forked from GitHub/gf-core
the first approximation for a statistical model consistent with dependent types in the abstract syntax
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kr.angelov
@@ -9,14 +9,17 @@ module PGF.Probabilistic
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, probTree
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, rankTreesByProbs
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, mkProbDefs
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) where
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import PGF.CId
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import PGF.Data
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import PGF.Macros
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import PGF.Type
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import PGF.Expr
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import qualified Data.Map as Map
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import Data.List (sortBy,partition)
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import Data.List (sortBy,partition,nub,mapAccumL)
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import Data.Maybe (fromMaybe, fromJust)
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-- | An abstract data structure which represents
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@@ -99,3 +102,179 @@ rankTreesByProbs pgf ts = sortBy (\ (_,p) (_,q) -> compare q p)
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[(t, probTree pgf t) | t <- ts]
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mkProbDefs :: PGF -> ([[CId]],[(CId,Type,[Equation])])
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mkProbDefs pgf =
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let cs = [(c,hyps,fns) | (c,(hyps0,fs,_)) <- Map.toList (cats (abstract pgf)),
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not (elem c [cidString,cidInt,cidFloat]),
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let hyps = zipWith (\(bt,_,ty) n -> (bt,mkCId ('v':show n),ty))
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hyps0
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[1..]
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fns = [(f,ty) | (_,f) <- fs,
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let Just (ty,_,_,_,_) = Map.lookup f (funs (abstract pgf))]
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]
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((_,css),eqss) = mapAccumL (\(ngen,css) (c,hyps,fns) ->
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let st0 = (1,Map.empty)
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((_,eqs_map),cs) = computeConstrs pgf st0 [(fn,[],es) | (fn,(DTyp _ _ es)) <- fns]
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(ngen', eqs) = mapAccumL (mkEquation eqs_map hyps) ngen fns
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ceqs = [(id,DTyp [] cidFloat [],reverse eqs) | (id,eqs) <- Map.toList eqs_map, not (null eqs)]
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in ((ngen',cs:css),(p_f c, mkType c hyps, eqs):ceqs)) (1,[]) cs
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in (reverse (concat css),concat eqss)
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where
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mkEImplArg bt e
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| bt == Explicit = e
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| otherwise = EImplArg e
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mkPImplArg bt p
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| bt == Explicit = p
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| otherwise = PImplArg p
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mkType c hyps =
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DTyp (hyps++[mkHypo (DTyp [] c es)]) cidFloat []
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where
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is = reverse [0..length hyps-1]
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es = [mkEImplArg bt (EVar i) | (i,(bt,_,_)) <- zip is hyps]
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sig = (funs (abstract pgf), \_ -> Nothing)
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mkEquation ceqs hyps ngen (fn,ty@(DTyp args _ es)) =
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let fs1 = case Map.lookup (p_f fn) ceqs of
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Nothing -> [mkApp (k_f fn) (map (\(i,_) -> EVar (k-i-1)) vs1)]
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Just eqs | null eqs -> []
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| otherwise -> [mkApp (p_f fn) (map (\(i,_) -> EVar (k-i-1)) vs1)]
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(ngen',fs2) = mapAccumL mkFactor2 ngen vs2
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fs3 = map mkFactor3 vs3
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eq = Equ (map mkTildeP xes++[PApp fn (zipWith mkArgP [1..] args)])
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(mkMult (fs1++fs2++fs3))
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in (ngen',eq)
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where
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xes = map (normalForm sig k env) es
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mkTildeP e =
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case e of
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EImplArg e -> PImplArg (PTilde e)
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e -> PTilde e
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mkArgP n (bt,_,_) = mkPImplArg bt (PVar (mkCId ('v':show n)))
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mkMult [] = ELit (LFlt 1)
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mkMult [e] = e
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mkMult es = mkApp (mkCId "mult") es
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mkFactor2 ngen (src,dst) =
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let vs = [EVar (k-i-1) | (i,ty) <- src]
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in (ngen+1,mkApp (p_i ngen) vs)
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mkFactor3 (i,DTyp _ c es) =
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let v = EVar (k-i-1)
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in mkApp (p_f c) (map (normalForm sig k env) es++[v])
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(k,env,vs1,vs2,vs3) = mkDeps ty
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mkDeps (DTyp args _ es) =
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let (k,env,dep1) = updateArgs 0 [] [] args
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dep2 = foldl (update k env) dep1 es
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(vs2,vs3) = closure k dep2 [] []
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vs1 = concat [src | (src,dst) <- dep2, elem k dst]
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in (k,map (\k -> VGen k []) env,vs1,reverse vs2,vs3)
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where
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updateArgs k env dep [] = (k,env,dep)
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updateArgs k env dep ((_,x,ty@(DTyp _ _ es)) : args) =
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let dep1 = foldl (update k env) dep es ++ [([(k,ty)],[])]
