# Rainbow, a termination proof certification tool
# See the COPYRIGHTS and LICENSE files.

The aim of Rainbow is to check the correctness of termination
certificates for various existing formats. The certification is
currently done by generating a Coq file based on the CoLoR
library. Coq is a powerful proof assistant and checker (see
http://coq.inria.fr) and CoLoR is a Coq library on rewriting and
termination (see https://github.com/fblanqui/color).

LICENSE: this file describes the license governing this tool.
COPYRIGHTS: this file describes the copyrights holders.
INSTALL: this file describes a compilation procedure.
THANKS: thanks to various people for their comments or help.

TPDB is the Termination Problem Data Base available at
http://dev.aspsimon.org/projects/termcomp/downloads/.

The main program is "convert". See INSTALL to build it. It allows you
to convert one problem/proof file from one format to another one. Do
"convert -h" to learn how to use it. We also provide some useful
scripts in the scripts directory:

- check_coq file.xml: convert a CPF file.xml into file.v and check it with coqc

- rename_tpdb: rename TPDB/CPF files to get valid Coq filenames

Various examples are provided in the directory examples/. Do "[g]make
examples" to compile them.

For checking proofs with Coq, make sure that your ~/.coqrc file
contains the following line, where <dir> is the directory where CoLoR
files have been compiled:

  Add Rec LoadPath "<dir>" as CoLoR.

Command for checking a CPF file:

convert -icpf file.cpf -ocoq > file.v && coqc -dont-load-proofs file.v

Or:

check_coq file.xml

-------------------------------------------------------
TPDB termination problems supported by Rainbow
-------------------------------------------------------

- TRS standard
- TRS relative
- TRS modulo equations l=r with Var(l)=Var(r) (e.g. associativity
  and commutativity) are translated into TRS relative
- SRS standard
- SRS relative

-------------------------------------------------------
Proof techniques supported by Rainbow
-------------------------------------------------------

- dependency pair transformation with or without marked symbols
- dependency graph decomposition based on unification
- polynomial interpretation
- matrix interpretation (standard, arctic and below-zero)
- argument filtering
- SRS or unary TRS reversal
- RPO
- loops
- root labelling
- flat context closure

See grammar/proof.xsd for details.

-------------------------------------------------------
Termination problems formats supported by Rainbow
-------------------------------------------------------

- the old TPDB format grammar/tpdb.html (file extensions .trs and .srs)
- the new TPDB format grammar/xtc.xsd (file extension .xtc)
- its own format grammar/problem.xsd (file extension .pb)

-------------------------------------------------------
Termination certificates formats supported by Rainbow
-------------------------------------------------------

- the new common format grammar/cpf.xsd (file extension .cpf)
- its own format grammar/proof.xsd (file extension .prf)

-------------------------------------------------------
Translation of TPDB variable names into CoLoR
-------------------------------------------------------

A variable in a TPDB rule (resp. equation) [LHS -> RHS | cond1, ...,
condn] (resp. [LHS == RHS]) is translated in CoLoR into a natural
number that is its leftmost position (starting from 0) in the list of
variables, computed in a depth-first manner, of the term
F(LHS,cond1,..,condn,RHS) (resp. F(LHS,RHS)) where F is some arbitrary
new symbol of the appropriate arity.

For instance, the rule f(y,y,x)->g(x,h(y)) is translated to
f(0,0,2)->g(2,h(0)) since the list of variables of the rule is
[y;y;x;x;y]. And the dependency pairs computed in CoLoR are
f(0,0,2)->g(2,h(0)) and f(0,0,2)->h(0).