diff --git a/docs/src/manpage.md b/docs/src/manpage.md
index aef0df1f31..831530aec1 100644
--- a/docs/src/manpage.md
+++ b/docs/src/manpage.md
@@ -3634,5 +3634,5 @@ MILLER(1)                                                            MILLER(1)
 
 
 
-                                  2023-08-26                         MILLER(1)
+                                  2023-08-27                         MILLER(1)
 </pre>
diff --git a/docs/src/manpage.txt b/docs/src/manpage.txt
index a4bb520495..43f2ed3865 100644
--- a/docs/src/manpage.txt
+++ b/docs/src/manpage.txt
@@ -3613,4 +3613,4 @@ MILLER(1)                                                            MILLER(1)
 
 
 
-                                  2023-08-26                         MILLER(1)
+                                  2023-08-27                         MILLER(1)
diff --git a/docs/src/missings.csv b/docs/src/missings.csv
new file mode 100644
index 0000000000..22abbc0424
--- /dev/null
+++ b/docs/src/missings.csv
@@ -0,0 +1,4 @@
+a,x,z,w
+red,7,,
+green,,242,zdatsyg
+blue,9,,
diff --git a/docs/src/missings.json b/docs/src/missings.json
new file mode 100644
index 0000000000..d1dfb13ad6
--- /dev/null
+++ b/docs/src/missings.json
@@ -0,0 +1,5 @@
+[
+  { "a": "red",   "x": 7 },
+  { "a": "green", "z": 242, "w": "zdatsyg" },
+  { "a": "blue",  "x": 9 }
+]
diff --git a/docs/src/reference-main-null-data.md b/docs/src/reference-main-null-data.md
index 6ddd2518f8..0de7c67c91 100644
--- a/docs/src/reference-main-null-data.md
+++ b/docs/src/reference-main-null-data.md
@@ -93,7 +93,7 @@ a=1,b=8
 x=9,b=10
 </pre>
 
-* Functions/operators which have one or more *empty* arguments produce empty output: e.g.
+* Most functions/operators which have one or more *empty* arguments produce empty output: e.g.
 
 <pre class="pre-highlight-in-pair">
 <b>echo 'x=2,y=3' | mlr put '$a=$x+$y'</b>
@@ -106,7 +106,7 @@ x=2,y=3,a=5
 <b>echo 'x=,y=3' | mlr put '$a=$x+$y'</b>
 </pre>
 <pre class="pre-non-highlight-in-pair">
-x=,y=3,a=
+x=,y=3,a=3
 </pre>
 
 <pre class="pre-highlight-in-pair">
@@ -125,6 +125,55 @@ with the exception that the `min` and `max` functions are special: if one argume
 x=,y=3,a=3,b=
 </pre>
 
+Likewise, empty works like 0 for addition and subtraction, and multiplication:
+
+<pre class="pre-highlight-in-pair">
+<b>echo 'x=,y=3' | mlr put '$a = $x + $y; $b = $x - $y; $c = $x * $y'</b>
+</pre>
+<pre class="pre-non-highlight-in-pair">
+x=,y=3,a=3,b=-3,c=3
+</pre>
+
+This is intended to follow the arithmetic rule for absent data (explained next). In particular:
+
+* For file formats allowing for heterogeneity in keys, e.g. JSON, you should be able to keep a running sum of some field, say `$x`. If a given record doesn't have `$x`, then `$x` will be absent for that record, and the sum should simply continue.
+* For CSV and TSV, which don't allow for hetrogeneity in keys, the _only_ way a value can be missing is to be empty.  Here, if a given record doesn't have `$x`, then `$x` will be empty for that record, and the sum should simply continue.
+
+<pre class="pre-highlight-in-pair">
+<b>cat missings.json</b>
+</pre>
+<pre class="pre-non-highlight-in-pair">
+[
+  { "a": "red",   "x": 7 },
+  { "a": "green", "z": 242, "w": "zdatsyg" },
+  { "a": "blue",  "x": 9 }
+]
+</pre>
+
+<pre class="pre-highlight-in-pair">
+<b>mlr --ijson --from missings.json put -q 'begin { @sum = 0 } @sum += $x; end { print @sum }'</b>
+</pre>
+<pre class="pre-non-highlight-in-pair">
+16
+</pre>
+
+<pre class="pre-highlight-in-pair">
+<b>cat missings.csv</b>
+</pre>
+<pre class="pre-non-highlight-in-pair">
+a,x,z,w
+red,7,,
+green,,242,zdatsyg
+blue,9,,
+</pre>
+
+<pre class="pre-highlight-in-pair">
+<b>mlr --icsv --from missings.csv put -q 'begin { @sum = 0 } @sum += $x; end { print @sum }'</b>
+</pre>
+<pre class="pre-non-highlight-in-pair">
+16
+</pre>
+
 * Functions of *absent* variables (e.g. `mlr put '$y = log10($nonesuch)'`) evaluate to absent, and arithmetic/bitwise/boolean operators with both operands being absent evaluate to absent. Arithmetic operators with one absent operand return the other operand. More specifically, absent values act like zero for addition/subtraction, and one for multiplication: Furthermore, **any expression which evaluates to absent is not stored in the left-hand side of an assignment statement**:
 
 <pre class="pre-highlight-in-pair">
@@ -145,8 +194,6 @@ x=2,y=3,a=2,b=3
 
 The reasoning is as follows:
 
-* Empty values are explicit in the data so they should explicitly affect accumulations: `mlr put '@sum += $x'` should accumulate numeric `x` values into the sum but an empty `x`, when encountered in the input data stream, should make the sum non-numeric. To work around this you can use the `is_not_null` function as follows: `mlr put 'is_not_null($x) { @sum += $x }'`
-
 * Absent stream-record values should not break accumulations, since Miller by design handles heterogeneous data: the running `@sum` in `mlr put '@sum += $x'` should not be invalidated for records which have no `x`.
 
