, synthPendingFailures := default } }

structure Lean.Meta.State :

MetaM monad state.

mctx : MetavarContext
cache : Cache
zetaDeltaFVarIds : FVarIdSet
When Context.trackZetaDelta == true, then any let-decl free variable that is zetaDelta-expanded by MetaM is stored in zetaDeltaFVarIds.
postponed : PersistentArray PostponedEntry
Array of postponed universe level constraints
diag : Diagnostics

Instances For

Lean.Meta.instInhabitedState

instance Lean.Meta.instInhabitedState :

Inhabited State

Equations

Lean.Meta.instInhabitedState = { default := { mctx := default, cache := default, zetaDeltaFVarIds := default, postponed := default, diag := default } }

structure Lean.Meta.SavedState :

Backtrackable state for the MetaM monad.

core : Core.SavedState
meta : State

Instances For

instance Lean.Meta.instNonemptySavedState :

Nonempty SavedState

opaque Lean.Meta.maxSynthPendingDepth :

Lean.Option Nat

structure Lean.Meta.Context :

Contextual information for the MetaM monad.

config : Lean.Meta.Config
configKey : UInt64
trackZetaDelta : Bool
When trackZetaDelta = true, we track all free variables that have been zetaDelta-expanded. That is, suppose the local context contains the declaration x : t := v, and we reduce x to v, then we insert x into State.zetaDeltaFVarIds. We use trackZetaDelta to discover which let-declarations let x := v; e can be represented as (fun x => e) v. When we find these declarations we set their nonDep flag with true. To find these let-declarations in a given term s, we 1- Reset State.zetaDeltaFVarIds 2- Set trackZetaDelta := true 3- Type-check s.
Note that, we do not include this field in the Config structure because this field is not taken into account while caching results. See also field zetaDeltaSet.
zetaDeltaSet : FVarIdSet
If config.zetaDelta := false, we may select specific local declarations to be unfolded using the field zetaDeltaSet. Note that, we do not include this field in the Config structure because this field is not taken into account while caching results. Moreover, we reset all caches whenever setting it.
lctx : LocalContext
Local context
localInstances : LocalInstances
Local instances in lctx.
defEqCtx? : Option DefEqContext
Not none when inside of an isDefEq test. See PostponedEntry.
synthPendingDepth : Nat
Track the number of nested synthPending invocations. Nested invocations can happen when the type class resolution invokes synthPending.
Remark: synthPending fails if synthPendingDepth > maxSynthPendingDepth.
canUnfold? : Option (Config → ConstantInfo → CoreM Bool)
A predicate to control whether a constant can be unfolded or not at whnf. Note that we do not cache results at whnf when canUnfold? is not none.
univApprox : Bool
When Config.univApprox := true, this flag is set to true when there is no progress processing universe constraints.
inTypeClassResolution : Bool
inTypeClassResolution := true when isDefEq is invoked at tryResolve in the type class resolution module. We don't use isDefEqProjDelta when performing TC resolution due to performance issues. This is not a great solution, but a proper solution would require a more sophisticased caching mechanism.

@[reducible, inline]

abbrev Lean.Meta.MetaM (α : Type) :

The MetaM monad is a core component of Lean's metaprogramming framework, facilitating the construction and manipulation of expressions (Lean.Expr) within Lean.

It builds on top of CoreM and additionally provides:

A LocalContext for managing free variables.
A MetavarContext for managing metavariables.
A Cache for caching results of the key MetaM operations.

The key operations provided by MetaM are:

inferType, which attempts to automatically infer the type of a given expression.
whnf, which reduces an expression to the point where the outermost part is no longer reducible but the inside may still contain unreduced expression.
isDefEq, which determines whether two expressions are definitionally equal, possibly assigning meta variables in the process.
forallTelescope and lambdaTelescope, which make it possible to automatically move into (nested) binders while updating the local context.

The following is a small example that demonstrates how to obtain and manipulate the type of a Fin expression:

import Lean

open Lean Meta

def getFinBound (e : Expr) : MetaM (Option Expr) := do
  let type ← whnf (← inferType e)
  let_expr Fin bound := type | return none
  return bound

def a : Fin 100 := 42

run_meta
  match ← getFinBound (.const ``a []) with
  | some limit => IO.println (← ppExpr limit)
  | none => IO.println "no limit found"

Equations

Lean.MetaM = ReaderT Lean.Meta.Context (StateRefT' IO.RealWorld Lean.Meta.State Lean.CoreM)

Instances For

@[always_inline]

instance Lean.Meta.instMonadMetaM :

Equations

Lean.Meta.instMonadMetaM = Monad.mk

instance Lean.Meta.instInhabitedMetaM {α : Type} :

Inhabited (MetaM α)

Equations

Lean.Meta.instInhabitedMetaM = { default := fun (x : Lean.Meta.Context) (x : ST.Ref IO.RealWorld Lean.Meta.State) => default }

instance Lean.Meta.instMonadLCtxMetaM :

MonadLCtx MetaM

Equations

Lean.Meta.instMonadLCtxMetaM = { getLCtx := do let __do_lift ← read pure __do_lift.lctx }

instance Lean.Meta.instMonadMCtxMetaM :

MonadMCtx MetaM

Equations

One or more equations did not get rendered due to their size.

instance Lean.Meta.instMonadEnvMetaM :

Equations

One or more equations did not get rendered due to their size.

instance Lean.Meta.instAddMessageContextMetaM :

AddMessageContext MetaM

Equations

Lean.Meta.instAddMessageContextMetaM = { addMessageContext := Lean.addMessageContextFull }

def Lean.Meta.saveState :

MetaM SavedState

Equations

Lean.Meta.saveState = do let __do_lift ← liftM Lean.Core.saveState let __do_lift_1 ← get pure { core := __do_lift, meta := __do_lift_1 }

def Lean.Meta.SavedState.restore (b : SavedState) :

Restore backtrackable parts of the state.

Equations

One or more equations did not get rendered due to their size.

@[specialize #[]]

def Lean.Meta.withRestoreOrSaveFull {α : Type} (reusableResult? : Option (α × SavedState)) (act : MetaM α) :

MetaM (α × SavedState)

Incremental reuse primitive: if reusableResult? is none, runs act and returns its result together with the saved monadic state after act including the heartbeats used by it. If reusableResult? on the other hand is some (a, state), restores full state including heartbeats used and returns (a, state).

The intention is for steps that support incremental reuse to initially pass none as reusableResult? and store the result and state in a snapshot. In a further run, if reuse is possible, reusableResult? should be set to the previous result and state, ensuring that the state after running withRestoreOrSaveFull is identical in both runs. Note however that necessarily this is only an approximation in the case of heartbeats as heartbeats used by withRestoreOrSaveFull itself after calling act as well as by reuse-handling code such as the one supplying reusableResult? are not accounted for.

Equations

One or more equations did not get rendered due to their size.

instance Lean.Meta.instMonadBacktrackSavedStateMetaM :

MonadBacktrack SavedState MetaM

Equations

Lean.Meta.instMonadBacktrackSavedStateMetaM = { saveState := Lean.Meta.saveState, restoreState := fun (s : Lean.Meta.SavedState) => s.restore }

@[inline]

def Lean.Meta.MetaM.run {α : Type} (x : MetaM α) (ctx : Context := { config := { foApprox := false, ctxApprox := false, quasiPatternApprox := false, constApprox := false, isDefEqStuckEx := false, unificationHints := true, proofIrrelevance := true, assignSyntheticOpaque := false, offsetCnstrs := true, transparency := TransparencyMode.default, etaStruct := EtaStructMode.all, univApprox := true, iota := true, beta := true, proj := ProjReductionKind.yesWithDelta, zeta := true, zetaDelta := true, zetaUnused := true }, configKey := Lean.Meta.Config.toKey✝ { foApprox := false, ctxApprox := false, quasiPatternApprox := false, constApprox := false, isDefEqStuckEx := false, unificationHints := true, proofIrrelevance := true, assignSyntheticOpaque := false, offsetCnstrs := true, transparency := TransparencyMode.default, etaStruct := EtaStructMode.all, univApprox := true, iota := true, beta := true, proj := ProjReductionKind.yesWithDelta, zeta := true, zetaDelta := true, zetaUnused := true }, trackZetaDelta := false, zetaDeltaSet := ∅, lctx := { fvarIdToDecl := { root := PersistentHashMap.Node.entries PersistentHashMap.mkEmptyEntriesArray }, decls := { root := PersistentArrayNode.node (Array.mkEmpty PersistentArray.branching.toNat), tail := Array.mkEmpty PersistentArray.branching.toNat, size := 0, shift := PersistentArray.initShift, tailOff := 0 } }, localInstances := #[], defEqCtx? := none, synthPendingDepth := 0, canUnfold? := none, univApprox := false, inTypeClassResolution := false }) (s : State := { mctx := { depth := 0, levelAssignDepth := 0, mvarCounter := 0, lDepth := { root := PersistentHashMap.Node.entries PersistentHashMap.mkEmptyEntriesArray }, decls := { root := PersistentHashMap.Node.entries PersistentHashMap.mkEmptyEntriesArray }, userNames := { root := PersistentHashMap.Node.entries PersistentHashMap.mkEmptyEntriesArray }, lAssignment := { root := PersistentHashMap.Node.entries PersistentHashMap.mkEmptyEntriesArray }, eAssignment := { root := PersistentHashMap.Node.entries PersistentHashMap.mkEmptyEntriesArray }, dAssignment := { root := PersistentHashMap.Node.entries PersistentHashMap.mkEmptyEntriesArray } }, cache := { inferType := { root := PersistentHashMap.Node.entries PersistentHashMap.mkEmptyEntriesArray }, funInfo := { root := PersistentHashMap.Node.entries PersistentHashMap.mkEmptyEntriesArray }, synthInstance := { root := PersistentHashMap.Node.entries PersistentHashMap.mkEmptyEntriesArray }, whnf := { root := PersistentHashMap.Node.entries PersistentHashMap.mkEmptyEntriesArray }, defEqTrans := { root := PersistentHashMap.Node.entries PersistentHashMap.mkEmptyEntriesArray }, defEqPerm := { root := PersistentHashMap.Node.entries PersistentHashMap.mkEmptyEntriesArray } }, zetaDeltaFVarIds := ∅, postponed := { root := PersistentArrayNode.node (Array.mkEmpty PersistentArray.branching.toNat), tail := Array.mkEmpty PersistentArray.branching.toNat, size := 0, shift := PersistentArray.initShift, tailOff := 0 }, diag := { unfoldCounter := { root := PersistentHashMap.Node.entries PersistentHashMap.mkEmptyEntriesArray }, heuristicCounter := { root := PersistentHashMap.Node.entries PersistentHashMap.mkEmptyEntriesArray }, instanceCounter := { root := PersistentHashMap.Node.entries PersistentHashMap.mkEmptyEntriesArray }, synthPendingFailures := { root := PersistentHashMap.Node.entries PersistentHashMap.mkEmptyEntriesArray } } }) :

