2 ms·

It reminds me the earliest implementations of Lisp where numbers have considered as lists of certain length.

cess11 3y ago
How would that work? I've only come across recursive function application as a way to implement Peano/Church numerals, similar to how it might be done in Prolog: natnum(0). natnum(s(N)) :- natnum(N).
- Drakim 3y ago
  I have no idea if this is actually the case with early Lisp, but when I was making my own vaguely Lisp-alike interpreter, it became awfully tempting to make everything into a list. After all, arrays are lists, strings are lists of characters, and even structs can be thought of as a list with unorthodox indexing. At one point I was faced with the fact that I only really had 2 datatypes in my interpreter, the list and the integer. So I bit the bullet and made my integer type into a list with one byte entry, thus reducing my total amount of datatypes to one. Every piece of my interpreter code always knew that it would get a list as inputs, and it was kinda beautiful. CPU-wise it was wasteful, but it reduced the interpreter size by a lot.
- EdwardCoffin 3y ago
  I believe the microprocessor from Steele's and Sussman's paper Design of a LISP-based microprocessor [1] used Peano numbers. [1] https://dl.acm.org/doi/pdf/10.1145/359024.359031 https://dl.acm.org/doi/pdf/10.1145/359024.359031
  - cess11 3y ago
    Under 10. Discussion they discuss the lack of numbers and how they're using CONS as a kind of 'add 1' and CAR/CDR as a kind of 'subtract 1' when calculating positions in memory, similar to how integer index/pointers might be used on a different type of machine, as if the length of a list would be an implicit pointer. They seem almost giddy about having designed a computer that can perform interesting mathematical tasks like integrals and derivatives without numbers.
mzl 3y ago
What Lisp would that be? Considering it is not (as far as I can see) mentioned in McCarthys History of Lisp (https://dl.acm.org/doi/pdf/10.1145/800025.1198360 https://dl.acm.org/doi/pdf/10.1145/800025.1198360) I think no actual Lisp used unary arithmetic based on list lengths. Sure, there might be toy examples used for teaching that did this, but that is a something different.

How would that work? I've only come across recursive function application as a way to implement Peano/Church numerals, similar to how it might be done in Prolog: natnum(0). natnum(s(N)) :- natnum(N).

Drakim 3y ago
I have no idea if this is actually the case with early Lisp, but when I was making my own vaguely Lisp-alike interpreter, it became awfully tempting to make everything into a list. After all, arrays are lists, strings are lists of characters, and even structs can be thought of as a list with unorthodox indexing. At one point I was faced with the fact that I only really had 2 datatypes in my interpreter, the list and the integer. So I bit the bullet and made my integer type into a list with one byte entry, thus reducing my total amount of datatypes to one. Every piece of my interpreter code always knew that it would get a list as inputs, and it was kinda beautiful. CPU-wise it was wasteful, but it reduced the interpreter size by a lot.
EdwardCoffin 3y ago
I believe the microprocessor from Steele's and Sussman's paper Design of a LISP-based microprocessor [1] used Peano numbers. [1] https://dl.acm.org/doi/pdf/10.1145/359024.359031 https://dl.acm.org/doi/pdf/10.1145/359024.359031
- cess11 3y ago
  Under 10. Discussion they discuss the lack of numbers and how they're using CONS as a kind of 'add 1' and CAR/CDR as a kind of 'subtract 1' when calculating positions in memory, similar to how integer index/pointers might be used on a different type of machine, as if the length of a list would be an implicit pointer. They seem almost giddy about having designed a computer that can perform interesting mathematical tasks like integrals and derivatives without numbers.

mzl 3y ago

What Lisp would that be? Considering it is not (as far as I can see) mentioned in McCarthys History of Lisp (https://dl.acm.org/doi/pdf/10.1145/800025.1198360 https://dl.acm.org/doi/pdf/10.1145/800025.1198360) I think no actual Lisp used unary arithmetic based on list lengths. Sure, there might be toy examples used for teaching that did this, but that is a something different.