 * Absent out-of-stream-variable values are precisely what allow you to write `mlr put '@sum += $x'`. Otherwise you would have to write `mlr put 'begin{@sum = 0}; @sum += $x'` -- which is tolerable -- but for `mlr put 'begin{...}; @sum[$a][$b] += $x'` you'd have to pre-initialize `@sum` for all values of `$a` and `$b` in your input data stream, which is intolerable.
@@ -198,10 +245,11 @@ If you're interested in a formal description of how empty and absent fields part
 <b>mlr help type-arithmetic-info</b>
 </pre>
 <pre class="pre-non-highlight-in-pair">
-(+)        | 1          2.5        (absent)   (error)   
-------     + ------     ------     ------     ------    
-1          | 2          3.5        1          (error)   
-2.5        | 3.5        5          2.5        (error)   
-(absent)   | 1          2.5        (absent)   (error)   
-(error)    | (error)    (error)    (error)    (error)   
+(+)        | 1          2.5       (empty)    (absent)   (error)   
+------     + ------     ------     ------     ------     ------    
+1          | 2          3.5        1          1          (error)   
+2.5        | 3.5        5          2.5        2.5        (error)   
+(empty)    | 1          2.5        (empty)    (absent)   (error)   
+(absent)   | 1          2.5        (absent)   (absent)   (error)   
+(error)    | (error)    (error)    (error)    (error)    (error)   
 </pre>
diff --git a/docs/src/reference-main-null-data.md.in b/docs/src/reference-main-null-data.md.in
index 4a9b446164..381a46522b 100644
--- a/docs/src/reference-main-null-data.md.in
+++ b/docs/src/reference-main-null-data.md.in
@@ -34,7 +34,7 @@ GENMD-RUN-COMMAND
 mlr sort -nr a data/sort-null.dat
 GENMD-EOF
 
-* Functions/operators which have one or more *empty* arguments produce empty output: e.g.
+* Most functions/operators which have one or more *empty* arguments produce empty output: e.g.
 
 GENMD-RUN-COMMAND
 echo 'x=2,y=3' | mlr put '$a=$x+$y'
@@ -54,6 +54,33 @@ GENMD-RUN-COMMAND
 echo 'x=,y=3' | mlr put '$a=min($x,$y);$b=max($x,$y)'
 GENMD-EOF
 
+Likewise, empty works like 0 for addition and subtraction, and multiplication:
+
+GENMD-RUN-COMMAND
+echo 'x=,y=3' | mlr put '$a = $x + $y; $b = $x - $y; $c = $x * $y'
+GENMD-EOF
+
+This is intended to follow the arithmetic rule for absent data (explained next). In particular:
+
+* For file formats allowing for heterogeneity in keys, e.g. JSON, you should be able to keep a running sum of some field, say `$x`. If a given record doesn't have `$x`, then `$x` will be absent for that record, and the sum should simply continue.
+* For CSV and TSV, which don't allow for hetrogeneity in keys, the _only_ way a value can be missing is to be empty.  Here, if a given record doesn't have `$x`, then `$x` will be empty for that record, and the sum should simply continue.
+
+GENMD-RUN-COMMAND
+cat missings.json
+GENMD-EOF
+
+GENMD-RUN-COMMAND
+mlr --ijson --from missings.json put -q 'begin { @sum = 0 } @sum += $x; end { print @sum }'
+GENMD-EOF
+
+GENMD-RUN-COMMAND
+cat missings.csv
+GENMD-EOF
+
+GENMD-RUN-COMMAND
+mlr --icsv --from missings.csv put -q 'begin { @sum = 0 } @sum += $x; end { print @sum }'
+GENMD-EOF
+
 * Functions of *absent* variables (e.g. `mlr put '$y = log10($nonesuch)'`) evaluate to absent, and arithmetic/bitwise/boolean operators with both operands being absent evaluate to absent. Arithmetic operators with one absent operand return the other operand. More specifically, absent values act like zero for addition/subtraction, and one for multiplication: Furthermore, **any expression which evaluates to absent is not stored in the left-hand side of an assignment statement**:
 
 GENMD-RUN-COMMAND
@@ -68,8 +95,6 @@ GENMD-EOF
 
 The reasoning is as follows:
 
-* Empty values are explicit in the data so they should explicitly affect accumulations: `mlr put '@sum += $x'` should accumulate numeric `x` values into the sum but an empty `x`, when encountered in the input data stream, should make the sum non-numeric. To work around this you can use the `is_not_null` function as follows: `mlr put 'is_not_null($x) { @sum += $x }'`
-
 * Absent stream-record values should not break accumulations, since Miller by design handles heterogeneous data: the running `@sum` in `mlr put '@sum += $x'` should not be invalidated for records which have no `x`.
 
 * Absent out-of-stream-variable values are precisely what allow you to write `mlr put '@sum += $x'`. Otherwise you would have to write `mlr put 'begin{@sum = 0}; @sum += $x'` -- which is tolerable -- but for `mlr put 'begin{...}; @sum[$a][$b] += $x'` you'd have to pre-initialize `@sum` for all values of `$a` and `$b` in your input data stream, which is intolerable.
diff --git a/docs/src/split_circle.csv b/docs/src/split_circle.csv
new file mode 100644
index 0000000000..6ea6a0a937
--- /dev/null
+++ b/docs/src/split_circle.csv
@@ -0,0 +1,4 @@
+color,shape,flag,k,index,quantity,rate
+red,circle,true,3,16,13.8103,2.9010
+yellow,circle,true,8,73,63.9785,4.2370
+yellow,circle,true,9,87,63.5058,8.3350
diff --git a/docs/src/split_square.csv b/docs/src/split_square.csv
new file mode 100644
index 0000000000..122663bfec
--- /dev/null
+++ b/docs/src/split_square.csv
@@ -0,0 +1,5 @@
+color,shape,flag,k,index,quantity,rate
+red,square,true,2,15,79.2778,0.0130
+red,square,false,4,48,77.5542,7.4670
+red,square,false,6,64,77.1991,9.5310
+purple,square,false,10,91,72.3735,8.2430
diff --git a/docs/src/split_triangle.csv b/docs/src/split_triangle.csv
new file mode 100644
index 0000000000..70bce77e6c
--- /dev/null
+++ b/docs/src/split_triangle.csv
@@ -0,0 +1,4 @@
+color,shape,flag,k,index,quantity,rate
+yellow,triangle,true,1,11,43.6498,9.8870
+purple,triangle,false,5,51,81.2290,8.5910
+purple,triangle,false,7,65,80.1405,5.8240
diff --git a/internal/pkg/bifs/arithmetic.go b/internal/pkg/bifs/arithmetic.go
index 86f6d1e7f9..871874e7e5 100644
--- a/internal/pkg/bifs/arithmetic.go
+++ b/internal/pkg/bifs/arithmetic.go
@@ -14,7 +14,7 @@ var upos_dispositions = [mlrval.MT_DIM]UnaryFunc{
 	/*INT    */ _1u___,
 	/*FLOAT  */ _1u___,
 	/*BOOL   */ _erro1,
-	/*VOID   */ _void1,
+	/*VOID   */ _zero1,
 	/*STRING */ _erro1,
 	/*ARRAY  */ _absn1,
 	/*MAP    */ _absn1,
@@ -43,7 +43,7 @@ var uneg_dispositions = [mlrval.MT_DIM]UnaryFunc{
 	/*INT    */ uneg_i_i,
 	/*FLOAT  */ uneg_f_f,
 	/*BOOL   */ _erro1,
-	/*VOID   */ _void1,
+	/*VOID   */ _zero1,
 	/*STRING */ _erro1,
 	/*ARRAY  */ _absn1,
 	/*MAP    */ _absn1,
@@ -97,11 +97,11 @@ func plus_f_ff(input1, input2 *mlrval.Mlrval) *mlrval.Mlrval {
 }
 
