Remark: in the paper "Counting Immutable Beans" the concepts of free and live variables coincide because the paper does not consider join points. For example, consider the function body B

let x := ctor_0;
jmp block_1 x

in a context where we have the join point block_1 defined as

block_1 (x : obj) : obj :=
let z := ctor_0 x y;
ret z

The variable y is live in the function body B since it occurs in block_1 which is "invoked" by B.

@[reducible, inline]

abbrev Lean.IR.IsLive.M (α : Type) : Type

We use State Context instead of ReaderT Context Id because we remove non local joint points from Context whenever we visit them instead of maintaining a set of visited non local join points.

Remark: we don't need to track local join points because we assume there is no variable or join point shadowing in our IR.

@[reducible, inline]

abbrev Lean.IR.IsLive.visitVar (w : Index) (x : VarId) : M Bool

@[reducible, inline]

abbrev Lean.IR.IsLive.visitJP (w : Index) (x : JoinPointId) : M Bool

@[reducible, inline]

abbrev Lean.IR.IsLive.visitArg (w : Index) (a : Arg) : M Bool

@[reducible, inline]

abbrev Lean.IR.IsLive.visitArgs (w : Index) (as : Array Arg) : M Bool

@[reducible, inline]

abbrev Lean.IR.IsLive.visitExpr (w : Index) (e : Expr) : M Bool

partial def Lean.IR.IsLive.visitFnBody (w : Index) : FnBody → M Bool

def Lean.IR.FnBody.hasLiveVar (b : FnBody) (ctx : LocalContext) (x : VarId) : Bool

Return true if x is live in the function body b in the context ctx.

Remark: the context only needs to contain all (free) join point declarations.

Recall that we say that a join point j is free in b if b contains FnBody.jmp j ys and j is not local.

@[reducible, inline]

abbrev Lean.IR.LiveVarSet : Type

@[reducible, inline]

abbrev Lean.IR.JPLiveVarMap : Type

instance Lean.IR.instInhabitedLiveVarSet : Inhabited LiveVarSet

def Lean.IR.mkLiveVarSet (x : VarId) : LiveVarSet

@[reducible, inline]

abbrev Lean.IR.LiveVars.Collector : Type

def Lean.IR.LiveVars.collectExpr : Expr → Collector

partial def Lean.IR.LiveVars.collectFnBody : FnBody → JPLiveVarMap → Collector

def Lean.IR.LiveVars.updateJPLiveVarMap (j : JoinPointId) (ys : Array Param) (v : FnBody) (m : JPLiveVarMap) : JPLiveVarMap

def Lean.IR.updateLiveVars (e : Expr) (v : LiveVarSet) : LiveVarSet

def Lean.IR.collectLiveVars (b : FnBody) (m : JPLiveVarMap) (v : LiveVarSet := ∅) : LiveVarSet