Operators Support
=================

Standard Python Operators
-------------------------

+----------------+------------------+-------------+----------------------+---------------------+------------------------+---------------------+--------------------------+------------------------+--------------------+---------------------------+----------------------+-----------------------+------------------------+-----------------------+-------------------------+------------------------------------+
| operator       | description      | hgraph name | TS[int] TS[float]    | TS[bool]            | TS[str]                | TS[enum]            | TS[date,datetime]        | TS[timedelta]          | TS[CompoundScalar] | TS[tuple]                 | TS[set]              | TS[dict]              | TSS[T]                 | TSL[TST, S]           | TSB[Schema]             | TSD[K, V]                          |
+================+==================+=============+======================+=====================+========================+=====================+==========================+========================+====================+===========================+======================+=======================+========================+=======================+=========================+====================================+
| a + b          | addition         | add\_       | ✅                   | ❌                  | ✅                     | ❌                  | ✅      b is timedelta   | ✅                     | ❌                 | ✅      concat tuples     | ❌                   | ❌                    | ❌                     | ✅      item-wise     | ✅      item-wise       | ❌                                 |
+----------------+------------------+-------------+----------------------+---------------------+------------------------+---------------------+--------------------------+------------------------+--------------------+---------------------------+----------------------+-----------------------+------------------------+-----------------------+-------------------------+------------------------------------+
| a - b          | subtraction      | sub\_       | ✅                   | ❌                  | ❌                     | ❌                  | ✅                       | ✅                     | ❌                 | ❌                        | ✅      set diff     | ✅      diff          | ✅      set difference | ✅      item-wise     | ✅      item-wise       | ✅      diff                       |
+----------------+------------------+-------------+----------------------+---------------------+------------------------+---------------------+--------------------------+------------------------+--------------------+---------------------------+----------------------+-----------------------+------------------------+-----------------------+-------------------------+------------------------------------+
| a \* b         | multiplication   | mul\_       | ✅                   | ❌                  | ✅      b is int       | ❌                  | ❌                       | ✅      b is int/float | ❌                 | ✅      b is int          | ❌                   | ❌                    | ❌                     | ✅      item-wise     | ✅      item-wise       | ❌                                 |
+----------------+------------------+-------------+----------------------+---------------------+------------------------+---------------------+--------------------------+------------------------+--------------------+---------------------------+----------------------+-----------------------+------------------------+-----------------------+-------------------------+------------------------------------+
| a / b          | true division    | div\_       | ✅                   | ❌                  | ❌                     | ❌                  | ❌                       | ✅      b is int/float | ❌                 | ❌                        | ❌                   | ❌                    | ❌                     | ✅      item-wise     | ✅      item-wise       | ❌                                 |
+----------------+------------------+-------------+----------------------+---------------------+------------------------+---------------------+--------------------------+------------------------+--------------------+---------------------------+----------------------+-----------------------+------------------------+-----------------------+-------------------------+------------------------------------+
| a // b         | floor division   | floordiv\_  | ✅                   | ❌                  | ❌                     | ❌                  | ❌                       | ❌                     | ❌                 | ❌                        | ❌                   | ❌                    | ❌                     | ✅      item-wise     | ✅      item-wise       | ❌                                 |
+----------------+------------------+-------------+----------------------+---------------------+------------------------+---------------------+--------------------------+------------------------+--------------------+---------------------------+----------------------+-----------------------+------------------------+-----------------------+-------------------------+------------------------------------+
| a % b          | modulo           | mod\_       | ✅                   | ❌                  | ❌                     | ❌                  | ❌                       | ❌                     | ❌                 | ❌                        | ❌                   | ❌                    | ❌                     | ✅      item-wise     | ✅      item-wise       | ❌                                 |
+----------------+------------------+-------------+----------------------+---------------------+------------------------+---------------------+--------------------------+------------------------+--------------------+---------------------------+----------------------+-----------------------+------------------------+-----------------------+-------------------------+------------------------------------+
| divmod(a, b)   | divmod           | divmod\_    | ✅                   | ❌                  | ❌                     | ❌                  | ❌                       | ❌                     | ❌                 | ❌                        | ❌                   | ❌                    | ❌                     | ❌                    | ❌                      | ❌                                 |
