Remove native script examples, this is now implemented in exec spec

shelley/chain-and-ledger/formal-spec/multi-sig.tex

@@ -751,16 +751,10 @@ \subsection{Native Script Interpreter}
 script as data type which can then be interpreted
 natively. Figure~\ref{fig:types-msig} shows the types and necessary functions
 for such a native script implementation. The type $\ScriptMSig$ is defined as a
-tree-structure which is either a single signature leaf node or a list of
-values of type $\ScriptMSig$ together with an integral threshold value.
-
-The validation of such a term is done as shown in the specialization of
-\fun{validateScript} for $\ScriptMSig$ as shown in Figure~\ref{fig:types-msig}.
-It checks for presence of a single signature in the set of signatures of a
-transaction as the base case and compares the number of validating nodes in the
-list with the threshold in the recursion case. The
-Appendix~\ref{sec:native-multi-sign} provides some examples of how this scheme
-can be used.
+tree-structure which is either a single signature leaf node or a list of values
+of type $\ScriptMSig$, which either requires all signatures to validate, at
+least one of the signatures to validate or at least the threshold value of $m$
+signatures to validate.
 
 \subsection{Lower Level Implementation Details}
 \label{sec:lower-level-impl}
@@ -804,94 +798,6 @@ \section{Summary}
 viable for any reason, e.g., script size or readiness of library, only the
 native script implementation could be pursued instead.
 
-\appendix
-
-\section{Native Multi-Signature Examples}
-\label{sec:native-multi-sign}
-
-\begin{verbatim}
-verifyCases :: ScriptMSig -> [(Set VKeyHash, Bool)] -> Bool
-verifyCases script cases =
-    and [ evalMultiSigScript script keyset == expected
-        | (keyset, expected) <- cases]
-
-mkVKeyHashSet :: [Int] -> Set VKeyHash
-mkVKeyHashSet = Set.fromList . map VKeyHash
-
-example1Of2 =
-  MultiSig 1 [SingleSig (VKeyHash 1), SingleSig (VKeyHash 2)]
-
-example1Of2_verify =
-    verifyCases
-      example1Of2
-      [ (mkVKeyHashSet [],    False)
-      , (mkVKeyHashSet [1],   True)
-      , (mkVKeyHashSet [2],   True)
-      , (mkVKeyHashSet [1,2], True)
-      , (mkVKeyHashSet [3],   False)
-      ]
-
-example2Of2 =
-  MultiSig 2 [SingleSig (VKeyHash 1), SingleSig (VKeyHash 2)]
-
-example2Of2_verify =
-    verifyCases
-      example2Of2
-      [ (mkVKeyHashSet [],      False)
-      , (mkVKeyHashSet [1],     False)
-      , (mkVKeyHashSet [2],     False)
-      , (mkVKeyHashSet [1,2],   True)
-      , (mkVKeyHashSet [3],     False)
-      , (mkVKeyHashSet [1,2,3], True)
-      ]
-
-exampleNestedOrAnd =
-  MultiSig 1 [ MultiSig 2 [SingleSig (VKeyHash 1), SingleSig (VKeyHash 2)]
-             , MultiSig 2 [SingleSig (VKeyHash 3), SingleSig (VKeyHash 4)]
-             ]
-
-exampleNestedAndOr =
-  MultiSig 2 [ MultiSig 1 [SingleSig (VKeyHash 1), SingleSig (VKeyHash 2)]
-             , MultiSig 1 [SingleSig (VKeyHash 3), SingleSig (VKeyHash 4)]
-             ]
-
-exampleNestedOrAnd_verify =
-    verifyCases
-      exampleNestedOrAnd
-      [ (keysset, expected)
-      | has1 <- [False, True]
-      , has2 <- [False, True]
-      , has3 <- [False, True]
-      , has4 <- [False, True]
-      , has5 <- [False, True]
-      , let keysset = mkVKeyHashSet $ [ 1 | has1 ]
-                                   ++ [ 2 | has2 ]
-                                   ++ [ 3 | has3 ]
-                                   ++ [ 4 | has4 ]
-                                   ++ [ 5 | has5 ]
-            expected = (has1 && has2)
-                    || (has3 && has4)
-      ]
-
-exampleNestedAndOr_verify =
-    verifyCases
-      exampleNestedAndOr
-      [ (keysset, expected)
-      | has1 <- [False, True]
-      , has2 <- [False, True]
-      , has3 <- [False, True]
-      , has4 <- [False, True]
-      , has5 <- [False, True]
-      , let keysset = mkVKeyHashSet $ [ 1 | has1 ]
-                                   ++ [ 2 | has2 ]
-                                   ++ [ 3 | has3 ]
-                                   ++ [ 4 | has4 ]
-                                   ++ [ 5 | has5 ]
-            expected = (has1 || has2)
-                    && (has3 || has4)
-      ]
-\end{verbatim}
-
 \addcontentsline{toc}{section}{References} \bibliographystyle{plainnat}
 \bibliography{references}