adp-multi-0.2.2: tests/ADP/Tests/RGExample.hs
{-# LANGUAGE DeriveDataTypeable #-}
{-
Example using the Reeder&Giegerich class of pseudoknots.
(with only the first canonization rule applied)
The grammar was taken from:
Markus E. Nebel and Frank Weinberg. Algebraic and Combinatorial Properties of Common
RNA Pseudoknot Classes with Applications. 2012.
The original algorithm (not in grammar form) can be found in:
Jens Reeder and Robert Giegerich. Design, implementation and evaluation of a practical
pseudoknot folding algorithm based on thermodynamics. BMC Bioinformatics, 5:104, 2004.
-}
module ADP.Tests.RGExample where
import Data.Typeable
import Data.Data
import ADP.Multi.All
import ADP.Multi.Rewriting.All
type RG_Algebra alphabet answer = (
EPS -> answer, -- nil
answer -> answer -> answer, -- left
answer -> answer -> answer -> answer, -- pair
answer -> answer -> answer -> answer -> answer -> answer -> answer, -- knot
answer -> answer -> answer, -- knot1
answer -> answer, -- knot2
(alphabet, alphabet) -> answer, -- basepair
alphabet -> answer, -- base
[answer] -> [answer] -- h
)
infixl ***
(***) :: (Eq b, Eq c) => RG_Algebra a b -> RG_Algebra a c -> RG_Algebra a (b,c)
alg1 *** alg2 = (nil,left,pair,knot,knot1,knot2,basepair,base,h) where
(nil',left',pair',knot',knot1',knot2',basepair',base',h') = alg1
(nil'',left'',pair'',knot'',knot1'',knot2'',basepair'',base'',h'') = alg2
nil a = (nil' a, nil'' a)
left (b1,b2) (s1,s2) = (left' b1 s1, left'' b2 s2)
pair (p1,p2) (s11,s21) (s12,s22) = (pair' p1 s11 s12, pair'' p2 s21 s22)
knot (k11,k21) (k12,k22) (s11,s21) (s12,s22) (s13,s23) (s14,s24) =
(knot' k11 k12 s11 s12 s13 s14, knot'' k21 k22 s21 s22 s23 s24)
knot1 (p1,p2) (k1,k2) = (knot1' p1 k1, knot1'' p2 k2)
knot2 (p1,p2) = (knot2' p1, knot2'' p2)
basepair a = (basepair' a, basepair'' a)
base a = (base' a, base'' a)
h xs = [ (x1,x2) |
x1 <- h' [ y1 | (y1,_) <- xs]
, x2 <- h'' [ y2 | (y1,y2) <- xs, y1 == x1]
]
-- This data type is used only for the enum algebra.
-- The type allows invalid trees which would be impossible to build
-- with the given grammar rules.
-- As an additional (programming) error check, a second debug enum algebra checks
-- the types via pattern-matching.
data Start = Nil
| Left' Start Start
| Pair Start Start Start
| Knot Start Start Start Start Start Start
| Knot1 Start Start
| Knot2 Start
| BasePair (Char, Char)
| Base Char
deriving (Eq, Show, Data, Typeable)
-- without consistency checks
enum :: RG_Algebra Char Start
enum = (\_->Nil,Left',Pair,Knot,Knot1,Knot2,BasePair,Base,id)
-- with consistency checks
enumDebug :: RG_Algebra Char Start
enumDebug = (nil,left,pair,knot,knot1,knot2,basepair,base,h) where
s' = [Nil, Left'{}, Pair{}, Knot{}]
k' = [Knot1 {}, Knot2 {}]
nil _ = Nil
left b@(Base _) s
| s `isOf` s' = Left' b s
pair p@(BasePair _) s1 s2
| [s1,s2] `areOf` s' = Pair p s1 s2
knot k1 k2 s1 s2 s3 s4
| [k1,k2] `areOf` k' && [s1,s2,s3,s4] `areOf` s' = Knot k1 k2 s1 s2 s3 s4
knot1 p@(BasePair _) k
| k `isOf` k' = Knot1 p k
knot2 p@(BasePair _) = Knot2 p
basepair = BasePair
base = Base
h = id
isOf l r = toConstr l `elem` map toConstr r
areOf l r = all (`isOf` r) l
maxBasepairs :: RG_Algebra Char Int
maxBasepairs = (nil,left,pair,knot,knot1,knot2,basepair,base,h) where
nil _ = 0
left a b = a + b
pair a b c = a + b + c
knot a b c d e f = a + b + c + d + e + f
knot1 a b = a + b
knot2 a = a
basepair _ = 1
base _ = 0
h [] = []
h xs = [maximum xs]
maxKnots :: RG_Algebra Char Int
maxKnots = (nil,left,pair,knot,knot1,knot2,basepair,base,h) where
nil _ = 0
left _ b = b
pair _ b c = b + c
knot _ _ c d e f = 1 + c + d + e + f
knot1 _ _ = 0
knot2 _ = 0
basepair _ = 0
base _ = 0
h [] = []
h xs = [maximum xs]
-- The left part is the structure and the right part the reconstructed input.
