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-rw-r--r--Semantic.hs286
1 files changed, 160 insertions, 126 deletions
diff --git a/Semantic.hs b/Semantic.hs
index e40f4bc..73b489e 100644
--- a/Semantic.hs
+++ b/Semantic.hs
@@ -1,5 +1,6 @@
import System( getArgs )
import Data.List
+import Data.Maybe
import qualified Data.Set as Set
import qualified Data.Map as Map
import TypeVar
@@ -30,7 +31,7 @@ instance Show Theorems where
data ArticleLine = Comment { commentString :: String }
- | Command { commandFunc :: ((Stack,Dictionary,Assumptions,Theorems)->(Stack,Dictionary,Assumptions,Theorems)) }
+ | Command { commandFunc :: ((Stack,Dictionary,Assumptions,Theorems) -> Maybe (Stack,Dictionary,Assumptions,Theorems)) }
@@ -68,49 +69,57 @@ parse n = Command (number n)
-name :: String -> ((Stack,Dictionary,Assumptions,Theorems) -> (Stack,Dictionary,Assumptions,Theorems))
+name :: String -> ((Stack,Dictionary,Assumptions,Theorems) -> Maybe (Stack,Dictionary,Assumptions,Theorems))
name str = \(s,d,a,t) ->
- let wordList = (separateBy '.') . removeEscChars . removeQuotes $ str
- name = Name (init wordList) (last wordList)
- s' = Stack $ ObjName name : (stackList s)
- in (s',d,a,t)
+ if (not . isName $ str)
+ then Nothing
+ else let wordList = (separateBy '.') . removeEscChars . removeQuotes $ str
+ name = Name (init wordList) (last wordList)
+ s' = Stack $ ObjName name : (stackList s)
+ in Just (s',d,a,t)
-number :: String -> ((Stack,Dictionary,Assumptions,Theorems) -> (Stack,Dictionary,Assumptions,Theorems))
-number n = \(s,d,a,t) -> (Stack $ ObjNum (read n) : (stackList s), d, a, t)
+number :: String -> ((Stack,Dictionary,Assumptions,Theorems) -> Maybe (Stack,Dictionary,Assumptions,Theorems))
+number n = \(s,d,a,t) ->
+ if (not . isNumber $ n)
+ then Nothing
+ else Just (Stack $ ObjNum (read n) : (stackList s), d, a, t)
-absTerm :: (Stack,Dictionary,Assumptions,Theorems) -> (Stack,Dictionary,Assumptions,Theorems)
+absTerm :: (Stack,Dictionary,Assumptions,Theorems) -> Maybe (Stack,Dictionary,Assumptions,Theorems)
absTerm (s,d,a,t) =
let stack = stackList s
op = (\x y -> TAbs (TVar y) x)
newTerm = ObjTerm $ op (objTerm $ stack!!0) (objVar $ stack!!1)
s' = Stack $ newTerm : (drop 2 stack)
- in (s',d,a,t)
+ in Just (s',d,a,t)
--- need to add guards to check that the variable is not free in the hypothesis
-absThm :: (Stack,Dictionary,Assumptions,Theorems) -> (Stack,Dictionary,Assumptions,Theorems)
+absThm :: (Stack,Dictionary,Assumptions,Theorems) -> Maybe (Stack,Dictionary,Assumptions,Theorems)
absThm (s,d,a,t) =
let stack = stackList s
- op = (\x y -> Theorem (thmHyp x)
- (mkEquals (TAbs (TVar y) (getlhs . thmCon $ x))
- (TAbs (TVar y) (getrhs . thmCon $ x))))
- theorem = ObjThm $ op (objThm $ stack!!0) (objVar $ stack!!1)
- s' = Stack $ theorem : (drop 2 stack)
- in (s',d,a,t)
-
-
-appTerm :: (Stack,Dictionary,Assumptions,Theorems) -> (Stack,Dictionary,Assumptions,Theorems)
+ oldthm = objThm $ stack!!0
+ var = objVar $ stack!!1
+ in if (Set.member (TVar var) (thmHyp oldthm))
+ then Nothing
