Lazy Discrimination Tree

This file defines a new type of discrimination tree optimized for rapid population of imported modules for use in tactics. It uses a lazy initialization strategy.

The discrimination tree can be created through createImportedEnvironment. This creates a discrimination tree from all imported modules in an environment using a callback that provides the entries as InitEntry values.

The function getMatch can be used to get the values that match the expression as well as an updated lazy discrimination tree that has elaborated additional parts of the tree.

inductive Lean.Meta.LazyDiscrTree.Key : Type

Discrimination tree key.

• const: Lake.Name → Nat → Lean.Meta.LazyDiscrTree.Key
• fvar: Lean.FVarId → Nat → Lean.Meta.LazyDiscrTree.Key
• lit: Lean.Literal → Lean.Meta.LazyDiscrTree.Key
• star: Lean.Meta.LazyDiscrTree.Key
• other: Lean.Meta.LazyDiscrTree.Key
• arrow: Lean.Meta.LazyDiscrTree.Key
• proj: Lake.Name → Nat → Nat → Lean.Meta.LazyDiscrTree.Key

instance Lean.Meta.LazyDiscrTree.instInhabitedKey : Inhabited Lean.Meta.LazyDiscrTree.Key

Equations

• Lean.Meta.LazyDiscrTree.instInhabitedKey = { default := Lean.Meta.LazyDiscrTree.Key.const default default }

instance Lean.Meta.LazyDiscrTree.instBEqKey : BEq Lean.Meta.LazyDiscrTree.Key

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• Lean.Meta.LazyDiscrTree.instBEqKey = { beq := Lean.Meta.LazyDiscrTree.beqKey✝ }

instance Lean.Meta.LazyDiscrTree.instReprKey : Repr Lean.Meta.LazyDiscrTree.Key

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• Lean.Meta.LazyDiscrTree.instReprKey = { reprPrec := Lean.Meta.LazyDiscrTree.reprKey✝ }

def Lean.Meta.LazyDiscrTree.Key.hash : Lean.Meta.LazyDiscrTree.Key → UInt64

Hash function

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instance Lean.Meta.LazyDiscrTree.Key.instHashable : Hashable Lean.Meta.LazyDiscrTree.Key

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• Lean.Meta.LazyDiscrTree.Key.instHashable = { hash := Lean.Meta.LazyDiscrTree.Key.hash }

instance Lean.Meta.LazyDiscrTree.instInhabitedTrie : {a : Type} → Inhabited (Lean.Meta.LazyDiscrTree.Trie a)

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• Lean.Meta.LazyDiscrTree.instInhabitedTrie = { default := { values := default, star := default, children := default, pending := default } }

instance Lean.Meta.LazyDiscrTree.instEmptyCollectionTrie {α : Type} : EmptyCollection (Lean.Meta.LazyDiscrTree.Trie α)

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• Lean.Meta.LazyDiscrTree.instEmptyCollectionTrie = { emptyCollection := { values := #[], star := 0, children := ∅, pending := #[] } }

structure Lean.Meta.LazyDiscrTree (α : Type) : Type

LazyDiscrTree is a variant of the discriminator tree datatype DiscrTree in Lean core that is designed to be efficiently initializable with a large number of patterns. This is useful in contexts such as searching an entire Lean environment for expressions that match a pattern.

Lazy discriminator trees achieve good performance by minimizing the amount of work that is done up front to build the discriminator tree. When first adding patterns to the tree, only the root discriminator key is computed and processing the remaining terms is deferred until demanded by a match.

• config : Lean.Meta.WhnfCoreConfig

  Configuration for normalization.

• tries : Array (Lean.Meta.LazyDiscrTree.Trie α)

  Backing array of trie entries. Should be owned by this trie.

