Technische Universität München,
Fakultät für Informatik
Lehrstuhl Informatik IV,
Research Group Automated Reasoning
E: Questions and Answers
To put it short, E is a theorem prover and PROLOG is a programming
language. Although they both can solve a common subset of problems,
there are some significant differences. E works in a bottom-up
fashion, systematically generating consequences from the set of input
clauses, until a contradictiom (i.e. a proof) has been found. PROLOG
uses SLD resolution to find a solution in a top-down depth-first
fashion, and, consequently, is not complete, i.e. it can run forever
although a solution exists.
Here is a list of the most important differences:
- Advantages of PROLOG:
- You can write procedural code with semi-explicit control flow
and cuts.
- PROLOG has a pretty rich set of predefined predicates,
i.e. numbers, arithmetic, I/O-Statements and so on.
- PROLOG
is a mature technology, and may be faster for some
classes of probems.
- Advantages of E:
- E has purely declarative semantics: a<-b. is fully
equivalent to a;~b. is fully equivalent to
~b;a. is fully equivalent to ~b<-~a. While E
allows procedural clauses (as in a:-b.), that is only
for compatibility with SETHEO. Procedural clauses are treated exactly
as declarative ones. The most natural clause representation for E
is probably a literal disjunction:
a=$true;b!=$true;c!=$true.
- E has a richer language, not restricted to Horn clauses (i.e. we
can write a;b <- c,d., meaning "if c and d then a or
b"). You can use explicitly negated atoms, as in ~a <-
b. (In fact, starting with E 0.82, E supports full first
order format in TPTP and TSTP syntax, for a much richer
input language).
- E has basically no predefined predicates and function
symbols. You want it - you specify it. No relying on cheesy
machine arithmetic ;-)
- E is complete. If the query follows from the axioms, E will find a
proof (well, theoretically - in practice the computer or the user may
run out of resources or patience) unless the user explicitly selects
an incomplete search strategy.
- E has a different (stronger) concept of equality on terms, not modulo
unification, but modulo an equational first-order theory (which
is part of the input problem).
- Due to clever search strategies, E may be faster for some classes
of problems.
You can try to get E and feed some simple PROLOG code into it to see
what happens (simple means "no numbers, no predefined predicates"). As
far as I know, the LOP syntax of E is a superset of basic PROLOG
without numbers and predefined symbols (but I am not very much into
PROLOG).
I'm now doing a lot of development work off-line on my laptop. As one
consequence, the snapshot was only updated very infrequently. As few
people used it, I just decided to discontinue it. Email me for the
latest version (you get the added benefit of a defined state ;-).
Not any longer. It did for some time, but finally feature creep has
caught up with this mysterious effect.
I did not have a good explanation for the effect while it
lasted. While I am always trying to cut some old cruft here and there,
I also keep adding new features. Some of the effect may be due to
random amounts of backup files or profiling data in the
directories. All in all, I just put it down as a strange and
interesting effect.
Because C++ sucks big rocks through small straws like nothing short of
a pack of giant vampire squids. Yes, really, that's the reason ;-)
Moreover, the latest versions are not called CLIB anymore, but just E.
Starting with E 0.22, each release version has received a
nickname. This usually is the name of a tea (or the corresponding tea
garden) which I drank a lot while programming the version.
- Risheehat is the name of a tea garden in Darjeeling
making one of the worlds finest first flush Darjeeling teas.
- Yunnan is a region in China producing a famous black
tea with a redish tint.
- Castleton is a very small tea garden in Darjeeling
making an excellent second flush Darjeeling tea.
- Jungpana is a tea garden in Darjeeling
making a very good and quite famous second flush Darjeeling tea.
- Lingia is a tea garden
making a very good first flush Darjeeling tea. It's nearly as
good as the Risheehat (in my opinion), but more expensive.
- Phuguri is a decent first flush
Darjeeling I tried during the work on E 0.5.
- Mim is a very fine first flush Darjeeling that,
surprisingly enough, can stand hard water fairly well, and which
I hence tend to drink a lot while travelling.
- Kanchanjangha is an ecologically produced tea from
Nepal. I quite like Nepalese tea, and tried to find a new
variety. It is not bad, but not up to the Darjeelings I am used
to (yes, I am a tea snob).
- North Tukvar is a somewhat bigger tea garden in
Darjeeling. Their claim to fame is that they managed to bring the
first tea of the 2001 harvesting period into my tea shop.
- Mullotar is a fairly large tea garden producing a quite
nice organically grown first flush that offers excellent value
for money (if you buy a kilogramm at a time ;-)
- Nuwara Eliya is one of the very best Ceylon (now Sri
Lanka) highland teas.
- Dhajea is a tea garden making a very good (not quite
great) first flush Darjeeling tea.
- Puttabong is another Darjeeling tea garden which
provided me with a very good new harvest first flush in 2003.
- Steinthal is a small, but quite old and famous
Darjeeling tea garden, with particularly good second flush teas.
- Tumsong is a medium sized garden in Eastern Darjeeling.
- Lung Ching or Dragon's Well Tea is a famous
(and quite good) gree tea from the Zhejiang province in mainland
China.
- Soom is a tea garden in Darjeeling supplying me with a
lot of new early harvest tea in 2005.
- Kanyam is a tea garden in Nepal. I am impressed - I
found that a 2005 first flush Kanyam was comparable to
my rather good Darjeelings!
- Singtom is a Darjeeling tea garden.
- Longview is another Darjeeling tea garden providing an
excellent 2007 first flush.
- Temi is a very good tea from Sikkim on the Southern
slopes of the Himalaya.
- Balasun is the tea estate in the Eastern Himalaya that
provided me with a very nice 2009 early harvest Darjeeling.
Yes, a couple of groups do work on theorem proving. The people at the
Argonne National Laboratories have a
fairly complete
list. There also is an introduction to automated
reasoning on the web, which has another list of
systems.There are a couple of theorem provers that had not insignificant
influence on the design of E:
- SETHEO
is a top-down model-elemination prover. It's fate is to be mated to E
and thus to form a composite prover. This shows
particularly in the fact that E's native input syntax is a
dialect of LOP as used by SETHEO.
- DISCOUNT
and Waldmeister
are two provers for unit-equational problems. Experiences with
DISCOUNT have had a profound effect on many design decisions
for E, in particular on the way search heuristics are
specified. The extremely impressive results of Waldmeister made
me choose perfect discrimination trees as the main indexing
structure in E.
- SPASS is the first high
performance theorem prover based on superposition I became
aware of. I use it as a benchmarking tool and for debugging
("If it's easy for SPASS it should be easy for E").
- Finally, Otter
(or, more exactly, discussions with it's main author, Bill McCune)
also gave me some ideas now incorporated into E. Bill has a new
system, Prover
9, that borrows from E in return.
- Vampire
is another high-performance theorem prover. E and Vampire are
about as far from each other as two high-performance
saturationg provers can be. However, there is a useful exchange
of ideas.
Stephan
Schulz,schulz@informatik.tu-muenchen.de, 5.7.2000