+ else let op = (\x y -> Theorem (thmHyp x)
+ (mkEquals (TAbs (TVar y) (getlhs . thmCon $ x))
+ (TAbs (TVar y) (getrhs . thmCon $ x))))
+ theorem = ObjThm $ op oldthm var
+ s' = Stack $ theorem : (drop 2 stack)
+ in Just (s',d,a,t)
+
+
+appTerm :: (Stack,Dictionary,Assumptions,Theorems) -> Maybe (Stack,Dictionary,Assumptions,Theorems)
appTerm (s,d,a,t) =
let stack = stackList s
op = (\x y -> TApp y x)
newTerm = ObjTerm $ op (objTerm $ stack!!0) (objTerm $ stack!!1)
s' = Stack $ newTerm : (drop 2 stack)
- in (s',d,a,t)
+ in Just (s',d,a,t)
-appThm :: (Stack,Dictionary,Assumptions,Theorems) -> (Stack,Dictionary,Assumptions,Theorems)
+appThm :: (Stack,Dictionary,Assumptions,Theorems) -> Maybe (Stack,Dictionary,Assumptions,Theorems)
appThm (s,d,a,t) =
let stack = stackList s
op = (\x y -> Theorem (Set.union (thmHyp x) (thmHyp y))
@@ -118,31 +127,36 @@ appThm (s,d,a,t) =
(TApp (getrhs . thmCon $ y) (getrhs . thmCon $ x))))
theorem = ObjThm $ op (objThm $ stack!!0) (objThm $ stack!!1)
s' = Stack $ theorem : (drop 2 stack)
- in (s',d,a,t)
+ in Just (s',d,a,t)
-assume :: (Stack,Dictionary,Assumptions,Theorems) -> (Stack,Dictionary,Assumptions,Theorems)
+assume :: (Stack,Dictionary,Assumptions,Theorems) -> Maybe (Stack,Dictionary,Assumptions,Theorems)
assume (s,d,a,t) =
let stack = stackList s
- op = (\x -> Theorem (Set.singleton x) x)
- theorem = ObjThm $ op (objTerm $ stack!!0)
- s' = Stack $ theorem : (tail stack)
- in (s',d,a,t)
+ term = objTerm $ stack!!0
+ in if (typeOf term /= typeBool)
+ then Nothing
+ else let op = (\x -> Theorem (Set.singleton x) x)
+ theorem = ObjThm $ op term
+ s' = Stack $ theorem : (tail stack)
+ in Just (s',d,a,t)
--- need to add guarding for all terms being of type bool
-axiom :: (Stack,Dictionary,Assumptions,Theorems) -> (Stack,Dictionary,Assumptions,Theorems)
+axiom :: (Stack,Dictionary,Assumptions,Theorems) -> Maybe (Stack,Dictionary,Assumptions,Theorems)
axiom (s,d,a,t) =
let stack = stackList s
assumptions = assumeSet a
- op = (\x y -> Theorem (Set.fromList y) x)
- theorem = ObjThm $ op (objTerm $ stack!!0) (map (objTerm) . objList $ stack!!1)
- s' = Stack $ theorem : (drop 2 stack)
- a' = Assumptions $ Set.insert theorem assumptions
- in (s',d,a',t)
+ termList = (map (objTerm) . objList $ stack!!1)
+ in if (filter (\x -> typeOf x /= typeBool) termList /= [])
+ then Nothing
+ else let op = (\x y -> Theorem (Set.fromList y) x)
+ theorem = ObjThm $ op (objTerm $ stack!!0) termList
+ s' = Stack $ theorem : (drop 2 stack)
+ a' = Assumptions $ Set.insert theorem assumptions
+ in Just (s',d,a',t)
-betaConv :: (Stack,Dictionary,Assumptions,Theorems) -> (Stack,Dictionary,Assumptions,Theorems)
+betaConv :: (Stack,Dictionary,Assumptions,Theorems) -> Maybe (Stack,Dictionary,Assumptions,Theorems)
betaConv (s,d,a,t) =
let stack = stackList s
op = (\x -> Theorem (Set.empty)
@@ -151,37 +165,37 @@ betaConv (s,d,a,t) =
(tAbsTerm . tAppLeft $ x))))
theorem = ObjThm $ op (objTerm $ stack!!0)
s' = Stack $ theorem : (tail stack)
- in (s',d,a,t)
+ in Just (s',d,a,t)