 var plus_dispositions = [mlrval.MT_DIM][mlrval.MT_DIM]BinaryFunc{
-	//       .  INT        FLOAT      BOOL   VOID   STRING ARRAY  MAP    FUNC    ERROR   NULL   ABSENT
-	/*INT    */ {plus_n_ii, plus_f_if, _erro, _void, _erro, _absn, _absn, _erro, _erro, _1___, _1___},
-	/*FLOAT  */ {plus_f_fi, plus_f_ff, _erro, _void, _erro, _absn, _absn, _erro, _erro, _1___, _1___},
+	//       .  INT         FLOAT      BOOL   VOID   STRING ARRAY  MAP    FUNC   ERROR  NULL   ABSENT
+	/*INT    */ {plus_n_ii, plus_f_if, _erro, _1___, _erro, _absn, _absn, _erro, _erro, _1___, _1___},
+	/*FLOAT  */ {plus_f_fi, plus_f_ff, _erro, _1___, _erro, _absn, _absn, _erro, _erro, _1___, _1___},
 	/*BOOL   */ {_erro, _erro, _erro, _erro, _erro, _absn, _absn, _erro, _erro, _erro, _erro},
-	/*VOID   */ {_void, _void, _erro, _void, _erro, _absn, _absn, _erro, _erro, _erro, _absn},
+	/*VOID   */ {_2___, _2___, _erro, _void, _erro, _absn, _absn, _erro, _erro, _erro, _absn},
 	/*STRING */ {_erro, _erro, _erro, _erro, _erro, _absn, _absn, _erro, _erro, _erro, _erro},
 	/*ARRAY  */ {_absn, _absn, _absn, _absn, _absn, _absn, _absn, _erro, _absn, _absn, _absn},
 	/*MAP    */ {_absn, _absn, _absn, _absn, _absn, _absn, _absn, _erro, _absn, _absn, _absn},
@@ -155,11 +155,11 @@ func minus_f_ff(input1, input2 *mlrval.Mlrval) *mlrval.Mlrval {
 }
 
 var minus_dispositions = [mlrval.MT_DIM][mlrval.MT_DIM]BinaryFunc{
-	//       .  INT         FLOAT       BOOL   VOID   STRING ARRAY  MAP    FUNC    ERROR   NULL   ABSENT
-	/*INT    */ {minus_n_ii, minus_f_if, _erro, _void, _erro, _absn, _absn, _erro, _erro, _1___, _1___},
-	/*FLOAT  */ {minus_f_fi, minus_f_ff, _erro, _void, _erro, _absn, _absn, _erro, _erro, _1___, _1___},
+	//       .  INT          FLOAT       BOOL   VOID   STRING ARRAY  MAP    FUNC   ERROR  NULL   ABSENT
+	/*INT    */ {minus_n_ii, minus_f_if, _erro, _1___, _erro, _absn, _absn, _erro, _erro, _1___, _1___},
+	/*FLOAT  */ {minus_f_fi, minus_f_ff, _erro, _1___, _erro, _absn, _absn, _erro, _erro, _1___, _1___},
 	/*BOOL   */ {_erro, _erro, _erro, _erro, _erro, _absn, _absn, _erro, _erro, _erro, _erro},
-	/*VOID   */ {_void, _void, _erro, _void, _erro, _absn, _absn, _erro, _erro, _erro, _absn},
+	/*VOID   */ {_n2__, _n2__, _erro, _void, _erro, _absn, _absn, _erro, _erro, _erro, _absn},
 	/*STRING */ {_erro, _erro, _erro, _erro, _erro, _absn, _absn, _erro, _erro, _erro, _erro},
 	/*ARRAY  */ {_absn, _absn, _absn, _absn, _absn, _absn, _absn, _erro, _absn, _absn, _absn},
 	/*MAP    */ {_absn, _absn, _absn, _absn, _absn, _absn, _absn, _erro, _absn, _absn, _absn},
@@ -229,11 +229,11 @@ func times_f_ff(input1, input2 *mlrval.Mlrval) *mlrval.Mlrval {
 }
 
 var times_dispositions = [mlrval.MT_DIM][mlrval.MT_DIM]BinaryFunc{
-	//       .  INT         FLOAT       BOOL   VOID   STRING ARRAY  MAP    FUNC    ERROR   NULL   ABSENT
-	/*INT    */ {times_n_ii, times_f_if, _erro, _void, _erro, _absn, _absn, _erro, _erro, _1___, _1___},
-	/*FLOAT  */ {times_f_fi, times_f_ff, _erro, _void, _erro, _absn, _absn, _erro, _erro, _1___, _1___},
+	//       .  INT          FLOAT       BOOL   VOID   STRING ARRAY  MAP    FUNC   ERROR  NULL   ABSENT
+	/*INT    */ {times_n_ii, times_f_if, _erro, _1___, _erro, _absn, _absn, _erro, _erro, _1___, _1___},
+	/*FLOAT  */ {times_f_fi, times_f_ff, _erro, _1___, _erro, _absn, _absn, _erro, _erro, _1___, _1___},
 	/*BOOL   */ {_erro, _erro, _erro, _erro, _erro, _absn, _absn, _erro, _erro, _erro, _erro},
-	/*VOID   */ {_void, _void, _erro, _void, _erro, _absn, _absn, _erro, _erro, _erro, _absn},
+	/*VOID   */ {_2___, _2___, _erro, _void, _erro, _absn, _absn, _erro, _erro, _erro, _absn},
 	/*STRING */ {_erro, _erro, _erro, _erro, _erro, _absn, _absn, _erro, _erro, _erro, _erro},
 	/*ARRAY  */ {_absn, _absn, _absn, _absn, _absn, _absn, _absn, _erro, _absn, _absn, _absn},
 	/*MAP    */ {_absn, _absn, _absn, _absn, _absn, _absn, _absn, _erro, _absn, _absn, _absn},
@@ -389,11 +389,11 @@ func dotplus_f_ff(input1, input2 *mlrval.Mlrval) *mlrval.Mlrval {
 }
 
