Why is bash errexit not behaving as expected in function calls?

Question

In the bash man page, it states:

Exit immediately if a pipeline (which may consist of a single simple command),
a subshell command enclosed in parentheses, or one of the commands executed as part of a command list enclosed by braces...

So I assumed that a function should be considered a command list enclosed by braces. However, if you apply a conditional to the function call, errexit no longer persists inside the function body and it executes the entire command list before returning. Even if you explicitly create a subshell inside the function with errexit enabled for that subshell, all commands in the command list are executed. Here is a simple example that demonstrates the issue:

function a() { b ; c ; d ; e ; }
function ap() { { b ; c ; d ; e ; } ; }
function as() { ( set -e ; b ; c ; d ; e ) ; }
function b() { false ; }
function c() { false ; }
function d() { false ; }
function e() { false ; }

---

( set -Eex ; a )
+ a
+ b
+ false

---

( set -Eex ; ap )
+ ap
+ b
+ false

---

( set -Eex ; as )
+ as
+ set -e
+ b
+ false

Now if I apply a conditional to each of them...

( set -Eex ; a || false )
+ a
+ b
+ false
+ c
+ false
+ d
+ false
+ e
+ false
+ false

---

( set -Eex ; ap || false )
+ ap
+ b
+ false
+ c
+ false
+ d
+ false
+ e
+ false
+ false

---

( set -Eex ; as )
+ as
+ set -e
+ b
+ false
+ c
+ false
+ d
+ false
+ e
+ false
+ false

Answer 1

You started to quote the manual but then you cut the bit that explained this behaviour, which was in the very next sentence:

-e Exit immediately if a pipeline, which may consist of a single simple command, a subshell command enclosed in parentheses, or one of the commands executed as part of a command list enclosed by braces returns a non-zero status. The shell does not exit if the command that fails is part of the command list immediately following a while or until keyword, part of the test in an if statement, part of any command executed in a && or || list except the command following the final && or ||, any command in a pipeline but the last, or if the command’s return status is being inverted with !.