Is IronScheme suitable for working through SICP?

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Will there be any incompatibilities with the code in SICP if I use IronScheme?

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There shouldn't be any significant incompatibilities.

If you find any, why not post them here (as problems to solve), to document them?

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You may want to use DrScheme (http://www.plt-scheme.org/) in 'Pretty Big' language mode and allow redefinition of initial bindings for working through code examples and exercises in SICP. I have been using it for trying out examples and exercises in SICP and have not run into any problems with the interpreter. It's also much more developed compared to IronScheme.