 var dot_plus_dispositions = [mlrval.MT_DIM][mlrval.MT_DIM]BinaryFunc{
-	//       .  INT           FLOAT         BOOL   VOID   STRING ARRAY  MAP    FUNC    ERROR   NULL   ABSENT
-	/*INT    */ {dotplus_i_ii, dotplus_f_if, _erro, _void, _erro, _absn, _absn, _erro, _erro, _1___, _1___},
-	/*FLOAT  */ {dotplus_f_fi, dotplus_f_ff, _erro, _void, _erro, _absn, _absn, _erro, _erro, _1___, _1___},
+	//       .  INT            FLOAT         BOOL   VOID   STRING ARRAY  MAP    FUNC   ERROR  NULL   ABSENT
+	/*INT    */ {dotplus_i_ii, dotplus_f_if, _erro, _1___, _erro, _absn, _absn, _erro, _erro, _1___, _1___},
+	/*FLOAT  */ {dotplus_f_fi, dotplus_f_ff, _erro, _1___, _erro, _absn, _absn, _erro, _erro, _1___, _1___},
 	/*BOOL   */ {_erro, _erro, _erro, _erro, _erro, _absn, _absn, _erro, _erro, _erro, _erro},
-	/*VOID   */ {_void, _void, _erro, _void, _erro, _absn, _absn, _erro, _erro, _erro, _absn},
+	/*VOID   */ {_2___, _2___, _erro, _void, _erro, _absn, _absn, _erro, _erro, _erro, _absn},
 	/*STRING */ {_erro, _erro, _erro, _erro, _erro, _absn, _absn, _erro, _erro, _erro, _erro},
 	/*ARRAY  */ {_absn, _absn, _absn, _absn, _absn, _absn, _absn, _erro, _absn, _absn, _absn},
 	/*MAP    */ {_absn, _absn, _absn, _absn, _absn, _absn, _absn, _erro, _absn, _absn, _absn},
@@ -425,11 +425,11 @@ func dotminus_f_ff(input1, input2 *mlrval.Mlrval) *mlrval.Mlrval {
 }
 
 var dotminus_dispositions = [mlrval.MT_DIM][mlrval.MT_DIM]BinaryFunc{
-	//       .  INT            FLOAT          BOOL   VOID   STRING ARRAY  MAP    FUNC    ERROR   NULL   ABSENT
-	/*INT    */ {dotminus_i_ii, dotminus_f_if, _erro, _void, _erro, _absn, _absn, _erro, _erro, _1___, _1___},
-	/*FLOAT  */ {dotminus_f_fi, dotminus_f_ff, _erro, _void, _erro, _absn, _absn, _erro, _erro, _1___, _1___},
+	//       .  INT             FLOAT          BOOL   VOID   STRING ARRAY  MAP    FUNC   ERROR  NULL   ABSENT
+	/*INT    */ {dotminus_i_ii, dotminus_f_if, _erro, _1___, _erro, _absn, _absn, _erro, _erro, _1___, _1___},
+	/*FLOAT  */ {dotminus_f_fi, dotminus_f_ff, _erro, _1___, _erro, _absn, _absn, _erro, _erro, _1___, _1___},
 	/*BOOL   */ {_erro, _erro, _erro, _erro, _erro, _absn, _absn, _erro, _erro, _erro, _erro},
-	/*VOID   */ {_void, _void, _erro, _void, _erro, _absn, _absn, _erro, _erro, _erro, _absn},
+	/*VOID   */ {_n2__, _n2__, _erro, _void, _erro, _absn, _absn, _erro, _erro, _erro, _absn},
 	/*STRING */ {_erro, _erro, _erro, _erro, _erro, _absn, _absn, _erro, _erro, _erro, _erro},
 	/*ARRAY  */ {_absn, _absn, _absn, _absn, _absn, _absn, _absn, _erro, _absn, _absn, _absn},
 	/*MAP    */ {_absn, _absn, _absn, _absn, _absn, _absn, _absn, _erro, _absn, _absn, _absn},
@@ -461,11 +461,11 @@ func dottimes_f_ff(input1, input2 *mlrval.Mlrval) *mlrval.Mlrval {
 }
 
 var dottimes_dispositions = [mlrval.MT_DIM][mlrval.MT_DIM]BinaryFunc{
-	//       .  INT            FLOAT          BOOL   VOID   STRING ARRAY  MAP    FUNC    ERROR   NULL   ABSENT
-	/*INT    */ {dottimes_i_ii, dottimes_f_if, _erro, _void, _erro, _absn, _absn, _erro, _erro, _1___, _1___},
-	/*FLOAT  */ {dottimes_f_fi, dottimes_f_ff, _erro, _void, _erro, _absn, _absn, _erro, _erro, _1___, _1___},
+	//       .  INT             FLOAT          BOOL   VOID   STRING ARRAY  MAP    FUNC   ERROR  NULL   ABSENT
+	/*INT    */ {dottimes_i_ii, dottimes_f_if, _erro, _1___, _erro, _absn, _absn, _erro, _erro, _1___, _1___},
+	/*FLOAT  */ {dottimes_f_fi, dottimes_f_ff, _erro, _1___, _erro, _absn, _absn, _erro, _erro, _1___, _1___},
 	/*BOOL   */ {_erro, _erro, _erro, _erro, _erro, _absn, _absn, _erro, _erro, _erro, _erro},
-	/*VOID   */ {_void, _void, _erro, _void, _erro, _absn, _absn, _erro, _erro, _erro, _absn},
+	/*VOID   */ {_n2__, _n2__, _erro, _void, _erro, _absn, _absn, _erro, _erro, _erro, _absn},
 	/*STRING */ {_erro, _erro, _erro, _erro, _erro, _absn, _absn, _erro, _erro, _erro, _erro},
 	/*ARRAY  */ {_absn, _absn, _absn, _absn, _absn, _absn, _absn, _erro, _absn, _absn, _absn},
 	/*MAP    */ {_absn, _absn, _absn, _absn, _absn, _absn, _absn, _erro, _absn, _absn, _absn},
diff --git a/internal/pkg/bifs/base.go b/internal/pkg/bifs/base.go
index 700cfab262..36aeb63d28 100644
--- a/internal/pkg/bifs/base.go
+++ b/internal/pkg/bifs/base.go
@@ -106,6 +106,11 @@ func _zero1(input1 *mlrval.Mlrval) *mlrval.Mlrval {
 	return mlrval.FromInt(0)
 }
 