CoreM (α × State)

Equations

x.run ctx s = (x ctx).run s

@[inline]

def Lean.Meta.MetaM.run' {α : Type} (x : MetaM α) (ctx : Context := { config := { foApprox := false, ctxApprox := false, quasiPatternApprox := false, constApprox := false, isDefEqStuckEx := false, unificationHints := true, proofIrrelevance := true, assignSyntheticOpaque := false, offsetCnstrs := true, transparency := TransparencyMode.default, etaStruct := EtaStructMode.all, univApprox := true, iota := true, beta := true, proj := ProjReductionKind.yesWithDelta, zeta := true, zetaDelta := true, zetaUnused := true }, configKey := Lean.Meta.Config.toKey✝ { foApprox := false, ctxApprox := false, quasiPatternApprox := false, constApprox := false, isDefEqStuckEx := false, unificationHints := true, proofIrrelevance := true, assignSyntheticOpaque := false, offsetCnstrs := true, transparency := TransparencyMode.default, etaStruct := EtaStructMode.all, univApprox := true, iota := true, beta := true, proj := ProjReductionKind.yesWithDelta, zeta := true, zetaDelta := true, zetaUnused := true }, trackZetaDelta := false, zetaDeltaSet := ∅, lctx := { fvarIdToDecl := { root := PersistentHashMap.Node.entries PersistentHashMap.mkEmptyEntriesArray }, decls := { root := PersistentArrayNode.node (Array.mkEmpty PersistentArray.branching.toNat), tail := Array.mkEmpty PersistentArray.branching.toNat, size := 0, shift := PersistentArray.initShift, tailOff := 0 } }, localInstances := #[], defEqCtx? := none, synthPendingDepth := 0, canUnfold? := none, univApprox := false, inTypeClassResolution := false }) (s : State := { mctx := { depth := 0, levelAssignDepth := 0, mvarCounter := 0, lDepth := { root := PersistentHashMap.Node.entries PersistentHashMap.mkEmptyEntriesArray }, decls := { root := PersistentHashMap.Node.entries PersistentHashMap.mkEmptyEntriesArray }, userNames := { root := PersistentHashMap.Node.entries PersistentHashMap.mkEmptyEntriesArray }, lAssignment := { root := PersistentHashMap.Node.entries PersistentHashMap.mkEmptyEntriesArray }, eAssignment := { root := PersistentHashMap.Node.entries PersistentHashMap.mkEmptyEntriesArray }, dAssignment := { root := PersistentHashMap.Node.entries PersistentHashMap.mkEmptyEntriesArray } }, cache := { inferType := { root := PersistentHashMap.Node.entries PersistentHashMap.mkEmptyEntriesArray }, funInfo := { root := PersistentHashMap.Node.entries PersistentHashMap.mkEmptyEntriesArray }, synthInstance := { root := PersistentHashMap.Node.entries PersistentHashMap.mkEmptyEntriesArray }, whnf := { root := PersistentHashMap.Node.entries PersistentHashMap.mkEmptyEntriesArray }, defEqTrans := { root := PersistentHashMap.Node.entries PersistentHashMap.mkEmptyEntriesArray }, defEqPerm := { root := PersistentHashMap.Node.entries PersistentHashMap.mkEmptyEntriesArray } }, zetaDeltaFVarIds := ∅, postponed := { root := PersistentArrayNode.node (Array.mkEmpty PersistentArray.branching.toNat), tail := Array.mkEmpty PersistentArray.branching.toNat, size := 0, shift := PersistentArray.initShift, tailOff := 0 }, diag := { unfoldCounter := { root := PersistentHashMap.Node.entries PersistentHashMap.mkEmptyEntriesArray }, heuristicCounter := { root := PersistentHashMap.Node.entries PersistentHashMap.mkEmptyEntriesArray }, instanceCounter := { root := PersistentHashMap.Node.entries PersistentHashMap.mkEmptyEntriesArray }, synthPendingFailures := { root := PersistentHashMap.Node.entries PersistentHashMap.mkEmptyEntriesArray } } }) :

Equations

x.run' ctx s = Prod.fst <$> x.run ctx s

@[inline]

def Lean.Meta.MetaM.toIO {α : Type} (x : MetaM α) (ctxCore : Core.Context) (sCore : Core.State) (ctx : Context := { config := { foApprox := false, ctxApprox := false, quasiPatternApprox := false, constApprox := false, isDefEqStuckEx := false, unificationHints := true, proofIrrelevance := true, assignSyntheticOpaque := false, offsetCnstrs := true, transparency := TransparencyMode.default, etaStruct := EtaStructMode.all, univApprox := true, iota := true, beta := true, proj := ProjReductionKind.yesWithDelta, zeta := true, zetaDelta := true, zetaUnused := true }, configKey := Lean.Meta.Config.toKey✝ { foApprox := false, ctxApprox := false, quasiPatternApprox := false, constApprox := false, isDefEqStuckEx := false, unificationHints := true, proofIrrelevance := true, assignSyntheticOpaque := false, offsetCnstrs := true, transparency := TransparencyMode.default, etaStruct := EtaStructMode.all, univApprox := true, iota := true, beta := true, proj := ProjReductionKind.yesWithDelta, zeta := true, zetaDelta := true, zetaUnused := true }, trackZetaDelta := false, zetaDeltaSet := ∅, lctx := { fvarIdToDecl := { root := PersistentHashMap.Node.entries PersistentHashMap.mkEmptyEntriesArray }, decls := { root := PersistentArrayNode.node (Array.mkEmpty PersistentArray.branching.toNat), tail := Array.mkEmpty PersistentArray.branching.toNat, size := 0, shift := PersistentArray.initShift, tailOff := 0 } }, localInstances := #[], defEqCtx? := none, synthPendingDepth := 0, canUnfold? := none, univApprox := false, inTypeClassResolution := false }) (s : State := { mctx := { depth := 0, levelAssignDepth := 0, mvarCounter := 0, lDepth := { root := PersistentHashMap.Node.entries PersistentHashMap.mkEmptyEntriesArray }, decls := { root := PersistentHashMap.Node.entries PersistentHashMap.mkEmptyEntriesArray }, userNames := { root := PersistentHashMap.Node.entries PersistentHashMap.mkEmptyEntriesArray }, lAssignment := { root := PersistentHashMap.Node.entries PersistentHashMap.mkEmptyEntriesArray }, eAssignment := { root := PersistentHashMap.Node.entries PersistentHashMap.mkEmptyEntriesArray }, dAssignment := { root := PersistentHashMap.Node.entries PersistentHashMap.mkEmptyEntriesArray } }, cache := { inferType := { root := PersistentHashMap.Node.entries PersistentHashMap.mkEmptyEntriesArray }, funInfo := { root := PersistentHashMap.Node.entries PersistentHashMap.mkEmptyEntriesArray }, synthInstance := { root := PersistentHashMap.Node.entries PersistentHashMap.mkEmptyEntriesArray }, whnf := { root := PersistentHashMap.Node.entries PersistentHashMap.mkEmptyEntriesArray }, defEqTrans := { root := PersistentHashMap.Node.entries PersistentHashMap.mkEmptyEntriesArray }, defEqPerm := { root := PersistentHashMap.Node.entries PersistentHashMap.mkEmptyEntriesArray } }, zetaDeltaFVarIds := ∅, postponed := { root := PersistentArrayNode.node (Array.mkEmpty PersistentArray.branching.toNat), tail := Array.mkEmpty PersistentArray.branching.toNat, size := 0, shift := PersistentArray.initShift, tailOff := 0 }, diag := { unfoldCounter := { root := PersistentHashMap.Node.entries PersistentHashMap.mkEmptyEntriesArray }, heuristicCounter := { root := PersistentHashMap.Node.entries PersistentHashMap.mkEmptyEntriesArray }, instanceCounter := { root := PersistentHashMap.Node.entries PersistentHashMap.mkEmptyEntriesArray }, synthPendingFailures := { root := PersistentHashMap.Node.entries PersistentHashMap.mkEmptyEntriesArray } } }) :

IO (α × Core.State × State)

Equations

x.toIO ctxCore sCore ctx s = do let __discr ← (x.run ctx s).toIO ctxCore sCore match __discr with | ((a, s), sCore) => pure (a, sCore, s)

def Lean.Meta.throwIsDefEqStuck {α : Type} :

Equations

Lean.Meta.throwIsDefEqStuck = throw (Lean.Exception.internal Lean.Meta.isDefEqStuckExceptionId)

