+
+-- Is the given core expression a lambda abstraction?
+is_lam :: CoreSyn.CoreExpr -> Bool
+is_lam (CoreSyn.Lam _ _) = True
+is_lam _ = False
+
+-- Is the given core expression of a function type?
+is_fun :: CoreSyn.CoreExpr -> Bool
+-- Treat Type arguments differently, because exprType is not defined for them.
+is_fun (CoreSyn.Type _) = False
+is_fun expr = (Type.isFunTy . CoreUtils.exprType) expr
+
+-- Is the given core expression polymorphic (i.e., does it accept type
+-- arguments?).
+is_poly :: CoreSyn.CoreExpr -> Bool
+-- Treat Type arguments differently, because exprType is not defined for them.
+is_poly (CoreSyn.Type _) = False
+is_poly expr = (Maybe.isJust . Type.splitForAllTy_maybe . CoreUtils.exprType) expr
+
+-- Is the given core expression a variable reference?
+is_var :: CoreSyn.CoreExpr -> Bool
+is_var (CoreSyn.Var _) = True
+is_var _ = False
+
+-- Can the given core expression be applied to something? This is true for
+-- applying to a value as well as a type.
+is_applicable :: CoreSyn.CoreExpr -> Bool
+is_applicable expr = is_fun expr || is_poly expr
+
+-- Does the given CoreExpr have any free type vars?
+has_free_tyvars :: CoreSyn.CoreExpr -> Bool
+has_free_tyvars = not . VarSet.isEmptyVarSet . (CoreFVs.exprSomeFreeVars Var.isTyVar)
+
+-- Turns a Var CoreExpr into the Id inside it. Will of course only work for
+-- simple Var CoreExprs, not complexer ones.
+exprToVar :: CoreSyn.CoreExpr -> Var.Id
+exprToVar (CoreSyn.Var id) = id