meaning of [ ]

[Rustom Mody]

On Monday, September 4, 2017 at 7:57:23 PM UTC+5:30, Rustom Mody wrote:
> On Monday, September 4, 2017 at 6:36:11 PM UTC+5:30, Ben Bacarisse wrote:
> > But [p for p in sys.path] is a list and "set-builder" notation is used
> > for sets.  Order is crucial for sys.path.  You say exactly that below so
> > I don't see how referring to sets helps anyone understand lists.
> 
> Clearly if the question was of *sets* vs *lists* the distinction is at least as
> crucial, maybe even more so than the similarity.
> The OP-question here however is one about comprehensions and it appears without
> the questioner realizing that — as Peter's answer showed
> 
> See the very first line of this:
> https://en.wikipedia.org/wiki/List_comprehension
> “List comprehension follows the form of the mathematical set-builder notation (set comprehension)”
>  
> ie its both historically and structurally linked
> IOW emphasising the incidental sequential nature of the computation 
> at the cost of the fundamental structure-preserving nature of the concept

Incomplete; I meant to say:

ie its both historically and structurally linked.
IOW emphasising the incidental sequential nature of the computation 
at the cost of the fundamental structure-preserving nature of the concept
seems to be some ()*&^$W# behavior on the part of people instructing python

The essential meaning of comprehensions is the following diagrams
not the for-loop implementation

If l is
[x₁, x₂,… xₙ ]

[f(x) for x in l]
means this picture:

[x₁,     x₂,…    xₙ ]
 ↓       ↓…      ↓

[f(x₁), f(x₂),… f(xₙ)]

Likewise
If s is
{x₁, x₂,… xₙ}

{f(x) for x in s} 
means this picture:

{x₁,     x₂, …   xₙ}
 ↓       ↓   …   ↓

{f(x₁), f(x₂),… f(xₙ)}