+// Return one (unary)
+func __one1(input1 *mlrval.Mlrval) *mlrval.Mlrval {
+	return mlrval.FromInt(1)
+}
+
 // Return null (unary)
 func _null1(input1 *mlrval.Mlrval) *mlrval.Mlrval {
 	return mlrval.NULL
diff --git a/internal/pkg/terminals/help/entry.go b/internal/pkg/terminals/help/entry.go
index 5fe7c9a9f7..17130fe26d 100644
--- a/internal/pkg/terminals/help/entry.go
+++ b/internal/pkg/terminals/help/entry.go
@@ -486,6 +486,7 @@ func helpTypeArithmeticInfo() {
 	mlrvals := []*mlrval.Mlrval{
 		mlrval.FromInt(1),
 		mlrval.FromFloat(2.5),
+		mlrval.VOID,
 		mlrval.ABSENT,
 		mlrval.ERROR,
 	}
@@ -497,17 +498,27 @@ func helpTypeArithmeticInfo() {
 			fmt.Printf("%-10s |", "(+)")
 		} else if i == -1 {
 			fmt.Printf("%-10s +", "------")
+		} else if mlrvals[i].IsVoid() {
+			fmt.Printf("%-10s |", "(empty)")
 		} else {
 			fmt.Printf("%-10s |", mlrvals[i].String())
 		}
 		for j := 0; j < n; j++ {
 			if i == -2 {
-				fmt.Printf(" %-10s", mlrvals[j].String())
+				if mlrvals[j].IsVoid() {
+					fmt.Printf("%-10s", "(empty)")
+				} else {
+					fmt.Printf(" %-10s", mlrvals[j].String())
+				}
 			} else if i == -1 {
 				fmt.Printf(" %-10s", "------")
 			} else {
 				sum := bifs.BIF_plus_binary(mlrvals[i], mlrvals[j])
-				fmt.Printf(" %-10s", sum.String())
+				if sum.IsVoid() {
+					fmt.Printf(" %-10s", "(empty)")
+				} else {
+					fmt.Printf(" %-10s", sum.String())
+				}
 			}
 		}
 		fmt.Println()
diff --git a/man/manpage.txt b/man/manpage.txt
index a4bb520495..43f2ed3865 100644
--- a/man/manpage.txt
+++ b/man/manpage.txt
@@ -3613,4 +3613,4 @@ MILLER(1)                                                            MILLER(1)
 
 
 
