{- |

Module : $Header$

Description : Maude Morphisms

Copyright : (c) Martin Kuehl, Uni Bremen 2008-2009

License : similar to LGPL, see HetCATS/LICENSE.txt or LIZENZ.txt

Maintainer : mkhl@informatik.uni-bremen.de

Stability : experimental

Portability : portable

Definition of morphisms for Maude.

-}

module Maude.Morphism (

Morphism(..),

SortMap,

OpMap,

applyRenamings,

fromSignRenamings,

fromSignsRenamings,

symbolMap,

empty,

identity,

isIdentity,

inclusion,

inverse,

compose,

isLegal,

isInclusion,

mapSentence,

renameSorts,

union,

setTarget,

qualifySorts,

extendWithSortRenaming,

getNewSorts

) where

import Maude.AS_Maude

import Maude.Symbol

import Maude.Meta

import Maude.Util

import Maude.Printing ()

import Maude.Sign (Sign)

import Maude.Sentence (Sentence)

import qualified Maude.Sign as Sign

import qualified Maude.Sentence as Sen

import Data.List (partition)

import Data.Maybe (fromJust)

import qualified Data.Set as Set

import qualified Data.Map as Map

import Common.Result (Result)

import qualified Common.Result as Result

import Common.Doc hiding (empty)

import Common.DocUtils (Pretty(..))

type SortMap = SymbolMap

type OpMap = SymbolMap

type LabelMap = SymbolMap

data Morphism = Morphism {

source :: Sign,

target :: Sign,

sortMap :: SortMap,

opMap :: OpMap,

labelMap :: LabelMap

} deriving (Show, Ord, Eq)

instance Pretty Morphism where

pretty mor = let

pr'pair txt left right = hsep

[txt, pretty left, text "to", pretty right]

pr'ops src tgt = pr'pair (text "op") src (getName tgt)

pr'map fun = vcat . map (uncurry fun) . Map.toList

smap = pr'map (pr'pair $ text "sort") $ sortMap mor

omap = pr'map pr'ops $ opMap mor

lmap = pr'map (pr'pair $ text "label") $ labelMap mor

in vcat [ smap, omap, lmap ]

-- text "\n\nTarget:" <$$> pretty $ target mor

-- mapSource :: (Sign -> Sign) -> Morphism -> Morphism

-- mapSource func mor = mor { source = func $ source mor }

mapTarget :: (Sign -> Sign) -> Morphism -> Morphism

mapTarget func mor = mor { target = func $ target mor }

mapSortMap :: (SymbolMap -> SymbolMap) -> Morphism -> Morphism

mapSortMap func mor = mor { sortMap = func $ sortMap mor }

mapOpMap :: (SymbolMap -> SymbolMap) -> Morphism -> Morphism

mapOpMap func mor = mor { opMap = func $ opMap mor }

mapLabelMap :: (SymbolMap -> SymbolMap) -> Morphism -> Morphism

mapLabelMap func mor = mor { labelMap = func $ labelMap mor }

-- | Separate Operator and other Renamings.

partitionRenamings :: [Renaming] -> ([Renaming], [Renaming])

partitionRenamings = let

is'op renaming = case renaming of

OpRenaming1 _ _ -> True

OpRenaming2 _ _ _ _ -> True

_ -> False

in partition is'op

renamingSymbolsMaybe :: Renaming -> Maybe (Symbol, Symbol)

renamingSymbolsMaybe rename = case rename of

SortRenaming src tgt -> Just (asSymbol src, asSymbol tgt)

LabelRenaming src tgt -> Just (asSymbol src, asSymbol tgt)

OpRenaming1 src (To tgt _) -> Just (asSymbol src, asSymbol tgt)

OpRenaming2 src dom cod (To tgt _) -> let

src' = getName src

tgt' = getName tgt

dom' = map asSymbol dom

cod' = asSymbol cod

in Just (Operator src' dom' cod', Operator tgt' dom' cod')