@[inline]

def Lean.Meta.liftMetaM {m : Type → Type u_1} {α : Type} [MonadLiftT MetaM m] (x : MetaM α) :

m α

Equations

Lean.Meta.liftMetaM x = liftM x

@[inline]

def Lean.Meta.mapMetaM {m : Type → Type u_1} [MonadControlT MetaM m] [Monad m] (f : {α : Type} → MetaM α → MetaM α) {α : Type} (x : m α) :

m α

Equations

Lean.Meta.mapMetaM f x = controlAt Lean.MetaM fun (runInBase : {β : Type} → m β → Lean.MetaM (stM Lean.MetaM m β)) => f (runInBase x)

@[inline]

def Lean.Meta.map1MetaM {m : Type → Type u_1} {β : Sort u_2} [MonadControlT MetaM m] [Monad m] (f : {α : Type} → (β → MetaM α) → MetaM α) {α : Type} (k : β → m α) :

m α

Equations

Lean.Meta.map1MetaM f k = controlAt Lean.MetaM fun (runInBase : {β : Type} → m β → Lean.MetaM (stM Lean.MetaM m β)) => f fun (b : β) => runInBase (k b)

@[inline]

def Lean.Meta.map2MetaM {m : Type → Type u_1} {β : Sort u_2} {γ : Sort u_3} [MonadControlT MetaM m] [Monad m] (f : {α : Type} → (β → γ → MetaM α) → MetaM α) {α : Type} (k : β → γ → m α) :

m α

Equations

Lean.Meta.map2MetaM f k = controlAt Lean.MetaM fun (runInBase : {β : Type} → m β → Lean.MetaM (stM Lean.MetaM m β)) => f fun (b : β) (c : γ) => runInBase (k b c)

@[inline]

def Lean.Meta.modifyCache (f : Cache → Cache) :

Equations

One or more equations did not get rendered due to their size.

def Lean.Meta.resetCache :

Equations

One or more equations did not get rendered due to their size.

@[inline]

def Lean.Meta.modifyInferTypeCache (f : InferTypeCache → InferTypeCache) :

Equations

One or more equations did not get rendered due to their size.

@[inline]

def Lean.Meta.modifyDefEqTransientCache (f : DefEqCache → DefEqCache) :

Equations

One or more equations did not get rendered due to their size.

@[inline]

def Lean.Meta.modifyDefEqPermCache (f : DefEqCache → DefEqCache) :

Equations

One or more equations did not get rendered due to their size.

def Lean.Meta.mkExprConfigCacheKey (expr : Expr) :

MetaM ExprConfigCacheKey

Equations

Lean.Meta.mkExprConfigCacheKey expr = do let __do_lift ← read pure { expr := expr, configKey := Lean.Meta.Context.configKey✝ __do_lift }

def Lean.Meta.mkDefEqCacheKey (lhs rhs : Expr) :

MetaM DefEqCacheKey

Equations

One or more equations did not get rendered due to their size.

def Lean.Meta.mkInfoCacheKey (expr : Expr) (nargs? : Option Nat) :

MetaM InfoCacheKey

Equations

Lean.Meta.mkInfoCacheKey expr nargs? = do let __do_lift ← read pure { configKey := Lean.Meta.Context.configKey✝ __do_lift, expr := expr, nargs? := nargs? }

@[inline]

def Lean.Meta.resetDefEqPermCaches :

Equations

Lean.Meta.resetDefEqPermCaches = Lean.Meta.modifyDefEqPermCache fun (x : Lean.Meta.DefEqCache) => { root := Lean.PersistentHashMap.Node.entries Lean.PersistentHashMap.mkEmptyEntriesArray }

@[inline]

def Lean.Meta.resetSynthInstanceCache :

Equations

One or more equations did not get rendered due to their size.

@[inline]

def Lean.Meta.modifyDiag (f : Diagnostics → Diagnostics) :

Equations

One or more equations did not get rendered due to their size.

def Lean.Meta.recordUnfold (declName : Name) :

If diagnostics are enabled, record that declName has been unfolded.

Equations

One or more equations did not get rendered due to their size.

def Lean.Meta.recordDefEqHeuristic (declName : Name) :

If diagnostics are enabled, record that heuristic for solving f a =?= f b has been used.

Equations

One or more equations did not get rendered due to their size.

def Lean.Meta.recordInstance (declName : Name) :

If diagnostics are enabled, record that instance declName was used during TC resolution.

Equations

One or more equations did not get rendered due to their size.

def Lean.Meta.recordSynthPendingFailure (type : Expr) :

If diagnostics are enabled, record that synth pending failures.

Equations

One or more equations did not get rendered due to their size.

def Lean.Meta.getLocalInstances :

MetaM LocalInstances

Equations

Lean.Meta.getLocalInstances = do let __do_lift ← read pure __do_lift.localInstances

def Lean.Meta.getConfig :

Equations

Lean.Meta.getConfig = do let __do_lift ← read pure (Lean.Meta.Context.config✝ __do_lift)

def Lean.Meta.getConfigWithKey :

MetaM ConfigWithKey

Equations

Lean.Meta.getConfigWithKey = do let __do_lift ← Lean.Meta.getConfig pure __do_lift.toConfigWithKey

def Lean.Meta.resetZetaDeltaFVarIds :

Equations

Lean.Meta.resetZetaDeltaFVarIds = modify fun (s : Lean.Meta.State) => { mctx := s.mctx, cache := s.cache, zetaDeltaFVarIds := ∅, postponed := s.postponed, diag := s.diag }

def Lean.Meta.getZetaDeltaFVarIds :

MetaM FVarIdSet

Equations

Lean.Meta.getZetaDeltaFVarIds = do let __do_lift ← get pure __do_lift.zetaDeltaFVarIds

def Lean.Meta.getPostponed :

MetaM (PersistentArray PostponedEntry)

Return the array of postponed universe level constraints.

Equations

Lean.Meta.getPostponed = do let __do_lift ← get pure __do_lift.postponed

def Lean.Meta.setPostponed (postponed : PersistentArray PostponedEntry) :

Set the array of postponed universe level constraints.

Equations

Lean.Meta.setPostponed postponed = modify fun (s : Lean.Meta.State) => { mctx := s.mctx, cache := s.cache, zetaDeltaFVarIds := s.zetaDeltaFVarIds, postponed := postponed, diag := s.diag }

@[inline]

def Lean.Meta.modifyPostponed (f : PersistentArray PostponedEntry → PersistentArray PostponedEntry) :

Modify the array of postponed universe level constraints.

Equations

Lean.Meta.modifyPostponed f = modify fun (s : Lean.Meta.State) => { mctx := s.mctx, cache := s.cache, zetaDeltaFVarIds := s.zetaDeltaFVarIds, postponed := f s.postponed, diag := s.diag }

def Lean.Meta.useEtaStruct (inductName : Name) :

useEtaStruct inductName return true if we eta for structures is enabled for for the inductive datatype inductName.

Recall we have three different settings: .none (never use it), .all (always use it), .notClasses (enabled only for structure-like inductive types that are not classes).

The parameter inductName affects the result only if the current setting is .notClasses.

Equations

One or more equations did not get rendered due to their size.

WARNING: The following 4 constants are a hack for simulating forward declarations. They are defined later using the export attribute. This is hackish because we have to hard-code the true arity of these definitions here, and make sure the C names match. We have used another hack based on IO.Refs in the past, it was safer but less efficient.

@[extern 6 lean_whnf]

opaque Lean.Meta.whnf :

Expr → MetaM Expr

Reduces an expression to its weak head normal form. This is when the "head" of the top-level expression has been fully reduced. The result may contain subexpressions that have not been reduced.

See Lean.Meta.whnfImp for the implementation.

@[extern 6 lean_infer_type]

opaque Lean.Meta.inferType :

Expr → MetaM Expr

Returns the inferred type of the given expression. Assumes the expression is type-correct.

The type inference algorithm does not do general type checking. Type inference only looks at subterms that are necessary for determining an expression's type, and as such if inferType succeeds it does not mean the term is type-correct. If an expression is sufficiently ill-formed that it prevents inferType from computing a type, then it will fail with a type error.

For typechecking during elaboration, see Lean.Meta.check. (Note that we do not guarantee that the elaborator typechecker is as correct or as efficient as the kernel typechecker. The kernel typechecker is invoked when a definition is added to the environment.)

Here are examples of type-incorrect terms for which inferType succeeds:

import Lean

open Lean Meta

/--
`@id.{1} Bool Nat.zero`.
In general, the type of `@id α x` is `α`.
-/
def e1 : Expr := mkApp2 (.const ``id [1]) (.const ``Bool []) (.const ``Nat.zero [])
#eval inferType e1
-- Lean.Expr.const `Bool []
#eval check e1
-- error: application type mismatch

/--
`let x : Int := Nat.zero; true`.
In general, the type of `let x := v; e`, if `e` does not reference `x`, is the type of `e`.
-/
def e2 : Expr := .letE `x (.const ``Int []) (.const ``Nat.zero []) (.const ``true []) false
#eval inferType e2
-- Lean.Expr.const `Bool []
#eval check e2
-- error: invalid let declaration

Here is an example of a type-incorrect term that makes inferType fail:

/--
`Nat.zero Nat.zero`
-/
def e3 : Expr := .app (.const ``Nat.zero []) (.const ``Nat.zero [])
#eval inferType e3
-- error: function expected

See Lean.Meta.inferTypeImp for the implementation of inferType.

