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sxeval - an evaluator for symbolic expressions

Symbolic expressions may be interpreted, i.e. evaluated.

Most sx.Objects evaluate to themselves.

sx.Symbols are resolved in an sxeval.Environment to a bound value. If no bound value is found, some actions are taken. See below for details.

A non-empty list is treated differently: its first object must evaluate to a "callable" object, i.e. a function. The other objects of the list are evaluated recursively and are treated as arguments for that function.

The first object of a list may alternatively evaluate to a "syntax" object, also a function. The function is called with the other objects of the list as its arguments. The result of the function call, typically a list, is then evaluated too. This allows some kind of meta-evaluation.

"Callable" and "syntax" objects are defined in the package sxbuiltins.

Evaluation works in three steps:

  1. The object is parsed according to the evaluation rules, resulting in an "expression" object (sxeval.Expr).
  2. Expression objects may be "reworked", into possibly simpler expression objects. For example, if a symbols's value cannot be changed, the symbol lookup can be replaced with its value.
  3. The expression is computed with respect to a given environment, resulting in an object.

This separation allowed to pre-compute the structure of an object, resulting in possibly faster execution time or less memory to store. Parsing an reworking can be done in advance, while computing can be done much later.

To make the steps of evaluation easier to handle, sxeval defines an "environment" type (sxeval.Environment) that provides appropriate functions. Its central attribute is the current "binding".

sxeval.Bindings are effectively just a mapping of sx.Symbols to an sx.Object. A sx.Symbol is bound to a sx.Object.

The are two types of bindings: a constant binding does not allow to update the sx.Object that is bound to the sx.Symbol. A variable binding allows this update.

sxeval.Bindings form a hierarchy: all but one have a parent binding. This allows to overwrite constant bindings somehow: create a child parent and bind the sx.Symbol to another sx.Object, and evaluate a sx.Object in the new child binding.

Resolving a sx.Symbol works as follows: when a sx.Symbol is looked up in a given environment, and it is not bound in that environments binding, the sx.Symbol is resolved in the parent binding.

Of course, there is a binding that does not have a parent binding: the root binding. If a sx.Symbol is not bound in the root binding, the lookup operation fails.