Replacing Or with List

Question

I'm having trouble with replacements involving Or. I think the trouble mainly comes from the fact that you can't simply replace Or[a_] -> a, since a is often an invalid expression (like b, c). I.e. List[Or[a, b]] /. Or[a,b] -> a, b gives an error.

I have expressions inside lists such as {a, Or[b, c], d} - but also expressions such as {a, Or[b, c]} etc. I want to find a good way to replace the Or[a, b] with a, b - this should be possible since everything is happening inside a list such that it is okay that a, b isn't a valid expression on its own. It will end up in something like {x,a,b,z}.

I have expressions like:

{{m[3]->0,mbar[3]->2},{m[3]->1,mbar[3]->1}||{m[3]->2,mbar[3]->0},id[1]}

Or in FullForm:

List[List[Rule[m[3],0],Rule[mbar[3],2]],Or[List[Rule[m[3],1],Rule[mbar[3],1]],List[Rule[m[3],2],Rule[mbar[3],0]]],id[1]]

What do you do with these annoying Or's (which I get from Solve/Reduce and are thus forced upon me)?

I can find solutions for specific cases (List[x_, Or[a_, b_], z_] -> List[x, a, b, z]), but I would prefer a solution that does not involve looking at the precise structure of every object that involves Or. The whole point is that I need the replacements to work on things that get spit out by reduce without doing it by hand.

Note: The structure should not vary very wildly however. I expect no Ors inside Ors and only a combination of Lists and Rules and numbers.

Answer 1

You can use ReplaceAll (/.) to replace any Head with another. In combination with Sequence:

{a, Or[b, c], d} /. Or -> Sequence

{a, b, c, d}

Answer 2

You can also use Block to temporarily set Or to Sequence:

exp = {{m[3] -> 0, mbar[3] -> 2}, 
       {m[3] -> 1, mbar[3] -> 1} || {m[3] -> 2, mbar[3] -> 0}, id[1]};

Block[{Or = Sequence}, exp]

{{m[3] -> 0, mbar[3] -> 2}, {m[3] -> 1, mbar[3] -> 1}, {m[3] -> 2, mbar[3] -> 0}, id[1]}

Answer 3

list = {a, Or[b, c], d, Or[k, m]};

Using MapApply (new in 13.1) and Splice (new in 12.1)

MapApply[Splice @* List] @ list

{a, b, c, d, k, m}