-                                  2023-08-26                         MILLER(1)
+                                  2023-08-27                         MILLER(1)
diff --git a/man/mlr.1 b/man/mlr.1
index 702d51667c..51320a9a88 100644
--- a/man/mlr.1
+++ b/man/mlr.1
@@ -2,12 +2,12 @@
 .\"     Title: mlr
 .\"    Author: [see the "AUTHOR" section]
 .\" Generator: ./mkman.rb
-.\"      Date: 2023-08-26
+.\"      Date: 2023-08-27
 .\"    Manual: \ \&
 .\"    Source: \ \&
 .\"  Language: English
 .\"
-.TH "MILLER" "1" "2023-08-26" "\ \&" "\ \&"
+.TH "MILLER" "1" "2023-08-27" "\ \&" "\ \&"
 .\" -----------------------------------------------------------------
 .\" * Portability definitions
 .\" ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
diff --git a/test/cases/dsl-absent-empty/0009/expout b/test/cases/dsl-absent-empty/0009/expout
index 0a9b64d06d..eaae444884 100644
--- a/test/cases/dsl-absent-empty/0009/expout
+++ b/test/cases/dsl-absent-empty/0009/expout
@@ -1,6 +1,6 @@
 x=1,y=2,z=3
-x=1,y=,z=
-x=,y=2,z=
+x=1,y=,z=1
+x=,y=2,z=2
 x=,y=,z=
 a=1,y=2,z=2
 a=1,y=
diff --git a/test/cases/dsl-absent-empty/0011/expout b/test/cases/dsl-absent-empty/0011/expout
index 46b9c18aa8..e13ed42e18 100644
--- a/test/cases/dsl-absent-empty/0011/expout
+++ b/test/cases/dsl-absent-empty/0011/expout
@@ -1,24 +1,24 @@
 s=2
 x=1,y=2
-s=
+s=2
 x=1,y=
-s=
+s=4
 x=,y=2
-s=
+s=4
 x=,y=
-s=
+s=6
 a=1,y=2
-s=
+s=6
 a=1,y=
-s=
+s=8
 a=,y=2
-s=
+s=8
 a=,y=
-s=
+s=8
 x=1,b=2
-s=
+s=8
 x=1,b=
-s=
+s=8
 x=,b=2
-s=
+s=8
 x=,b=
diff --git a/test/cases/dsl-absent-empty/0013/expout b/test/cases/dsl-absent-empty/0013/expout
index 35bd567868..68ab9a155d 100644
--- a/test/cases/dsl-absent-empty/0013/expout
+++ b/test/cases/dsl-absent-empty/0013/expout
@@ -1,6 +1,6 @@
 x=int,y=int,z=int
-x=int,y=empty,z=empty
-x=empty,y=int,z=empty
+x=int,y=empty,z=int
+x=empty,y=int,z=int
 x=empty,y=empty,z=empty
 a=1,y=int,z=int,x=absent
 a=1,y=empty,x=absent,z=absent
diff --git a/test/cases/dsl-absent-empty/0015/expout b/test/cases/dsl-absent-empty/0015/expout
index cfcebeab9c..bef580d780 100644
--- a/test/cases/dsl-absent-empty/0015/expout
+++ b/test/cases/dsl-absent-empty/0015/expout
@@ -1,12 +1,12 @@
 x=int,y=int,z=absent,s=int
-x=int,y=empty,z=absent,s=empty
-x=empty,y=int,z=absent,s=empty
-x=empty,y=empty,z=absent,s=empty
-a=1,y=int,x=absent,z=absent,s=empty
-a=1,y=empty,x=absent,z=absent,s=empty
-a=,y=int,x=absent,z=absent,s=empty
-a=,y=empty,x=absent,z=absent,s=empty
-x=int,b=2,y=absent,z=absent,s=empty
-x=int,b=,y=absent,z=absent,s=empty
-x=empty,b=2,y=absent,z=absent,s=empty
-x=empty,b=,y=absent,z=absent,s=empty
+x=int,y=empty,z=absent,s=int
+x=empty,y=int,z=absent,s=int
+x=empty,y=empty,z=absent,s=int
+a=1,y=int,x=absent,z=absent,s=int
+a=1,y=empty,x=absent,z=absent,s=int
+a=,y=int,x=absent,z=absent,s=int
+a=,y=empty,x=absent,z=absent,s=int
+x=int,b=2,y=absent,z=absent,s=int
+x=int,b=,y=absent,z=absent,s=int
+x=empty,b=2,y=absent,z=absent,s=int
+x=empty,b=,y=absent,z=absent,s=int
diff --git a/test/cases/dsl-absent-empty/0018/expout b/test/cases/dsl-absent-empty/0018/expout
index 5f0fd1b7cb..245f83dfe6 100644
--- a/test/cases/dsl-absent-empty/0018/expout
+++ b/test/cases/dsl-absent-empty/0018/expout
@@ -1,4 +1,4 @@
 x=1	ostype=absent	xtype=int	nstype=int	nsum=1
-x=	osum=1	ostype=int	xtype=empty	nstype=empty	nsum=
-x=7	osum=	ostype=empty	xtype=int	nstype=empty	nsum=
-sum=
+x=	osum=1	ostype=int	xtype=empty	nstype=int	nsum=1
+x=7	osum=1	ostype=int	xtype=int	nstype=int	nsum=8
+sum=8
diff --git a/test/cases/dsl-absent-empty/0019/expout b/test/cases/dsl-absent-empty/0019/expout
index 5f0fd1b7cb..245f83dfe6 100644
--- a/test/cases/dsl-absent-empty/0019/expout
+++ b/test/cases/dsl-absent-empty/0019/expout
@@ -1,4 +1,4 @@
 x=1	ostype=absent	xtype=int	nstype=int	nsum=1
-x=	osum=1	ostype=int	xtype=empty	nstype=empty	nsum=
-x=7	osum=	ostype=empty	xtype=int	nstype=empty	nsum=
-sum=
+x=	osum=1	ostype=int	xtype=empty	nstype=int	nsum=1
+x=7	osum=1	ostype=int	xtype=int	nstype=int	nsum=8
+sum=8
diff --git a/test/cases/dsl-absent-empty/0024/expout b/test/cases/dsl-absent-empty/0024/expout
index e65c673b38..d9c7706251 100644
