Context

The notion of a context is a universal one.

A set of name-value (or name-concept) directed pairs or bindings is called an environment or a context (when it is being passing along).

In logic it corresponds to the set \(\Gamma\)

In programming it is the global namespace.

A local context in programming is a lexical closure which captures the values of all “free” variables.

Expressions are always evaluated within some context and can contain occurrences of the names (references) found in that context.

This is the core of any system of logic. What is already proven is in \(\G\).

The evaluator will use the definitions associated with these names as rules for simplifiying (reducing) expressions.

Mathematical thinking is a whole way of looking at things, of stripping them down to their numerical, structural, or logical essentials, and of analyzing the underlying patterns.

The meaning of an expression is its value and there are no other effects, hidden or otherwise, in any procedure for actually obtaining it. Furthermore,

Expressions can be evaluated by a basically simple process of substitution and simplification, using both primitive rules and rules supplied by the programmer in the form of definitions.

Conceptually this is a set of ordered pairs (or relations).

In the classic (old-school) terms a context is represented as an alist or a list of pairs.