-cons :: (Stack,Dictionary,Assumptions,Theorems) -> (Stack,Dictionary,Assumptions,Theorems)
+cons :: (Stack,Dictionary,Assumptions,Theorems) -> Maybe (Stack,Dictionary,Assumptions,Theorems)
cons (s,d,a,t) =
let stack = stackList s
op = (\x y -> y : x)
newList = ObjList $ op (objList $ stack!!0) (stack!!1)
s' = Stack $ newList : (drop 2 stack)
- in (s',d,a,t)
+ in Just (s',d,a,t)
-constant :: (Stack,Dictionary,Assumptions,Theorems) -> (Stack,Dictionary,Assumptions,Theorems)
+constant :: (Stack,Dictionary,Assumptions,Theorems) -> Maybe (Stack,Dictionary,Assumptions,Theorems)
constant (s,d,a,t) =
let stack = stackList s
op = (\x -> Const x)
constant = ObjConst $ op (objName $ stack!!0)
s' = Stack $ constant : (tail stack)
- in (s',d,a,t)
+ in Just (s',d,a,t)
-constTerm :: (Stack,Dictionary,Assumptions,Theorems) -> (Stack,Dictionary,Assumptions,Theorems)
+constTerm :: (Stack,Dictionary,Assumptions,Theorems) -> Maybe (Stack,Dictionary,Assumptions,Theorems)
constTerm (s,d,a,t) =
let stack = stackList s
op = (\x y -> TConst y x)
newType = ObjTerm $ op (objType $ stack!!0) (objConst $ stack!!1)
s' = Stack $ newType : (drop 2 stack)
- in (s',d,a,t)
+ in Just (s',d,a,t)
-deductAntisym :: (Stack,Dictionary,Assumptions,Theorems) -> (Stack,Dictionary,Assumptions,Theorems)
+deductAntisym :: (Stack,Dictionary,Assumptions,Theorems) -> Maybe (Stack,Dictionary,Assumptions,Theorems)
deductAntisym (s,d,a,t) =
let stack = stackList s
op = (\x y -> Theorem (Set.union (Set.delete (thmCon $ x) (thmHyp $ y))
@@ -189,110 +203,118 @@ deductAntisym (s,d,a,t) =
(mkEquals (thmCon $ y) (thmCon $ x)))
theorem = ObjThm $ op (objThm $ stack!!0) (objThm $ stack!!1)
s' = Stack $ theorem : (drop 2 stack)
- in (s',d,a,t)
+ in Just (s',d,a,t)
-def :: (Stack,Dictionary,Assumptions,Theorems) -> (Stack,Dictionary,Assumptions,Theorems)
+def :: (Stack,Dictionary,Assumptions,Theorems) -> Maybe (Stack,Dictionary,Assumptions,Theorems)
def (s,d,a,t) =
let stack = stackList s
d' = Dictionary $ Map.insert (objNum $ stack!!0) (stack!!1) (dictionMap d)
s' = Stack $ tail stack
- in (s',d',a,t)
+ in Just (s',d',a,t)
-defineConst :: (Stack,Dictionary,Assumptions,Theorems) -> (Stack,Dictionary,Assumptions,Theorems)
+defineConst :: (Stack,Dictionary,Assumptions,Theorems) -> Maybe (Stack,Dictionary,Assumptions,Theorems)
defineConst (s,d,a,t) =
let stack = stackList s
- op1 = (\x -> Const x)
- op2 = (\x y -> Theorem Set.empty (mkEquals x y))
- constant = ObjConst $ op1 (objName $ stack!!1)
- constTerm = TConst (objConst $ constant) (typeOf (objTerm $ stack!!0))
- theorem = ObjThm $ op2 constTerm (objTerm $ stack!!0)
- s' = Stack $ theorem : constant : (drop 2 stack)
- in (s',d,a,t)
-
-
-defineTypeOp :: (Stack,Dictionary,Assumptions,Theorems) -> (Stack,Dictionary,Assumptions,Theorems)
+ term = objTerm $ stack!!0
+ in if (freeVars term /= Set.empty || typeVarsInTerm term /= typeVarsInType (typeOf term))
+ then Nothing
+ else let op1 = (\x -> Const x)
+ op2 = (\x y -> Theorem Set.empty (mkEquals x y))
+ constant = ObjConst $ op1 (objName $ stack!!1)