@[extern 7 lean_is_expr_def_eq]

opaque Lean.Meta.isExprDefEqAux :

Expr → Expr → MetaM Bool

@[extern 7 lean_is_level_def_eq]

opaque Lean.Meta.isLevelDefEqAux :

Level → Level → MetaM Bool

@[extern 6 lean_synth_pending]

opaque Lean.Meta.synthPending :

MVarId → MetaM Bool

def Lean.Meta.whnfForall (e : Expr) :

Equations

Lean.Meta.whnfForall e = do let e' ← Lean.Meta.whnf e if e'.isForall = true then pure e' else pure e

def Lean.Meta.withIncRecDepth {n : Type → Type u_1} [MonadControlT MetaM n] [Monad n] {α : Type} (x : n α) :

n α

Equations

Lean.Meta.withIncRecDepth x = Lean.Meta.mapMetaM (fun {α : Type} => Lean.withIncRecDepth) x

def Lean.Meta.mkFreshExprMVarAt (lctx : LocalContext) (localInsts : LocalInstances) (type : Expr) (kind : MetavarKind := MetavarKind.natural) (userName : Name := Name.anonymous) (numScopeArgs : Nat := 0) :

Equations

One or more equations did not get rendered due to their size.

def Lean.Meta.mkFreshLevelMVar :

Equations

Lean.Meta.mkFreshLevelMVar = do let mvarId ← Lean.mkFreshLMVarId Lean.modifyMCtx fun (mctx : Lean.MetavarContext) => mctx.addLevelMVarDecl mvarId pure (Lean.mkLevelMVar mvarId)

def Lean.Meta.mkFreshExprMVar (type? : Option Expr) (kind : MetavarKind := MetavarKind.natural) (userName : Name := Name.anonymous) :

Equations

Lean.Meta.mkFreshExprMVar type? kind userName = Lean.Meta.mkFreshExprMVarImpl✝ type? kind userName

def Lean.Meta.mkFreshTypeMVar (kind : MetavarKind := MetavarKind.natural) (userName : Name := Name.anonymous) :

Equations

Lean.Meta.mkFreshTypeMVar kind userName = do let u ← Lean.Meta.mkFreshLevelMVar Lean.Meta.mkFreshExprMVar (some (Lean.mkSort u)) kind userName

def Lean.Meta.mkFreshExprMVarWithId (mvarId : MVarId) (type? : Option Expr := none) (kind : MetavarKind := MetavarKind.natural) (userName : Name := Name.anonymous) :

Equations

One or more equations did not get rendered due to their size.
Lean.Meta.mkFreshExprMVarWithId mvarId (some type) kind userName = Lean.Meta.mkFreshExprMVarWithIdCore✝ mvarId type kind userName

def Lean.Meta.mkFreshLevelMVars (num : Nat) :

MetaM (List Level)

Equations

Lean.Meta.mkFreshLevelMVars num = num.foldM (fun (x : Nat) (x : x < num) (us : List Lean.Level) => do let __do_lift ← Lean.Meta.mkFreshLevelMVar pure (__do_lift :: us)) []

def Lean.Meta.mkFreshLevelMVarsFor (info : ConstantInfo) :

MetaM (List Level)

Equations

Lean.Meta.mkFreshLevelMVarsFor info = Lean.Meta.mkFreshLevelMVars info.numLevelParams

def Lean.Meta.mkConstWithFreshMVarLevels (declName : Name) :

Create a constant with the given name and new universe metavariables. Example: mkConstWithFreshMVarLevels `Monad returns @Monad.{?u, ?v}

Equations

Lean.Meta.mkConstWithFreshMVarLevels declName = do let info ← Lean.getConstInfo declName let __do_lift ← Lean.Meta.mkFreshLevelMVarsFor info pure (Lean.mkConst declName __do_lift)

def Lean.Meta.getTransparency :

MetaM TransparencyMode

Return current transparency setting/mode.

Equations

Lean.Meta.getTransparency = do let __do_lift ← Lean.Meta.getConfig pure __do_lift.transparency

def Lean.Meta.shouldReduceAll :

Equations

Lean.Meta.shouldReduceAll = do let __do_lift ← Lean.Meta.getTransparency pure (__do_lift == Lean.Meta.TransparencyMode.all)

def Lean.Meta.shouldReduceReducibleOnly :

Equations

Lean.Meta.shouldReduceReducibleOnly = do let __do_lift ← Lean.Meta.getTransparency pure (__do_lift == Lean.Meta.TransparencyMode.reducible)

def Lean.MVarId.findDecl? (mvarId : MVarId) :

MetaM (Option MetavarDecl)

Return some mvarDecl where mvarDecl is mvarId declaration in the current metavariable context. Return none if mvarId has no declaration in the current metavariable context.

Equations

mvarId.findDecl? = do let __do_lift ← Lean.getMCtx pure (__do_lift.findDecl? mvarId)

def Lean.MVarId.getDecl (mvarId : MVarId) :

MetaM MetavarDecl

Return mvarId declaration in the current metavariable context. Throw an exception if mvarId is not declared in the current metavariable context.

Equations

One or more equations did not get rendered due to their size.

def Lean.MVarId.getKind (mvarId : MVarId) :

MetaM MetavarKind

Return mvarId kind. Throw an exception if mvarId is not declared in the current metavariable context.

Equations

mvarId.getKind = do let __do_lift ← mvarId.getDecl pure __do_lift.kind

def Lean.Meta.isSyntheticMVar (e : Expr) :

Return true if e is a synthetic (or synthetic opaque) metavariable

Equations

One or more equations did not get rendered due to their size.

def Lean.MVarId.setKind (mvarId : MVarId) (kind : MetavarKind) :

Set mvarId kind in the current metavariable context.

Equations

mvarId.setKind kind = Lean.modifyMCtx fun (mctx : Lean.MetavarContext) => mctx.setMVarKind mvarId kind

def Lean.MVarId.setType (mvarId : MVarId) (type : Expr) :

Update the type of the given metavariable. This function assumes the new type is definitionally equal to the current one

Equations

mvarId.setType type = Lean.modifyMCtx fun (mctx : Lean.MetavarContext) => mctx.setMVarType mvarId type

def Lean.MVarId.isReadOnly (mvarId : MVarId) :

Return true if the given metavariable is "read-only". That is, its depth is different from the current metavariable context depth.

Equations

mvarId.isReadOnly = do let __do_lift ← mvarId.getDecl let __do_lift_1 ← Lean.getMCtx pure (__do_lift.depth != __do_lift_1.depth)

def Lean.MVarId.isReadOnlyOrSyntheticOpaque (mvarId : MVarId) :

Returns true if mvarId.isReadOnly returns true or if mvarId is a synthetic opaque metavariable.

Recall isDefEq will not assign a value to mvarId if mvarId.isReadOnlyOrSyntheticOpaque.

Equations

One or more equations did not get rendered due to their size.

def Lean.LMVarId.getLevel (mvarId : LMVarId) :

Return the level of the given universe level metavariable.

Equations

One or more equations did not get rendered due to their size.

def Lean.LMVarId.isReadOnly (mvarId : LMVarId) :

Return true if the given universe metavariable is "read-only". That is, its depth is different from the current metavariable context depth.

Equations

mvarId.isReadOnly = do let __do_lift ← mvarId.getLevel let __do_lift_1 ← Lean.getMCtx pure (decide (__do_lift < __do_lift_1.levelAssignDepth))

def Lean.MVarId.setUserName (mvarId : MVarId) (newUserName : Name) :

Set the user-facing name for the given metavariable.

Equations

mvarId.setUserName newUserName = Lean.modifyMCtx fun (mctx : Lean.MetavarContext) => mctx.setMVarUserName mvarId newUserName

def Lean.FVarId.throwUnknown {α : Type} (fvarId : FVarId) :

Throw an exception saying fvarId is not declared in the current local context.

Equations

fvarId.throwUnknown = Lean.throwError (Lean.toMessageData "unknown free variable '" ++ Lean.toMessageData (Lean.mkFVar fvarId) ++ Lean.toMessageData "'")

def Lean.FVarId.findDecl? (fvarId : FVarId) :

MetaM (Option LocalDecl)

Return some decl if fvarId is declared in the current local context.

Equations

fvarId.findDecl? = do let __do_lift ← Lean.getLCtx pure (__do_lift.find? fvarId)

def Lean.FVarId.getDecl (fvarId : FVarId) :

MetaM LocalDecl

Return the local declaration for the given free variable. Throw an exception if local declaration is not in the current local context.

Equations

fvarId.getDecl = do let __do_lift ← Lean.getLCtx match __do_lift.find? fvarId with | some d => pure d | none => liftM fvarId.throwUnknown

def Lean.FVarId.getType (fvarId : FVarId) :

Return the type of the given free variable.

Equations

fvarId.getType = do let __do_lift ← fvarId.getDecl pure __do_lift.type

def Lean.FVarId.getBinderInfo (fvarId : FVarId) :

MetaM BinderInfo

Return the binder information for the given free variable.

Equations

fvarId.getBinderInfo = do let __do_lift ← fvarId.getDecl pure __do_lift.binderInfo

def Lean.FVarId.getValue? (fvarId : FVarId) :

MetaM (Option Expr)

Return some value if the given free variable is a let-declaration, and none otherwise.

Equations

fvarId.getValue? = do let __do_lift ← fvarId.getDecl pure __do_lift.value?

def Lean.FVarId.getUserName (fvarId : FVarId) :

Return the user-facing name for the given free variable.

Equations

fvarId.getUserName = do let __do_lift ← fvarId.getDecl pure __do_lift.userName

def Lean.FVarId.isLetVar (fvarId : FVarId) :

Return true is the free variable is a let-variable.

Equations

fvarId.isLetVar = do let __do_lift ← fvarId.getDecl pure __do_lift.isLet

def Lean.Meta.getFVarLocalDecl (fvar : Expr) :

MetaM LocalDecl

Get the local declaration associated to the given Expr in the current local context. Fails if the given expression is not a fvar or if no such declaration exists.

Equations

Lean.Meta.getFVarLocalDecl fvar = fvar.fvarId!.getDecl

def Lean.FVarId.hasForwardDeps (fvarId : FVarId) :

Returns true if another local declaration in the local context depends on fvarId.

Equations

One or more equations did not get rendered due to their size.

def Lean.Meta.getLocalDeclFromUserName (userName : Name) :

MetaM LocalDecl

Given a user-facing name for a free variable, return its declaration in the current local context. Throw an exception if free variable is not declared.