• roots : Lean.HashMap Lean.Meta.LazyDiscrTree.Key Lean.Meta.LazyDiscrTree.TrieIndex

  Map from discriminator trie roots to the index.

instance Lean.Meta.LazyDiscrTree.instInhabited {α : Type} : Inhabited (Lean.Meta.LazyDiscrTree α)

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def Lean.Meta.LazyDiscrTree.patternPath (e : Lean.Expr) (config : Lean.Meta.WhnfCoreConfig) : Lean.MetaM (Array Lean.Meta.LazyDiscrTree.Key)

Create a key path from an expression using the function used for patterns.

This differs from Lean.Meta.DiscrTree.mkPath and targetPath in that the expression should uses free variables rather than meta-variables for holes.

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def Lean.Meta.LazyDiscrTree.targetPath (e : Lean.Expr) (config : Lean.Meta.WhnfCoreConfig) : Lean.MetaM (Array Lean.Meta.LazyDiscrTree.Key)

Create a key path from an expression we are matching against.

This should have mvars instantiated where feasible.

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def Lean.Meta.LazyDiscrTree.dropKeyAux {α : Type} (next : Lean.Meta.LazyDiscrTree.TrieIndex) (rest : List Lean.Meta.LazyDiscrTree.Key) : Lean.Meta.LazyDiscrTree.MatchM α Unit

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def Lean.Meta.LazyDiscrTree.dropKey {α : Type} (t : Lean.Meta.LazyDiscrTree α) (path : List Lean.Meta.LazyDiscrTree.Key) : Lean.MetaM (Lean.Meta.LazyDiscrTree α)

This drops a specific key from the lazy discrimination tree so that all the entries matching that key exactly are removed.

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structure Lean.Meta.LazyDiscrTree.MatchResult (α : Type) : Type

A match result contains the terms formed from matching a term against patterns in the discrimination tree.

• elts : Array (Array (Array α))

  The elements in the match result.

  The top-level array represents an array from score values to the results with that score. A score is the number of non-star matches in a pattern against the term, and thus bounded by the size of the term being matched against. The elements of this array are themselves arrays of non-empty arrays so that we can defer concatenating results until needed.

def Lean.Meta.LazyDiscrTree.MatchResult.size {α : Type} (mr : Lean.Meta.LazyDiscrTree.MatchResult α) : Nat

Number of elements in result

Equations

• mr.size = Array.foldl (fun (i : Nat) (a : Array (Array α)) => Array.foldl (fun (n : Nat) (a : Array α) => n + a.size) i a 0) 0 mr.elts 0

@[specialize #[]]

def Lean.Meta.LazyDiscrTree.MatchResult.appendResultsAux {α : Type} {β : Type u_1} (mr : Lean.Meta.LazyDiscrTree.MatchResult α) (a : Array β) (f : Nat → α → β) : Array β

Append results to array

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def Lean.Meta.LazyDiscrTree.MatchResult.appendResults {α : Type} (mr : Lean.Meta.LazyDiscrTree.MatchResult α) (a : Array α) : Array α

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• mr.appendResults a = mr.appendResultsAux a fun (x : Nat) (a : α) => a

structure Lean.Meta.LazyDiscrTree.PartialMatch : Type

• todo : Array Lean.Expr
• score : Nat
• c : Lean.Meta.LazyDiscrTree.TrieIndex

instance Lean.Meta.LazyDiscrTree.instInhabitedPartialMatch : Inhabited Lean.Meta.LazyDiscrTree.PartialMatch

Equations

• Lean.Meta.LazyDiscrTree.instInhabitedPartialMatch = { default := { todo := default, score := default, c := default } }

def Lean.Meta.LazyDiscrTree.getMatch {α : Type} (d : Lean.Meta.LazyDiscrTree α) (e : Lean.Expr) : Lean.MetaM (Lean.Meta.LazyDiscrTree.MatchResult α × Lean.Meta.LazyDiscrTree α)

Find values that match e in d.

The results are ordered so that the longest matches in terms of number of non-star keys are first with ties going to earlier operators first.

