Extract formula call from schema

[DominiqueMakowski]

Say I am interested in getting things like the model matrix and coef names from a formula. As far as I'm aware, the current shortest method to do that is:

using DataFrames
using StatsModels

df = DataFrame(x = rand(100), y = rand(100))

f = @formula(y ~ 1 + x)
f = apply_schema(f, schema(f, df))

modelmatrix(f, df)
coefnames(f)

I was wondering whether it was possible to add a method to extract back the formula call from schema(f, df), which would then allow us to make apply_schema() dispatch directly on a schema and get all the necessary info, and be able to write something like

f = apply_schema(schema(@formula(y ~ 1 + x), df))

# Or 

f = schema(@formula(y ~ 1 + x), df) |> 
        apply_schema

Alternatively, this would allow other methods to implicitly call apply_schema() on a schema. I am not familiar with the code base so I'm not sure this makes sense, but I think in essence what I am asking is ways to reduce the repeated input of the same objects.