advancedresearch/poi

In order to explain how Poi works, one needs to explain a bit about Path Semantics.Path Semantics is an extremely expressive language for mathematical programming, Path Semantics is often used in combination with Category Theory, Logic, etc.A "path" (or "normal path") is a way of navigating between functions, for example:Translated into words, this sentence means:In normal programming, there is no way to express this idea directly, Composition in path-space is just function composition:If one imagines computation = 2D, then computation + path-space = 3D.Path Semantics can be thought of as "point-free style" sub-set of equations. The more general and expressive a theory is, the harder it is to do proof search.As a consequence, theorem proving along both computation + path-space is In Path Semantics, if you say "the natural numbers", you mean the natural numbers, not the natural numbers as described by the Peano axioms. This is what the "semantics" in Path Semantics means.It is possible to express ideas in Path Semantics which are believed to be true, Path Semantics requires no or little type checking in the "point-free style".Poi is designed to be used as a Rust library.It means that anybody can create their own tools on top of Poi, advanced path semantical knowledge.A symbol contains every domain-specific symbol and "avatar extensions" This means that point-free transformations on functions sometimes can compute stuff, without explicitly needing to reference the concrete value directly.