Equations

One or more equations did not get rendered due to their size.

def Lean.Meta.getFVarFromUserName (userName : Name) :

Given a user-facing name for a free variable, return the free variable or throw if not declared.

Equations

Lean.Meta.getFVarFromUserName userName = do let d ← Lean.Meta.getLocalDeclFromUserName userName pure (Lean.Expr.fvar d.fvarId)

@[inline]

def Lean.Meta.liftMkBindingM {α : Type} (x : MetavarContext.MkBindingM α) :

Lift a MkBindingM monadic action x to MetaM.

Equations

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def Lean.Expr.abstractRangeM (e : Expr) (n : Nat) (xs : Array Expr) :

Similar to abstracM but consider only the first min n xs.size entries in xs

It is also similar to Expr.abstractRange, but handles metavariables correctly. It uses elimMVarDeps to ensure e and the type of the free variables xs do not contain a metavariable ?m s.t. local context of ?m contains a free variable in xs.

Equations

e.abstractRangeM n xs = Lean.Meta.liftMkBindingM (Lean.MetavarContext.abstractRange e n xs)

def Lean.Expr.abstractM (e : Expr) (xs : Array Expr) :

Replace free (or meta) variables xs with loose bound variables. Similar to Expr.abstract, but handles metavariables correctly.

Equations

e.abstractM xs = e.abstractRangeM xs.size xs

def Lean.Meta.collectForwardDeps (toRevert : Array Expr) (preserveOrder : Bool) :

MetaM (Array Expr)

Collect forward dependencies for the free variables in toRevert. Recall that when reverting free variables xs, we must also revert their forward dependencies.

Equations

Lean.Meta.collectForwardDeps toRevert preserveOrder = Lean.Meta.liftMkBindingM (Lean.MetavarContext.collectForwardDeps toRevert preserveOrder)

def Lean.Meta.mkForallFVars (xs : Array Expr) (e : Expr) (usedOnly : Bool := false) (usedLetOnly : Bool := true) (binderInfoForMVars : BinderInfo := BinderInfo.implicit) :

Takes an array xs of free variables or metavariables and a term e that may contain those variables, and abstracts and binds them as universal quantifiers.

if usedOnly = true then only variables that the expression body depends on will appear.
if usedLetOnly = true same as usedOnly except for let-bound variables. (That is, local constants which have been assigned a value.)

Equations

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def Lean.Meta.mkLambdaFVars (xs : Array Expr) (e : Expr) (usedOnly : Bool := false) (usedLetOnly : Bool := true) (etaReduce : Bool := false) (binderInfoForMVars : BinderInfo := BinderInfo.implicit) :

Takes an array xs of free variables and metavariables and a body term e and creates fun ..xs => e, suitably abstracting e and the types in xs.

Equations

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def Lean.Meta.mkLetFVars (xs : Array Expr) (e : Expr) (usedLetOnly : Bool := true) (binderInfoForMVars : BinderInfo := BinderInfo.implicit) :

Equations

Lean.Meta.mkLetFVars xs e usedLetOnly binderInfoForMVars = Lean.Meta.mkLambdaFVars xs e false usedLetOnly false binderInfoForMVars

def Lean.Meta.mkFunUnit (a : Expr) :

fun _ : Unit => a

Equations

Lean.Meta.mkFunUnit a = do let __do_lift ← liftM (Lean.mkFreshUserName `x) pure (Lean.mkLambda __do_lift Lean.BinderInfo.default (Lean.mkConst `Unit) a)

def Lean.Meta.elimMVarDeps (xs : Array Expr) (e : Expr) (preserveOrder : Bool := false) :

Equations

Lean.Meta.elimMVarDeps xs e preserveOrder = if xs.isEmpty = true then pure e else Lean.Meta.liftMkBindingM (Lean.MetavarContext.elimMVarDeps xs e preserveOrder)

@[inline]

def Lean.Meta.withConfig {n : Type → Type u_1} [MonadControlT MetaM n] [Monad n] {α : Type} (f : Config → Config) :

n α → n α

withConfig f x executes x using the updated configuration object obtained by applying f.

Equations

One or more equations did not get rendered due to their size.

@[inline]

def Lean.Meta.withConfigWithKey {n : Type → Type u_1} [MonadControlT MetaM n] [Monad n] {α : Type} (c : ConfigWithKey) :

n α → n α

Equations

One or more equations did not get rendered due to their size.

@[inline]

def Lean.Meta.withCanUnfoldPred {n : Type → Type u_1} [MonadControlT MetaM n] [Monad n] {α : Type} (p : Config → ConstantInfo → CoreM Bool) :

n α → n α

Equations

One or more equations did not get rendered due to their size.

@[inline]

def Lean.Meta.withIncSynthPending {n : Type → Type u_1} [MonadControlT MetaM n] [Monad n] {α : Type} :

n α → n α

Equations

One or more equations did not get rendered due to their size.

@[inline]

def Lean.Meta.withInTypeClassResolution {n : Type → Type u_1} [MonadControlT MetaM n] [Monad n] {α : Type} :

n α → n α

Equations

One or more equations did not get rendered due to their size.

@[inline]

def Lean.Meta.withFreshCache {n : Type → Type u_1} [MonadControlT MetaM n] [Monad n] {α : Type} :

n α → n α

Equations

One or more equations did not get rendered due to their size.

@[inline]

def Lean.Meta.withTrackingZetaDelta {n : Type → Type u_1} [MonadControlT MetaM n] [Monad n] {α : Type} :

n α → n α

Executes x tracking zetaDelta reductions Config.trackZetaDelta := true

Equations

One or more equations did not get rendered due to their size.

def Lean.Meta.withZetaDeltaSet {n : Type → Type u_1} [MonadControlT MetaM n] [Monad n] {α : Type} (s : FVarIdSet) :

n α → n α

withZetaDeltaSet s x executes x with zetaDeltaSet := s. The cache is reset while executing x if s is not empty.

Equations

One or more equations did not get rendered due to their size.

def Lean.Meta.withTrackingZetaDeltaSet {n : Type → Type u_1} [MonadControlT MetaM n] [Monad n] {α : Type} (s : FVarIdSet) :

n α → n α

Similar to withZetaDeltaSet, but also enables withTrackingZetaDelta if s is not empty.

Equations

One or more equations did not get rendered due to their size.

@[inline]

def Lean.Meta.withoutProofIrrelevance {n : Type → Type u_1} [MonadControlT MetaM n] [Monad n] {α : Type} (x : n α) :

n α

Equations

One or more equations did not get rendered due to their size.

@[inline]

def Lean.Meta.withTransparency {n : Type → Type u_1} [MonadControlT MetaM n] [Monad n] {α : Type} (mode : TransparencyMode) :

n α → n α

Equations

Lean.Meta.withTransparency mode = Lean.Meta.mapMetaM fun {α : Type} => withReader fun (x : Lean.Meta.Context) => Lean.Meta.Context.setTransparency✝ x mode

@[inline]

def Lean.Meta.withDefault {n : Type → Type u_1} [MonadControlT MetaM n] [Monad n] {α : Type} (x : n α) :

n α

withDefault x executes x using the default transparency setting.

Equations

Lean.Meta.withDefault x = Lean.Meta.withTransparency Lean.Meta.TransparencyMode.default x

@[inline]

def Lean.Meta.withReducible {n : Type → Type u_1} [MonadControlT MetaM n] [Monad n] {α : Type} (x : n α) :

n α

withReducible x executes x using the reducible transparency setting. In this setting only definitions tagged as [reducible] are unfolded.

Equations

Lean.Meta.withReducible x = Lean.Meta.withTransparency Lean.Meta.TransparencyMode.reducible x

@[inline]

def Lean.Meta.withReducibleAndInstances {n : Type → Type u_1} [MonadControlT MetaM n] [Monad n] {α : Type} (x : n α) :

n α

withReducibleAndInstances x executes x using the .instances transparency setting. In this setting only definitions tagged as [reducible] or type class instances are unfolded.

Equations

Lean.Meta.withReducibleAndInstances x = Lean.Meta.withTransparency Lean.Meta.TransparencyMode.instances x

@[inline]

def Lean.Meta.withAtLeastTransparency {n : Type → Type u_1} [MonadControlT MetaM n] [Monad n] {α : Type} (mode : TransparencyMode) :

n α → n α

Execute x ensuring the transparency setting is at least mode. Recall that .all > .default > .instances > .reducible.

Equations

One or more equations did not get rendered due to their size.

@[inline]

def Lean.Meta.withAssignableSyntheticOpaque {n : Type → Type u_1} [MonadControlT MetaM n] [Monad n] {α : Type} (x : n α) :

n α

Execute x allowing isDefEq to assign synthetic opaque metavariables.

Equations

One or more equations did not get rendered due to their size.

@[inline]

def Lean.Meta.savingCache {n : Type → Type u_1} [MonadControlT MetaM n] [Monad n] {α : Type} :

n α → n α

Equations

Lean.Meta.savingCache = Lean.Meta.mapMetaM fun {α : Type} => Lean.Meta.savingCacheImpl✝

def Lean.Meta.getTheoremInfo (info : ConstantInfo) :

MetaM (Option ConstantInfo)

Equations

Lean.Meta.getTheoremInfo info = do let __do_lift ← Lean.Meta.shouldReduceAll if __do_lift = true then pure (some info) else pure none

def Lean.Meta.withNewLocalInstance {n : Type → Type u_1} [MonadControlT MetaM n] [Monad n] {α : Type} (className : Name) (fvar : Expr) :

n α → n α

Add entry { className := className, fvar := fvar } to localInstances, and then execute continuation k.

