Experimental working commit, programm will compile

But the Proof that the domain of the local function
is not right. Also if in the definition of our local
function we just use f(x) = x then we get a technical
ambigus parse

8 files changed, 42 insertions, 21 deletions

diff --git a/library/topology/urysohn2.tex b/library/topology/urysohn2.tex
index 8e5261e..05ea180 100644
--- a/library/topology/urysohn2.tex
+++ b/library/topology/urysohn2.tex
@@ -44,10 +44,14 @@
 \begin{proof}
 
 
+    Define $f : X \to \reals$ such that  $f(x) = $
+    \begin{cases}
+        &(x + x) , x \in X
+        % & x ,x \in X    <- will result in technicly ambigus parse
+    \end{cases}
 
-
+    Trivial.
     
-    Contradiction.
     
 \end{proof}
 
diff --git a/source/Checking.hs b/source/Checking.hs
index 817c477..6d55ee1 100644
--- a/source/Checking.hs
+++ b/source/Checking.hs
@@ -543,7 +543,7 @@ checkProof = \case
         checkCalc calc
         assume [Asm (calcResult calc)]
         checkProof continue
-    DefineFunctionMathy funVar domVar ranVar argVar definitions continue -> do
+    DefineFunctionMathy funVar argVar domVar ranExpr definitions continue -> do
         -- We have f: X \to Y and x \mapsto ...  
         -- definition is a nonempty list of (expresssion e, formula phi)
         -- such that f(x) =  e if phi(x)
@@ -558,8 +558,8 @@ checkProof = \case
         setGoals [makeForall [argVar] ((TermVar argVar `IsElementOf` TermVar domVar) `Iff` subdomainConjuctionLocalFunction argVar definitions )] -- check the disjunct union
         tellTasks
 
-        assume [Asm (makeForall [argVar] ((TermVar argVar `IsElementOf` TermVar domVar) `Implies` (TermOp ApplySymbol [TermVar funVar, TermVar argVar] `IsElementOf` TermVar ranVar)))] -- function f from \dom(f) \to \ran(f)
-        assume (functionSubdomianExpression funVar argVar definitions) --behavior on the subdomians
+        assume [Asm (makeForall [argVar] ((TermVar argVar `IsElementOf` TermVar domVar) `Implies` (TermOp ApplySymbol [TermVar funVar, TermVar argVar] `IsElementOf` ranExpr)))] -- function f from \dom(f) \to \ran(f)
+        assume (functionSubdomianExpression funVar argVar (NonEmpty.toList definitions)) --behavior on the subdomians
         setGoals goals
         checkProof continue
 
@@ -571,9 +571,10 @@ subdomainConjuctionLocalFunction argVar defintions =
     in TermVar argVar `IsElementOf` makeConjunction stmts
 
 
-functionSubdomianExpression :: VarSymbol -> VarSymbol -> NonEmpty (Term, Formula) -> [Asm]
-functionSubdomianExpression f a nxs = case nxs of
-    x:|xs -> singleFunctionSubdomianExpression f a x : functionSubdomianExpression f a (NonEmpty.fromList xs)
+functionSubdomianExpression :: VarSymbol -> VarSymbol -> [(Term, Formula)] -> [Asm]
+functionSubdomianExpression f a (x:xs) = singleFunctionSubdomianExpression f a x : functionSubdomianExpression f a xs
+functionSubdomianExpression _ _ [] = []
+
     
 
 singleFunctionSubdomianExpression :: VarSymbol -> VarSymbol -> (Term, Formula) -> Asm
diff --git a/source/Meaning.hs b/source/Meaning.hs
index ab98c9a..4a21fa3 100644
--- a/source/Meaning.hs
+++ b/source/Meaning.hs
@@ -606,9 +606,9 @@ glossProof = \case
             then Sem.DefineFunction funVar argVar <$> glossExpr valueExpr <*> glossExpr domExpr <*> glossProof proof
             else error "mismatched variables in function definition."
     