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env1 | x == wildCId = env
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| otherwise = k : env
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in updateArgs (k+1) env1 dep1 args
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update k env dep e =
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case e of
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EApp e1 e2 -> update k env (update k env dep e1) e2
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EFun _ -> dep
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EVar i -> let (dep1,(src,dst):dep2) = splitAt (env !! i) dep
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in dep1++(src,k:dst):dep2
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closure k [] vs2 vs3 = (vs2,vs3)
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closure k ((src,dst):deps) vs2 vs3
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| null dst = closure k deps vs2 (vs3++src)
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| otherwise =
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let (deps1,deps2) = partition (\(src',dst') -> not (null [v1 | v1 <- dst, v2 <- dst', v1 == v2])) deps
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deps3 = (src,dst):deps1
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src2 = concatMap fst deps3
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dst2 = [v | v <- concatMap snd deps3
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, lookup v src2 == Nothing]
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dep2 = (src2,dst2)
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dst' = nub dst
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in if null deps1
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then if dst' == [k]
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then closure k deps2 vs2 vs3
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else closure k deps2 ((src,dst') : vs2) vs3
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else closure k (dep2 : deps2) vs2 vs3
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mkNewSig src =
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DTyp (mkArgs 0 0 [] src) cidFloat []
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where
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mkArgs k l env [] = []
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mkArgs k l env ((i,DTyp _ c es) : src)
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| i == k = let ty = DTyp [] c (map (normalForm sig k env) es)
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in (Explicit,wildCId,ty) : mkArgs (k+1) (l+1) (VGen l [] : env) src
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| otherwise = mkArgs (k+1) l (VMeta 0 env [] : env) src
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type CState = (Int,Map.Map CId [Equation])
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computeConstrs :: PGF -> CState -> [(CId,[Patt],[Expr])] -> (CState,[[CId]])
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computeConstrs pgf (ngen,eqs_map) fns@((id,pts,[]):rest)
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| null rest =
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let eqs_map' =
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Map.insertWith (++) (p_f id)
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(if null pts
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then []
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else [Equ pts (ELit (LFlt 1.0))])
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eqs_map
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in ((ngen,eqs_map'),[])
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| otherwise =
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let (st,ks) = mapAccumL mk_k (ngen,eqs_map) fns
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mk_k (ngen,eqs_map) (id,pts,[])
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| null pts = ((ngen,eqs_map),k_f id)
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| otherwise = let eqs_map' =
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Map.insertWith (++)
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(p_f id)
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[Equ pts (EFun (k_i ngen))]
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eqs_map
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in ((ngen+1,eqs_map'),k_i ngen)
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in (st,[ks])
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computeConstrs pgf st fns =
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let (st',res) = mapAccumL (\st (p,fns) -> computeConstrs pgf st fns)
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st
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(computeConstr fns)
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in (st',concat res)
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where
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computeConstr fns = merge (split fns (Map.empty,[]))
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merge (cns,vrs) =
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[(p,fns++[(id,ps++[p],es) | (id,ps,es) <- vrs])
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| (p,fns) <- concatMap addArgs (Map.toList cns)]
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++
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if null vrs
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then []
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else [(PWild,[(id,ps++[PWild],es) | (id,ps,es) <- vrs])]
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where
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addArgs (cn,fns) = addArg (length args) cn [] fns
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where
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Just (ty@(DTyp args _ es),_,_,_,_) = Map.lookup cn (funs (abstract pgf))
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addArg 0 cn ps fns = [(PApp cn (reverse ps),fns)]
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addArg n cn ps fns = concat [addArg (n-1) cn (arg:ps) fns' | (arg,fns') <- computeConstr fns]
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split [] (cns,vrs) = (cns,vrs)
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split ((id, ps, e:es):fns) (cns,vrs) = split fns (extract e [])
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where
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extract (EFun cn) args = (Map.insertWith (++) cn [(id,ps,args++es)] cns, vrs)
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extract (EVar i) args = (cns, (id,ps,es):vrs)
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extract (EApp e1 e2) args = extract e1 (e2:args)
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extract (ETyped e ty) args = extract e args
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extract (EImplArg e) args = extract e args
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p_f c = mkCId ("p_"++showCId c)
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p_i i = mkCId ("p_"++show i)
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k_f f = mkCId ("k_"++showCId f)
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k_i i = mkCId ("k_"++show i)
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