Equations

Lean.Meta.withNewLocalInstance className fvar = Lean.Meta.mapMetaM fun {α : Type} => Lean.Meta.withNewLocalInstanceImp✝ className fvar

def Lean.Meta.isClass? (type : Expr) :

MetaM (Option Name)

isClass? type return some ClsName if type is an instance of the class ClsName. Example:

#eval do
  let x ← mkAppM ``Inhabited #[mkConst ``Nat]
  IO.println (← isClass? x)
  -- (some Inhabited)

Equations

One or more equations did not get rendered due to their size.

def Lean.Meta.withNewLocalInstances {n : Type → Type u_1} [MonadControlT MetaM n] [Monad n] {α : Type} (fvars : Array Expr) (j : Nat) :

n α → n α

Equations

Lean.Meta.withNewLocalInstances fvars j = Lean.Meta.mapMetaM fun {α : Type} => Lean.Meta.withNewLocalInstancesImpAux✝ fvars j

def Lean.Meta.forallTelescope {n : Type → Type u_1} [MonadControlT MetaM n] [Monad n] {α : Type} (type : Expr) (k : Array Expr → Expr → n α) (cleanupAnnotations : Bool := false) :

n α

Given type of the form forall xs, A, execute k xs A. This combinator will declare local declarations, create free variables for them, execute k with updated local context, and make sure the cache is restored after executing k.

If cleanupAnnotations is true, we apply Expr.cleanupAnnotations to each type in the telescope.

Equations

One or more equations did not get rendered due to their size.

def Lean.Meta.mapForallTelescope' (f : Expr → Expr → MetaM Expr) (forallTerm : Expr) :

Given a monadic function f that takes a type and a term of that type and produces a new term, lifts this to the monadic function that opens a ∀ telescope, applies f to the body, and then builds the lambda telescope term for the new term.

Equations

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def Lean.Meta.mapForallTelescope (f : Expr → MetaM Expr) (forallTerm : Expr) :

Given a monadic function f that takes a term and produces a new term, lifts this to the monadic function that opens a ∀ telescope, applies f to the body, and then builds the lambda telescope term for the new term.

Equations

Lean.Meta.mapForallTelescope f forallTerm = Lean.Meta.mapForallTelescope' (fun (x e : Lean.Expr) => f e) forallTerm

def Lean.Meta.forallTelescopeReducing {n : Type → Type u_1} [MonadControlT MetaM n] [Monad n] {α : Type} (type : Expr) (k : Array Expr → Expr → n α) (cleanupAnnotations : Bool := false) :

n α

Similar to forallTelescope, but given type of the form forall xs, A, it reduces A and continues building the telescope if it is a forall.

If cleanupAnnotations is true, we apply Expr.cleanupAnnotations to each type in the telescope.

Equations

One or more equations did not get rendered due to their size.

def Lean.Meta.forallBoundedTelescope {n : Type → Type u_1} [MonadControlT MetaM n] [Monad n] {α : Type} (type : Expr) (maxFVars? : Option Nat) (k : Array Expr → Expr → n α) (cleanupAnnotations : Bool := false) :

n α

Similar to forallTelescopeReducing, stops constructing the telescope when it reaches size maxFVars.

If cleanupAnnotations is true, we apply Expr.cleanupAnnotations to each type in the telescope.

Equations

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def Lean.Meta.lambdaLetTelescope {n : Type → Type u_1} [MonadControlT MetaM n] [Monad n] {α : Type} (e : Expr) (k : Array Expr → Expr → n α) (cleanupAnnotations : Bool := false) :

n α

Similar to lambdaTelescope but for lambda and let expressions.

If cleanupAnnotations is true, we apply Expr.cleanupAnnotations to each type in the telescope.

Equations

One or more equations did not get rendered due to their size.

def Lean.Meta.lambdaTelescope {n : Type → Type u_1} [MonadControlT MetaM n] [Monad n] {α : Type} (e : Expr) (k : Array Expr → Expr → n α) (cleanupAnnotations : Bool := false) :

n α

Given e of the form fun ..xs => A, execute k xs A. This combinator will declare local declarations, create free variables for them, execute k with updated local context, and make sure the cache is restored after executing k.

If cleanupAnnotations is true, we apply Expr.cleanupAnnotations to each type in the telescope.

Equations

One or more equations did not get rendered due to their size.

def Lean.Meta.lambdaBoundedTelescope {n : Type → Type u_1} [MonadControlT MetaM n] [Monad n] {α : Type} (e : Expr) (maxFVars : Nat) (k : Array Expr → Expr → n α) (cleanupAnnotations : Bool := false) :

n α

Given e of the form fun ..xs ..ys => A, execute k xs (fun ..ys => A) where xs.size ≤ maxFVars. This combinator will declare local declarations, create free variables for them, execute k with updated local context, and make sure the cache is restored after executing k.

If cleanupAnnotations is true, we apply Expr.cleanupAnnotations to each type in the telescope.

Equations

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def Lean.Meta.getParamNames (declName : Name) :

MetaM (Array Name)

Return the parameter names for the given global declaration.

Equations

One or more equations did not get rendered due to their size.

def Lean.Meta.forallMetaTelescope (e : Expr) (kind : MetavarKind := MetavarKind.natural) :

MetaM (Array Expr × Array BinderInfo × Expr)

Given e of the form forall ..xs, A, this combinator will create a new metavariable for each x in xs and instantiate A with these. Returns a product containing

the new metavariables
the binder info for the xs
the instantiated A

Equations

Lean.Meta.forallMetaTelescope e kind = Lean.Meta.forallMetaTelescopeReducingAux✝ e false none kind

def Lean.Meta.forallMetaTelescopeReducing (e : Expr) (maxMVars? : Option Nat := none) (kind : MetavarKind := MetavarKind.natural) :

MetaM (Array Expr × Array BinderInfo × Expr)

Similar to forallMetaTelescope, but if e = forall ..xs, A it will reduce A to construct further mvars.

Equations

Lean.Meta.forallMetaTelescopeReducing e maxMVars? kind = Lean.Meta.forallMetaTelescopeReducingAux✝ e true maxMVars? kind

def Lean.Meta.forallMetaBoundedTelescope (e : Expr) (maxMVars : Nat) (kind : MetavarKind := MetavarKind.natural) :

MetaM (Array Expr × Array BinderInfo × Expr)

Similar to forallMetaTelescopeReducing, stops constructing the telescope when it reaches size maxMVars.

Equations

Lean.Meta.forallMetaBoundedTelescope e maxMVars kind = Lean.Meta.forallMetaTelescopeReducingAux✝ e true (some maxMVars) kind

def Lean.Meta.lambdaMetaTelescope (e : Expr) (maxMVars? : Option Nat := none) :

MetaM (Array Expr × Array BinderInfo × Expr)

Similar to forallMetaTelescopeReducingAux but for lambda expressions.

Equations

Lean.Meta.lambdaMetaTelescope e maxMVars? = Lean.Meta.lambdaMetaTelescope.process maxMVars? #[] #[] 0 e

partial def Lean.Meta.lambdaMetaTelescope.process (maxMVars? : Option Nat := none) (mvars : Array Expr) (bis : Array BinderInfo) (j : Nat) (type : Expr) :

MetaM (Array Expr × Array BinderInfo × Expr)

def Lean.Meta.withLocalDecl {n : Type → Type u_1} [MonadControlT MetaM n] [Monad n] {α : Type} (name : Name) (bi : BinderInfo) (type : Expr) (k : Expr → n α) (kind : LocalDeclKind := LocalDeclKind.default) :

n α

Create a free variable x with name, binderInfo and type, add it to the context and run in k. Then revert the context.

Equations

Lean.Meta.withLocalDecl name bi type k kind = Lean.Meta.map1MetaM (fun {α : Type} (k : Lean.Expr → Lean.MetaM α) => Lean.Meta.withLocalDeclImp✝ name bi type k kind) k

def Lean.Meta.withLocalDeclD {n : Type → Type u_1} [MonadControlT MetaM n] [Monad n] {α : Type} (name : Name) (type : Expr) (k : Expr → n α) :

n α

Equations

Lean.Meta.withLocalDeclD name type k = Lean.Meta.withLocalDecl name Lean.BinderInfo.default type k

def Lean.Meta.withLocalDeclNoLocalInstanceUpdate {α : Type} (name : Name) (bi : BinderInfo) (type : Expr) (x : Expr → MetaM α) :

Similar to withLocalDecl, but it does not check whether the new variable is a local instance or not.

Equations

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def Lean.Meta.withLocalDecls {n : Type → Type u_1} [MonadControlT MetaM n] [Monad n] {α : Type} [Inhabited α] (declInfos : Array (Name × BinderInfo × (Array Expr → n Expr))) (k : Array Expr → n α) :

n α

Append an array of free variables xs to the local context and execute k xs. declInfos takes the form of an array consisting of:

the name of the variable
the binder info of the variable
a type constructor for the variable, where the array consists of all of the free variables defined prior to this one. This is needed because the type of the variable may depend on prior variables.

See withLocalDeclsD and withLocalDeclsDND for simplier variants.

Equations

Lean.Meta.withLocalDecls declInfos k = Lean.Meta.withLocalDecls.loop declInfos k #[]

partial def Lean.Meta.withLocalDecls.loop {n : Type → Type u_1} [MonadControlT MetaM n] [Monad n] {α : Type} (declInfos : Array (Name × BinderInfo × (Array Expr → n Expr))) (k : Array Expr → n α) [Inhabited α] (acc : Array Expr) :

n α

def Lean.Meta.withLocalDeclsD {n : Type → Type u_1} [MonadControlT MetaM n] [Monad n] {α : Type} [Inhabited α] (declInfos : Array (Name × (Array Expr → n Expr))) (k : Array Expr → n α) :

n α

Variant of withLocalDecls using Binderinfo.default

Equations

One or more equations did not get rendered due to their size.

def Lean.Meta.withLocalDeclsDND {n : Type → Type u_1} [MonadControlT MetaM n] [Monad n] {α : Type} [Inhabited α] (declInfos : Array (Name × Expr)) (k : Array Expr → n α) :

n α

Simpler variant of withLocalDeclsD for bringing variables into scope whose types do not depend on each other.

