2 added 18 characters in body
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Haskell, 5764 bytes

map unwords.g.words
g(h:t)=(show h('"':h++"\""):t):map(h:)(g t)
g _=[]

Try it online!Try it online!

Outputs a list of strings. Based on nimi's answer.

Haskell, 57 bytes

map unwords.g.words
g(h:t)=(show h:t):map(h:)(g t)
g _=[]

Try it online!

Outputs a list of strings. Based on nimi's answer.

Haskell, 64 bytes

map unwords.g.words
g(h:t)=(('"':h++"\""):t):map(h:)(g t)
g _=[]

Try it online!

Outputs a list of strings. Based on nimi's answer.

1
source | link

Haskell, 57 bytes

map unwords.g.words
g(h:t)=(show h:t):map(h:)(g t)
g _=[]

Try it online!

Outputs a list of strings. Based on nimi's answer.