+----------------+------------------+-------------+----------------------+---------------------+------------------------+---------------------+--------------------------+------------------------+--------------------+---------------------------+----------------------+-----------------------+------------------------+-----------------------+-------------------------+------------------------------------+
| a \*\* b       | pow              | pow\_       | ✅                   | ❌                  | ❌                     | ❌                  | ❌                       | ❌                     | ❌                 | ❌                        | ❌                   | ❌                    | ❌                     | ✅      item-wise     | ✅      item-wise       | ❌                                 |
+----------------+------------------+-------------+----------------------+---------------------+------------------------+---------------------+--------------------------+------------------------+--------------------+---------------------------+----------------------+-----------------------+------------------------+-----------------------+-------------------------+------------------------------------+
| a << b         | left shift       | lshift\_    | ✅                   | ❌                  | ❌                     | ❌                  | ❌                       | ❌                     | ❌                 | ❓ shift items left       | ❌                   | ❌                    | ❌                     | ✅      item-wise     | ✅      item-wise       | ❌                                 |
+----------------+------------------+-------------+----------------------+---------------------+------------------------+---------------------+--------------------------+------------------------+--------------------+---------------------------+----------------------+-----------------------+------------------------+-----------------------+-------------------------+------------------------------------+
| a >> b         | right shift      | rshift\_    | ✅                   | ❌                  | ❌                     | ❌                  | ❌                       | ❌                     | ❌                 | ❌                        | ❌                   | ❌                    | ❌                     | ✅      item-wise     | ✅      item-wise       | ❌                                 |
+----------------+------------------+-------------+----------------------+---------------------+------------------------+---------------------+--------------------------+------------------------+--------------------+---------------------------+----------------------+-----------------------+------------------------+-----------------------+-------------------------+------------------------------------+
| a & b          | bitwise and      | bit_and     | ✅                   | ✅                  | ❌                     | ❌                  | ❌                       | ❌                     | ❌                 | ❌                        | ✅      intersection | ❓ intersection       | ✅      intersection   | ✅      item-wise     | ✅      item-wise       | ✅      intersection               |
+----------------+------------------+-------------+----------------------+---------------------+------------------------+---------------------+--------------------------+------------------------+--------------------+---------------------------+----------------------+-----------------------+------------------------+-----------------------+-------------------------+------------------------------------+
| a | b          | bitwise or       | bit_or      | ✅                   | ✅                  | ❌                     | ❌                  | ❌                       | ❌                     | ❌                 | ❌                        | ✅      union        | ❓ union              | ✅      union          | ✅      item-wise     | ✅      item-wise       | ✅      merge                      |
+----------------+------------------+-------------+----------------------+---------------------+------------------------+---------------------+--------------------------+------------------------+--------------------+---------------------------+----------------------+-----------------------+------------------------+-----------------------+-------------------------+------------------------------------+
| a ^ b          | bitwise xor      | bit_xor     | ✅                   | ✅                  | ❌                     | ❌                  | ❌                       | ❌                     | ❌                 | ❌                        | ✅      symm. diff   | ❓ symm. diff         | ✅      symm. diff     | ✅      item-wise     | ✅      item-wise       | ✅      symm. diff                 |
+----------------+------------------+-------------+----------------------+---------------------+------------------------+---------------------+--------------------------+------------------------+--------------------+---------------------------+----------------------+-----------------------+------------------------+-----------------------+-------------------------+------------------------------------+
| a == b         | equal            | eq\_        | ✅                   | ✅                  | ✅                     | ✅                  | ✅                       | ✅                     | ✅                 | ✅                        | ✅                   | ✅                    | ✅                     | ✅      single bool   | ✅      single bool     | ✅                                 |
+----------------+------------------+-------------+----------------------+---------------------+------------------------+---------------------+--------------------------+------------------------+--------------------+---------------------------+----------------------+-----------------------+------------------------+-----------------------+-------------------------+------------------------------------+
| a != b         | not equal        | ne\_        | ✅                   | ✅                  | ✅                     | ✅                  | ✅                       | ✅                     | ✅                 | ✅                        | ✅                   | ✅                    | ✅                     | ✅      single bool   | ✅      single bool     | ✅                                 |
+----------------+------------------+-------------+----------------------+---------------------+------------------------+---------------------+--------------------------+------------------------+--------------------+---------------------------+----------------------+-----------------------+------------------------+-----------------------+-------------------------+------------------------------------+