Equations

• d.getMatch e = Lean.Meta.withReducible (Lean.Meta.LazyDiscrTree.runMatch d (Lean.Meta.LazyDiscrTree.getMatchCore d.roots e))

instance Lean.Meta.LazyDiscrTree.instInhabitedPreDiscrTree : {a : Type} → Inhabited (Lean.Meta.LazyDiscrTree.PreDiscrTree a)

Equations

• Lean.Meta.LazyDiscrTree.instInhabitedPreDiscrTree = { default := { roots := default, tries := default } }

def Lean.Meta.LazyDiscrTree.PreDiscrTree.append {α : Type} (x : Lean.Meta.LazyDiscrTree.PreDiscrTree α) (y : Lean.Meta.LazyDiscrTree.PreDiscrTree α) : Lean.Meta.LazyDiscrTree.PreDiscrTree α

Merge two discrimination trees.

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instance Lean.Meta.LazyDiscrTree.PreDiscrTree.instAppendPreDiscrTree {α : Type} : Append (Lean.Meta.LazyDiscrTree.PreDiscrTree α)

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• Lean.Meta.LazyDiscrTree.PreDiscrTree.instAppendPreDiscrTree = { append := Lean.Meta.LazyDiscrTree.PreDiscrTree.append }

@[reducible]

structure Lean.Meta.LazyDiscrTree.InitEntry (α : Type) : Type

Initial entry in lazy discrimination tree

• key : Lean.Meta.LazyDiscrTree.Key

  Return root key for an entry.

• entry : Lean.Meta.LazyDiscrTree.LazyEntry α

  Returns rest of entry for later insertion.

def Lean.Meta.LazyDiscrTree.InitEntry.fromExpr {α : Type} (expr : Lean.Expr) (value : α) (config : optParam Lean.Meta.WhnfCoreConfig { iota := true, beta := true, proj := Lean.Meta.ProjReductionKind.yesWithDelta, zeta := true, zetaDelta := true }) : Lean.MetaM (Lean.Meta.LazyDiscrTree.InitEntry α)

Constructs an initial entry from an expression and value.

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def Lean.Meta.LazyDiscrTree.InitEntry.mkSubEntry {α : Type} (e : Lean.Meta.LazyDiscrTree.InitEntry α) (idx : Nat) (value : α) (config : optParam Lean.Meta.WhnfCoreConfig { iota := true, beta := true, proj := Lean.Meta.ProjReductionKind.yesWithDelta, zeta := true, zetaDelta := true }) : Lean.MetaM (Lean.Meta.LazyDiscrTree.InitEntry α)

Creates an entry for a subterm of an initial entry.

This is slightly more efficient than using fromExpr on subterms since it avoids a redundant call to whnf.

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structure Lean.Meta.LazyDiscrTree.Cache : Type

• ngen : Lean.NameGenerator
• core : Lean.Core.Cache
• meta : Lean.Meta.Cache

def Lean.Meta.LazyDiscrTree.Cache.empty (ngen : Lean.NameGenerator) : Lean.Meta.LazyDiscrTree.Cache

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def Lean.Meta.LazyDiscrTree.matchPrefix (s : String) (pre : String) : Bool

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• Lean.Meta.LazyDiscrTree.matchPrefix s pre = (s.startsWith pre && (s.drop pre.length).all Char.isDigit)

def Lean.Meta.LazyDiscrTree.isInternalDetail : Lake.Name → Bool

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def Lean.Meta.LazyDiscrTree.blacklistInsertion (env : Lean.Environment) (declName : Lake.Name) : Bool

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instance Lean.Meta.LazyDiscrTree.instInhabitedInitResults {α : Type} : Inhabited (Lean.Meta.LazyDiscrTree.InitResults α)

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• Lean.Meta.LazyDiscrTree.instInhabitedInitResults = { default := { tree := { roots := ∅, tries := #[] }, errors := #[] } }

def Lean.Meta.LazyDiscrTree.InitResults.append {α : Type} (x : Lean.Meta.LazyDiscrTree.InitResults α) (y : Lean.Meta.LazyDiscrTree.InitResults α) : Lean.Meta.LazyDiscrTree.InitResults α

Combine two initial results.