-    Raw.DefineFunctionMathy funVar domVar ranVar funVar2 argVar definitions proof -> do
+    Raw.DefineFunctionMathy funVar domVar ranExpr funVar2 argVar definitions proof -> do
         if funVar == funVar2
-            then Sem.DefineFunctionMathy funVar domVar ranVar argVar <$> (glossLocalFunctionExprDef `each` definitions) <*> glossProof proof
+            then Sem.DefineFunctionMathy funVar argVar domVar <$> glossExpr ranExpr <*> (glossLocalFunctionExprDef `each` definitions) <*> glossProof proof
             else error "missmatched function names"
     Raw.Calc calc proof ->
         Sem.Calc <$> glossCalc calc <*> glossProof proof
diff --git a/source/Syntax/Abstract.hs b/source/Syntax/Abstract.hs
index 6372c87..13691e7 100644
--- a/source/Syntax/Abstract.hs
+++ b/source/Syntax/Abstract.hs
@@ -373,7 +373,7 @@ data Proof
     
     
     
-    | DefineFunctionMathy VarSymbol VarSymbol VarSymbol VarSymbol VarSymbol (NonEmpty (Expr, Formula)) Proof
+    | DefineFunctionMathy VarSymbol VarSymbol Expr VarSymbol VarSymbol (NonEmpty (Expr, Formula)) Proof
     -- ^ Local function definition, but in this case we give the domain and target an the rules for $xs$ in some sub domains.
     -- 
     deriving (Show, Eq, Ord)
diff --git a/source/Syntax/Adapt.hs b/source/Syntax/Adapt.hs
index 3cff497..4b43bc6 100644
--- a/source/Syntax/Adapt.hs
+++ b/source/Syntax/Adapt.hs
@@ -34,8 +34,8 @@ scanChunk ltoks =
             matchOrErr struct "struct definition" pos
         Located{startPos = pos, unLocated = (BeginEnv "inductive")} :_ ->
             matchOrErr inductive "inductive definition" pos
-        Located{startPos = pos, unLocated = (BeginEnv "signature")} :_ ->
-            matchOrErr signatureIntro "signature" pos
+        --Located{startPos = pos, unLocated = (BeginEnv "signature")} :_ ->
+        --    matchOrErr signatureIntro "signature" pos
         _ -> []
 
 adaptChunks :: [[Located Token]] -> Lexicon -> Lexicon
diff --git a/source/Syntax/Concrete.hs b/source/Syntax/Concrete.hs
index 69280c1..fe08fec 100644
--- a/source/Syntax/Concrete.hs
+++ b/source/Syntax/Concrete.hs
@@ -373,16 +373,16 @@ grammar lexicon@Lexicon{..} = mdo
     --     3 & \text{else}     
     -- \end{cases}
 
-    functionDefineCase <- rule $ (,) <$> expr <*> (_ampersand *> formula)
+    functionDefineCase <- rule $ (,) <$> (_ampersand *> (expr <|> exprVar )) <*> (_comma *> formula)
     defineFunctionMathy <-  rule    $ DefineFunctionMathy 
                                     <$> (_define *> beginMath *> varSymbol)           -- Define $ f
                                     <*> (_colon *> varSymbol)                           -- : 'var' \to 'var'
-                                    <*> (_to *> varSymbol <* endMath <* _suchThat) 
+                                    <*> (_to *> expr <* endMath <* _suchThat) 
                                     -- <*> (_suchThat  *> align (many1 ((_ampersand *> varSymbol <* _mapsto) <*> exprApp <*> (_ampersand *> formula))))
                                     -- <*> (_suchThat  *> align (many1 (varSymbol <* exprApp <*  formula)))
-                                    <*> varSymbol <*> varSymbol <* symbol "="
-                                    <*> many1 functionDefineCase
-                                    <*> proof 
+                                    <*> (beginMath *> varSymbol) <*> (paren varSymbol <* _eq <* endMath)
+                                    <*> cases (many1 functionDefineCase)
+                                    <*> proof
 
 
 
@@ -644,6 +644,9 @@ group body = token InvisibleBraceL *> body <* token InvisibleBraceR <?> "\"{...}
 align :: Prod r Text (Located Token) a -> Prod r Text (Located Token) a
 align body = begin "align*" *> body <* end "align*"
 
