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Prevaricating. But you get (most of) a good new essay out of it.

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Simon Brooke 2023-04-03 10:22:06 +01:00
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# M-Expressions
# Interpreting M-Expressions
M-Expressions ('mexprs') are the grammar which John McCarthy origininally used to write Lisp, and the grammar in which many of the function definitions in the [Lisp 1.5 Programmer's Manual](https://www.softwarepreservation.org/projects/LISP/book/LISP%201.5%20Programmers%20Manual.pdf) are stated. However, I have not seen anywhere a claim that Lisp 1.5 could *read* M-Expressions, and it is not clear to me whether it was even planned that it should do so.
M-Expressions ('mexprs') are the grammar which John McCarthy origininally used to write Lisp, and the grammar in which many of the function definitions in the [Lisp 1.5 Programmer's Manual](https://www.softwarepreservation.org/projects/LISP/book/LISP%201.5%20Programmers%20Manual.pdf) are stated. However, I have not seen anywhere a claim that Lisp 1.5 could *read* M-Expressions, and it is not clear to me whether it was even planned that it should do so, although the discussion on [page 10](https://www.softwarepreservation.org/projects/LISP/book/LISP%201.5%20Programmers%20Manual.pdf#page=18) suggests that it was.
Rather, it seems to me probably that M-Expressions were only ever a grammar intended to be written on paper, like [Backus Naur Form](https://en.wikipedia.org/wiki/Backus%E2%80%93Naur_form), to describe and to reason about algorithms.
Rather, it seems to me possible that M-Expressions were only ever a grammar intended to be written on paper, like [Backus Naur Form](https://en.wikipedia.org/wiki/Backus%E2%80%93Naur_form), to describe and to reason about algorithms. I think at the point
at which the M-Expression grammar was written, the idea of the [universal Lisp function](https://www.softwarepreservation.org/projects/LISP/book/LISP%201.5%20Programmers%20Manual.pdf#page=18)
I set out to make Beowulf read M-Expressions essentially out of curiousity, to see whether it could be done. I had this idea that if it could be done, I could implement most of Lisp 1.5 simply by copying in the M-Expression definitions out of the manual.
@ -45,7 +46,7 @@ is
((QUOTE T) (QUOTE F))))))
```
This is certainly more prolix and more awkward, but it also risks being flat wrong.
This is certainly more prolix and more awkward.
Is the value of `NIL` the atom `NIL`, or is it the empty list `()`? If the former, then the translation from the M-Expression above is correct. However, that means that recursive functions which recurse down a list seeking the end will fail. So the latter must be the case.
@ -57,8 +58,10 @@ Is the value of `NIL` the atom `NIL`, or is it the empty list `()`? If the forme
I think there is an ambiguity in referencing constants which are not bound to themselves in the M-Expression notation as given in the manual. This is particularly problematic with regards to `NIL` and `F`, but there may be others instances.
However, so long as `F` is bound to `NIL`, and `NIL` is also bound to `NIL` (both of which are true by default, although changeable by the user), and `NIL` is the special marker used in the `CDR` of the last cons cell of a flat list, this is a difference which in practice does not make a difference. I still find it worrying, though, that rebinding variables could lead to disaster.
### Curly braces
The use of curly braces is not defined in the grammar as stated on page 10. They are not used in the initial definition of `APPLY` on page 13, but they are used in the more developed restatement on page 70. I believe they are to be read as indicating a `DO` statement -- a list of function calls to be made sequentially but without strict functional dependence on one another -- but I don't find the exposition here particularly clear and I'm not sure of this.
The use of curly braces is not defined in the grammar as stated on page 10. They are not used in the initial definition of `APPLY` on page 13, but they are used in the more developed restatement on page 70. I believe they are to be read as indicating a section of assembly code to be assembled by the [Lisp Assembly Program](https://www.softwarepreservation.org/projects/LISP/book/LISP%201.5%20Programmers%20Manual.pdf#page=81) -- but I don't find the exposition here particularly clear and I'm not sure of this.
Consequently, the M-Expression interpreter in Beowulf does not interpret curly braces.