inductive Lean.Compiler.LCNF.UnreachableBranches.Value : Type

The abstract domain of the interpreter. Representing sets of values of a certain type.

• bot : Value

  Undefined, could be anything we have no information.

• top : Value

  All values are possible.

• ctor (i : Name) (vs : Array Value) : Value

  A certain constructor with a certain sets of parameters is possible.

• choice (vs : List Value) : Value

  A set of values are possible.

def Lean.Compiler.LCNF.UnreachableBranches.instInhabitedValue.default : Value

@[implicit_reducible]

instance Lean.Compiler.LCNF.UnreachableBranches.instInhabitedValue : Inhabited Value

def Lean.Compiler.LCNF.UnreachableBranches.Value.maxValueDepth : Nat

partial def Lean.Compiler.LCNF.UnreachableBranches.Value.beq : Value → Value → Bool

@[implicit_reducible]

instance Lean.Compiler.LCNF.UnreachableBranches.Value.instBEq : BEq Value

partial def Lean.Compiler.LCNF.UnreachableBranches.Value.toFormat : Value → Format

@[implicit_reducible]

instance Lean.Compiler.LCNF.UnreachableBranches.Value.instRepr : Repr Value

def Lean.Compiler.LCNF.UnreachableBranches.Value.inductValOfCtor (ctorName : Name) (env : Environment) : InductiveVal

partial def Lean.Compiler.LCNF.UnreachableBranches.Value.addChoice (env : Environment) (vs : List Value) (v : Value) : List Value

Fuse v into vs. That is do not only append but if we see that v is a constructor that is already contained within vs try to detect the difference between these values and merge them accordingly into a choice node further down the tree.

partial def Lean.Compiler.LCNF.UnreachableBranches.Value.merge (env : Environment) (v1 v2 : Value) : Value

Merge two values into one. bot is the neutral element, top the annihilator.

def Lean.Compiler.LCNF.UnreachableBranches.Value.truncate (env : Environment) (v : Value) : Value

Make sure constructors of recursive inductive datatypes can only occur once in each path. Values at depth > maxValueDepth are also approximated at top. We use this function to implement a simple widening operation for our abstract interpreter. Recall the widening functions is used to ensure termination in abstract interpreters.

def Lean.Compiler.LCNF.UnreachableBranches.Value.widening (env : Environment) (v1 v2 : Value) : Value

Widening operator that guarantees termination in our abstract interpreter.

partial def Lean.Compiler.LCNF.UnreachableBranches.Value.containsCtor : Value → Name → Bool

Check whether a certain constructor is part of a Value by name. Note that both top and bot will always true here. For bot this is because we have no information about the Value so just to be sure we don't claim the absence of a certain constructor.

def Lean.Compiler.LCNF.UnreachableBranches.Value.getCtorArgs : Value → Name → Option (Array Value)

Obtain the arguments of a certain constructor within the Value.

def Lean.Compiler.LCNF.UnreachableBranches.Value.ofNat (n : Nat) : Value

def Lean.Compiler.LCNF.UnreachableBranches.Value.ofLCNFLit : LitValue → Value

partial def Lean.Compiler.LCNF.UnreachableBranches.Value.proj (env : Environment) : Value → Nat → Value

partial def Lean.Compiler.LCNF.UnreachableBranches.Value.isLiteral : Value → Bool

We say that a Value is a literal iff it is only a tree of Value.ctor nodes.

def Lean.Compiler.LCNF.UnreachableBranches.Value.getLiteral (v : Value) : CompilerM (Option (Array (CodeDecl Purity.pure) × FVarId))

Attempt to turn a Value that is representing a literal into a set of auxiliary declarations + the final FVarId of the declaration that contains the actual literal. If it is not a literal return none.

@[reducible, inline]

abbrev Lean.Compiler.LCNF.UnreachableBranches.FunctionSummaries : Type

A map from function names to the Value that the abstract interpreter produced for them.

opaque Lean.Compiler.LCNF.UnreachableBranches.functionSummariesExt : SimplePersistentEnvExtension (Name × Value) FunctionSummaries

Storing FunctionSummaries for all functions in a .olean.

def Lean.Compiler.LCNF.UnreachableBranches.addFunctionSummary (env : Environment) (fid : Name) (v : Value) : Environment

Add a Value for a function name.

def Lean.Compiler.LCNF.UnreachableBranches.getFunctionSummary? (env : Environment) (fid : Name) : Option Value

Obtain the Value for a function name if possible.

