问题
I'm building a web-based programming language partially inspired by Prolog and Haskell (don't laugh).
It already has quite a bit of functionality, you can check out the prototype at http://www.lastcalc.com/. You can see the source here and read about the architecture here. Remember it's a prototype.
Currently LastCalc cannot simplify expressions or solve equations. Rather than hard-coding this in Java, I would like to enhance the fundamental language such that it can be extended to do these things using nothing but the language itself (as with Prolog). Unlike Prolog, LastCalc has a more powerful search algorithm, Prolog is "depth-first search with backtracking", LastCalc currently uses a heuristic best-first search.
Before delving into this I want to understand more about how other systems solve this problem, particularly Mathematica / Wolfram Alpha.
I assume the idea, at least in the general case, is that you give the system a bunch of rules for manipulation of equations (like a*(b+c) = a*b + a+c) specify the goal (eg. isolate variable x) and then let it loose.
So, my questions are:
- Is my assumption correct?
- What is the search strategy for applying rules? eg. depth first, breadth first, depth first with iterative deepening, some kind of best first?
- If it is "best first", what heuristics are used to determine whether it is likely that a particular rule application has got us closer to our goal?
I'd also appreciate any other advice (except for "give up" - I regularly ignore that piece of advice and doing so has served me well ;).
回答1:
I dealt with such questions myself some time ago. I then found this document about simplification of expressions. It is titled Rule-based Simplification of Expressions and shows some details about simplification in Mupad, which later became a part of Matlab.
According to this document, your assumption is correct. There is a set of rules for manipulation of expressions. A heuristic quality metric is is used as a target function for simplification.
回答2:
Wolfram alpha is developed by Mathematica
- mathematica is stephen wolphram's brainchild. Mathematica 1.0 was released in 1988. mathematica is much like maple and they both rely heavily on older software libraries like LaPack.
- The libraries that these programs are, based on, and often simply, legacy software. They've been around, and modified, for a very long time.
If you would like to know about the background programs running, sagemath is a free open source alternative; you could possible reverse engineer the solutions to your questions:
SageMath.org
来源：https://stackoverflow.com/questions/18727737/how-does-a-system-like-wolfram-alpha-or-mathematica-solve-equations