movements

[lambda.git] / topics / week12_list_and_tree_zippers.mdwn

diff --git a/topics/week12_list_and_tree_zippers.mdwn b/topics/week12_list_and_tree_zippers.mdwn
index 2f5d5dc..89d83b6 100644 (file)
--- a/topics/week12_list_and_tree_zippers.mdwn
+++ b/topics/week12_list_and_tree_zippers.mdwn
@@ -1,3 +1,5 @@
+<!-- λ ◊ ≠ ∃ Λ ∀ ≡ α β γ ρ ω φ ψ Ω ○ μ η δ ζ ξ ⋆ ★ • ∙ ● ⚫ 𝟎 𝟏 𝟐 𝟘 𝟙 𝟚 𝟬 𝟭 𝟮 ⇧ (U+2e17) ¢ -->
+

 [[!toc]]
 
 ##List Zippers##
 [[!toc]]
 
 ##List Zippers##


@@ -213,7 +215,7 @@ siblings of the focussed tree:
 
     Branch (Leaf 2, Leaf 3), ([], [Leaf 4])
 
 
     Branch (Leaf 2, Leaf 3), ([], [Leaf 4])
 

-We still need to add the rest of the context.  But just computed that
+We still need to add the rest of the context.  But we just computed that

 context a minute ago.  It was ([Leaf 1], []).  If we add it here, we get:
 
     Branch (Leaf 2, Leaf 3), ([], [Leaf 4], ([Leaf 1], [])
 context a minute ago.  It was ([Leaf 1], []).  If we add it here, we get:
 
     Branch (Leaf 2, Leaf 3), ([], [Leaf 4], ([Leaf 1], [])


@@ -223,13 +225,13 @@ Here's the type suggested by this idea:
     type context = Root | Context of (tree list) * (tree list) * context
     type zipper = tree * context
 
     type context = Root | Context of (tree list) * (tree list) * context
     type zipper = tree * context
 

-We can gloss `Context of (tree list) * (tree list) * context` as 
-`Context of (left siblings) * (right siblings) * (context of parent)`.
+We can gloss the triple `(tree list) * (tree list) * context` as 
+`(left siblings) * (right siblings) * (context of parent)`.

 
 Here, then, is the full tree zipper we've been looking for:
 
 
 Here, then, is the full tree zipper we've been looking for:
 

-  (Branch [Leaf 2; Leaf 3],
-   Context ([], [Leaf 4], Context ([Leaf 1], [], Root)))
+    (Branch [Leaf 2; Leaf 3],
+     Context ([], [Leaf 4], Context ([Leaf 1], [], Root)))

 
 Just as with the simple list zipper, note that elements that are near
 the focussed element in the tree are near the focussed element in the
 
 Just as with the simple list zipper, note that elements that are near
 the focussed element in the tree are near the focussed element in the


@@ -266,50 +268,33 @@ probably not represent siblings with a list zipper, but with something
 more special-purpose and economical.
 
 With these functions, we can refocus on any part of the tree.
 more special-purpose and economical.
 
 With these functions, we can refocus on any part of the tree.

-Here's a complete tour:
+Let's abbreviate a tree zipper like this:
+
+    [2;3], ([] [4] ([1], [], Root)) 
+
+    ≡ (Branch [Leaf 2; Leaf 3],
+       Context ([], [Leaf 4], Context ([Leaf 1], [], Root)))
+
+Then we can take a tour of the original tree like this:

 
 <pre>
 
 <pre>

-# let z1 = (t1, Root);;
-val z1 : zipper =
-  (Branch [Leaf 1; Branch [Branch [Leaf 2; Leaf 3]; Leaf 4]], Root)
-# let z2 = downleft z1;;
-val z2 : zipper =
-  (Leaf 1, Context ([], [Branch [Branch [Leaf 2; Leaf 3]; Leaf 4]], Root))
-# let z3 = right z2;;
-val z3 : zipper =
-  (Branch [Branch [Leaf 2; Leaf 3]; Leaf 4], Context ([Leaf 1], [], Root))
-# let z4 = downleft z3;;
-val z4 : zipper =
-  (Branch [Leaf 2; Leaf 3],
-   Context ([], [Leaf 4], Context ([Leaf 1], [], Root)))
-# let z5 = downleft z4;;
-val z5 : zipper =
-  (Leaf 2,
-   Context ([], [Leaf 3],
-    Context ([], [Leaf 4], Context ([Leaf 1], [], Root))))
-# let z6 = right z5;;
-val z6 : zipper =
-  (Leaf 3,
-   Context ([Leaf 2], [],
-    Context ([], [Leaf 4], Context ([Leaf 1], [], Root))))
-# let z7 = up z6;;
-val z7 : zipper =
-  (Branch [Leaf 2; Leaf 3],
-   Context ([], [Leaf 4], Context ([Leaf 1], [], Root)))
-# let z8 = right z7;;
-val z8 : zipper =
-  (Leaf 4,
-   Context ([Branch [Leaf 2; Leaf 3]], [], Context ([Leaf 1], [], Root)))
-# let z9 = up z8;;
-val z9 : zipper =
-  (Branch [Branch [Leaf 2; Leaf 3]; Leaf 4], Context ([Leaf 1], [], Root))
-# let z10 = up z9;;
-val z10 : zipper =
-  (Branch [Leaf 1; Branch [Branch [Leaf 2; Leaf 3]; Leaf 4]], Root)
-# z10 = z1;;
-- : bool = true
-# z10 == z1;;
-- : bool = false
+_|__
+|  |
+1  |
+  _|__
+  |  |
+  |  4
+ _|__
+ |  |
+ 2  3
+
+    [1;[[2;3];4]],Root           =                                                              [1;[[2;3];4]],Root
+  downleft                                                                                               up
+1, ([],[[2;3];4],Root) right [[2;3];4],([1],[],Root)                                            [[2;3];4],([1],[],Root)
+                           downleft                                                                      up                                
+                        [2;3],([],[4],([1],[],Root))         [2;3],([],[4],([1],[],Root)) right 4,([2;3],[],([1],[],Root))
+                      downleft                                           up
+                    2, ([],[3],([],[4],([1],[],Root))) right 3, ([2],[],([],[4],([1],[],Root)))

 </pre>
 
 Here's more on zippers:
 </pre>
 
 Here's more on zippers: