mustafasrepo opened a new issue, #8064:
URL: https://github.com/apache/arrow-datafusion/issues/8064

   ### Is your feature request related to a problem or challenge?
   
   In the existing code base we have two different methods to keep track of 
equivalences in the `Arc<dyn PhysicalPlan>`.
   Which are `equivalence_properties` and `ordering_equivalence_properties`. 
   
   As a background `EquivalenceProperties` keeps track of equivalent columns 
such as `a=b=c`, `e=f`.
   `OrderingEquivalenceProperties` alternative orderings that table satisfies. 
such `[a ASC, b ASC]`, and `[c ASC, d ASC]`.
   `OrderingEquivalenceProperties` keeps track of constant expressions also 
(e.g expression that are known to have a constant value. This can arise after 
filter, join, etc.).
   
   Inherently, this information is coupled, as an example 
   Assume that 
   - existing table satisfies following orderings `[a ASC, b ASC]` and `[c ASC, 
d ASC]`.
   - table have equivalent columns `a=e`.
   - It is known that `f` is constant.
   
   If an operator requires ordering at its input `[e ASC, f ASC, b ASC]`. 
During the analysis for whether this requirement is satisfied by existing 
ordering, we need to consider all orderings, equivalences, and constants at the 
same time.
   
   Following naive algorithm can be followed for this analysis (Please note 
that algorithm in this PR is more elaborate.)
   - Remove constant expressions from the requirement (This converts 
requirement `[e ASC, f ASC, b ASC]` to `[e ASC, b ASC]`)
   - Rewrite requirement such that it uses only representative expression for 
each distinct equivalent group (This converts requirement `[e ASC, b ASC]` to 
`[a ASC, b ASC]`). 
   - Apply same procedures above each of the orderings inside the 
`OrderingEquivalences` (This converts ordering `[a ASC, b ASC]` to `[a ASC, b 
ASC]` and `[c ASC, d ASC]` to `[c ASC, d ASC]` no change ). 
   - Check whether normalized requirement `[a ASC, b ASC]` is satisfied by any 
of normalized orderings `[a ASC, b ASC]`, `[c ASC, d ASC]`.
   
   As can be seen from the example above. Keeping track of these information 
separately, is a bit cumbersome. 
   
   Also for the user implementing new functionality is a bit hard, and existing 
APIs are a bit involved also. Such as `ordering_satisfy`, 
`requirements_compatible`, etc.
   
   I think it is better to unify these information in a single `struct` so that
   - We can expose better, and more friendly `API`s from struct.
   - Move utils, functions, to method calls
   - Keep the invariants in the state (not relying on correct arguments). 
   - All of the implementations, algorithms resides in a single place, and 
logic is not scatterred in different files.
   
   ### Describe the solution you'd like
   
   _No response_
   
   ### Describe alternatives you've considered
   
   _No response_
   
   ### Additional context
   
   _No response_


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