| a < b          | less             | lt\_        | ✅                   | ✅                  | ✅                     | ✅      value       | ✅                       | ✅                     | ❌                 | ✅                        | ✅                   | ❌                    | ❌                     | ❌                    | ❌                      | ❌                                 |
+----------------+------------------+-------------+----------------------+---------------------+------------------------+---------------------+--------------------------+------------------------+--------------------+---------------------------+----------------------+-----------------------+------------------------+-----------------------+-------------------------+------------------------------------+
| a <= b         | less or equal    | le\_        | ✅                   | ✅                  | ✅                     | ✅      value       | ✅                       | ✅                     | ❌                 | ✅                        | ✅                   | ❌                    | ❌                     | ❌                    | ❌                      | ❌                                 |
+----------------+------------------+-------------+----------------------+---------------------+------------------------+---------------------+--------------------------+------------------------+--------------------+---------------------------+----------------------+-----------------------+------------------------+-----------------------+-------------------------+------------------------------------+
| a > b          | greater          | gt\_        | ✅                   | ✅                  | ✅                     | ✅      value       | ✅                       | ✅                     | ❌                 | ✅                        | ✅                   | ❌                    | ❌                     | ❌                    | ❌                      | ❌                                 |
+----------------+------------------+-------------+----------------------+---------------------+------------------------+---------------------+--------------------------+------------------------+--------------------+---------------------------+----------------------+-----------------------+------------------------+-----------------------+-------------------------+------------------------------------+
| a >= b         | greater or equal | ge\_        | ✅                   | ✅                  | ✅                     | ✅      value       | ✅                       | ✅                     | ❌                 | ✅                        | ✅                   | ❌                    | ❌                     | ❌                    | ❌                      | ❌                                 |
+----------------+------------------+-------------+----------------------+---------------------+------------------------+---------------------+--------------------------+------------------------+--------------------+---------------------------+----------------------+-----------------------+------------------------+-----------------------+-------------------------+------------------------------------+
| -a             | unary negative   | neg\_       | ✅                   | ❌                  | ❌                     | ❌                  | ❌                       | ✅                     | ❌                 | ❌                        | ❌                   | ❌                    | ❌                     | ✅      item-wise     | ✅      item-wise       | ❌                                 |
+----------------+------------------+-------------+----------------------+---------------------+------------------------+---------------------+--------------------------+------------------------+--------------------+---------------------------+----------------------+-----------------------+------------------------+-----------------------+-------------------------+------------------------------------+
| +a             | unary positive   | pos\_       | ✅                   | ❌                  | ❌                     | ❌                  | ❌                       | ✅                     | ❌                 | ❌                        | ❌                   | ❌                    | ❌                     | ✅      item-wise     | ✅      item-wise       | ❌                                 |
+----------------+------------------+-------------+----------------------+---------------------+------------------------+---------------------+--------------------------+------------------------+--------------------+---------------------------+----------------------+-----------------------+------------------------+-----------------------+-------------------------+------------------------------------+
| ~a             | inversion        | invert\_    | ✅                   | ✅                  | ❌                     | ❌                  | ❌                       | ❌                     | ❌                 | ❌                        | ❌                   | ❌                    | ❌                     | ✅      item-wise     | ✅      item-wise       | ❌                                 |
+----------------+------------------+-------------+----------------------+---------------------+------------------------+---------------------+--------------------------+------------------------+--------------------+---------------------------+----------------------+-----------------------+------------------------+-----------------------+-------------------------+------------------------------------+
| abs(a)         | abs              | abs\_       | ✅                   | ❌                  | ❌                     | ❌                  | ❌                       | ✅                     | ❌                 | ❌                        | ❌                   | ❌                    | ❌                     | ✅      item-wise     | ✅      item-wise       | ❌                                 |
+----------------+------------------+-------------+----------------------+---------------------+------------------------+---------------------+--------------------------+------------------------+--------------------+---------------------------+----------------------+-----------------------+------------------------+-----------------------+-------------------------+------------------------------------+
| a[b]           | getitem          | getitem\_   | ❌                   | ❌                  | ❌                     | ❌                  | ❌                       | ❌                     | ❌                 | ✅                        | ❌                   | ✅                    | ❌                     | ✅      item by index | ✅      item by index   | ✅                                 |
