diff --git a/src/Convert/Scoper.hs b/src/Convert/Scoper.hs
index eaa45a6..6cd1ed4 100644
--- a/src/Convert/Scoper.hs
+++ b/src/Convert/Scoper.hs
@@ -40,6 +40,7 @@ module Convert.Scoper
     , withinProcedure
     , withinProcedureM
     , scopeModuleItemT
+    , Replacements
     ) where
 
 import Control.Monad.State.Strict
diff --git a/src/Convert/TypeOf.hs b/src/Convert/TypeOf.hs
index baed014..551cd5c 100644
--- a/src/Convert/TypeOf.hs
+++ b/src/Convert/TypeOf.hs
@@ -3,6 +3,14 @@
  - Author: Zachary Snow <zach@zachjs.com>
  -
  - Conversion for the `type` operator
+ -
+ - This conversion is responsible for explicit type resolution throughout sv2v.
+ - It uses Scoper to resolve hierarchical expressions in a scope-aware manner.
+ -
+ - Some other conversions, such as the dimension query and streaming
+ - concatenation conversions, defer the resolution of type information to this
+ - conversion pass by producing nodes with the `type` operator during
+ - elaboration.
  -}
 
 module Convert.TypeOf (convert) where
@@ -19,9 +27,15 @@ convert :: [AST] -> [AST]
 convert = map $ traverseDescriptions $ partScoper
     traverseDeclM traverseModuleItemM traverseGenItemM traverseStmtM
 
+-- internal representation of a fully implicit type
 pattern UnknownType :: Type
 pattern UnknownType = Implicit Unspecified []
 
+-- single bit 4-state `logic` type
+pattern UnitType :: Type
+pattern UnitType = IntegerVector TLogic Unspecified []
+
+-- insert the given declaration into the scope, and convert an TypeOfs within
 traverseDeclM :: Decl -> Scoper Type Decl
 traverseDeclM decl = do
     item <- traverseModuleItemM (MIPackageItem $ Decl decl)
@@ -29,7 +43,7 @@ traverseDeclM decl = do
     case decl' of
         Variable Local UnknownType ident [] Nil -> do
             -- functions with no return type implicitly return a single bit
-            insertElem ident $ IntegerVector TLogic Unspecified []
+            insertElem ident UnitType
             return decl'
         Variable d t ident a e -> do
             let t' = injectRanges t a
@@ -46,6 +60,7 @@ traverseDeclM decl = do
         ParamType{} -> return decl'
         CommentDecl{} -> return decl'
 
+-- convert TypeOf in a ModuleItem
 traverseModuleItemM :: ModuleItem -> Scoper Type ModuleItem
 traverseModuleItemM (Genvar x) = do
     insertElem x $ IntegerAtom TInteger Unspecified
@@ -53,12 +68,15 @@ traverseModuleItemM (Genvar x) = do
 traverseModuleItemM item =
     traverseTypesM (traverseNestedTypesM traverseTypeM) item
 
+-- convert TypeOf in a GenItem
 traverseGenItemM :: GenItem -> Scoper Type GenItem
 traverseGenItemM = traverseGenItemExprsM traverseExprM
 
+-- convert TypeOf in a Stmt
 traverseStmtM :: Stmt -> Scoper Type Stmt
 traverseStmtM = traverseStmtExprsM traverseExprM
 
+-- convert TypeOf in a Expr
 traverseExprM :: Expr -> Scoper Type Expr
 traverseExprM = traverseNestedExprsM $ traverseExprTypesM $
     traverseNestedTypesM traverseTypeM
@@ -67,6 +85,8 @@ traverseTypeM :: Type -> Scoper Type Type
 traverseTypeM (TypeOf expr) = typeof expr
 traverseTypeM other = return other
 
+-- attempts to find the given (potentially hierarchical or generate-scoped)
+-- expression in the available scope information
 lookupTypeOf :: Expr -> Scoper Type Type
 lookupTypeOf expr = do
     details <- lookupElemM expr
@@ -75,15 +95,18 @@ lookupTypeOf expr = do
         Just (_, replacements, typ) ->
             return $ if Map.null replacements
                 then typ
-                else rewriteType typ
-            where
-                rewriteType = traverseNestedTypes $ traverseTypeExprs $
-                    traverseNestedExprs replace
-                replace :: Expr -> Expr
-                replace (Ident x) =
-                    Map.findWithDefault (Ident x) x replacements
-                replace other = other
+                else rewriteType replacements typ
+    where
+        rewriteType :: Replacements -> Type -> Type
+        rewriteType replacements = traverseNestedTypes $ traverseTypeExprs $
+            traverseNestedExprs (replace replacements)
+        replace :: Replacements -> Expr -> Expr
+        replace replacements (Ident x) =
+            Map.findWithDefault (Ident x) x replacements
+        replace _ other = other
 