Equations

One or more equations did not get rendered due to their size.

def Lean.Meta.withNewBinderInfos {n : Type → Type u_1} [MonadControlT MetaM n] [Monad n] {α : Type} (bs : Array (FVarId × BinderInfo)) (k : n α) :

n α

Equations

Lean.Meta.withNewBinderInfos bs k = Lean.Meta.mapMetaM (fun {α : Type} (k : Lean.MetaM α) => Lean.Meta.withNewBinderInfosImp✝ bs k) k

def Lean.Meta.withInstImplicitAsImplict {α : Type} (xs : Array Expr) (k : MetaM α) :

Execute k using a local context where any x in xs that is tagged as instance implicit is treated as a regular implicit.

Equations

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def Lean.Meta.withLetDecl {n : Type → Type u_1} [MonadControlT MetaM n] [Monad n] {α : Type} (name : Name) (type val : Expr) (k : Expr → n α) (kind : LocalDeclKind := LocalDeclKind.default) :

n α

Add the local declaration <name> : <type> := <val> to the local context and execute k x, where x is a new free variable corresponding to the let-declaration. After executing k x, the local context is restored.

Equations

Lean.Meta.withLetDecl name type val k kind = Lean.Meta.map1MetaM (fun {α : Type} (k : Lean.Expr → Lean.MetaM α) => Lean.Meta.withLetDeclImp✝ name type val k kind) k

def Lean.Meta.withLocalInstancesImp {α : Type} (decls : List LocalDecl) (k : MetaM α) :

Equations

One or more equations did not get rendered due to their size.

def Lean.Meta.withLocalInstances {n : Type → Type u_1} [MonadControlT MetaM n] [Monad n] {α : Type} (decls : List LocalDecl) :

n α → n α

Register any local instance in decls

Equations

Lean.Meta.withLocalInstances decls = Lean.Meta.mapMetaM fun {α : Type} => Lean.Meta.withLocalInstancesImp decls

def Lean.Meta.withExistingLocalDecls {n : Type → Type u_1} [MonadControlT MetaM n] [Monad n] {α : Type} (decls : List LocalDecl) :

n α → n α

withExistingLocalDecls decls k, adds the given local declarations to the local context, and then executes k. This method assumes declarations in decls have valid FVarIds. After executing k, the local context is restored.

Remark: this method is used, for example, to implement the match-compiler. Each match-alternative commes with a local declarations (corresponding to pattern variables), and we use withExistingLocalDecls to add them to the local context before we process them.

Equations

Lean.Meta.withExistingLocalDecls decls = Lean.Meta.mapMetaM fun {α : Type} => Lean.Meta.withExistingLocalDeclsImp✝ decls

def Lean.Meta.withReplaceFVarId {α : Type} (fvarId : FVarId) (e : Expr) :

MetaM α → MetaM α

Removes fvarId from the local context, and replaces occurrences of it with e. It is the responsibility of the caller to ensure that e is well-typed in the context of any occurrence of fvarId.

Equations

One or more equations did not get rendered due to their size.

def Lean.Meta.withNewMCtxDepth {n : Type → Type u_1} [MonadControlT MetaM n] [Monad n] {α : Type} (k : n α) (allowLevelAssignments : Bool := false) :

n α

withNewMCtxDepth k executes k with a higher metavariable context depth, where metavariables created outside the withNewMCtxDepth (with a lower depth) cannot be assigned. If allowLevelAssignments is set to true, then the level metavariable depth is not increased, and level metavariables from the outer scope can be assigned. (This is used by TC synthesis.)

Equations

Lean.Meta.withNewMCtxDepth k allowLevelAssignments = Lean.Meta.mapMetaM (fun {α : Type} => Lean.Meta.withNewMCtxDepthImp✝ allowLevelAssignments) k

def Lean.Meta.withLCtx {n : Type → Type u_1} [MonadControlT MetaM n] [Monad n] {α : Type} (lctx : LocalContext) (localInsts : LocalInstances) :

n α → n α

withLCtx lctx localInsts k replaces the local context and local instances, and then executes k. The local context and instances are restored after executing k. This method assumes that the local instances in localInsts are in the local context lctx.

Equations

Lean.Meta.withLCtx lctx localInsts = Lean.Meta.mapMetaM fun {α : Type} => Lean.Meta.withLocalContextImp✝ lctx localInsts

def Lean.Meta.withLCtx' {n : Type → Type u_1} [MonadControlT MetaM n] [Monad n] {α : Type} (lctx : LocalContext) :

n α → n α

Simpler version of withLCtx which just updates the local context. It is the resposability of the caller ensure the local instances are also properly updated.

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def Lean.Meta.withErasedFVars {n : Type → Type} [MonadControlT MetaM n] [Monad n] {α : Type} [MonadLCtx n] [MonadLiftT MetaM n] (fvarIds : Array FVarId) (k : n α) :

n α

Runs k in a local environment with the fvarIds erased.

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def Lean.MVarId.withContext {n : Type → Type u_1} [MonadControlT MetaM n] [Monad n] {α : Type} (mvarId : MVarId) :

n α → n α

Executes x using the given metavariable LocalContext and LocalInstances. The type class resolution cache is flushed when executing x if its LocalInstances are different from the current ones.

Equations

mvarId.withContext = Lean.Meta.mapMetaM fun {α : Type} => Lean.Meta.withMVarContextImp✝ mvarId

def Lean.Meta.withMCtx {n : Type → Type u_1} [MonadControlT MetaM n] [Monad n] {α : Type} (mctx : MetavarContext) :

n α → n α

withMCtx mctx k replaces the metavariable context and then executes k. The metavariable context is restored after executing k.

This method is used to implement the type class resolution procedure.

Equations

Lean.Meta.withMCtx mctx = Lean.Meta.mapMetaM fun {α : Type} => Lean.Meta.withMCtxImp✝ mctx

def Lean.Meta.withoutModifyingMCtx {n : Type → Type u_1} [MonadControlT MetaM n] [Monad n] {α : Type} :

n α → n α

withoutModifyingMCtx k executes k and then restores the metavariable context.

Equations

Lean.Meta.withoutModifyingMCtx = Lean.Meta.mapMetaM fun {α : Type} (x : Lean.MetaM α) => do let mctx ← Lean.getMCtx tryFinally x do Lean.Meta.resetCache Lean.setMCtx mctx

@[inline]

def Lean.Meta.approxDefEq {n : Type → Type u_1} [MonadControlT MetaM n] [Monad n] {α : Type} :

n α → n α

Execute x using approximate unification: foApprox, ctxApprox and quasiPatternApprox.

Equations

Lean.Meta.approxDefEq = Lean.Meta.mapMetaM fun {α : Type} => Lean.Meta.approxDefEqImp✝

@[inline]

def Lean.Meta.fullApproxDefEq {n : Type → Type u_1} [MonadControlT MetaM n] [Monad n] {α : Type} :

n α → n α

Similar to approxDefEq, but uses all available approximations. We don't use constApprox by default at approxDefEq because it often produces undesirable solution for monadic code. For example, suppose we have pure (x > 0) which has type ?m Prop. We also have the goal [Pure ?m]. Now, assume the expected type is IO Bool. Then, the unification constraint ?m Prop =?= IO Bool could be solved as ?m := fun _ => IO Bool using constApprox, but this spurious solution would generate a failure when we try to solve [Pure (fun _ => IO Bool)]

Equations

Lean.Meta.fullApproxDefEq = Lean.Meta.mapMetaM fun {α : Type} => Lean.Meta.fullApproxDefEqImp✝

def Lean.Meta.normalizeLevel (u : Level) :

Instantiate assigned universe metavariables in u, and then normalize it.

Equations

Lean.Meta.normalizeLevel u = do let u ← Lean.instantiateLevelMVars u pure u.normalize

def Lean.Meta.whnfR (e : Expr) :

whnf with reducible transparency.

Equations

Lean.Meta.whnfR e = Lean.Meta.withTransparency Lean.Meta.TransparencyMode.reducible (Lean.Meta.whnf e)

def Lean.Meta.whnfD (e : Expr) :

whnf with default transparency.

Equations

Lean.Meta.whnfD e = Lean.Meta.withTransparency Lean.Meta.TransparencyMode.default (Lean.Meta.whnf e)

def Lean.Meta.whnfI (e : Expr) :

whnf with instances transparency.

Equations

Lean.Meta.whnfI e = Lean.Meta.withTransparency Lean.Meta.TransparencyMode.instances (Lean.Meta.whnf e)

def Lean.Meta.whnfAtMostI (e : Expr) :

whnf with at most instances transparency.

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def Lean.Meta.setInlineAttribute (declName : Name) (kind : Compiler.InlineAttributeKind := Compiler.InlineAttributeKind.inline) :

Mark declaration declName with the attribute [inline]. This method does not check whether the given declaration is a definition.

Recall that this attribute can only be set in the same module where declName has been declared.

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def Lean.Meta.instantiateForall (e : Expr) (ps : Array Expr) :

Given e of the form forall (a_1 : A_1) ... (a_n : A_n), B[a_1, ..., a_n] and p_1 : A_1, ... p_n : A_n, return B[p_1, ..., p_n].

Equations

Lean.Meta.instantiateForall e ps = Lean.Meta.instantiateForallAux✝ ps 0 e

def Lean.Meta.instantiateLambda (e : Expr) (ps : Array Expr) :

Given e of the form fun (a_1 : A_1) ... (a_n : A_n) => t[a_1, ..., a_n] and p_1 : A_1, ... p_n : A_n, return t[p_1, ..., p_n]. It uses whnf to reduce e if it is not a lambda

Equations

Lean.Meta.instantiateLambda e ps = Lean.Meta.instantiateLambdaAux✝ ps 0 e

def Lean.Meta.ppExprWithInfos (e : Expr) :

MetaM FormatWithInfos

Pretty-print the given expression.

