You should maybe look for bindings to other symbolic algebra software, but I haven't heard of it (there was a Jane Street Summer Project about that a few years ago, but I'm not sure there was any deliverable produced). I don't see right know what representation give to a semantic space with Min and Max functions.Įdit: Regarding external libraries, I don't know any and I'm not sure there are. For example, for polynomial fractions, the semantic space would be something like:Īnd poly = (multiplicity * var * degree) list Enter functions in standard mathematical notation, using x as independent variable. The composition of both transformations will naturally give you a normalization procedure, without having to worry for example about direction of the Add rewriting (some arbitrary choice will arise naturally from your reification function). Online Calculator is a simple web application that lets you perform advanced calculations, plot 2D and 3D graphs, and make symbolic calculations such as differentiation. Find a suitable (unique) representation for objects of sem, then an evaluation function expr -> sem, then finally (if you wish to, but you don't need to for equality checking for example) a reification sem -> expr. Take a more semantic approach of giving a 'semantic' of your values : an element in expr is really a notation for a mathematical object that lives in the type sem. But then you have an equation system for which you need to show Church-Rosser and normalization dirty business indeed. That can be done by directing the equations that you know are true : from Add(a,Add(b,c)) = Add(Add(a,b),c) you will derive either Add(a,Add(b,c)) -> Add(Add(a,b),c) or the other way around. I know of two different ways to find normal forms for your expressions expr :ĭefine rewrite rules expr -> expr that correspond to your intuition, and show that they are normalizing. For Min and Max, I don't know I suppose the simplest way is to consider them as if/then/else tests, and make them float to the top of your expressions (duplicating stuff in the process), for example P(Max(Q,R)) would be rewritten into P(if Q>R then Q else R), and then in if Q>R then P(Q) else P(R). If you drop out Min and Max, normal forms are easy: they're elements of the field of fractions on your variables, I mean P/Q where P, Q are polynomials.

Links to papers that present representations for normal forms and/or algorithms for construction/ simplification/ comparison would also help.Īlso, if you know of an Ocaml library that does this let me know. That can be written easily if I know how. The above representation will probably not work too good.Ĭan someone point me out how I should approach this? I don't necessary need code. a + b - a = 0 or a + 1 > a) I need to have some sort of normal form and operate on it. I imagine that in order to perform useful and efficient computation (eg. More exactly I would represent an expression in the following way (Caml code): type sym_expr_t = My problem: symbolic expression manipulation.Ī symbolic expression is built starting from integer constants and variable with the help of operators like +, -, *, /, min,max.

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