Documentation

Lean.Meta.LazyDiscrTree

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 createImportedDiscrTree. This creates a discrimination tree from all public 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.

Discrimination tree key.

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    Returns true iff the argument should be treated as a "wildcard" by the discrimination tree.

    This includes proofs, instance implicit arguments, implicit arguments, and terms of the form noIndexing t

    This is a clone of Lean.Meta.DiscrTree.ignoreArg and mainly added to avoid coupling between DiscrTree and LazyDiscrTree while both are potentially subject to independent changes.

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      Returns true if e is one of the following

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        Returns true if e is one of the following

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          Eliminate loose bound variables via beta-reduction.

          This is primarily used to reduce pi-terms ∀(x : P), T into non-dependent functions P → T. The latter has a more specific discrimination tree key .arrow.. and this improves the accuracy of the discrimination tree.

          Clone of Lean.Meta.DiscrTree.elimLooseBVarsByBeta. See it for more discussion.

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              @[reducible, inline]

              An unprocessed entry in the lazy discrimination tree.

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                @[reducible]

                Index identifying trie in a discrimination tree.

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                  Discrimination tree trie. See LazyDiscrTree.

                  • node :: (
                  • )
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                    Push lazy entry to trie.

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                    • { values := vs, star := star, children := cs, pending := p }.pushPending x✝ = { values := vs, star := star, children := cs, pending := p.push x✝ }
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                      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.

                      • tries : Array (Trie α)

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

                      • Map from discriminator trie roots to the index.

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                        Specialization of Lean.Meta.DiscrTree.pushArgs

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                          Initial capacity for key and todo vector.

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                            Get the root key and rest of terms of an expression using the specified config.

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                              partial def Lean.Meta.LazyDiscrTree.buildPath (op : BoolArray ExprExprMetaM (Key × Array Expr)) (root : Bool) (todo : Array Expr) (keys : Array 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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                                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.runMatch {α β : Type} (d : LazyDiscrTree α) (m : MatchM α β) :
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                                    def Lean.Meta.LazyDiscrTree.newTrie {m : TypeType u_1} {α : Type} [Monad m] [MonadState (Array (Trie α)) m] (e : LazyEntry α) :

                                    Create a new trie with the given lazy entry.

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                                      Add a lazy entry to an existing trie.

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                                          This evaluates all lazy entries in a trie and updates values, starIdx, and children accordingly.

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                                                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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                                                  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.

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                                                      Number of elements in result

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                                                        @[specialize #[]]
                                                        def Lean.Meta.LazyDiscrTree.MatchResult.appendResultsAux {α : Type} {β : Type u_1} (mr : MatchResult α) (a : Array β) (f : Natαβ) :

                                                        Append results to array

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                                                              partial def Lean.Meta.LazyDiscrTree.getMatchLoop {α : Type} (cases : Array PartialMatch) (result : MatchResult α) :

                                                              Evaluate all partial matches and add resulting matches to MatchResult.

                                                              The partial matches are stored in an array that is used as a stack. When adding multiple partial matches to explore next, to ensure the order of results matches user expectations, this code must add paths we want to prioritize and return results earlier are added last.

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                                                                  Find values that match e in root.

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                                                                    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.

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                                                                      Structure for quickly initializing a lazy discrimination tree with a large number of elements using concurrent functions for generating entries.

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                                                                          Add an entry to the pre-discrimination tree.

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                                                                            Convert a pre-discrimination tree to a lazy discrimination tree.

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                                                                              Merge two discrimination trees.

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                                                                                Initial entry in lazy discrimination tree

                                                                                • key : Key

                                                                                  Return root key for an entry.

                                                                                • entry : LazyEntry α

                                                                                  Returns rest of entry for later insertion.

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                                                                                  def Lean.Meta.LazyDiscrTree.InitEntry.fromExpr {α : Type} (expr : Expr) (value : α) :

                                                                                  Constructs an initial entry from an expression and value.