+----------------+------------------+-------------+----------------------+---------------------+------------------------+---------------------+--------------------------+------------------------+--------------------+---------------------------+----------------------+-----------------------+------------------------+-----------------------+-------------------------+------------------------------------+
| a.b            | getattr          | getattr\_   | ❌                   | ❌                  | ❌                     | ❌                  | ❌                       | ❌                     | ✅                 | ❌                        | ❌                   | ❌                    | ❌                     | ❌                    | ✅      item by name    | ✅      if values is a schema type |
+----------------+------------------+-------------+----------------------+---------------------+------------------------+---------------------+--------------------------+------------------------+--------------------+---------------------------+----------------------+-----------------------+------------------------+-----------------------+-------------------------+------------------------------------+
| &nbsp;         |                  |             |                      |                     |                        |                     |                          |                        |                    |                           |                      |                       |                        |                       |                         |                                    |
+----------------+------------------+-------------+----------------------+---------------------+------------------------+---------------------+--------------------------+------------------------+--------------------+---------------------------+----------------------+-----------------------+------------------------+-----------------------+-------------------------+------------------------------------+
| not\_(a)       | not              | not\_       | ✅                   | ✅                  | ✅                     | ❌                  | ✅                       | ✅                     | ❌                 | ✅                        | ✅                   | ✅                    | ✅                     | ❌                    | ❌                      | ✅                                 |
+----------------+------------------+-------------+----------------------+---------------------+------------------------+---------------------+--------------------------+------------------------+--------------------+---------------------------+----------------------+-----------------------+------------------------+-----------------------+-------------------------+------------------------------------+
| and\_(a, b)    | and              | and\_       | ✅                   | ✅                  | ✅                     | ❌                  | ✅                       | ✅                     | ❌                 | ✅                        | ✅                   | ✅                    | ✅                     | ❌                    | ❌                      | ❌                                 |
+----------------+------------------+-------------+----------------------+---------------------+------------------------+---------------------+--------------------------+------------------------+--------------------+---------------------------+----------------------+-----------------------+------------------------+-----------------------+-------------------------+------------------------------------+
| or\_(a, b)     | or               | or\_        | ✅                   | ✅                  | ✅                     | ❌                  | ✅                       | ✅                     | ❌                 | ✅                        | ✅                   | ✅                    | ✅                     | ❌                    | ❌                      | ❌                                 |
+----------------+------------------+-------------+----------------------+---------------------+------------------------+---------------------+--------------------------+------------------------+--------------------+---------------------------+----------------------+-----------------------+------------------------+-----------------------+-------------------------+------------------------------------+
| len\_(a)       | len              | len\_       | ❌                   | ❌                  | ✅                     | ❌                  | ❌                       | ❌                     | ❌                 | ✅                        | ✅                   | ✅                    | ✅                     | ✅                    | ✅      number of items | ✅                                 |
+----------------+------------------+-------------+----------------------+---------------------+------------------------+---------------------+--------------------------+------------------------+--------------------+---------------------------+----------------------+-----------------------+------------------------+-----------------------+-------------------------+------------------------------------+
| &nbsp;         |                  |             |                      |                     |                        |                     |                          |                        |                    |                           |                      |                       |                        |                       |                         |                                    |
+----------------+------------------+-------------+----------------------+---------------------+------------------------+---------------------+--------------------------+------------------------+--------------------+---------------------------+----------------------+-----------------------+------------------------+-----------------------+-------------------------+------------------------------------+
| min\_(\*args)  | multi-arg min    | min\_       | ✅                   | ✅                  | ✅                     | ✅      value       | ✅                       | ✅                     | ❌                 | ❌                        | ❌                   | ❌                    | ❌                     | ✅      item-wise     | ✅      item-wise       | ❌                                 |