+ constTerm = TConst (objConst $ constant) (typeOf (objTerm $ stack!!0))
+ theorem = ObjThm $ op2 constTerm (objTerm $ stack!!0)
+ s' = Stack $ theorem : constant : (drop 2 stack)
+ in Just (s',d,a,t)
+
+
+defineTypeOp :: (Stack,Dictionary,Assumptions,Theorems) -> Maybe (Stack,Dictionary,Assumptions,Theorems)
defineTypeOp (s,d,a,t) =
let stack = stackList s
oldthm = objThm $ stack!!0
namelist = map (objName) . objList $ stack!!1
- rep = Const . objName $ stack!!2
- abst = Const . objName $ stack!!3
- n = TypeOp . objName $ stack!!4
- rtype = typeOf . tAppRight . thmCon $ oldthm
- atype = AType (map (\x -> TypeVar x) namelist) n
- r' = TVar (Var (Name [] "r'") rtype)
- a' = TVar (Var (Name [] "a'") atype)
- reptype = typeFunc atype rtype
- abstype = typeFunc rtype atype
- repTerm = TConst rep reptype
- absTerm = TConst abst abstype
- rthm = Theorem Set.empty (mkEquals (TApp (tAppLeft . thmCon $ oldthm) r')
- (mkEquals (TApp repTerm (TApp absTerm r')) r'))
- athm = Theorem Set.empty (mkEquals (TApp absTerm (TApp repTerm a')) a')
- s' = Stack $ (ObjThm rthm) : (ObjThm athm) : (ObjConst rep) : (ObjConst abst) : (ObjTyOp n) : (drop 5 stack)
- in (s',d,a,t)
-
-
-eqMp :: (Stack,Dictionary,Assumptions,Theorems) -> (Stack,Dictionary,Assumptions,Theorems)
+ in if ((typeVarsInTerm . tAppLeft . thmCon $ oldthm) /= (Set.fromList . map (\x -> TypeVar x) $ namelist) ||
+ (length namelist) /= (length . nub $ namelist))
+ then Nothing
+ else let rep = Const . objName $ stack!!2
+ abst = Const . objName $ stack!!3
+ n = TypeOp . objName $ stack!!4
+ rtype = typeOf . tAppRight . thmCon $ oldthm
+ atype = AType (map (\x -> TypeVar x) namelist) n
+ r' = TVar (Var (Name [] "r'") rtype)
+ a' = TVar (Var (Name [] "a'") atype)
+ reptype = typeFunc atype rtype
+ abstype = typeFunc rtype atype
+ repTerm = TConst rep reptype
+ absTerm = TConst abst abstype
+ rthm = Theorem Set.empty (mkEquals (TApp (tAppLeft . thmCon $ oldthm) r')
+ (mkEquals (TApp repTerm (TApp absTerm r')) r'))
+ athm = Theorem Set.empty (mkEquals (TApp absTerm (TApp repTerm a')) a')
+ s' = Stack $ (ObjThm rthm) : (ObjThm athm) : (ObjConst rep) : (ObjConst abst) : (ObjTyOp n) : (drop 5 stack)
+ in Just (s',d,a,t)
+
+
+eqMp :: (Stack,Dictionary,Assumptions,Theorems) -> Maybe (Stack,Dictionary,Assumptions,Theorems)
eqMp (s,d,a,t) =
let stack = stackList s
- op = (\x y -> if (thmCon x == (getlhs (thmCon y))) then
- Theorem (Set.union (thmHyp x) (thmHyp y))
- (getrhs (thmCon y))
- else error "Theorem consequents not alpha equivalent in eqMp")
- theorem = ObjThm $ op (objThm $ stack!!0) (objThm $ stack!!1)
- s' = Stack $ theorem : (drop 2 stack)
- in (s',d,a,t)
+ thm1 = objThm $ stack!!0
+ thm2 = objThm $ stack!!1
+ in if ((thmCon thm1) /= (getlhs . thmCon $ thm2))
+ then Nothing
+ else let op = (\x y -> Theorem (Set.union (thmHyp x) (thmHyp y))
+ (getrhs (thmCon y)))
+ theorem = ObjThm $ op thm1 thm2
+ s' = Stack $ theorem : (drop 2 stack)
+ in Just (s',d,a,t)
-nil :: (Stack,Dictionary,Assumptions,Theorems) -> (Stack,Dictionary,Assumptions,Theorems)
-nil (s,d,a,t) = (Stack $ ObjList [] : (stackList s), d, a, t)
