This is (in some ways) a followup on Subset error with new cmdstanr version.

After concertation with @avehtari, we’ve decided to update the name of the function to include the suffix _lpmf. Nothing too hard: I update the stan-math and the stanc3 code, notably doing an edit to `Utils.ml`

:

```
let is_distribution_name s =
(not
( String.is_suffix s ~suffix:"_cdf_log"
|| String.is_suffix s ~suffix:"_ccdf_log"
|| String.equal s "laplace_marginal_poisson_log_lpmf"))
&& List.exists
~f:(fun suffix -> String.is_suffix s ~suffix)
distribution_suffices
```

With these changes, I can compile and run a model that uses the following line

```
target += laplace_marginal_poisson_log_lpmf(y | n_samples, ye, K, phi,
x, delta, delta_int, theta_0);
```

and in the short term, that’s all I need.

What about

```
y ~ laplace_marginal_poisson_log(n_samples, ye, ...);
```

I get the following message

```
Ill-typed arguments to '~' statement. No distribution 'laplace_marginal_poisson_log' was found with the correct signature.
```

which is a transpiler issue. Fair enough, I didn’t do much to indicate laplace_marginal_poisson_log was a distribution. The relevant edit in `Stan_math_signatures.ml`

should be

```
let distributions =
[ (full_lpmf, "beta_binomial", [DVInt; DVInt; DVReal; DVReal])
; (full_lpdf, "beta", [DVReal; DVReal; DVReal])
. . .
; ([Lpmf], "lapalce_marginal_poisson_log",
[ (DataOnly, UArray UInt); (DataOnly, UArray UInt)
; ( AutoDiffable
, UFun
( [ (AutoDiffable, UVector); (DataOnly, UArray UVector)
; (DataOnly, UArray UReal); (DataOnly, UArray UInt) ]
, ReturnType UMatrix ) )
; (AutoDiffable, UVector); (DataOnly, UArray UVector)
; (DataOnly, UArray UReal); (DataOnly, UArray UInt)
; (AutoDiffable, UVector) ]) ]
```

which prompts the error message

```
MacBook-Pro:stanc3 charlesm$ dune runtest test/integration
File "src/middle/Stan_math_signatures.ml", line 192, characters 5-9:
Error: This variant expression is expected to have type fkind list
The constructor Lpmf does not belong to type list
MacBook-Pro:stanc3 charlesm$ dune runtest test/integration
File "src/middle/Stan_math_signatures.ml", line 193, characters 6-29:
Error: This expression has type 'a * 'b
but an expression was expected of type dimensionality
```

I’m not sure what the error is here. I also assume there are some additional moving parts from using qualifier arguments. Any help would be very much welcomed.