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def Lean.Meta.ppExpr (e : Expr) :

Pretty-print the given expression.

Equations

Lean.Meta.ppExpr e = (fun (x : Lean.FormatWithInfos) => x.fmt) <$> Lean.Meta.ppExprWithInfos e

@[inline]

def Lean.Meta.orElse {α : Type} (x : MetaM α) (y : Unit → MetaM α) :

Equations

Lean.Meta.orElse x y = do let s ← Lean.saveState tryCatch x fun (x : Lean.Exception) => do s.restore y ()

instance Lean.Meta.instOrElseMetaM {α : Type} :

OrElse (MetaM α)

Equations

Lean.Meta.instOrElseMetaM = { orElse := Lean.Meta.orElse }

instance Lean.Meta.instAlternativeMetaM :

Alternative MetaM

Equations

Lean.Meta.instAlternativeMetaM = Alternative.mk (fun {x : Type} => Lean.throwError (Lean.toMessageData "failed")) fun {α : Type} => Lean.Meta.orElse

@[inline]

def Lean.Meta.orelseMergeErrors {m : Type → Type u_1} {α : Type} [MonadControlT MetaM m] [Monad m] (x y : m α) (mergeRef : Syntax → Syntax → Syntax := fun (r₁ x : Syntax) => r₁) (mergeMsg : MessageData → MessageData → MessageData := fun (m₁ m₂ : MessageData) => m₁ ++ MessageData.ofFormat Format.line ++ MessageData.ofFormat Format.line ++ m₂) :

m α

Similar to orelse, but merge errors. Note that internal errors are not caught. The default mergeRef uses the ref (position information) for the first message. The default mergeMsg combines error messages using Format.line ++ Format.line as a separator.

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def Lean.Meta.mapErrorImp {α : Type} (x : MetaM α) (f : MessageData → MessageData) :

Execute x, and apply f to the produced error message

Equations

Lean.Meta.mapErrorImp x f = tryCatch x fun (ex : Lean.Exception) => match ex with | Lean.Exception.error ref msg => throw (Lean.Exception.error ref (f msg)) | ex => throw ex

@[inline]

def Lean.Meta.mapError {m : Type → Type u_1} {α : Type} [MonadControlT MetaM m] [Monad m] (x : m α) (f : MessageData → MessageData) :

m α

Equations

Lean.Meta.mapError x f = controlAt Lean.MetaM fun (runInBase : {β : Type} → m β → Lean.MetaM (stM Lean.MetaM m β)) => Lean.Meta.mapErrorImp (runInBase x) f

def Lean.Meta.sortFVarIds (fvarIds : Array FVarId) :

MetaM (Array FVarId)

Sort free variables using an order x < y iff x was defined before y. If a free variable is not in the local context, we use their id.

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def Lean.Meta.isInductivePredicate? (declName : Name) :

MetaM (Option InductiveVal)

Return some info if declName is an inductive predicate where info : InductiveVal. That is, inductive type in Prop.

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def Lean.Meta.isInductivePredicate (declName : Name) :

Return true if declName is an inductive predicate. That is, inductive type in Prop.

Equations

Lean.Meta.isInductivePredicate declName = do let __do_lift ← Lean.Meta.isInductivePredicate? declName pure __do_lift.isSome

def Lean.Meta.isListLevelDefEqAux :

List Level → List Level → MetaM Bool

Equations

Lean.Meta.isListLevelDefEqAux [] [] = pure true
Lean.Meta.isListLevelDefEqAux (u :: us) (v :: vs) = (Lean.Meta.isLevelDefEqAux u v <&&> Lean.Meta.isListLevelDefEqAux us vs)
Lean.Meta.isListLevelDefEqAux x✝¹ x✝ = pure false

def Lean.Meta.getNumPostponed :

Equations

Lean.Meta.getNumPostponed = do let __do_lift ← Lean.Meta.getPostponed pure __do_lift.size

def Lean.Meta.getResetPostponed :

MetaM (PersistentArray PostponedEntry)

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def Lean.Meta.mkLevelStuckErrorMessage (entry : PostponedEntry) :

MetaM MessageData

Equations

Lean.Meta.mkLevelStuckErrorMessage entry = Lean.Meta.mkLevelErrorMessageCore✝ "stuck at solving universe constraint" entry

def Lean.Meta.mkLevelErrorMessage (entry : PostponedEntry) :

MetaM MessageData

Equations

Lean.Meta.mkLevelErrorMessage entry = Lean.Meta.mkLevelErrorMessageCore✝ "failed to solve universe constraint" entry

def Lean.Meta.processPostponed (mayPostpone : Bool := true) (exceptionOnFailure : Bool := false) :

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partial def Lean.Meta.processPostponed.loop (mayPostpone : Bool := true) (exceptionOnFailure : Bool := false) :

@[specialize #[]]

def Lean.Meta.checkpointDefEq (x : MetaM Bool) (mayPostpone : Bool := true) :

checkpointDefEq x executes x and process all postponed universe level constraints produced by x. We keep the modifications only if processPostponed return true and x returned true.

If mayPostpone == false, all new postponed universe level constraints must be solved before returning. We currently try to postpone universe constraints as much as possible, even when by postponing them we are not sure whether x really succeeded or not.

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def Lean.Meta.isLevelDefEq (u v : Level) :

Determines whether two universe level expressions are definitionally equal to each other.

Equations

Lean.Meta.isLevelDefEq u v = Lean.Meta.checkpointDefEq (Lean.Meta.isLevelDefEqAux u v)

def Lean.Meta.isExprDefEq (t s : Expr) :

See isDefEq.

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@[reducible, inline]

abbrev Lean.Meta.isDefEq (t s : Expr) :

Determines whether two expressions are definitionally equal to each other.

To control how metavariables are assigned and unified, metavariables and their context have a "depth". Given a metavariable ?m and a MetavarContext mctx, ?m is not assigned if ?m.depth != mctx.depth. The combinator withNewMCtxDepth x will bump the depth while executing x. So, withNewMCtxDepth (isDefEq a b) is isDefEq without any mvar assignment happening whereas isDefEq a b will assign any metavariables of the current depth in a and b to unify them.

For matching (where only mvars in b should be assigned), we create the term inside the withNewMCtxDepth. For an example, see Lean.Meta.Simp.tryTheoremWithExtraArgs?

Equations

Lean.Meta.isDefEq t s = Lean.Meta.isExprDefEq t s

def Lean.Meta.isExprDefEqGuarded (a b : Expr) :

Equations

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@[reducible, inline]

abbrev Lean.Meta.isDefEqGuarded (t s : Expr) :

Similar to isDefEq, but returns false if an exception has been thrown.

Equations

Lean.Meta.isDefEqGuarded t s = Lean.Meta.isExprDefEqGuarded t s

def Lean.Meta.isDefEqNoConstantApprox (t s : Expr) :

Equations

Lean.Meta.isDefEqNoConstantApprox t s = Lean.Meta.approxDefEq (Lean.Meta.isDefEq t s)

@[extern lean_checked_assign]

opaque Lean.MVarId.checkedAssign (mvarId : MVarId) (val : Expr) :

Returns true if mvarId := val was successfully assigned. This method uses the same assignment validation performed by isDefEq, but it does not check whether the types match.

def Lean.Meta.etaExpand (e : Expr) :

Eta expand the given expression. Example:

etaExpand (mkConst ``Nat.add)

produces fun x y => Nat.add x y

Equations

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def Lean.Meta.instantiateMVarsIfMVarApp (e : Expr) :

If e is of the form ?m ... instantiate metavars

Equations

Lean.Meta.instantiateMVarsIfMVarApp e = if e.getAppFn.isMVar = true then Lean.instantiateMVars e else pure e

instance Lean.Meta.instTypeNameRealizeConstantResult :

TypeName Lean.Meta.RealizeConstantResult✝

Equations

Lean.Meta.instTypeNameRealizeConstantResult = Lean.Meta.inst✝

def Lean.Meta.realizeConst (forConst constName : Name) (realize : MetaM Unit) :

Makes the helper constant constName that is derived from forConst available in the environment. enableRealizationsForConst forConst must have been called first on this environment branch. If this is the first environment branch requesting constName to be realized (atomically), realize is called with the environment and options at the time of calling enableRealizationsForConst if forConst is from the current module and the state just after importing (when enableRealizationsForImports should be called) otherwise, thus helping achieve deterministic results despite the non-deterministic choice of which thread is tasked with realization. In other words, the state after calling realizeConst is as if realize had been called immediately after enableRealizationsForConst forConst, though the effects of this call are visible only after calling realizeConst. See below for more details on the replayed effects.

realizeConst cannot check what other data is captured in the realize closure, so it is best practice to extract it into a separate function and pay close attention to the passed arguments, if any. realize must return with constName added to the environment, at which point all callers of realizeConst with this constName will be unblocked and have access to an updated version of their own environment containing any new constants realize added, including recursively realized constants. Traces, diagnostics, and raw std stream output are reported at all callers via Core.logSnapshotTask (so that the location of generated diagnostics is deterministic). Note that, as realize is run using the options at declaration time of forConst, trace options must be set prior to that (or, for imported constants, on the cmdline) in order to be active. The environment extension state at the end of realize is available to each caller via EnvExtension.findStateAsync for constName. If realize throws an exception or fails to add constName to the environment, an appropriate diagnostic is reported to all callers but no constants are added to the environment.

Equations

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def Lean.Meta.realizeConst.realizeAndReport (constName : Name) (realize : MetaM Unit) (coreCtx : Core.Context) (env : Environment) (opts : Options) :

BaseIO (Environment × Dynamic)

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