+----------------+------------------+-------------+----------------------+---------------------+------------------------+---------------------+--------------------------+------------------------+--------------------+---------------------------+----------------------+-----------------------+------------------------+-----------------------+-------------------------+------------------------------------+
| max\_(\*args)  | multi-arg max    | max\_       | ✅                   | ✅                  | ✅                     | ✅      value       | ✅                       | ✅                     | ❌                 | ❌                        | ❌                   | ❌                    | ❌                     | ✅      item-wise     | ✅      item-wise       | ❌                                 |
+----------------+------------------+-------------+----------------------+---------------------+------------------------+---------------------+--------------------------+------------------------+--------------------+---------------------------+----------------------+-----------------------+------------------------+-----------------------+-------------------------+------------------------------------+
| sum\_(\*args)  | multi-arg sum    | sum\_       | ✅                   | ✅                  | ✅                     | ❌                  | ❌                       | ✅                     | ❌                 | ✅                        | ❌                   | ❌                    | ❌                     | ✅      item-wise     | ✅      item-wise       | ❌                                 |
+----------------+------------------+-------------+----------------------+---------------------+------------------------+---------------------+--------------------------+------------------------+--------------------+---------------------------+----------------------+-----------------------+------------------------+-----------------------+-------------------------+------------------------------------+
| min\_(a)       | unary min        | min\_       | ✅      running min  | ✅      running min | ✅      running min    | ✅      running min | ✅      running min      | ✅      running min    | ❌                 | ✅      min item          | ✅      min item     | ✅      min value     | ✅      min item       | ✅      min item      | ✅      min item        | ✅      min value                  |
+----------------+------------------+-------------+----------------------+---------------------+------------------------+---------------------+--------------------------+------------------------+--------------------+---------------------------+----------------------+-----------------------+------------------------+-----------------------+-------------------------+------------------------------------+
| max\_(a)       | unary max        | max\_       | ✅      running max  | ✅      running max | ✅      running max    | ✅      running max | ✅      running max      | ✅      running max    | ❌                 | ✅      max item          | ✅      max item     | ✅      max value     | ✅      max item       | ✅      max item      | ✅      max item        | ✅      max value                  |
+----------------+------------------+-------------+----------------------+---------------------+------------------------+---------------------+--------------------------+------------------------+--------------------+---------------------------+----------------------+-----------------------+------------------------+-----------------------+-------------------------+------------------------------------+
| sum\_(a)       | unary sum        | sum\_       | ✅      running sum  | ✅      running sum | ✅      running sum    | ❌                  | ❌                       | ✅      running sum    | ❌                 | ✅      sum items         | ✅      sum items    | ✅      sum values    | ✅      sum items      | ✅      sum items     | ✅      sum items       | ✅      sum value                  |
+----------------+------------------+-------------+----------------------+---------------------+------------------------+---------------------+--------------------------+------------------------+--------------------+---------------------------+----------------------+-----------------------+------------------------+-----------------------+-------------------------+------------------------------------+
| &nbsp;         |                  |             |                      |                     |                        |                     |                          |                        |                    |                           |                      |                       |                        |                       |                         |                                    |
+----------------+------------------+-------------+----------------------+---------------------+------------------------+---------------------+--------------------------+------------------------+--------------------+---------------------------+----------------------+-----------------------+------------------------+-----------------------+-------------------------+------------------------------------+
| contains(a, b) | b in a           | contains\_  | ❌                   | ❌                  | ✅      substring find | ❌                  | ❌                       | ❌                     | ❌                 | ✅                        | ✅                   | ✅      key find      | ✅                     | ❌                    | ❌                      | ✅                                 |
+----------------+------------------+-------------+----------------------+---------------------+------------------------+---------------------+--------------------------+------------------------+--------------------+---------------------------+----------------------+-----------------------+------------------------+-----------------------+-------------------------+------------------------------------+
| is_empty(a)    | empty test       | is_empty    | ❌                   | ❌                  | ✅                     | ❌                  | ❌                       | ❌                     | ❌                 | ✅                        | ✅                   | ✅                    | ✅                     | ❌                    | ❌                      | ✅                                 |
+----------------+------------------+-------------+----------------------+---------------------+------------------------+---------------------+--------------------------+------------------------+--------------------+---------------------------+----------------------+-----------------------+------------------------+-----------------------+-------------------------+------------------------------------+
