3 ms·

A symbolic language is something like mathematica. Mathematica does evaluation as term rewriting with rules for how to rewrite all sorts of things - and if it c

A symbolic language is something like mathematica. Mathematica does evaluation as term rewriting with rules for how to rewrite all sorts of things - and if it can't find matching rules, it leaves the expression in the same symbolic form as the input.

bmitc 4y ago
You can do that with symbolic expressions in all the languages I listed.
- sterlind 4y ago
  In Mathematica, the equivalent of a "function call" would be something like f[x,y]. I can write and run that, and it won't give an error if f, x or y aren't defined. Fundamentally, all atoms in the language are terms of symbols. Expressions are broken down by patterns until they're reduced as far as they can be, then the language happily stops and returns how far it got. It's like Lisp, if everything in Lisp were quoted, and eval consisted of pattern matching and applying substitution rules. As an example, say in Haskell I have foo x y = x + 2/y. Can you write a function that takes any function in, and replaces all + with *? in Mathematica you can: foo[x_,y_] := x + 2/y; foo[x,y] /. l_ + r_ -> l*r. I'm sure you can do this stuff in other languages if you try hard enough. Some kind of reflection in Haskell or F#. In Lisp, grab and quote the definition of foo and apply macro machinery to it. But that's not the tao of those languages, while it is the essence of Mathematica.
  - chowells 4y ago
    > Some kind of reflection in Haskell In Haskell you can only do that kind of manipulation at compile time. At run time, the source code is long gone. And even at compile time, expressions are a very different type than code that can be run. Haskell just isn't anything like a symbolic language. As pointed out way upthread, it provides lots of hooks for programmers to have nice syntax for entry points to symbolic systems - if someone writes one.

3 ms·

A symbolic language is something like mathematica. Mathematica does evaluation as term rewriting with rules for how to rewrite all sorts of things - and if it c

by chowells 4y ago

bmitc 4y ago
You can do that with symbolic expressions in all the languages I listed.
- sterlind 4y ago
  In Mathematica, the equivalent of a "function call" would be something like f[x,y]. I can write and run that, and it won't give an error if f, x or y aren't defined. Fundamentally, all atoms in the language are terms of symbols. Expressions are broken down by patterns until they're reduced as far as they can be, then the language happily stops and returns how far it got. It's like Lisp, if everything in Lisp were quoted, and eval consisted of pattern matching and applying substitution rules. As an example, say in Haskell I have foo x y = x + 2/y. Can you write a function that takes any function in, and replaces all + with *? in Mathematica you can: foo[x_,y_] := x + 2/y; foo[x,y] /. l_ + r_ -> l*r. I'm sure you can do this stuff in other languages if you try hard enough. Some kind of reflection in Haskell or F#. In Lisp, grab and quote the definition of foo and apply macro machinery to it. But that's not the tao of those languages, while it is the essence of Mathematica.
  - chowells 4y ago
    > Some kind of reflection in Haskell In Haskell you can only do that kind of manipulation at compile time. At run time, the source code is long gone. And even at compile time, expressions are a very different type than code that can be run. Haskell just isn't anything like a symbolic language. As pointed out way upthread, it provides lots of hooks for programmers to have nice syntax for entry points to symbolic systems - if someone writes one.