@[reducible, inline]

abbrev Lean.Compiler.LCNF.UnreachableBranches.Assignment : Type

A map from variable identifiers to the Value produced by the abstract interpreter for them.

structure Lean.Compiler.LCNF.UnreachableBranches.InterpContext : Type

The context of InterpM.

• decls : Array (Decl Purity.pure)

  The list of Decls we are operating on in InterpM. This can be a single declaration or a mutual block of declarations where their analysis might influence each other as we approach the fixpoint.

• currFnIdx : Nat

  The index of the function we are currently operating on in decls.

structure Lean.Compiler.LCNF.UnreachableBranches.InterpState : Type

• assignments : Array Assignment

  Assignments of functions in the InterpContext.

• funVals : Array Value

  Values of functions in the InterpContext use during computation of the fixpoint. Afterwards they are stored into the Environment.

@[reducible, inline]

abbrev Lean.Compiler.LCNF.UnreachableBranches.InterpM (α : Type) : Type

The monad which powers the abstract interpreter.

def Lean.Compiler.LCNF.UnreachableBranches.getAssignment : InterpM Assignment

Get the variable Assignment of the current function.

def Lean.Compiler.LCNF.UnreachableBranches.getFunVal (funIdx : Nat) : InterpM Value

Get the Value of a certain function in the current block by index.

def Lean.Compiler.LCNF.UnreachableBranches.findFunVal? (declName : Name) : InterpM (Option Value)

def Lean.Compiler.LCNF.UnreachableBranches.modifyAssignment (f : Assignment → Assignment) : InterpM Unit

Run f on the variable Assignment of the current function.

def Lean.Compiler.LCNF.UnreachableBranches.findVarValue (var : FVarId) : InterpM Value

Obtain the Value associated with var from the context of InterpM. If none is available return Value.bot.

def Lean.Compiler.LCNF.UnreachableBranches.findArgValue (arg : Arg Purity.pure) : InterpM Value

Find the value of arg using the logic of findVarValue.

def Lean.Compiler.LCNF.UnreachableBranches.updateVarAssignment (var : FVarId) (newVal : Value) : InterpM Unit

Update the assignment of var by merging the current value with newVal.

def Lean.Compiler.LCNF.UnreachableBranches.resetVarAssignment (var : FVarId) : InterpM Unit

Set the value of var to bot.

def Lean.Compiler.LCNF.UnreachableBranches.updateCurrFnSummary (v : Value) : InterpM Unit

Widen the value of the current function by v.

def Lean.Compiler.LCNF.UnreachableBranches.updateFunDeclParamsAssignment (params : Array (Param Purity.pure)) (args : Array (Arg Purity.pure)) : InterpM Bool

Return true if the assignment of at least one parameter has been updated. Furthermore if we see that params.size != args.size we know that this is a partial application and set the values of the remaining parameters to top since it is impossible to track what will happen with them from here on.

def Lean.Compiler.LCNF.UnreachableBranches.updateFunDeclParamsTop (params : Array (Param Purity.pure)) : InterpM Bool

partial def Lean.Compiler.LCNF.UnreachableBranches.interpCode : Code Purity.pure → InterpM Unit

The actual abstract interpreter on a block of Code.

def Lean.Compiler.LCNF.UnreachableBranches.inferStep : InterpM Bool

Rerun the abstract interpreter on all declarations except of the unsafe ones. Return whether any Value got updated in the process.

partial def Lean.Compiler.LCNF.UnreachableBranches.inferMain (n : Nat := 0) : InterpM Unit

Run inferStep until it reaches a fix point.

def Lean.Compiler.LCNF.UnreachableBranches.elimDead (assignment : Assignment) (decl : Decl Purity.pure) : CompilerM (Decl Purity.pure)

Use the information produced by the abstract interpreter to:

• Eliminate branches that we know cannot be hit
• Eliminate values that we know have to be constants.

def Lean.Compiler.LCNF.Decl.elimDeadBranches (decls : Array (Decl Purity.pure)) : CompilerM (Array (Decl Purity.pure))

def Lean.Compiler.LCNF.elimDeadBranches : Pass