[BUG] @callbacks not being registered when @app.callback and @callback with duplicate outputs are used

I'm aware that this is an edge case, but it's something we believe should be documented (and eventually fixed) in case someone runs into a similar issue.

The general recommendation would be to choose between @app.callback and @callback to use consistently across the app, even though combining them sometimes works, like in the following case:

@callback(
    Output("div1", "children", allow_duplicate=True),
    Input("b1", "n_clicks"),
    prevent_initial_call=True
)
...

@app.callback(
    Output("div1", "children"),
    Input("b2", "n_clicks"),
    prevent_initial_call=True
)

Description of the issue

If we have something like this in the code:

@app.callback(
    Output("div1", "children"),
    Input("b1", "n_clicks"),
    prevent_initial_call=True
)
...

@callback(
    Output("div1", "children"),
    Input("b2", "n_clicks"),
    prevent_initial_call=True
)

any callback defined with @callback will not work. Every callback defined with @app.callback will still work.

The code for the video app is at the end of this message.

https://github.com/user-attachments/assets/39899de0-8fdd-472e-8f7a-20789105774c

Defining duplicate callbacks like this is wrong according to the documentation. However, instead of this "all @callbacks not working" behaviour, we should see a "duplicate output warning" (see next section for more details).

Variations of the issue:

• The order in which the @app.callback and @callback callbacks are defined for the duplicate output doesn't affect the occurrence of the issue (it happens either way).
• If prevent_initial_call=True is not specified for (at least) @app.callback (the one with the duplicate output), the expected error will be raised:

dash.exceptions.DuplicateCallback: The callback `div1.children` provided with `dash.callback` was already assigned with `app.callback`.

• However, if prevent_initial_call=True is specified for @app.callback and not for @callback (the ones for the duplicate outputs), the issue will still occur, i.e. no error will be raised.

The last two points mean that:

• This will raise the expected error/exception:

@app.callback(
    Output("div1", "children"),
    Input("b1", "n_clicks"),
)
...
@callback(
    Output("div1", "children"),
    Input("b2", "n_clicks"),
    prevent_initial_call=True
)

• This will cause the issue - no error will be raised and other callbacks defined with @callback will not work.

@app.callback(
    Output("div1", "children"),
    Input("b1", "n_clicks"),
    prevent_initial_call=True
)
...
@callback(
    Output("div1", "children"),
    Input("b2", "n_clicks"),
)

If both callbacks are defined with @callback or @app.callback, the (expected) error appears in the debug menu. The app is loaded but no callback (not even the ones defined with @app.callback work:

https://github.com/user-attachments/assets/7d98a477-ae3a-4fd6-aa28-593341f5d450

If the callbacks are defined as the docs specify, with prevent_initial_call=True and allow_duplicate=True, like this, every callback will work (no matter if they are defined with @callback or @app.callback`):

@app.callback(
    Output("div1", "children", allow_duplicate=True),
    Input("b1", "n_clicks"),
    prevent_initial_call=True
)
...
@callback(
    Output("div1", "children"),
    Input("b2", "n_clicks"),
    prevent_initial_call=True
)

Expected behavior

Any case where callbacks with duplicate outputs are defined incorrectly should raise the below exception or an error in the debug menu:

dash.exceptions.DuplicateCallback: The callback `div1.children` provided with `dash.callback` was already assigned with `app.callback`.

So these two cases (and potentially more) should raise the exception:

# CASE 1: prevent_initial_call in app.callback and callback
@app.callback(
    Output("div1", "children"),
    Input("b1", "n_clicks"),
    prevent_initial_call=True
)
...

@callback(
    Output("div1", "children"),
    Input("b2", "n_clicks"),
    prevent_initial_call=True
)

# CASE 2: only prevent_initial_call in app.callback 
@app.callback(
    Output("div1", "children"),
    Input("b1", "n_clicks"),
    prevent_initial_call=True
)
...
@callback(
    Output("div1", "children"),
    Input("b2", "n_clicks"),
)

Code to reproduce the issue

dash==3.2.0

import dash
from dash import dcc, html, Input, Output, State, callback, ctx

app = dash.Dash(__name__)

app.layout = html.Div([
    html.H3("callback 1: @callback, output=div1 - without duplicate_output=True"),
    html.Button(id="b1", children="Trigger callback 1"),
    html.Div(id="div1", children="callbacks 1 or 2 not triggered yet"),
    ####
    html.H3("callback 2: @app.callback, output=div1"),
    html.Button(id="b2", children="Trigger callback 2"),
    ###
    html.H3("callback 3: @app.callback, output=div3"),
    html.Button(id="b3", children="Trigger callback 3"),
    html.Div(id="div3", children="callback 3 not triggered yet"),
    ####
    html.H3("callback 4: @callback, output=div4"),
    html.Button(id="b4", children="Trigger callback 4"),
    html.Div(id="div4", children="callback 4 not triggered yet"),
])

# this one won't work
@callback(
    Output("div1", "children"),
    Input("b1", "n_clicks"),
    prevent_initial_call=True
)
def update_div1_with_b1(b1):
    return f"Callback 1 triggered by {ctx.triggered_id} and {b1} clicks"

# this one will work
@app.callback(
    Output("div1", "children"),
    Input("b2", "n_clicks"),
    prevent_initial_call=True
)
def update_div1_with_b2(b2):
    return f"Callback 2 triggered by {ctx.triggered_id} and {b2} clicks"

# this one will work
@app.callback(
    Output("div3", "children"),
    Input("b3", "n_clicks"),
    prevent_initial_call=True
)
def update_div3(b3):
    return f"Callback 3 triggered by {ctx.triggered_id} and {b3} clicks"

# this one won't work
@callback(
    Output("div4", "children"),
    Input("b4", "n_clicks"),
    prevent_initial_call=True
)
def update_div4(b4):
    return f"Callback 4 triggered by {ctx.triggered_id} and {b4} clicks"

if __name__ == '__main__':
    app.run(debug=True) 

Start by running the provided Dash 3.2.0 reproduction and compare callback registration when using @callback and @app.callback with duplicate outputs and prevent_initial_call=True. Trace the registration path that produces the reported behavior, then verify that the duplicate-output case raises DuplicateCallback while unrelated callbacks still work.