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for instance get doctor racket for windows and you can start writing code.
It supports Scheme as well, not that I fond any difference yet.
I would suggest newLISP. It is open source, cross platform and comes with a nice GUI. Although it is not stricly either Scheme or common LISP I have been able to adapt the course examples easily. See: http://www.newlisp.org/
I second the DrRacket recommendation. Its what I am using and it works great. Just use the #lang planet neil/sicp directive and click run and you are all set.
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My problem using Scheme was that every time I wrote some expression or evaluated some expression, instead of simply doing the action the program would instead go like "REPL define XP problem go to z-dr" or any other unintelligible expression. Is Racket supposed to solve this problem?
I do not know about Racket but have just tried out TinyScheme and found it good for running the examples presented in this course. http://tinyscheme.sourceforge.net/home.html It implements most of R5RS (the Revised5 Report on the Algorithmic Language Scheme), that is standard Scheme. If you want the Edwin editor you should go for mit-scheme, but TinyScheme is enough for me
Racket is interactive, so as soon as you type in some s-expression, and hit enter, it is evaluated. There are some nice demos at YouTube, you may want to check those out.