Power vs Safety

I heard one time the idea that one should use the least powerful tool powerful enough to solve a problem. I didn't understand this at the time, but I've recently come to an understanding (not necessarily the meaning of the person who wrote it).

My first interpretation of this idea was that one should use the tool (I'm thinking in particular about programming languages, but this is more general then just that) with the fewest features. I thought I would rather use the *most* powerful tool I could find. I can understand, for example, not embedding a full programming language into a program if all you want is to let users enter arithmetic expressions, but not, for example, using BASIC rather than Haskell if its an option. You can benefit from simplicity, but I don't see an advantage to using languages without useful features just because you don't strictly *need* them.

Recently I came to another interpretation of this idea. It is common in computer science for there to be a series of systems of varying power that can solve increasingly difficult problems. The catch is that the more powerful the systems the weaker the statements one can make about them. This is true in automata theory (FSM < DFM < Pushdown Automata < Nondeterministic Pushdown Automata < Turing Machine, (although DFM < FSM as well)), the typed lambda calculus (the hierarchy is less obvious (at least to me), but much research goes into coming up with powerful systems (the calculus of constructions, for example) that are still weaker than the untyped lambda calculus to retain properties such as strong normalization or confluence), optimization theory (where you classify problems by the weakest form of optimization that can solve them), recursion theory (primitive recursion < mu-recursion (that about all I know about recursion theory)), abstract grammars (regular grammars < context free grammars < context sensitive grammar < universal grammar). Each of these situations (and more, I'm sure) have many more levels between the ones I happen to have heard of.

Taking automata as an example, each level in that hierarchy can solve all problems solvable by ones lower down, but can't solve all problems solvable by ones at higher levels. However, at each level we lose some assurances about termination or resource use. Finite automata are guaranteed to terminate, but the more powerful Turing Machines are not. Expressions typeable in the polymorphic lambda calculus reduce to a normal form, where untyped expressions do not always have such a form. Equality of regular grammars is decidable, but not so for context free grammars in general. We won't have strange optimization techniques like Genetic Algorithms if every problem were linear.

This is really a very common situation, where we would like to determine the least powerful system powerful enough to solve our problem simply so that we can make as many assurances about the solution as possible. This is also one of the ways that things like closure operators and adjunctions come into computer science ("the least thing great enough to" or "the greatest thing less then"). I think it may even be a fundamental part of computation in some way that I don't know how to formalize. Regardless, it is certainly true that a great deal of effort goes into doing exactly this- using the least powerful tool powerful enough to solve a problem.