Induction.hs revision 3d3889e0cefcdce9b3f43c53aaa201943ac2e895
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2b4130336e941b7d01c78a6da55449a4c6eca609Till MossakowskiModule : $Header$
2b4130336e941b7d01c78a6da55449a4c6eca609Till MossakowskiDescription : Derive induction schemes from sort generation constraints
2b4130336e941b7d01c78a6da55449a4c6eca609Till MossakowskiCopyright : (c) Till Mossakowski, Rainer Grabbe and Uni Bremen 2002-2006
2b4130336e941b7d01c78a6da55449a4c6eca609Till MossakowskiLicense : GPLv2 or higher, see LICENSE.txt
2b4130336e941b7d01c78a6da55449a4c6eca609Till MossakowskiMaintainer : till@informatik.uni-bremen.de
2b4130336e941b7d01c78a6da55449a4c6eca609Till MossakowskiStability : provisional
2b4130336e941b7d01c78a6da55449a4c6eca609Till MossakowskiPortability : portable
59d823de481014f68b8b024474bffac150b56e1eWiebke HerdingWe provide both second-order induction schemes as well as their
cc6df32dd55910aac7de12b30cc5049d96b8f770Wiebke Herdinginstantiation to specific first-order formulas.
e4e1509ff358e739fddf1483ad39467e0e1becc2Christian Maedermodule CASL.Induction (inductionScheme, generateInductionLemmas) where
e4e1509ff358e739fddf1483ad39467e0e1becc2Christian Maederimport CASL.Quantification (flatVAR_DECLs)
b1f52a36d45c5031c462291e263cec114975add1Wiebke Herdingimport Common.Utils (combine, number)
b1f52a36d45c5031c462291e263cec114975add1Wiebke Herdingimport qualified Data.Set as Set
b1f52a36d45c5031c462291e263cec114975add1Wiebke Herding{- | derive a second-order induction scheme from a sort generation constraint
b1f52a36d45c5031c462291e263cec114975add1Wiebke Herdingthe second-order predicate variables are represented as predicate
2b4130336e941b7d01c78a6da55449a4c6eca609Till Mossakowskisymbols P[s], where s is a sort -}
b1f52a36d45c5031c462291e263cec114975add1Wiebke HerdinginductionScheme :: FormExtension f => [Constraint] -> FORMULA f
b1f52a36d45c5031c462291e263cec114975add1Wiebke HerdinginductionScheme constrs =
b1f52a36d45c5031c462291e263cec114975add1Wiebke Herding induction $ map predSubst constrs
2b4130336e941b7d01c78a6da55449a4c6eca609Till Mossakowski where sorts = map newSort constrs
b1f52a36d45c5031c462291e263cec114975add1Wiebke Herding injective = isInjectiveList sorts
2b4130336e941b7d01c78a6da55449a4c6eca609Till Mossakowski predSubst constr =
2b4130336e941b7d01c78a6da55449a4c6eca609Till Mossakowski (constr, \ t -> Predication predSymb [t] nullRange)
b1f52a36d45c5031c462291e263cec114975add1Wiebke Herding predSymb = Qual_pred_name ident typ nullRange
b1f52a36d45c5031c462291e263cec114975add1Wiebke Herding Id ts cs ps =
b1f52a36d45c5031c462291e263cec114975add1Wiebke Herding if injective then newSort constr else origSort constr
b1f52a36d45c5031c462291e263cec114975add1Wiebke Herding ident = Id [mkSimpleId $ genNamePrefix ++ "P_"
error ("CASL.Induction. mkPrems: "
-> [AS_Anno.Named (FORMULA f)] -- ^ all goals of a theory
-> [AS_Anno.Named (FORMULA f)]
findVar s [] = error ("CASL.generateInductionLemmas:\n"
indSorts = Set.fromList $ map newSort singleDts
case dropWhile (not . (`Set.member` indSorts) . snd) vs of