doc-src/Codegen/Thy/document/Introduction.tex

 \noindent%
 \hspace*{0pt}module Example where {\char123}\\
 \hspace*{0pt}\\
 \hspace*{0pt}data Queue a = AQueue [a] [a];\\
 \hspace*{0pt}\\
-\hspace*{0pt}empty ::~forall a.~Queue a;\\
-\hspace*{0pt}empty = AQueue [] [];\\
-\hspace*{0pt}\\
-\hspace*{0pt}dequeue ::~forall a.~Queue a -> (Maybe a,~Queue a);\\
-\hspace*{0pt}dequeue (AQueue [] []) = (Nothing,~AQueue [] []);\\
-\hspace*{0pt}dequeue (AQueue xs (y :~ys)) = (Just y,~AQueue xs ys);\\
-\hspace*{0pt}dequeue (AQueue (v :~va) []) =\\
+\hspace*{0pt}empty ::~forall a.~Example.Queue a;\\
+\hspace*{0pt}empty = Example.AQueue [] [];\\
+\hspace*{0pt}\\
+\hspace*{0pt}dequeue ::~forall a.~Example.Queue a -> (Maybe a,~Example.Queue a);\\
+\hspace*{0pt}dequeue (Example.AQueue [] []) = (Nothing,~Example.AQueue [] []);\\
+\hspace*{0pt}dequeue (Example.AQueue xs (y :~ys)) = (Just y,~Example.AQueue xs ys);\\
+\hspace*{0pt}dequeue (Example.AQueue (v :~va) []) =\\
 \hspace*{0pt} ~let {\char123}\\
 \hspace*{0pt} ~~~(y :~ys) = reverse (v :~va);\\
-\hspace*{0pt} ~{\char125}~in (Just y,~AQueue [] ys);\\
-\hspace*{0pt}\\
-\hspace*{0pt}enqueue ::~forall a.~a -> Queue a -> Queue a;\\
-\hspace*{0pt}enqueue x (AQueue xs ys) = AQueue (x :~xs) ys;\\
+\hspace*{0pt} ~{\char125}~in (Just y,~Example.AQueue [] ys);\\
+\hspace*{0pt}\\
+\hspace*{0pt}enqueue ::~forall a.~a -> Example.Queue a -> Example.Queue a;\\
+\hspace*{0pt}enqueue x (Example.AQueue xs ys) = Example.AQueue (x :~xs) ys;\\
 \hspace*{0pt}\\
 \hspace*{0pt}{\char125}%
 \end{isamarkuptext}%
 \isamarkuptrue%
 %