+-- determines the type of an expression based on the available scope information
+-- according the semantics defined in IEEE 1800-2017, especially Section 11.6
 typeof :: Expr -> Scoper Type Type
 typeof (Number n) =
     return $ IntegerVector TLogic sg [r]
@@ -91,14 +114,7 @@ typeof (Number n) =
         r = (RawNum $ size - 1, RawNum 0)
         size = numberBitLength n
         sg = if numberIsSigned n then Signed else Unspecified
-typeof (Call (Ident "$unsigned") (Args [e] [])) =
-    typeof e
-typeof (Call (Ident "$signed") (Args [e] [])) =
-    typeof e
-typeof (Call (Ident "$clog2") (Args [_] [])) =
-    return $ IntegerAtom TInteger Unspecified
-typeof (Call (Ident x) _) =
-    typeof $ Ident x
+typeof (Call (Ident x) args) = typeofCall x args
 typeof (orig @ (Bit e _)) = do
     t <- typeof e
     case t of
@@ -120,10 +136,8 @@ typeof (orig @ (Range e mode r)) = do
 typeof (orig @ (Dot e x)) = do
     t <- typeof e
     case t of
-        Struct _ fields [] ->
-            return $ fieldsType fields
-        Union _ fields [] ->
-            return $ fieldsType fields
+        Struct _ fields [] -> return $ fieldsType fields
+        Union _  fields [] -> return $ fieldsType fields
         _ -> lookupTypeOf orig
     where
         fieldsType :: [Field] -> Type
@@ -132,23 +146,8 @@ typeof (orig @ (Dot e x)) = do
                 Just typ -> typ
                 Nothing -> TypeOf orig
 typeof (Cast (Right s) _) = return $ typeOfSize s
-typeof (UniOp UniSub  e  ) = typeof e
-typeof (UniOp BitNot  e  ) = typeof e
-typeof (UniOp LogNot  _  ) = return $ IntegerVector TLogic Unspecified []
-typeof (BinOp Pow     e _) = typeof e
-typeof (BinOp ShiftL  e _) = typeof e
-typeof (BinOp ShiftR  e _) = typeof e
-typeof (BinOp ShiftAL e _) = typeof e
-typeof (BinOp ShiftAR e _) = typeof e
-typeof (BinOp Add     a b) = largerSizeType a b
-typeof (BinOp Sub     a b) = largerSizeType a b
-typeof (BinOp Mul     a b) = largerSizeType a b
-typeof (BinOp Div     a b) = largerSizeType a b
-typeof (BinOp Mod     a b) = largerSizeType a b
-typeof (BinOp BitAnd  a b) = largerSizeType a b
-typeof (BinOp BitXor  a b) = largerSizeType a b
-typeof (BinOp BitXnor a b) = largerSizeType a b
-typeof (BinOp BitOr   a b) = largerSizeType a b
+typeof (UniOp op expr) = typeofUniOp op expr
+typeof (BinOp op a b) = typeofBinOp op a b
 typeof (Mux   _       a b) = largerSizeType a b
 typeof (Concat      exprs) = return $ typeOfSize $ concatSize exprs
 typeof (Repeat reps exprs) = return $ typeOfSize size
@@ -158,12 +157,65 @@ typeof (String str) =
     where
         r = (RawNum $ len - 1, RawNum 0)
         len = if null str then 1 else 8 * unescapedLength str
-        unescapedLength :: String -> Integer
-        unescapedLength [] = 0
-        unescapedLength ('\\' : _ : rest) = 1 + unescapedLength rest
-        unescapedLength (_        : rest) = 1 + unescapedLength rest
 typeof other = lookupTypeOf other
 
