# 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).