+nil :: (Stack,Dictionary,Assumptions,Theorems) -> Maybe (Stack,Dictionary,Assumptions,Theorems)
+nil (s,d,a,t) = Just (Stack $ ObjList [] : (stackList s), d, a, t)
-opType :: (Stack,Dictionary,Assumptions,Theorems) -> (Stack,Dictionary,Assumptions,Theorems)
+opType :: (Stack,Dictionary,Assumptions,Theorems) -> Maybe (Stack,Dictionary,Assumptions,Theorems)
opType (s,d,a,t) =
let stack = stackList s
op = (\x y -> AType x y)
newType = ObjType $ op (map (objType) . objList $ stack!!0) (objTyOp $ stack!!1)
s' = Stack $ newType : (drop 2 stack)
- in (s',d,a,t)
+ in Just (s',d,a,t)
-pop :: (Stack,Dictionary,Assumptions,Theorems) -> (Stack,Dictionary,Assumptions,Theorems)
-pop (s,d,a,t) = (Stack $ tail (stackList s),d,a,t)
+pop :: (Stack,Dictionary,Assumptions,Theorems) -> Maybe (Stack,Dictionary,Assumptions,Theorems)
+pop (s,d,a,t) = Just (Stack $ tail (stackList s),d,a,t)
-ref :: (Stack,Dictionary,Assumptions,Theorems) -> (Stack,Dictionary,Assumptions,Theorems)
+ref :: (Stack,Dictionary,Assumptions,Theorems) -> Maybe (Stack,Dictionary,Assumptions,Theorems)
ref (s,d,a,t) =
let stack = stackList s
dictionary = dictionMap d
object = dictionary Map.! (objNum $ stack!!0)
s' = Stack $ object : tail stack
- in (s',d,a,t)
+ in Just (s',d,a,t)
-refl :: (Stack,Dictionary,Assumptions,Theorems) -> (Stack,Dictionary,Assumptions,Theorems)
+refl :: (Stack,Dictionary,Assumptions,Theorems) -> Maybe (Stack,Dictionary,Assumptions,Theorems)
refl (s,d,a,t) =
let stack = stackList s
op = (\x -> Theorem Set.empty (mkEquals x x))
theorem = ObjThm $ op (objTerm $ stack!!0)
s' = Stack $ theorem : (tail stack)
- in (s',d,a,t)
+ in Just (s',d,a,t)
-remove :: (Stack,Dictionary,Assumptions,Theorems) -> (Stack,Dictionary,Assumptions,Theorems)
+remove :: (Stack,Dictionary,Assumptions,Theorems) -> Maybe (Stack,Dictionary,Assumptions,Theorems)
remove (s,d,a,t) =
let stack = stackList s
dictionary = dictionMap d
object = dictionary Map.! (objNum $ stack!!0)
s' = Stack $ object : tail stack
d' = Dictionary $ Map.delete (objNum $ stack!!0) dictionary
- in (s',d',a,t)
+ in Just (s',d',a,t)
-subst :: (Stack,Dictionary,Assumptions,Theorems) -> (Stack,Dictionary,Assumptions,Theorems)
+subst :: (Stack,Dictionary,Assumptions,Theorems) -> Maybe (Stack,Dictionary,Assumptions,Theorems)
subst (s,d,a,t) =
let stack = stackList s
op = (\x y -> Theorem (Set.map (substitute y) (thmHyp x))
@@ -304,67 +326,79 @@ subst (s,d,a,t) =
theorem = ObjThm $ op (objThm $ stack!!0) (substitution $ stack!!1)
s' = Stack $ theorem : (drop 2 stack)
- in (s',d,a,t)
+ in Just (s',d,a,t)
-thm :: (Stack,Dictionary,Assumptions,Theorems) -> (Stack,Dictionary,Assumptions,Theorems)
+thm :: (Stack,Dictionary,Assumptions,Theorems) -> Maybe (Stack,Dictionary,Assumptions,Theorems)
thm (s,d,a,t) =
let stack = stackList s
theorems = theoremSet t
- op = (\x y z -> Theorem (Set.fromList (alphaConvertList (Set.toList . thmHyp $ z) y))
- (alphaConvert (thmCon z) x))
- theorem = ObjThm $ op (objTerm $ stack!!0) (map (objTerm) . objList $ stack!!1) (objThm $ stack!!2)