prettyprint :: RG_Algebra Char ([String],[String])
prettyprint = (nil,left,pair,knot,knot1,knot2,basepair,base,h) where
nil _ = ([""],[""])
left (bl,br) (sl,sr) =
(
[concat $ bl ++ sl],
[concat $ br ++ sr]
)
pair ([p1l,p2l],[p1r,p2r]) (s1l,s1r) (s2l,s2r) =
(
[concat $ [p1l] ++ s1l ++ [p2l] ++ s2l],
[concat $ [p1r] ++ s1r ++ [p2r] ++ s2r]
)
knot ([k11l,k12l],[k11r,k12r]) ([k21l,k22l],[k21r,k22r]) (s1l,s1r) (s2l,s2r) (s3l,s3r) (s4l,s4r) =
let (k11l',k12l') = square k11l k12l
in
(
[concat $ [k11l'] ++ s1l ++ [k21l] ++ s2l ++ [k12l'] ++ s3l ++ [k22l] ++ s4l],
[concat $ [k11r] ++ s1r ++ [k21r] ++ s2r ++ [k12r] ++ s3r ++ [k22r] ++ s4r]
)
knot1 ([p1l,p2l],[p1r,p2r]) ([k1l,k2l],[k1r,k2r]) =
(
[concat $ [k1l] ++ [p1l], concat $ [p2l] ++ [k2l]],
[concat $ [k1r] ++ [p1r], concat $ [p2r] ++ [k2r]]
)
knot2 (pl,pr) = (pl, pr)
basepair (b1,b2) = (["(",")"], [[b1],[b2]])
base b = (["."], [[b]])
h = id
square l r = (map (const '[') l, map (const ']') r)
pstree :: RG_Algebra Char String
pstree = (nil,left,pair,knot,knot1,knot2,basepair,base,h) where
nil _ = "\\function{(\\op{f}_3,\\op{r}_0)}"
left b s = "\\pstree{\\function{(\\op{f}_1,\\op{r}_1)}}{" ++ b ++ s ++ "}"
pair p s1 s2 = "\\pstree{\\function{(\\op{f}_2,\\op{r}_2})}{" ++ p ++ s1 ++ s2 ++ "}"
knot k1 k2 s1 s2 s3 s4 = "\\pstree{\\function{(\\op{f}_4,\\op{r}_3)}}{" ++ k1 ++ k2 ++ s1 ++ s2 ++ s3 ++ s4 ++ "}"
knot1 p k = "\\pstree{\\function{(\\op{f}_5,\\op{r}_4})}{" ++ k ++ p ++ "}"
knot2 p = "\\pstree{\\function{(\\op{f}_6,\\op{id})}}{" ++ p ++ "}"
basepair (p1,p2) = "\\pstree{\\function{(\\op{f}_7,\\op{id})}}{\\terminalvec{" ++ [p1] ++ "}{" ++ [p2] ++ "}}"
base b = "\\pstree{\\function{(\\op{f}_8,\\op{id})}}{\\terminal{" ++ [b] ++ "}}"
h = id
pstreeYield :: RG_Algebra Char String
pstreeYield = (nil,left,pair,knot,knot1,knot2,basepair,base,h) where
nil _ = "\\function{\\op{r}_0}"
left b s = "\\pstree{\\function{\\op{r}_1}}{" ++ b ++ s ++ "}"
pair p s1 s2 = "\\pstree{\\function{\\op{r}_2}}{" ++ p ++ s1 ++ s2 ++ "}"
knot k1 k2 s1 s2 s3 s4 = "\\pstree{\\function{\\op{r}_3}}{" ++ k1 ++ k2 ++ s1 ++ s2 ++ s3 ++ s4 ++ "}"
