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[Axiom-developer] Embedding Axiom (Hickey and fold/unfold) and rule base

From: Tim Daly
Subject: [Axiom-developer] Embedding Axiom (Hickey and fold/unfold) and rule based programming
Date: Sat, 21 Nov 2009 11:58:54 -0500
User-agent: Thunderbird (Windows/20090302)

Martin Baker wrote:
On Friday 20 November 2009 23:17:25 Tim Daly wrote:
There is an excellent talk by Rich Hickey about modelling time, identity, values,
perception, state, memory, etc.


While I was watching this talk I was wondering about the difference between the mainstream computing issues verses mathematical computing issues.

I get the impression that the mainstream issue, from this talk, is about how to run multiple algorithms in parallel?

If we are trying to solve a set of equations, is there a natural parallelism ? For the reasons discussed in the talk, should a rule based method be preferred wherever possible and explicit coding of algorithms be discouraged?

Martin Baker


I don't know but I have some thoughts on the subject.

The first comment is that I have deep experience in rule based programming (I was a team member on a commercial rule-based programming product at IBM, we also built a huge expert system (FAME) on a combination rule-based/knowedge-rep system I built (KROPS), one of my two thesis topics was on the subject of rules, I use them in work on our current
Function Extraction project, etc)

I fear rule-based programming. It has the siren-song subtle appeal of being very easy to state "WHEN this DO thisthing". When you get into a problem, the solution is to add another rule to solve that particular case. Ultimately, you end up in a situation like the dinosaur in the tarpit... he can lift any leg but he cannot get out of the pit.

Rule based systems are subject to two general classes of failure. Either they simply stop because no rule applies or they go into an infinite loop because a prior state repeats. I do not know of a general way to verify and validate a rule based program (which was the subject of the thesis). In fact, they are extremely hard to debug. You can't use "print" statements or debuggers. Tracing is a swamp of output. Every rule could
be perfectly correct and the program is still wrong (witness the dinosaur).

Worse yet, the whole system working system can become unhinged by the addition of
just one "obviously correct" rule.

The second problem with rule-based programming is that they are not generally designed to be "theory-aware". For instance, you can write rules in Axiom to do simplification by pattern matching. You could write rules such as "divide each side by a constant". The problem is "what if the constant is zero?".... Ok, we can fix that with a rule... But now someone wants to use your simplification ruleset in a different domain (e.g. a domain which is non-associative for instance)... where does your ruleset assume associative? How does that assumption affect other rules? What if I want to apply "obviously correct" formulas (e.g. x = sqrt(x^2))? But is this correct if x=-1? Theory-aware systems need to be built on a consistent world based on consistent axioms. This kind of effort feels like a
"Principia" approach which Godel undermined.

I don't think rules will operate correctly in parallel either (although I have not tried). For rules to operate effectively they need to perceive (to use Hickey's term) the world in some consistent state. But a parallel system will undermine that assumption. A parallel dinosaur could be in a state with all of its feet out of the tar since each process is "lifting" one foot, (the dinosaur effectively "jumped") but the problem isn't solved.

Hickey is advocating pure functions which move from state to state, which look a lot like rules but they can be much more theory aware and they can be applied in a
procedural way.

Curiously, Hickey does not define functions on Identities, claiming
they are an emergent property of states. But we do reason about Identities also (they are meta-states, I guess). The river may not be the same from moment to moment except before the river flows and after the river dries up. The Identity of
a river has a lifetime above and beyond its states.


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