| type\_(a)      | type             | type\_      | ✅      int or float | ✅      bool        | ✅      str            | ✅      enum        | ✅      date or datetime | ✅      timedelta      | ✅                 | ✅      tuple[...]        | ✅      set[...]     | ✅      set[...]      | ❌                     | ❌                    | ❌                      | ❌                                 |
+----------------+------------------+-------------+----------------------+---------------------+------------------------+---------------------+--------------------------+------------------------+--------------------+---------------------------+----------------------+-----------------------+------------------------+-----------------------+-------------------------+------------------------------------+
| str\_(a)       | str              | str\_       | ✅                   | ✅                  | ✅      no-op          | ✅                  | ✅                       | ✅                     | ✅                 | ✅                        | ✅                   | ✅                    | ✅                     | ✅                    | ✅                      | ✅                                 |
+----------------+------------------+-------------+----------------------+---------------------+------------------------+---------------------+--------------------------+------------------------+--------------------+---------------------------+----------------------+-----------------------+------------------------+-----------------------+-------------------------+------------------------------------+
| &nbsp;         |                  |             |                      |                     |                        |                     |                          |                        |                    |                           |                      |                       |                        |                       |                         |                                    |
+----------------+------------------+-------------+----------------------+---------------------+------------------------+---------------------+--------------------------+------------------------+--------------------+---------------------------+----------------------+-----------------------+------------------------+-----------------------+-------------------------+------------------------------------+

convert
-------

+------------------------+------------------------+----------+---------+--------------------+----------------------+----------------------+------------------------------+--------------------+-------------+-----------------------------+--------------------------------------------------------------+
| from \ to              | TS[T], T is int, float | TS[bool] | TS[str] | TS[CompoundScalar] | TS[tuple]            | TS[set]              | TS[dict]                     | TSS[T]             | TSL[TST, S] | TSB[Schema]                 | TSD[K, V]                                                    |
+========================+========================+==========+=========+====================+======================+======================+==============================+====================+=============+=============================+==============================================================+
| TS[T], T is int, float | ✅                     | ✅       | ✅      |                    | ✅      tuple of one | ✅      tuple of one | ✅      key and value inputs | ✅      set of one |             |                             |                                                              |
+------------------------+------------------------+----------+---------+--------------------+----------------------+----------------------+------------------------------+--------------------+-------------+-----------------------------+--------------------------------------------------------------+
| TS[bool]               | ✅                     | ✅       | ✅      |                    | ✅      tuple of one | ✅      tuple of one |                              |                    |             |                             |                                                              |
+------------------------+------------------------+----------+---------+--------------------+----------------------+----------------------+------------------------------+--------------------+-------------+-----------------------------+--------------------------------------------------------------+
| TS[str]                | ✅                     | ✅       | ✅      |                    | ✅      tuple of one | ✅      tuple of one |                              | ✅      set of one |             |                             |                                                              |
+------------------------+------------------------+----------+---------+--------------------+----------------------+----------------------+------------------------------+--------------------+-------------+-----------------------------+--------------------------------------------------------------+
| TS[CompoundScalar]     | ❌                     | ✅       | ✅      | ✅                 |                      |                      |                              |                    |             | ✅                          |                                                              |
+------------------------+------------------------+----------+---------+--------------------+----------------------+----------------------+------------------------------+--------------------+-------------+-----------------------------+--------------------------------------------------------------+
| TS[tuple]              | ❌                     | ✅       | ✅      |                    | ✅                   | ✅                   | ✅      key and value tuples | ✅                 | ✅          |                             |                                                              |
+------------------------+------------------------+----------+---------+--------------------+----------------------+----------------------+------------------------------+--------------------+-------------+-----------------------------+--------------------------------------------------------------+
| TS[set]                | ❌                     | ✅       | ✅      |                    | ✅                   | ✅                   |                              | ✅                 |             |                             | ✅      if supplied a value                                  |