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instance Lean.Meta.LazyDiscrTree.InitResults.instAppendInitResults {α : Type} : Append (Lean.Meta.LazyDiscrTree.InitResults α)

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• Lean.Meta.LazyDiscrTree.InitResults.instAppendInitResults = { append := Lean.Meta.LazyDiscrTree.InitResults.append }

def Lean.Meta.LazyDiscrTree.getChildNgen {M : Type → Type} [Monad M] [Lean.MonadNameGenerator M] : M Lean.NameGenerator

Equations

• Lean.Meta.LazyDiscrTree.getChildNgen = do let ngen ← Lean.getNGen match ngen.mkChild with | (cngen, ngen) => do Lean.setNGen ngen pure cngen

def Lean.Meta.LazyDiscrTree.createLocalPreDiscrTree {α : Type} (cctx : Lean.Core.Context) (ngen : Lean.NameGenerator) (env : Lean.Environment) (d : Lean.Meta.LazyDiscrTree.ImportData) (act : Lake.Name → Lean.ConstantInfo → Lean.MetaM (Array (Lean.Meta.LazyDiscrTree.InitEntry α))) : BaseIO (Lean.Meta.LazyDiscrTree.PreDiscrTree α)

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def Lean.Meta.LazyDiscrTree.dropKeys {α : Type} (t : Lean.Meta.LazyDiscrTree α) (keys : List (List Lean.Meta.LazyDiscrTree.Key)) : Lean.MetaM (Lean.Meta.LazyDiscrTree α)

Equations

• t.dropKeys keys = List.foldlM (fun (x : Lean.Meta.LazyDiscrTree α) (x_1 : List Lean.Meta.LazyDiscrTree.Key) => x.dropKey x_1) t keys

def Lean.Meta.LazyDiscrTree.logImportFailure {m : Type → Type} [Monad m] [Lean.MonadLog m] [Lean.AddMessageContext m] [Lean.MonadOptions m] (f : Lean.Meta.LazyDiscrTree.ImportFailure) : m Unit

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def Lean.Meta.LazyDiscrTree.createImportedDiscrTree {m : Type → Type} {α : Type} [Monad m] [Lean.MonadLog m] [Lean.AddMessageContext m] [Lean.MonadOptions m] [MonadLiftT BaseIO m] (cctx : Lean.Core.Context) (ngen : Lean.NameGenerator) (env : Lean.Environment) (act : Lake.Name → Lean.ConstantInfo → Lean.MetaM (Array (Lean.Meta.LazyDiscrTree.InitEntry α))) (constantsPerTask : optParam Nat 1000) : m (Lean.Meta.LazyDiscrTree α)

Create a discriminator tree for imported environment.

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def Lean.Meta.LazyDiscrTree.createImportedDiscrTree.go {m : Type → Type} {α : Type} [Monad m] [MonadLiftT BaseIO m] (cctx : Lean.Core.Context) (env : Lean.Environment) (act : Lake.Name → Lean.ConstantInfo → Lean.MetaM (Array (Lean.Meta.LazyDiscrTree.InitEntry α))) (constantsPerTask : optParam Nat 1000) (n : Nat) (ngen : Lean.NameGenerator) (tasks : Array (Task (Lean.Meta.LazyDiscrTree.InitResults α))) (start : Nat) (cnt : Nat) (idx : Nat) : m (Array (Task (Lean.Meta.LazyDiscrTree.InitResults α)))

Allocate constants to tasks according to constantsPerTask.

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def Lean.Meta.LazyDiscrTree.findImportMatches {α : Type} (ext : Lean.EnvExtension (IO.Ref (Option (Lean.Meta.LazyDiscrTree α)))) (addEntry : Lake.Name → Lean.ConstantInfo → Lean.MetaM (Array (Lean.Meta.LazyDiscrTree.InitEntry α))) (droppedKeys : optParam (List (List Lean.Meta.LazyDiscrTree.Key)) []) (constantsPerTask : optParam Nat 1000) (ty : Lean.Expr) : Lean.MetaM (Lean.Meta.LazyDiscrTree.MatchResult α)

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structure Lean.Meta.LazyDiscrTree.ModuleDiscrTreeRef (α : Type) : Type

A discriminator tree for the current module's declarations only.