+cases :: Prod r Text (Located Token) a -> Prod r Text (Located Token) a
+cases body = begin "cases" *> body <* end "cases"
+
 
 maybeVarToken :: Located Token -> Maybe VarSymbol
 maybeVarToken ltok = case unLocated ltok of
diff --git a/source/Syntax/Internal.hs b/source/Syntax/Internal.hs
index 0e3361d..7046161 100644
--- a/source/Syntax/Internal.hs
+++ b/source/Syntax/Internal.hs
@@ -436,7 +436,7 @@ data Proof
     | Define VarSymbol Term Proof
     | DefineFunction VarSymbol VarSymbol Term Term Proof
 
-    | DefineFunctionMathy VarSymbol VarSymbol VarSymbol VarSymbol (NonEmpty (Term, Formula)) Proof
+    | DefineFunctionMathy VarSymbol VarSymbol VarSymbol Term (NonEmpty (Term, Formula)) Proof
 
 deriving instance Show Proof
 deriving instance Eq   Proof
diff --git a/source/Syntax/Token.hs b/source/Syntax/Token.hs
index cb3f4cb..52da86a 100644
--- a/source/Syntax/Token.hs
+++ b/source/Syntax/Token.hs
@@ -189,6 +189,7 @@ toks = whitespace *> goNormal id <* eof
                 Nothing -> pure (f [])
                 Just t@Located{unLocated = BeginEnv "math"} -> goMath (f . (t:))
                 Just t@Located{unLocated = BeginEnv "align*"} -> goMath (f . (t:))
+                Just t@Located{unLocated = BeginEnv "cases"} -> goMath (f . (t:))
                 Just t -> goNormal (f . (t:))
         goText f = do
             r <- optional textToken
@@ -204,6 +205,7 @@ toks = whitespace *> goNormal id <* eof
                 Nothing -> pure (f [])
                 Just t@Located{unLocated = EndEnv "math"} -> goNormal (f . (t:))
                 Just t@Located{unLocated = EndEnv "align*"} -> goNormal (f . (t:))
+                Just t@Located{unLocated = EndEnv "cases"} -> goNormal (f . (t:))
                 Just t@Located{unLocated = BeginEnv "text"} -> goText (f . (t:))
                 Just t@Located{unLocated = BeginEnv "explanation"} -> goText (f . (t:))
                 Just t -> goMath (f . (t:))
@@ -219,12 +221,12 @@ toks = whitespace *> goNormal id <* eof
 -- | Parses a single normal mode token.
 tok :: Lexer (Located Token)
 tok =
-    word <|> var <|> symbol <|> mathBegin <|> alignBegin <|> begin <|> end <|> opening <|> closing <|> label <|> ref <|> command
+    word <|> var <|> symbol <|> mathBegin <|> alignBegin <|> casesBegin <|> begin <|> end <|> opening <|> closing <|> label <|> ref <|> command
 
 -- | Parses a single math mode token.
 mathToken :: Lexer (Located Token)
 mathToken =
-    var <|> symbol <|> number <|> begin <|> alignEnd <|> end <|> opening <|> closing <|> beginText <|> beginExplanation <|> mathEnd <|> command
+    var <|> symbol <|> number <|> begin <|> alignEnd <|> casesEnd <|> end <|> opening <|> closing <|> beginText <|> beginExplanation <|> mathEnd <|> command
 
 beginText :: Lexer (Located Token)
 beginText = lexeme do
@@ -277,6 +279,11 @@ alignBegin = guardM isTextMode *> lexeme do
     setMathMode
     pure (BeginEnv "align*")
 
+casesBegin :: Lexer (Located Token)
+casesBegin = guardM isTextMode *> lexeme do
+    Char.string "\\begin{cases}"
+    setMathMode
+    pure (BeginEnv "cases")
 
 -- | Parses a single end math token.
 mathEnd :: Lexer (Located Token)
@@ -291,6 +298,12 @@ alignEnd = guardM isMathMode *> lexeme do
     setTextMode
     pure (EndEnv "align*")
 
+casesEnd :: Lexer (Located Token)
+casesEnd = guardM isMathMode *> lexeme do
+    Char.string "\\end{cases}"
+    setTextMode
+    pure (EndEnv "cases")
+
 
 -- | Parses a word. Words are returned casefolded, since we want to ignore their case later on.
 word :: Lexer (Located Token)