--- a/test/cases/dsl-absent-empty/0024/expout
+++ b/test/cases/dsl-absent-empty/0024/expout
@@ -1,4 +1,4 @@
 x=1	xtype=int	sum=11	stype=int
-x=	xtype=empty	sum=	stype=empty
+x=	xtype=empty	sum=10	stype=int
 y=	xtype=absent	sum=10	stype=int
 x=7	xtype=int	sum=17	stype=int
diff --git a/test/cases/dsl-absent-empty/0025/expout b/test/cases/dsl-absent-empty/0025/expout
index 1f25de3ba8..1c914b16e0 100644
--- a/test/cases/dsl-absent-empty/0025/expout
+++ b/test/cases/dsl-absent-empty/0025/expout
@@ -1,4 +1,4 @@
 x=1	xtype=int	sum=11	stype=int
-x=	xtype=empty	sum=	stype=empty
+x=	xtype=empty	sum=10	stype=int
 y=	xtype=absent	sum=999	stype=int
 x=7	xtype=int	sum=17	stype=int
diff --git a/test/cases/dsl-null-empty-handling/0005/expout b/test/cases/dsl-null-empty-handling/0005/expout
index 578780bf4c..ffaf4cbd05 100644
--- a/test/cases/dsl-null-empty-handling/0005/expout
+++ b/test/cases/dsl-null-empty-handling/0005/expout
@@ -1,3 +1,3 @@
 x=1,y=2,s=hello,z=3
-x=1,y=,s=,z=
+x=1,y=,s=,z=1
 x=,y=,s=hurrah,z=
diff --git a/test/cases/dsl-null-empty-handling/0018/expout b/test/cases/dsl-null-empty-handling/0018/expout
index 533c22c7c9..16af929a2b 100644
--- a/test/cases/dsl-null-empty-handling/0018/expout
+++ b/test/cases/dsl-null-empty-handling/0018/expout
@@ -1,6 +1,6 @@
 x=1	y=2	xy=3	sy=2	xt=1
-x=1	y=	xy=	xt=1
-x=	y=2	xy=	sy=2
+x=1	y=	xy=1	xt=1
+x=	y=2	xy=2	sy=2
 x=	y=	xy=
 a=1	y=2	xy=2	sy=2
 a=1	y=
diff --git a/test/cases/dsl-null-empty-handling/0019/expout b/test/cases/dsl-null-empty-handling/0019/expout
index 12833dc938..8f1ee88802 100644
--- a/test/cases/dsl-null-empty-handling/0019/expout
+++ b/test/cases/dsl-null-empty-handling/0019/expout
@@ -1,11 +1,11 @@
 x=1	y=2	xy=3	sy=5	xt=1	st=3
-x=1	y=	xy=	sy=	xt=1	st=3
-x=	y=2	xy=	sy=5	st=3
-x=	y=	xy=	sy=	st=3
+x=1	y=	xy=1	sy=3	xt=1	st=3
+x=	y=2	xy=2	sy=5	st=3
+x=	y=	xy=	sy=3	st=3
 a=1	y=2	xy=2	sy=5	st=3
-a=1	y=	sy=	st=3
+a=1	y=	sy=3	st=3
 a=	y=2	xy=2	sy=5	st=3
-a=	y=	sy=	st=3
+a=	y=	sy=3	st=3
 x=1	b=2	xy=1	sy=3	xt=1	st=3
 x=1	b=	xy=1	sy=3	xt=1	st=3
 x=	b=2	sy=3	st=3
diff --git a/test/cases/dsl-null-empty-handling/0020/expout b/test/cases/dsl-null-empty-handling/0020/expout
index bac8fc502c..40c4af232d 100644
--- a/test/cases/dsl-null-empty-handling/0020/expout
+++ b/test/cases/dsl-null-empty-handling/0020/expout
@@ -1,12 +1,12 @@
 x=1	y=2	xy=3	sy=2	xt=5	st=4
-x=1	y=	xy=	xt=5	st=4
-x=	y=2	xy=	sy=2	xt=	st=4
-x=	y=	xy=	xt=	st=4
+x=1	y=	xy=1	xt=5	st=4
+x=	y=2	xy=2	sy=2	xt=4	st=4
+x=	y=	xy=	xt=4	st=4
 a=1	y=2	xy=2	sy=2	xt=4	st=4
 a=1	y=	xt=4	st=4
 a=	y=2	xy=2	sy=2	xt=4	st=4
 a=	y=	xt=4	st=4
 x=1	b=2	xy=1	xt=5	st=4
 x=1	b=	xy=1	xt=5	st=4
-x=	b=2	xt=	st=4
-x=	b=	xt=	st=4
+x=	b=2	xt=4	st=4
+x=	b=	xt=4	st=4
diff --git a/test/cases/dsl-null-empty-handling/0021/expout b/test/cases/dsl-null-empty-handling/0021/expout
index a57679797d..76d169e421 100644
--- a/test/cases/dsl-null-empty-handling/0021/expout
+++ b/test/cases/dsl-null-empty-handling/0021/expout
@@ -1,12 +1,12 @@
 x=1	y=2	xy=3	sy=5	xt=5	st=7
-x=1	y=	xy=	sy=	xt=5	st=7
-x=	y=2	xy=	sy=5	xt=	st=7
-x=	y=	xy=	sy=	xt=	st=7
+x=1	y=	xy=1	sy=3	xt=5	st=7
+x=	y=2	xy=2	sy=5	xt=4	st=7
+x=	y=	xy=	sy=3	xt=4	st=7
 a=1	y=2	xy=2	sy=5	xt=4	st=7
-a=1	y=	sy=	xt=4	st=7
+a=1	y=	sy=3	xt=4	st=7
 a=	y=2	xy=2	sy=5	xt=4	st=7
-a=	y=	sy=	xt=4	st=7
+a=	y=	sy=3	xt=4	st=7
 x=1	b=2	xy=1	sy=3	xt=5	st=7
 x=1	b=	xy=1	sy=3	xt=5	st=7
-x=	b=2	sy=3	xt=	st=7
-x=	b=	sy=3	xt=	st=7
+x=	b=2	sy=3	xt=4	st=7
+x=	b=	sy=3	xt=4	st=7
diff --git a/test/cases/dsl-null-empty-handling/0022/expout b/test/cases/dsl-null-empty-handling/0022/expout
index b8d0e6ef30..2ec0bac9c6 100644
--- a/test/cases/dsl-null-empty-handling/0022/expout
+++ b/test/cases/dsl-null-empty-handling/0022/expout
@@ -1,6 +1,6 @@
 x=1	y=2	xy=-1	sy=2	xt=1
-x=1	y=	xy=	xt=1
-x=	y=2	xy=	sy=2
+x=1	y=	xy=1	xt=1
+x=	y=2	xy=-2	sy=2
 x=	y=	xy=
 a=1	y=2	xy=2	sy=2
 a=1	y=
diff --git a/test/cases/dsl-null-empty-handling/0023/expout b/test/cases/dsl-null-empty-handling/0023/expout
index 60236a2bfe..5490ccccde 100644
--- a/test/cases/dsl-null-empty-handling/0023/expout
+++ b/test/cases/dsl-null-empty-handling/0023/expout
@@ -1,11 +1,11 @@
 x=1	y=2	xy=-1	sy=1	xt=1	st=3
-x=1	y=	xy=	sy=	xt=1	st=3
-x=	y=2	xy=	sy=1	st=3