TermMap _ _ -> Nothing

renamingSymbols :: Renaming -> (Symbol, Symbol)

renamingSymbols = fromJust . renamingSymbolsMaybe

applyRenamings :: Morphism -> [Renaming] -> Morphism

applyRenamings mor rens = let

(ops, rest) = partitionRenamings rens

add'ops = flip (foldr applyOpRenaming) ops

add'rest = flip (foldr applyRenaming) rest

in add'rest . add'ops $ mor

-- | create a Morphism from an initial signature and a list of Renamings

fromSignRenamings :: Sign -> [Renaming] -> Morphism

fromSignRenamings = applyRenamings . identity

-- TODO: Handle Attrs in Op Renamings.

applyOpRenaming :: Renaming -> Morphism -> Morphism

applyOpRenaming rename = let

syms = renamingSymbols rename

add'op = mapOpMap $ uncurry Map.insert syms

use'op = mapTarget . uncurry Sign.renameOp syms

in case rename of

OpRenaming1 _ (To _ attrs) -> use'op attrs . add'op

OpRenaming2 _ _ _ (To _ attrs) -> use'op attrs . add'op

_ -> id

applyRenaming :: Renaming -> Morphism -> Morphism

applyRenaming rename = let

syms = renamingSymbols rename

add'sort = mapSortMap $ uncurry Map.insert syms

use'sort = mapTarget $ uncurry Sign.renameSort syms

ren'sort = mapOpMap $ uncurry renameSortOpMap syms

add'labl = mapLabelMap $ uncurry Map.insert syms

use'labl = mapTarget $ uncurry Sign.renameLabel syms

in case rename of

SortRenaming _ _ -> ren'sort . use'sort . add'sort

LabelRenaming _ _ -> use'labl . add'labl

_ -> id

-- | create a Morphism from the initial signatures and a list of Renamings

fromSignsRenamings :: Sign -> Sign -> [Renaming] -> Morphism

fromSignsRenamings sign1 sign2 rens = let

(ops, rest) = partitionRenamings rens

add'ops = flip (foldr insertOpRenaming) ops

add'rest = flip (foldr insertRenaming) rest

mor = inclusion sign1 sign2

in add'rest . add'ops $ mor

-- TODO: Handle Attrs in Op Renamings.

insertOpRenaming :: Renaming -> Morphism -> Morphism

insertOpRenaming rename = let

syms = renamingSymbols rename

add'op = mapOpMap $ uncurry Map.insert syms

in case rename of

OpRenaming1 _ _ -> add'op

OpRenaming2 _ _ _ _ -> add'op

_ -> id

insertRenaming :: Renaming -> Morphism -> Morphism

insertRenaming rename = let

syms = renamingSymbols rename

add'sort = mapSortMap $ uncurry Map.insert syms

ren'sort = mapOpMap $ uncurry renameSortOpMap syms

add'labl = mapLabelMap $ uncurry Map.insert syms

in case rename of

SortRenaming _ _ -> ren'sort . add'sort

LabelRenaming _ _ -> add'labl

_ -> id

-- | Rename sorts in the profiles of an operator map.

renameSortOpMap :: Symbol -> Symbol -> OpMap -> OpMap

renameSortOpMap from to = Map.map $ mapSorts $ Map.singleton from to

-- | extract the SymbolMap of a Morphism

symbolMap :: Morphism -> SymbolMap

symbolMap mor = Map.unions [sortMap mor, opMap mor, labelMap mor]

-- | the empty Morphism

empty :: Morphism

empty = identity Sign.empty

-- | the identity Morphism

identity :: Sign -> Morphism

identity sign = inclusion sign sign

-- | the inclusion Morphism

inclusion :: Sign -> Sign -> Morphism

inclusion src tgt = Morphism {

source = src,

target = tgt,

sortMap = Map.empty,

opMap = Map.empty,

labelMap = Map.empty

}

-- | the inverse Morphism

inverse :: Morphism -> Result Morphism

inverse mor = let

invertMap = Map.foldWithKey (flip Map.insert) Map.empty

in return Morphism {

source = target mor,

target = source mor,

sortMap = invertMap $ sortMap mor,

opMap = invertMap $ opMap mor,

labelMap = invertMap $ labelMap mor

}

-- | the composition of two Morphisms

compose :: Morphism -> Morphism -> Result Morphism

compose f g

| target f /= source g = fail

"target of the first and source of the second morphism are different"

| otherwise = let

-- Take SymbolMap |mp| of each Morphism.