- s' = Stack $ drop 3 stack
- t' = Theorems $ Set.insert theorem theorems
- in (s',d,a,t')
-
-
-typeOp :: (Stack,Dictionary,Assumptions,Theorems) -> (Stack,Dictionary,Assumptions,Theorems)
+ term = objTerm $ stack!!0
+ termlist = map (objTerm) . objList $ stack!!1
+ oldthm = objThm $ stack!!2
+ in if ((term /= (thmCon oldthm)) || (Set.fromList termlist /= thmHyp oldthm))
+ then Nothing
+ else let op = (\x y z -> Theorem (Set.fromList (alphaConvertList (Set.toList . thmHyp $ z) y))
+ (alphaConvert (thmCon z) x))
+ theorem = ObjThm $ op term termlist oldthm
+ s' = Stack $ drop 3 stack
+ t' = Theorems $ Set.insert theorem theorems
+ in Just (s',d,a,t')
+
+
+typeOp :: (Stack,Dictionary,Assumptions,Theorems) -> Maybe (Stack,Dictionary,Assumptions,Theorems)
typeOp (s,d,a,t) =
let stack = stackList s
op = (\x -> TypeOp x)
typeOp = ObjTyOp $ op (objName $ stack!!0)
s' = Stack $ typeOp : (tail stack)
- in (s',d,a,t)
+ in Just (s',d,a,t)
-var :: (Stack,Dictionary,Assumptions,Theorems) -> (Stack,Dictionary,Assumptions,Theorems)
+var :: (Stack,Dictionary,Assumptions,Theorems) -> Maybe (Stack,Dictionary,Assumptions,Theorems)
var (s,d,a,t) =
let stack = stackList s
- op = (\x y -> Var y x)
- var = ObjVar $ op (objType $ stack!!0) (objName $ stack!!1)
- s' = Stack $ var : (drop 2 stack)
- in (s',d,a,t)
+ n = objName $ stack!!1
+ in if (nameSpace n /= [])
+ then Nothing
+ else let op = (\x y -> Var y x)
+ var = ObjVar $ op (objType $ stack!!0) n
+ s' = Stack $ var : (drop 2 stack)
+ in Just (s',d,a,t)
-varTerm :: (Stack,Dictionary,Assumptions,Theorems) -> (Stack,Dictionary,Assumptions,Theorems)
+varTerm :: (Stack,Dictionary,Assumptions,Theorems) -> Maybe (Stack,Dictionary,Assumptions,Theorems)
varTerm (s,d,a,t) =
let stack = stackList s
op = (\x -> TVar x)
term = ObjTerm $ op (objVar $ stack!!0)
s' = Stack $ term : (tail stack)
- in (s',d,a,t)
+ in Just (s',d,a,t)
-varType :: (Stack,Dictionary,Assumptions,Theorems) -> (Stack,Dictionary,Assumptions,Theorems)
+varType :: (Stack,Dictionary,Assumptions,Theorems) -> Maybe (Stack,Dictionary,Assumptions,Theorems)
varType (s,d,a,t) =
let stack = stackList s
- op = (\x -> TypeVar x)
- newType = ObjType $ op (objName $ stack!!0)
- s' = Stack $ newType : (tail stack)
- in (s',d,a,t)
+ n = objName $ stack!!0
+ in if (nameSpace n /= [])
+ then Nothing
+ else let op = (\x -> TypeVar x)
+ newType = ObjType $ op n
+ s' = Stack $ newType : (tail stack)
+ in Just (s',d,a,t)
-doSemanticCheck :: [String] -> (Stack,Dictionary,Assumptions,Theorems)
+doSemanticCheck :: [String] -> Maybe (Stack,Dictionary,Assumptions,Theorems)
doSemanticCheck =
let s = Stack []
d = Dictionary Map.empty
a = Assumptions Set.empty
t = Theorems Set.empty
- op = (\x y -> case y of (Comment _) -> x
- (Command z) -> z x)
- in (foldl' (op) (s,d,a,t)) . (map (parse))
+ op = (\x y -> case x of (Nothing) -> Nothing
+ (Just w) -> case y of (Comment _) -> x
+ (Command z) -> z w)
+ in (foldl' (op) (Just (s,d,a,t))) . (map (parse))
-- important to use foldl here so commands get applied in the correct order