Programming Languages as Mathematical Representations
To those of you with math backgrounds....
A random conversation, about math and machine learning, led me to wondering - LISP & lambda calculus aside - is it reasonable to view programming languages as mathematical representations?
After all - a program represents a set of logical/mathematical relationships - be it descriptive, a model, or a series of operations - not unlike the way a set of differential equations can model a physical system (and be used to predict behavior).
Are there fundamental differences, beyond the symbology and grammars, that differentiate a set of equations from a program?
I ask this partly out of intellectual curiosity, and partly because, when it comes to analyzing and modeling systems, my mind tends to think in terms of code, rather than formulas - and I kind of wonder if there's really something fundamentally different about the thought process, or is it more akin to the difference between, say, differential and integral forms?
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