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                                                                                    def Lean.Meta.LazyDiscrTree.InitEntry.mkSubEntry {α : Type} (e : InitEntry α) (idx : Nat) (value : 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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                                                                                      Information about a failed import.

                                                                                      • module : Name

                                                                                        Module with constant that import failed on.

                                                                                      • const : Name

                                                                                        Constant that import failed on.

                                                                                      • exception : Exception

                                                                                        Exception that triggers error.

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                                                                                        Information generation from imported modules.

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                                                                                              def Lean.Meta.LazyDiscrTree.addConstImportData {α : Type} (cctx : Core.Context) (env : Environment) (modName : Name) (d : ImportData) (cacheRef : IO.Ref Cache) (tree : PreDiscrTree α) (act : NameConstantInfoMetaM (Array (InitEntry α))) (name : Name) (constInfo : ConstantInfo) :
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                                                                                                Contains the pre discrimination tree and any errors occurring during initialization of the library search tree.

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                                                                                                  Combine two initial results.

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                                                                                                  • { tree := yv, errors := ye }.append { tree := yv_1, errors := ye_1 } = { tree := yv ++ yv_1, errors := ye ++ ye_1 }
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                                                                                                      partial def Lean.Meta.LazyDiscrTree.loadImportedModule {α : Type} (cctx : Core.Context) (env : Environment) (act : NameConstantInfoMetaM (Array (InitEntry α))) (d : ImportData) (cacheRef : IO.Ref Cache) (tree : PreDiscrTree α) (mname : Name) (mdata : ModuleData) (i : Nat := 0) :
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                                                                                                        def Lean.Meta.LazyDiscrTree.combineGet {α : Type u_1} [Append α] (z : α) (tasks : Array (Task α)) :
                                                                                                        α

                                                                                                        Get the results of each task and merge using combining function

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                                                                                                                  def Lean.Meta.LazyDiscrTree.createImportedDiscrTree {m : TypeType} {α : Type} [Monad m] [MonadLog m] [AddMessageContext m] [MonadOptions m] [MonadLiftT BaseIO m] (cctx : Core.Context) (ngen : NameGenerator) (env : Environment) (act : NameConstantInfoMetaM (Array (InitEntry α))) (constantsPerTask : Nat := 1000) :

                                                                                                                  Create a discriminator tree for imported environment.

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                                                                                                                    Creates the core context used for initializing a tree using the current context.

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                                                                                                                      def Lean.Meta.LazyDiscrTree.findImportMatches {α : Type} (ext : EnvExtension (IO.Ref (Option (LazyDiscrTree α)))) (addEntry : NameConstantInfoMetaM (Array (InitEntry α))) (droppedKeys : List (List Key) := []) (constantsPerTask : Nat := 1000) (ty : Expr) :
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                                                                                                                        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.

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                                                                                                                          Create a discriminator tree for current module declarations.

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                                                                                                                            def Lean.Meta.LazyDiscrTree.createModuleTreeRef {α : Type} (entriesForConst : NameConstantInfoMetaM (Array (InitEntry α))) (droppedKeys : List (List Key)) :

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

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                                                                                                                              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 β : Type} (moduleTreeRef : ModuleDiscrTreeRef α) (ext : EnvExtension (IO.Ref (Option (LazyDiscrTree α)))) (addEntry : NameConstantInfoMetaM (Array (InitEntry α))) (droppedKeys : List (List Key) := []) (constantsPerTask : Nat := 1000) (adjustResult : Natαβ) (ty : Expr) :

                                                                                                                                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 : EnvExtension (IO.Ref (Option (LazyDiscrTree α)))) (addEntry : NameConstantInfoMetaM (Array (InitEntry α))) (droppedKeys : List (List Key) := []) (constantsPerTask : Nat := 1000) (ty : Expr) :

                                                                                                                                  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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