SMathML Reference

1 Introduction

MathML is a markup language based on XML for describing mathematics. Though MathML is human-readable-and-writable, it is human-readable-and-writable in the same sense that XML is human-readable-and-writable. So we have to provide users with methods of combination and abstraction to help them organize ideas about mathematical presentation and content.

SMathML is a DSL embedded in Scheme for expressing MathML (and also HTML), which is based on a hierarchical structure: $[user-defined abstractions] \to [primitive abstractions] \to [SXML] \to [HTML/XML] .$ It also provides a general way inspired by Oleg Kiselyov's SXSLT to create transformations of SXML, which is just a representation of HTML/XML as S-expressions. The boundary between primitive abstractions and user-defined abstractions is intended to be vague and the users are encouraged to create fundamental abstractions to his own taste.

2 Basic Elements of SMathML

3 Transformations of SMathML

4 Examples

4.1 The Fibonacci Sequence

(MB (let ((fib (lambda (n)
                 (let iter ((a 0) (b 1) (c 0))
                   (if (= c n)
                       a
                       (iter b (+ a b) (+ c 1))))))
          (&fib (lambda (n) (app 'fib n)))
          (seq (range 13)))
      (set-attr*
       (&table (list (map &fib seq) (map fib seq)))
       'frame "solid" 'rowlines "solid" 'columnlines "solid")))

\begin{matrix} fib (0) & fib (1) & fib (2) & fib (3) & fib (4) & fib (5) & fib (6) & fib (7) & fib (8) & fib (9) & fib (10) & fib (11) & fib (12) \\ 0 & 1 & 1 & 2 & 3 & 5 & 8 & 13 & 21 & 34 & 55 & 89 & 144 \end{matrix}

4.2 The Binomial Theorem

(MB (&= (^ (@+ $x $y) $n)
        (sum (&= $k $0) $n
             (&i* (comb $n $k) (^ $x (&- $n $k)) $y^k))))

{(x + y)}^{n} = \sum_{k = 0}^{n} (\binom{n}{k}) x^{n - k} y^{k}