-- Convert each SymbolMap to a function.

-- Compose those functions.

map'map :: (Morphism -> SymbolMap) -> Symbol -> Symbol

map'map mp = mapAsFunction (mp g) . mapAsFunction (mp f)

-- Map |x| via the composed SymbolMaps |mp| of both Morphisms.

-- Insert the renaming mapping into a SymbolMap.

insert :: (Morphism -> SymbolMap) -> Symbol -> SymbolMap -> SymbolMap

insert mp x = let y = map'map mp x

in if x == y then id else Map.insert x y

-- Map each symbol in |items| via the combined SymbolMaps |mp|.

compose'map :: (Morphism -> SymbolMap) -> (Sign -> SymbolSet) -> SymbolMap

compose'map mp items = if Map.null (mp g)

-- if the SymbolMap of |g| is empty, we use the one from |f|

then mp f

-- otherwise we start with the SymbolSet from |source f|

-- and construct a combined SymbolMap by applying both

-- SymbolMaps (from |f| and |g|) to each item in |insert|

else Set.fold (insert mp) Map.empty $ items (source f)

-- We want a morphism from |source f| to |target g|.

mor = inclusion (source f) (target g)

in return mor {

sortMap = compose'map sortMap getSorts,

opMap = compose'map opMap getOps,

labelMap = compose'map labelMap getLabels

}

-- | check that a Morphism is legal

isLegal :: Morphism -> Bool

isLegal mor = let

src = source mor

tgt = target mor

smap = sortMap mor

omap = opMap mor

lmap = labelMap mor

subset mp items = let mapped = Set.map $ mapAsFunction mp

in Set.isSubsetOf (mapped $ items src) $ items tgt

lg'source = Sign.isLegal src

lg'sortMap = subset smap getSorts

lg'opMap = subset omap getOps

lg'labelMap = subset lmap getLabels

lg'target = Sign.isLegal tgt

in all id [lg'source, lg'sortMap, lg'opMap, lg'labelMap, lg'target]

-- | check that a Morphism is the identity

isIdentity :: Morphism -> Bool

isIdentity mor = source mor == target mor

-- | check that a Morphism is an Inclusion

isInclusion :: Morphism -> Bool

isInclusion mor = let

null'sortMap = Map.null (sortMap mor)

null'opMap = Map.null (opMap mor)

null'labelMap = Map.null (labelMap mor)

in all id [null'sortMap, null'opMap, null'labelMap]

-- | translate a Sentence along a Morphism

mapSentence :: Morphism -> Sentence -> Result Sentence

mapSentence mor = let

smap = mapSorts (sortMap mor)

omap = mapOps (opMap mor)

lmap = mapLabels (labelMap mor)

in return . lmap . smap . omap

union :: Morphism -> Morphism -> Morphism

union m1 m2 = let apply func items = func (items m1) (items m2)

in Morphism {

source = apply Sign.union source,

target = apply Sign.union target,

sortMap = apply Map.union sortMap,

opMap = apply Map.union opMap,

labelMap = apply Map.union labelMap

}

setTarget :: Sign -> Morphism -> Morphism

setTarget sign morph = morph {target = sign}

renameSorts :: Morphism -> Symbols -> Symbols

renameSorts = mapSorts . sortMap

qualifySorts :: Morphism -> Qid -> Symbols -> Morphism

qualifySorts mor qid syms = let

insert symb = Map.insert symb $ qualify qid symb

smap = foldr insert Map.empty syms

q'tgt = mapTarget $ mapSorts smap

q'smap = mapSortMap $ mapSorts smap

x'smap = mapSortMap $ Map.union smap

in q'tgt . x'smap . q'smap $ mor

-- FIXME: Code duplication!

extendWithSortRenaming :: Symbol -> Symbol -> Morphism -> Morphism

extendWithSortRenaming src tgt = let

add'sort = mapSortMap $ Map.insert src tgt

use'sort = mapTarget $ Sign.renameSort src tgt

ren'sort = mapOpMap $ renameSortOpMap src tgt

in ren'sort . use'sort . add'sort

getNewSorts :: [Symbol] -> Morphism -> [Symbol]

getNewSorts ss morph = mapSorts (sortMap morph) ss