Note. We use different discriminator trees for imported and current module declarations since imported declarations are typically much more numerous but not changed after the environment is created.

• ref : IO.Ref (Lean.Meta.LazyDiscrTree α)

def Lean.Meta.LazyDiscrTree.createModuleDiscrTree {α : Type} (entriesForConst : Lake.Name → Lean.ConstantInfo → Lean.MetaM (Array (Lean.Meta.LazyDiscrTree.InitEntry α))) : Lean.CoreM (Lean.Meta.LazyDiscrTree α)

Create a discriminator tree for current module declarations.

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def Lean.Meta.LazyDiscrTree.createModuleTreeRef {α : Type} (entriesForConst : Lake.Name → Lean.ConstantInfo → Lean.MetaM (Array (Lean.Meta.LazyDiscrTree.InitEntry α))) (droppedKeys : List (List Lean.Meta.LazyDiscrTree.Key)) : Lean.MetaM (Lean.Meta.LazyDiscrTree.ModuleDiscrTreeRef α)

Creates reference for lazy discriminator tree that only contains this module's definitions.

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def Lean.Meta.LazyDiscrTree.findModuleMatches {α : Type} (moduleRef : Lean.Meta.LazyDiscrTree.ModuleDiscrTreeRef α) (ty : Lean.Expr) : Lean.MetaM (Lean.Meta.LazyDiscrTree.MatchResult α)

Returns candidates from this module in this module that match the expression.

• moduleRef is a references to a lazy discriminator tree only containing this module's definitions.

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def Lean.Meta.LazyDiscrTree.findMatchesExt {α : Type} {β : Type} (moduleTreeRef : Lean.Meta.LazyDiscrTree.ModuleDiscrTreeRef α) (ext : Lean.EnvExtension (IO.Ref (Option (Lean.Meta.LazyDiscrTree α)))) (addEntry : Lake.Name → Lean.ConstantInfo → Lean.MetaM (Array (Lean.Meta.LazyDiscrTree.InitEntry α))) (droppedKeys : optParam (List (List Lean.Meta.LazyDiscrTree.Key)) []) (constantsPerTask : optParam Nat 1000) (adjustResult : Nat → α → β) (ty : Lean.Expr) : Lean.MetaM (Array β)

findMatchesExt searches for entries in a lazily initialized discriminator tree.

It provides some additional capabilities beyond findMatches to adjust results based on priority and cache module declarations

• modulesTreeRef points to the discriminator tree for local environment. Used for caching and created by createLocalTree.
• ext should be an environment extension with an IO.Ref for caching the import lazy discriminator tree.
• addEntry is the function for creating discriminator tree entries from constants.
• droppedKeys contains keys we do not want to consider when searching for matches. It is used for dropping very general keys.
• constantsPerTask stores number of constants in imported modules used to decide when to create new task.
• adjustResult takes the priority and value to produce a final result.
• ty is the expression type.

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def Lean.Meta.LazyDiscrTree.findMatches {α : Type} (ext : Lean.EnvExtension (IO.Ref (Option (Lean.Meta.LazyDiscrTree α)))) (addEntry : Lake.Name → Lean.ConstantInfo → Lean.MetaM (Array (Lean.Meta.LazyDiscrTree.InitEntry α))) (droppedKeys : optParam (List (List Lean.Meta.LazyDiscrTree.Key)) []) (constantsPerTask : optParam Nat 1000) (ty : Lean.Expr) : Lean.MetaM (Array α)

findMatches searches for entries in a lazily initialized discriminator tree.

• ext should be an environment extension with an IO.Ref for caching the import lazy discriminator tree.
• addEntry is the function for creating discriminator tree entries from constants.
• droppedKeys contains keys we do not want to consider when searching for matches. It is used for dropping very general keys.

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