 \begin{isamarkuptext}%
 \isatypewriter%
 \noindent%
 \hspace*{0pt}module Example where {\char123}\\
 \hspace*{0pt}\\
-\hspace*{0pt}data Nat = Zero{\char95}nat | Suc Nat;\\
-\hspace*{0pt}\\
-\hspace*{0pt}plus{\char95}nat ::~Nat -> Nat -> Nat;\\
-\hspace*{0pt}plus{\char95}nat (Suc m) n = plus{\char95}nat m (Suc n);\\
-\hspace*{0pt}plus{\char95}nat Zero{\char95}nat n = n;\\
+\hspace*{0pt}data Nat = Zero{\char95}nat | Suc Example.Nat;\\
+\hspace*{0pt}\\
+\hspace*{0pt}plus{\char95}nat ::~Example.Nat -> Example.Nat -> Example.Nat;\\
+\hspace*{0pt}plus{\char95}nat (Example.Suc m) n = Example.plus{\char95}nat m (Example.Suc n);\\
+\hspace*{0pt}plus{\char95}nat Example.Zero{\char95}nat n = n;\\
 \hspace*{0pt}\\
 \hspace*{0pt}class Semigroup a where {\char123}\\
 \hspace*{0pt} ~mult ::~a -> a -> a;\\
 \hspace*{0pt}{\char125};\\
 \hspace*{0pt}\\
-\hspace*{0pt}class (Semigroup a) => Monoid a where {\char123}\\
+\hspace*{0pt}class (Example.Semigroup a) => Monoid a where {\char123}\\
 \hspace*{0pt} ~neutral ::~a;\\
 \hspace*{0pt}{\char125};\\
 \hspace*{0pt}\\
-\hspace*{0pt}pow ::~forall a.~(Monoid a) => Nat -> a -> a;\\
-\hspace*{0pt}pow Zero{\char95}nat a = neutral;\\
-\hspace*{0pt}pow (Suc n) a = mult a (pow n a);\\
-\hspace*{0pt}\\
-\hspace*{0pt}mult{\char95}nat ::~Nat -> Nat -> Nat;\\
-\hspace*{0pt}mult{\char95}nat Zero{\char95}nat n = Zero{\char95}nat;\\
-\hspace*{0pt}mult{\char95}nat (Suc m) n = plus{\char95}nat n (mult{\char95}nat m n);\\
-\hspace*{0pt}\\
-\hspace*{0pt}neutral{\char95}nat ::~Nat;\\
-\hspace*{0pt}neutral{\char95}nat = Suc Zero{\char95}nat;\\
-\hspace*{0pt}\\
-\hspace*{0pt}instance Semigroup Nat where {\char123}\\
-\hspace*{0pt} ~mult = mult{\char95}nat;\\
+\hspace*{0pt}pow ::~forall a.~(Example.Monoid a) => Example.Nat -> a -> a;\\
+\hspace*{0pt}pow Example.Zero{\char95}nat a = Example.neutral;\\
+\hspace*{0pt}pow (Example.Suc n) a = Example.mult a (Example.pow n a);\\
+\hspace*{0pt}\\
+\hspace*{0pt}mult{\char95}nat ::~Example.Nat -> Example.Nat -> Example.Nat;\\
+\hspace*{0pt}mult{\char95}nat Example.Zero{\char95}nat n = Example.Zero{\char95}nat;\\
+\hspace*{0pt}mult{\char95}nat (Example.Suc m) n = Example.plus{\char95}nat n (Example.mult{\char95}nat m n);\\
+\hspace*{0pt}\\
+\hspace*{0pt}neutral{\char95}nat ::~Example.Nat;\\
+\hspace*{0pt}neutral{\char95}nat = Example.Suc Example.Zero{\char95}nat;\\
+\hspace*{0pt}\\
+\hspace*{0pt}instance Example.Semigroup Example.Nat where {\char123}\\
+\hspace*{0pt} ~mult = Example.mult{\char95}nat;\\
 \hspace*{0pt}{\char125};\\
 \hspace*{0pt}\\
-\hspace*{0pt}instance Monoid Nat where {\char123}\\
-\hspace*{0pt} ~neutral = neutral{\char95}nat;\\
+\hspace*{0pt}instance Example.Monoid Example.Nat where {\char123}\\
+\hspace*{0pt} ~neutral = Example.neutral{\char95}nat;\\
 \hspace*{0pt}{\char125};\\
 \hspace*{0pt}\\
-\hspace*{0pt}bexp ::~Nat -> Nat;\\
-\hspace*{0pt}bexp n = pow n (Suc (Suc Zero{\char95}nat));\\
+\hspace*{0pt}bexp ::~Example.Nat -> Example.Nat;\\
+\hspace*{0pt}bexp n = Example.pow n (Example.Suc (Example.Suc Example.Zero{\char95}nat));\\
 \hspace*{0pt}\\
 \hspace*{0pt}{\char125}%
 \end{isamarkuptext}%
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 %

 \hspace*{0pt} ~type 'a monoid\\
 \hspace*{0pt} ~val semigroup{\char95}monoid :~'a monoid -> 'a semigroup\\
 \hspace*{0pt} ~val neutral :~'a monoid -> 'a\\
 \hspace*{0pt} ~val pow :~'a monoid -> nat -> 'a -> 'a\\
 \hspace*{0pt} ~val mult{\char95}nat :~nat -> nat -> nat\\
+\hspace*{0pt} ~val semigroup{\char95}nat :~nat semigroup\\
 \hspace*{0pt} ~val neutral{\char95}nat :~nat\\
-\hspace*{0pt} ~val semigroup{\char95}nat :~nat semigroup\\
 \hspace*{0pt} ~val monoid{\char95}nat :~nat monoid\\
 \hspace*{0pt} ~val bexp :~nat -> nat\\
 \hspace*{0pt}end = struct\\
 \hspace*{0pt}\\
 \hspace*{0pt}datatype nat = Zero{\char95}nat | Suc of nat;\\

 \hspace*{0pt} ~| pow A{\char95}~(Suc n) a = mult (semigroup{\char95}monoid A{\char95}) a (pow A{\char95}~n a);\\
 \hspace*{0pt}\\
 \hspace*{0pt}fun mult{\char95}nat Zero{\char95}nat n = Zero{\char95}nat\\
 \hspace*{0pt} ~| mult{\char95}nat (Suc m) n = plus{\char95}nat n (mult{\char95}nat m n);\\
 \hspace*{0pt}\\
+\hspace*{0pt}val semigroup{\char95}nat = {\char123}mult = mult{\char95}nat{\char125}~:~nat semigroup;\\
+\hspace*{0pt}\\
 \hspace*{0pt}val neutral{\char95}nat :~nat = Suc Zero{\char95}nat;\\
-\hspace*{0pt}\\
-\hspace*{0pt}val semigroup{\char95}nat = {\char123}mult = mult{\char95}nat{\char125}~:~nat semigroup;\\
 \hspace*{0pt}\\
 \hspace*{0pt}val monoid{\char95}nat = {\char123}semigroup{\char95}monoid = semigroup{\char95}nat,~neutral = neutral{\char95}nat{\char125}\\
 \hspace*{0pt} ~:~nat monoid;\\
 \hspace*{0pt}\\
 \hspace*{0pt}fun bexp n = pow monoid{\char95}nat n (Suc (Suc Zero{\char95}nat));\\