Lambda the Ultimate

I'm doing work on designing languages for probabilistic reasoning.

In probability theory, it seems that random variables play the part of a bridge between the informal and the formal. They are defined as functions

Z : Omega -> S

where Omega and S are "sample spaces" (sets that can be quantified by probability measures). Formally, Omega and S are both well-defined. In practice, Omega seems to be regarded as the set of all possible realities, which Z can operate on and return formal values in S. (It seems that it has to be, or probability users couldn't use probability theory to theorize about real-world phenomena.)

I was recently reading Olin Shivers's excellent dissertation, in which he states that free variables can be seen as bridging the informal with the formal. In other words, a program that consists of just an identifier "x" (assuming valid programs can have free variables) can be taken as meaning

x  ; to be changed later by some external, informal process

or that the context of "x", which "x" will be embedded in later by an external process, will determine its value.

I'm interested in explaining random variables in familiar terms. Besides Shivers's observation, I've had I/O functions suggested. What have you come across that can be regarded as bridging the informal and the formal?

Neil T

Hello All,

I hope this is not off topic.

Jacques Pitrat (one of France's first Artificial Intelligence researcher, working on symbolic and declarative meta-knowledge.) has just published his Malice constraint satisfaction problem solver (GPLv3 licence).

While the user interface of Malice is very primitive, the ideas and formalisms implemented inside Malice could interest some people.

I also found his book Artificial Beings (the conscience of a conscious machine) interesting, and provocative, explaining the interest of reflective software systems.

Regards.

See here.