<p>Is it by any chance just <a href="https://en.wikipedia.org/wiki/Computer_algebra_system" rel="nofollow noreferrer">this</a> (otherwise Google was no help)? I've seen throwaway remarks on this site by SK_Logic and Jorg-W-Mittag that use this term but I'm not entirely convinced and cannot find it used anywhere else.</p>

<terminology>
What is a CAS language?
CC BY-SA 4.0
2023-09-03T05:53:27.993Z
Related question: https://cs.stackexchange.com/questions/134846/how-can-a-computer-deal-with-real-numbers
Pseudonym
CC BY-SA 4.0
2023-09-04T08:57:10.400Z
Yes, I indeed meant languages of the Computer Algebra Systems, such as MACSYMA, Mathematica, Axiom, etc. Keep in mind that not all CASes have language frontends (e.g., SymPy is just built on top of Python, no CAS-specific language semantics involved), hence the distinction between CAS and CAS languages.
SK-logic
<p>Yes, CAS is a typical abbreviation for “computer algebra system”, languages like Maple and Mathematica. This is the usage in the references from those users I can find:</p>
<ul>
<li><p><a href="https://langdev.stackexchange.com/questions/6/what-are-the-advantages-and-disadvantages-of-implementing-reals-as-rationals#comment2369_6">From SK-Logic</a>, on a question about representing reals as rationals:</p>
<blockquote>
<p>Every single CAS language does this, for very obvious reasons.</p>
</blockquote>
</li>
<li><p><a href="https://langdev.stackexchange.com/a/1837">From Jorg W Mittag</a>:</p>
<blockquote>
<p>It gets more interesting when you get into geometry, though. You can't avoid roots and trigonometry here, so you will quickly run into irrational and transcendental numbers. Same for finance, where you will encounter logarithms at some point.</p>
<p>Here, you have two choices: turn your language into a CAS (with all the complexity that carries) or punt to some sort of inexact type.</p>
</blockquote>
</li>
</ul>
<p>Both of these are clearly referring to computer algebra systems, where numbers are represented by mathematical expressions producing them.</p>

CC BY-SA 4.0
2023-09-02T19:20:53.613Z
2023-09-02T19:20:53.613Z
Michael Homer
CC BY-SA 4.0
2023-09-03T05:53:10.343Z
I've never seen one, but there's no reason why you couldn't have CLP(Tarski): constraint logic programming with the first-order theory of reals. I haven't checked, but I'm sure there are SMT solvers that support it, too.
Pseudonym
CC BY-SA 4.0
2023-09-03T18:00:32.840Z
But it's not actually called a "CAS language" except by SK-Logic in that one quote from this Stack Exchange site (PLDI) right?
Nike Dattani
CC BY-SA 4.0
2023-09-03T20:46:40.563Z
@NikeDattani Anyone would call a "language that is used inside a CAS" a "CAS language."
Bergi
CC BY-SA 4.0
2023-09-04T09:01:55.777Z
I meant languages that are built specifically for CAS as CAS languages. You don't need to have a special language - see SymPy for an example of the opposite, but historically most CAS had a language front-end with some very specific semantics - MACSYMA (and Maxima after it), Mathematica, Axiom, MAPLE, and, yes, SMT-LIB I'd also put under this category.
SK-logic
CC BY-SA 4.0
2023-09-05T20:06:49.823Z
@SK-logic In that vein I'd call sympy a CAS library.
Barmar
# What is a CAS language?
Posted by: username_0 on 2023-09-02
Is it by any chance just [this](https://en.wikipedia.org/wiki/Computer_algebra_system) (otherwise Google was no help)? I've seen throwaway remarks on this site by SK\_Logic and Jorg-W-Mittag that use this term but I'm not entirely convinced and cannot find it used anywhere else.
**Tags:** terminology
> **Comments:**
> **username_1**: Related question: https://cs.stackexchange.com/questions/134846/how-can-a-computer-deal-with-real-numbers  
> **username_2**: Yes, I indeed meant languages of the Computer Algebra Systems, such as MACSYMA, Mathematica, Axiom, etc. Keep in mind that not all CASes have language frontends (e.g., SymPy is just built on top of Python, no CAS-specific language semantics involved), hence the distinction between CAS and CAS languages.  
---
## 1 answers
### Answer by username_3 on 2023-09-02. Score: 8 | Accepted answer
Yes, CAS is a typical abbreviation for “computer algebra system”, languages like Maple and Mathematica. This is the usage in the references from those users I can find:

* [From SK-Logic](https://langdev.stackexchange.com/questions/6/what-are-the-advantages-and-disadvantages-of-implementing-reals-as-rationals#comment2369_6), on a question about representing reals as rationals:

  > Every single CAS language does this, for very obvious reasons.
* [From Jorg W Mittag](https://langdev.stackexchange.com/a/1837):

  > It gets more interesting when you get into geometry, though. You can't avoid roots and trigonometry here, so you will quickly run into irrational and transcendental numbers. Same for finance, where you will encounter logarithms at some point.
  >
  > Here, you have two choices: turn your language into a CAS (with all the complexity that carries) or punt to some sort of inexact type.

Both of these are clearly referring to computer algebra systems, where numbers are represented by mathematical expressions producing them.
> **Comments:**
> **username_1** (2023-09-03): I've never seen one, but there's no reason why you couldn't have CLP(Tarski): constraint logic programming with the first-order theory of reals. I haven't checked, but I'm sure there are SMT solvers that support it, too.  
> **username_4** (2023-09-03): But it's not actually called a "CAS language" except by SK-Logic in that one quote from this Stack Exchange site (PLDI) right?  
> **username_5** (2023-09-03): @NikeDattani Anyone would call a "language that is used inside a CAS" a "CAS language."  
> **username_2** (2023-09-04): I meant languages that are built specifically for CAS as CAS languages. You don't need to have a special language - see SymPy for an example of the opposite, but historically most CAS had a language front-end with some very specific semantics - MACSYMA (and Maxima after it), Mathematica, Axiom, MAPLE, and, yes, SMT-LIB I'd also put under this category.  
> **username_6** (2023-09-05): @SK-logic In that vein I'd call sympy a CAS library.  
---
