Update examples for recursive destruct of conditionals and matches

examples/bts/264_destruct_if.mlw

+use list.List
+use list.Length
+use int.Int
 
 constant x: int
 
 predicate p int
 
+(**********************)
+(* Simple destruction *)
+(**********************)
+
 axiom H: if x = 42 then p 1 else p 2
 
-goal g: p 3
-
-use list.List
-use list.Length
-use int.Int
+goal g: p 0
 
 constant l: list int
 
-axiom H': match l with
+axiom H1: match l with
 | Nil -> p 4
 | Cons x y -> p (x+length y)
 | Cons _ (Cons y Nil) -> p y
@@ -21,19 +24,64 @@ axiom H': match l with
 | Cons _ (Cons _ (Cons _ _)) -> p 5
 end
 
-goal g': p 6
+goal g1: p 1
+
+(**********************)
+(* As and or patterns *)
+(**********************)
 
-axiom H'': match l with
+axiom H2: match l with
 | Nil -> p 1
 | Cons x Nil | Cons _ (Cons x Nil) -> p x
-| Cons _ (Cons _ _ as l') -> p (length l')
+| Cons _ (Cons _ _ as l1) -> p (length l1)
 end
 
-goal g'': p 7
+goal g2: p 2
 
-axiom H''': match l with
-| Cons _ (Cons _ _ as l') as l'' -> p (length l'+length l'')
+axiom H3: match l with
+| Cons _ (Cons _ _ as l1) as l2 -> p (length l1+length l2)
 | _ -> p 0
 end
 
-goal g''': p 8
\ No newline at end of file
+goal g3: p 3
+
+(*************************)
+(* Recursive destruction *)
+(*************************)
+
+axiom H4:
+  if p x then
+    (if p (x+1) then
+       p 1
+     else
+       p 2)
+  else p 3
+
+goal g4: p 4
+
+axiom H5: match l with
+| Cons x (Cons y _) ->
+  if x = y then
+    p 1 \/ p 2
+  else
+    p 3 /\ p 4
+| _ -> true
+end
+
+(*********************************************************************************)
+(* Interaction between recursive destruction of conditionals and of implications *)
+(*********************************************************************************)
+
+goal g5: p 5
+
+axiom H6: p 1 -> if p 2 then p 3 else p 4
+
+goal g6: p 6
+
+axiom H7: if p 1 then p 2 -> p 3 else p 4
+
+goal g7: p 7
+
+axiom H8: if p 1 then if p 2 then (p 3 -> p 4) else p 5 else p 6
+
+goal g8: p 8
\ No newline at end of file

examples/bts/264_destruct_if/why3session.xml

@@ -14,37 +14,117 @@
   </goal>
  </transf>
  </goal>
- <goal name="g&#39;">
- <transf name="destruct" arg1="H&#39;">
-  <goal name="g&#39;.0">
+ <goal name="g1">
+ <transf name="destruct" arg1="H1">
+  <goal name="g1.0">
   </goal>
-  <goal name="g&#39;.1">
+  <goal name="g1.1">
   </goal>
-  <goal name="g&#39;.2">
+  <goal name="g1.2">
   </goal>
-  <goal name="g&#39;.3">
+  <goal name="g1.3">
   </goal>
-  <goal name="g&#39;.4">
+  <goal name="g1.4">
   </goal>
  </transf>
  </goal>
- <goal name="g&#39;&#39;">
- <transf name="destruct" arg1="H&#39;&#39;">
-  <goal name="g&#39;&#39;.0">
+ <goal name="g2">
+ <transf name="destruct" arg1="H2">
+  <goal name="g2.0">
   </goal>
-  <goal name="g&#39;&#39;.1">
+  <goal name="g2.1">
   </goal>
-  <goal name="g&#39;&#39;.2">
+  <goal name="g2.2">
   </goal>
-  <goal name="g&#39;&#39;.3">
+  <goal name="g2.3">
   </goal>
  </transf>
  </goal>
- <goal name="g&#39;&#39;&#39;">
- <transf name="destruct" arg1="H&#39;&#39;&#39;">
-  <goal name="g&#39;&#39;&#39;.0">
+ <goal name="g3">
+ <transf name="destruct" arg1="H3">
+  <goal name="g3.0">
   </goal>
-  <goal name="g&#39;&#39;&#39;.1">
+  <goal name="g3.1">
+  </goal>
+ </transf>
+ </goal>
+ <goal name="g4">
+ <transf name="destruct" arg1="H4">
+  <goal name="g4.0">
+  </goal>
+  <goal name="g4.1">
+  </goal>
+ </transf>
+ <transf name="destruct_rec" arg1="H4">
+  <goal name="g4.0">
+  </goal>
+  <goal name="g4.1">
+  </goal>
+  <goal name="g4.2">
+  </goal>
+ </transf>
+ </goal>
+ <goal name="g5">
+ <transf name="destruct" arg1="H5">
+  <goal name="g5.0">
+  </goal>
+  <goal name="g5.1">
+  </goal>
+ </transf>
+ <transf name="destruct_rec" arg1="H5">
+  <goal name="g5.0">
+  </goal>
+  <goal name="g5.1">
+  </goal>
+  <goal name="g5.2">
+  </goal>
+  <goal name="g5.3">
+  </goal>
+ </transf>
+ </goal>
+ <goal name="g6">
+ <transf name="destruct" arg1="H6">
+  <goal name="g6.0" expl="destruct premise">
+  </goal>
+  <goal name="g6.1">
+  </goal>
+ </transf>
+ <transf name="destruct_rec" arg1="H6">
+  <goal name="g6.0" expl="destruct premise">
+  </goal>
+  <goal name="g6.1">
+  </goal>
+  <goal name="g6.2">
+  </goal>
+ </transf>
+ </goal>
+ <goal name="g7">
+ <transf name="destruct" arg1="H7">
+  <goal name="g7.0">
+  </goal>
+  <goal name="g7.1">
+  </goal>
+ </transf>
+ <transf name="destruct_rec" arg1="H7">
+  <goal name="g7.0">
+  </goal>
+  <goal name="g7.1">
+  </goal>
+ </transf>
+ </goal>
+ <goal name="g8">
+ <transf name="destruct" arg1="H8">
+  <goal name="g8.0">
+  </goal>
+  <goal name="g8.1">
+  </goal>
+ </transf>
+ <transf name="destruct_rec" arg1="H8">
+  <goal name="g8.0">
+  </goal>
+  <goal name="g8.1">
+  </goal>
+  <goal name="g8.2">
   </goal>
  </transf>
  </goal>