About all this Lisp fuzz
CyberFonic: The axioms you refer to is Church's lambda calculus, the seminal material may be found on John McCarthy's website: http://www-formal.stanford.edu/jmc.  The stuff is like 1960's !There are basically two main camps, Lisp-1 and Lisp-2 and consequently two divergent major families, Scheme and Common Lisp.  From my recollection, the "Lisp Wars" started with hardware implementations, Symbolics vs. Lisp Machines, et al., see http://en.wikipedia.org/wiki/Symbolics.My take is that the hardware implementations came at a time when CPU speeds and memory capacities where not up to the demands of integrated Lisp environments.  By the time speed and memory were sufficient to host Lisp, the world of IT got preoccupied with x86 architecture and Windows.  Neither of these being suitable (in 1980's) as a production Lisp hosting environment.In the hands of an expert Lisper, any version of Lisp quickly becomes extremely productive.  The issues of libraries (FFI) and compilation are addressed in different ways, it's like you have a choice!  It's like asking a guitarist why there are so many brands of guitars? Why don't they all use ____ (insert your pref. brand).To research further, I suggest looking-up "John McCarthy", "Guy Steele", "Richard Gabriel", "Symbolics", "Lisp Machine" on Wikipedia and Google.