-x=	y=	xy=	sy=	st=3
+x=1	y=	xy=1	sy=3	xt=1	st=3
+x=	y=2	xy=-2	sy=1	st=3
+x=	y=	xy=	sy=3	st=3
 a=1	y=2	xy=2	sy=1	st=3
-a=1	y=	sy=	st=3
+a=1	y=	sy=3	st=3
 a=	y=2	xy=2	sy=1	st=3
-a=	y=	sy=	st=3
+a=	y=	sy=3	st=3
 x=1	b=2	xy=1	sy=3	xt=1	st=3
 x=1	b=	xy=1	sy=3	xt=1	st=3
 x=	b=2	sy=3	st=3
diff --git a/test/cases/dsl-null-empty-handling/0024/expout b/test/cases/dsl-null-empty-handling/0024/expout
index decc36a948..df8e604895 100644
--- a/test/cases/dsl-null-empty-handling/0024/expout
+++ b/test/cases/dsl-null-empty-handling/0024/expout
@@ -1,12 +1,12 @@
 x=1	y=2	xy=-1	sy=2	xt=-3	st=4
-x=1	y=	xy=	xt=-3	st=4
-x=	y=2	xy=	sy=2	xt=	st=4
-x=	y=	xy=	xt=	st=4
+x=1	y=	xy=1	xt=-3	st=4
+x=	y=2	xy=-2	sy=2	xt=-4	st=4
+x=	y=	xy=	xt=-4	st=4
 a=1	y=2	xy=2	sy=2	xt=4	st=4
 a=1	y=	xt=4	st=4
 a=	y=2	xy=2	sy=2	xt=4	st=4
 a=	y=	xt=4	st=4
 x=1	b=2	xy=1	xt=-3	st=4
 x=1	b=	xy=1	xt=-3	st=4
-x=	b=2	xt=	st=4
-x=	b=	xt=	st=4
+x=	b=2	xt=-4	st=4
+x=	b=	xt=-4	st=4
diff --git a/test/cases/dsl-null-empty-handling/0025/expout b/test/cases/dsl-null-empty-handling/0025/expout
index c19e412d0b..ab04b574e9 100644
--- a/test/cases/dsl-null-empty-handling/0025/expout
+++ b/test/cases/dsl-null-empty-handling/0025/expout
@@ -1,12 +1,12 @@
 x=1	y=2	xy=-1	sy=1	xt=-3	st=-1
-x=1	y=	xy=	sy=	xt=-3	st=-1
-x=	y=2	xy=	sy=1	xt=	st=-1
-x=	y=	xy=	sy=	xt=	st=-1
+x=1	y=	xy=1	sy=3	xt=-3	st=-1
+x=	y=2	xy=-2	sy=1	xt=-4	st=-1
+x=	y=	xy=	sy=3	xt=-4	st=-1
 a=1	y=2	xy=2	sy=1	xt=4	st=-1
-a=1	y=	sy=	xt=4	st=-1
+a=1	y=	sy=3	xt=4	st=-1
 a=	y=2	xy=2	sy=1	xt=4	st=-1
-a=	y=	sy=	xt=4	st=-1
+a=	y=	sy=3	xt=4	st=-1
 x=1	b=2	xy=1	sy=3	xt=-3	st=-1
 x=1	b=	xy=1	sy=3	xt=-3	st=-1
-x=	b=2	sy=3	xt=	st=-1
-x=	b=	sy=3	xt=	st=-1
+x=	b=2	sy=3	xt=-4	st=-1
+x=	b=	sy=3	xt=-4	st=-1
diff --git a/test/cases/dsl-null-empty-handling/0026/expout b/test/cases/dsl-null-empty-handling/0026/expout
index 5ed9ed8076..b96c6e6612 100644
--- a/test/cases/dsl-null-empty-handling/0026/expout
+++ b/test/cases/dsl-null-empty-handling/0026/expout
@@ -1,6 +1,6 @@
 x=1	y=2	xy=2	sy=2	xt=1
-x=1	y=	xy=	xt=1
-x=	y=2	xy=	sy=2
+x=1	y=	xy=1	xt=1
+x=	y=2	xy=2	sy=2
 x=	y=	xy=
 a=1	y=2	xy=2	sy=2
 a=1	y=
diff --git a/test/cases/dsl-null-empty-handling/0027/expout b/test/cases/dsl-null-empty-handling/0027/expout
index 70c01ab4bb..8b51ffa510 100644
--- a/test/cases/dsl-null-empty-handling/0027/expout
+++ b/test/cases/dsl-null-empty-handling/0027/expout
@@ -1,11 +1,11 @@
 x=1	y=2	xy=2	sy=6	xt=1	st=3
-x=1	y=	xy=	sy=	xt=1	st=3
-x=	y=2	xy=	sy=6	st=3
-x=	y=	xy=	sy=	st=3
+x=1	y=	xy=1	sy=3	xt=1	st=3
+x=	y=2	xy=2	sy=6	st=3
+x=	y=	xy=	sy=3	st=3
 a=1	y=2	xy=2	sy=6	st=3
-a=1	y=	sy=	st=3
+a=1	y=	sy=3	st=3
 a=	y=2	xy=2	sy=6	st=3
-a=	y=	sy=	st=3
+a=	y=	sy=3	st=3
 x=1	b=2	xy=1	sy=3	xt=1	st=3
 x=1	b=	xy=1	sy=3	xt=1	st=3
 x=	b=2	sy=3	st=3
diff --git a/test/cases/dsl-null-empty-handling/0028/expout b/test/cases/dsl-null-empty-handling/0028/expout
index 862ac3fc46..ccb1e4fa7b 100644
--- a/test/cases/dsl-null-empty-handling/0028/expout
+++ b/test/cases/dsl-null-empty-handling/0028/expout
@@ -1,12 +1,12 @@
 x=1	y=2	xy=2	sy=2	xt=4	st=4
-x=1	y=	xy=	xt=4	st=4
-x=	y=2	xy=	sy=2	xt=	st=4
-x=	y=	xy=	xt=	st=4
+x=1	y=	xy=1	xt=4	st=4
+x=	y=2	xy=2	sy=2	xt=4	st=4
+x=	y=	xy=	xt=4	st=4
 a=1	y=2	xy=2	sy=2	xt=4	st=4
 a=1	y=	xt=4	st=4
 a=	y=2	xy=2	sy=2	xt=4	st=4
 a=	y=	xt=4	st=4
 x=1	b=2	xy=1	xt=4	st=4
 x=1	b=	xy=1	xt=4	st=4
-x=	b=2	xt=	st=4
-x=	b=	xt=	st=4
+x=	b=2	xt=4	st=4
+x=	b=	xt=4	st=4
diff --git a/test/cases/dsl-null-empty-handling/0029/expout b/test/cases/dsl-null-empty-handling/0029/expout
index c6d1029429..e5309caf0c 100644
--- a/test/cases/dsl-null-empty-handling/0029/expout
+++ b/test/cases/dsl-null-empty-handling/0029/expout
@@ -1,12 +1,12 @@
 x=1	y=2	xy=2	sy=6	xt=4	st=12
-x=1	y=	xy=	sy=	xt=4	st=12
-x=	y=2	xy=	sy=6	xt=	st=12
-x=	y=	xy=	sy=	xt=	st=12
+x=1	y=	xy=1	sy=3	xt=4	st=12
+x=	y=2	xy=2	sy=6	xt=4	st=12
+x=	y=	xy=	sy=3	xt=4	st=12
 a=1	y=2	xy=2	sy=6	xt=4	st=12
-a=1	y=	sy=	xt=4	st=12
+a=1	y=	sy=3	xt=4	st=12
 a=	y=2	xy=2	sy=6	xt=4	st=12
-a=	y=	sy=	xt=4	st=12
+a=	y=	sy=3	xt=4	st=12
 x=1	b=2	xy=1	sy=3	xt=4	st=12
 x=1	b=	xy=1	sy=3	xt=4	st=12
-x=	b=2	sy=3	xt=	st=12
-x=	b=	sy=3	xt=	st=12
+x=	b=2	sy=3	xt=4	st=12
+x=	b=	sy=3	xt=4	st=12