+-- length of a string literal in characters
+unescapedLength :: String -> Integer
+unescapedLength [] = 0
+unescapedLength ('\\' : _ : rest) = 1 + unescapedLength rest
+unescapedLength (_        : rest) = 1 + unescapedLength rest
+
+-- type of a standard (non-member) function call
+typeofCall :: String -> Args -> Scoper Type Type
+typeofCall "$unsigned" (Args [e] []) = typeof e
+typeofCall "$signed"   (Args [e] []) = typeof e
+typeofCall "$clog2"    (Args [_] []) =
+    return $ IntegerAtom TInteger Unspecified
+typeofCall fnName _ = typeof $ Ident fnName
+
+-- type of a unary operator expression
+typeofUniOp :: UniOp -> Expr -> Scoper Type Type
+typeofUniOp UniAdd e = typeof e
+typeofUniOp UniSub e = typeof e
+typeofUniOp BitNot e = typeof e
+typeofUniOp _ _ =
+    -- unary reductions and logical negation
+    return UnitType
+
+-- type of a binary operator expression (Section 11.6.1)
+typeofBinOp :: BinOp -> Expr -> Expr -> Scoper Type Type
+typeofBinOp op a b =
+    case op of
+        LogAnd  -> unitType
+        LogOr   -> unitType
+        LogImp  -> unitType
+        LogEq   -> unitType
+        Eq      -> unitType
+        Ne      -> unitType
+        TEq     -> unitType
+        TNe     -> unitType
+        WEq     -> unitType
+        WNe     -> unitType
+        Lt      -> unitType
+        Le      -> unitType
+        Gt      -> unitType
+        Ge      -> unitType
+        Pow     -> typeof a
+        ShiftL  -> typeof a
+        ShiftR  -> typeof a
+        ShiftAL -> typeof a
+        ShiftAR -> typeof a
+        Add     -> largerSizeType a b
+        Sub     -> largerSizeType a b
+        Mul     -> largerSizeType a b
+        Div     -> largerSizeType a b
+        Mod     -> largerSizeType a b
+        BitAnd  -> largerSizeType a b
+        BitXor  -> largerSizeType a b
+        BitXnor -> largerSizeType a b
+        BitOr   -> largerSizeType a b
+    where unitType = return UnitType
+
 -- produces a type large enough to hold either expression
 largerSizeType :: Expr -> Expr -> Scoper Type Type
 largerSizeType a (Number (Based 1 _ _ _ _)) = typeof a
diff --git a/test/basic/typeof_op.sv b/test/basic/typeof_op.sv
new file mode 100644
index 0000000..3e925fc
--- /dev/null
+++ b/test/basic/typeof_op.sv
@@ -0,0 +1,55 @@
+`define TEST(expr) \
+    $display(`"expr = %b; $bits(expr) = %0d`", (expr), $bits(expr));
+
+module top;
+    initial begin
+
+        `TEST(4'b1011)
+        `TEST(5'b01110)
+
+        `TEST(! 3'b101)
+        `TEST(~ 3'b101)
+        `TEST(+ 3'b101)
+        `TEST(- 3'b101)
+        `TEST(& 3'b101)
+        `TEST(~& 3'b101)
+        `TEST(| 3'b101)
+        `TEST(~| 3'b101)
+        `TEST(^ 3'b101)
+        `TEST(~^ 3'b101)
+
+        `TEST(4'b1011 && 5'b01110)
+        `TEST(4'b1011 || 5'b01110)
+        `TEST(4'b1011 & 5'b01110)
+        `TEST(4'b1011 ^ 5'b01110)
+        `TEST(4'b1011 ~^ 5'b01110)
+        `TEST(4'b1011 | 5'b01110)
+        `TEST(4'b1011 << 5'b01110)
+        `TEST(4'b1011 >> 5'b01110)
+        `TEST(4'b1011 <<< 5'b01110)
+        `TEST(4'b1011 >>> 5'b01110)
+        `TEST(4'b1011 == 5'b01110)
+        `TEST(4'b1011 != 5'b01110)
+        `TEST(4'b1011 === 5'b01110)
+        `TEST(4'b1011 !== 5'b01110)
+        `TEST(4'b1011 < 5'b01110)
+        `TEST(4'b1011 <= 5'b01110)
+        `TEST(4'b1011 > 5'b01110)
+        `TEST(4'b1011 >= 5'b01110)
+
+        // TODO: iverilog incorrectly handles width of these
+        // `TEST(4'b1011 * 5'b01110)
+        // `TEST(4'b1011 / 5'b01110)
+        // `TEST(4'b1011 % 5'b01110)
+        // `TEST(4'b1011 + 5'b01110)
+        // `TEST(4'b1011 - 5'b01110)
+        // `TEST(4'b1011 ** 5'b01110)
+
+        // TODO: not yet supported by iverilog
+        // `TEST(4'b1011 -> 5'b01110)
+        // `TEST(4'b1011 <-> 5'b01110)
+        // `TEST(4'b1011 ==? 5'b01110)
+        // `TEST(4'b1011 !=? 5'b01110)
+
+    end
+endmodule
diff --git a/test/basic/typeof_op.v b/test/basic/typeof_op.v
new file mode 100644
index 0000000..b798b77
--- /dev/null
+++ b/test/basic/typeof_op.v
@@ -0,0 +1 @@
+`include "typeof_op.sv"