knot1 p k = "\\pstree{\\function{\\op{r}_4}}{" ++ k ++ p ++ "}"
knot2 p = "\\pstree{\\function{\\op{id}}}{" ++ p ++ "}"
basepair (p1,p2) = "\\pstree{\\function{\\op{id}}}{\\terminalvec{" ++ [p1] ++ "}{" ++ [p2] ++ "}}"
base b = "\\pstree{\\function{\\op{id}}}{\\terminal{" ++ [b] ++ "}}"
h = id
pstreeEval :: RG_Algebra Char String
pstreeEval = (nil,left,pair,knot,knot1,knot2,basepair,base,h) where
nil _ = "\\function{\\op{f}_3}"
left b s = "\\pstree{\\function{\\op{f}_1}}{" ++ b ++ s ++ "}"
pair p s1 s2 = "\\pstree{\\function{\\op{f}_2})}{" ++ p ++ s1 ++ s2 ++ "}"
knot k1 k2 s1 s2 s3 s4 = "\\pstree{\\function{\\op{f}_4}}{" ++ k1 ++ k2 ++ s1 ++ s2 ++ s3 ++ s4 ++ "}"
knot1 p k = "\\pstree{\\function{\\op{f}_5}}{" ++ k ++ p ++ "}"
knot2 p = "\\pstree{\\function{\\op{f}_6}}{" ++ p ++ "}"
basepair (p1,p2) = "\\pstree{\\function{\\op{f}_7}}{\\terminalvec{" ++ [p1] ++ "}{" ++ [p2] ++ "}}"
base b = "\\pstree{\\function{\\op{f}_8}}{\\terminal{" ++ [b] ++ "}}"
h = id
rgknot :: RG_Algebra Char answer -> String -> [answer]
rgknot algebra inp =
let
(nil,left,pair,knot,knot1,knot2,basepair,base,h) = algebra
rewritePair, rewriteKnot :: Dim1
rewritePair [p1,p2,s1,s2] = [p1,s1,p2,s2]
rewriteKnot [k11,k12,k21,k22,s1,s2,s3,s4] = [k11,s1,k21,s2,k12,s3,k22,s4]
s = tabulated1 $
yieldSize1 (0,Nothing) $
nil <<< EPS >>> id1 |||
left <<< b ~~~ s >>> id1 |||
pair <<< p ~~~ s ~~~ s >>> rewritePair |||
knot <<< k ~~~ k ~~~ s ~~~ s ~~~ s ~~~ s >>> rewriteKnot
... h
b = tabulated1 $
base <<< 'a' >>> id1 |||
base <<< 'u' >>> id1 |||
base <<< 'c' >>> id1 |||
base <<< 'g' >>> id1
... h
p = tabulated2 $
basepair <<< ('a', 'u') >>> id2 |||
basepair <<< ('u', 'a') >>> id2 |||
basepair <<< ('c', 'g') >>> id2 |||
basepair <<< ('g', 'c') >>> id2 |||
basepair <<< ('g', 'u') >>> id2 |||
basepair <<< ('u', 'g') >>> id2
... h
rewriteKnot1 :: Dim2
rewriteKnot1 [p1,p2,k1,k2] = ([k1,p1],[p2,k2])
k = tabulated2 $
yieldSize2 (1,Nothing) (1,Nothing) $
knot1 <<< p ~~~ k >>> rewriteKnot1 |||
knot2 <<< p >>> id2
... h
z = mk inp
tabulated1 = table1 z
tabulated2 = table2 z
in axiom z s