We know for preparing a COBOL program before it can be executed using a RUN jcl we need to compile it and then link edit it so that we have a load module which can be run using the JCL. "; ; ; ; My question is if we have only one cobol program which is stand alone, then do we need to link edit it before it can be executed. Please give a detailed explaination

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Yes. Even a "standalone" program still has to interact with the Operating System which is made possible byt the linkedit.
You could also just perform a
compile followed by and link and
'go' which will not produced a
load module that is stored in
a library. The 'GO' step executes the 'module' on the
fly.
This might be something one might do during testing.
Once tested/verified you would to want to incur the compile/link process for each
subsequent execution of the
program.............
"Once tested/verified you would to want to incur the compile/link process for each
subsequent execution of the
program............."
I suspect this is a typo and should say NOT WANT TO INCUR . . .
Also, it is usually best to compile and link the module to a load module so that testing will be as close to the "real world" as possible.
You always need to pass the program through the link editor. There are always externals calls that need linking. If you have a compiled module, just run the linkedit step. That will save a little time.