+------------------------+------------------------+----------+---------+--------------------+----------------------+----------------------+------------------------------+--------------------+-------------+-----------------------------+--------------------------------------------------------------+
| TS[dict]               | ❌                     | ✅       | ✅      |                    |                      |                      | ✅                           |                    |             | ✅      for uniform schemas | ✅                                                           |
+------------------------+------------------------+----------+---------+--------------------+----------------------+----------------------+------------------------------+--------------------+-------------+-----------------------------+--------------------------------------------------------------+
| TSS[T]                 | ❌                     | ✅       | ✅      |                    | ✅                   | ✅                   |                              |                    |             |                             | ✅      if supplied a value                                  |
+------------------------+------------------------+----------+---------+--------------------+----------------------+----------------------+------------------------------+--------------------+-------------+-----------------------------+--------------------------------------------------------------+
| TSL[TST, S]            | ❌                     | ✅       | ✅      |                    | ✅                   |                      | ✅      ints for keys        |                    | ✅          |                             | ✅      with int keys, or use combine with a tuple of keys   |
+------------------------+------------------------+----------+---------+--------------------+----------------------+----------------------+------------------------------+--------------------+-------------+-----------------------------+--------------------------------------------------------------+
| TSB[Schema]            | ❌                     | ✅       | ✅      | ✅                 |                      |                      |                              |                    |             | ✅                          | ✅      if the schema is uniform                             |
+------------------------+------------------------+----------+---------+--------------------+----------------------+----------------------+------------------------------+--------------------+-------------+-----------------------------+--------------------------------------------------------------+
| TSD[K, V]              | ❌                     | ✅       | ✅      |                    |                      |                      | ✅                           |                    |             | ✅      for uniform schemas | ✅                                                           |
+------------------------+------------------------+----------+---------+--------------------+----------------------+----------------------+------------------------------+--------------------+-------------+-----------------------------+--------------------------------------------------------------+

combine
-------

+-----------------------------------+----------------------+---------+-------------------------------------+---------+-------------+-------------+---------------------------------+
| from \ to                         | TS[tuple]            | TS[set] | TS[Mapping]                         | TSS[T]  | TSL[TST, S] | TSB[Schema] | TSD[K, V]                       |
+===================================+======================+=========+=====================================+=========+=============+=============+=================================+
| TS[T], T is int, float, bool, str | ✅                   | ✅      | ✅      from two inputs for K and V | ✅      |             |             | ✅      for two inputs, K and V |
+-----------------------------------+----------------------+---------+-------------------------------------+---------+-------------+-------------+---------------------------------+
| TS[tuple]                         | ✅      same as sums | ✅      | ✅      from two inputs for K and V | ✅      |             |             | ✅      for two inputs, K and V |
+-----------------------------------+----------------------+---------+-------------------------------------+---------+-------------+-------------+---------------------------------+
| TS[set]                           |                      |         |                                     | ✅      |             |             |                                 |
+-----------------------------------+----------------------+---------+-------------------------------------+---------+-------------+-------------+---------------------------------+
| TS[Mapping]                       |                      |         |                                     |         |             |             | ✅                              |
+-----------------------------------+----------------------+---------+-------------------------------------+---------+-------------+-------------+---------------------------------+
| TSS[T]                            |                      |         |                                     | ✅      |             |             |                                 |
+-----------------------------------+----------------------+---------+-------------------------------------+---------+-------------+-------------+---------------------------------+
| TSD[K, V]                         |                      |         |                                     |         |             |             | ✅                              |
+-----------------------------------+----------------------+---------+-------------------------------------+---------+-------------+-------------+---------------------------------+

emit
----

+------------------------+-------------+
| input type             | output type |
+========================+=============+
| TS[tuple[SCALAR, ...]] | TS[SCALAR]  |
+------------------------+-------------+
| TS[set[SCALAR]]        | TS[SCALAR]  |
+------------------------+-------------+
| TS[Mapping[K, V]]      | TS[V]       |
+------------------------+-------------+
| TSS[SCALAR]            | TS[SCALAR]  |
+------------------------+-------------+
| TSL[T, SIZE]           | T           |
+------------------------+-------------+
| TSD[K, V]              | V           |
+------------------------+-------------+