@@ -16,24 +16,18 @@ Tests whether the tree address `a` is in the head or the tail of a noun.
16Produces the constant atom `%2` if it is within the head (subtree `+2`), or
16Produces the constant atom `%2` if it is within the head (subtree `+2`), or
17the constant atom `%3` if it is within the tail (subtree `+3`).
17the constant atom `%3` if it is within the tail (subtree `+3`).
19−In the Urbit binary-tree system, a parent at address `n` will always have its
20−children at address `2n` (the head) and address `2n+1` (the tail).
23−Accepts
20+#### Accepts
26`a` is an atom.
22`a` is an atom.
28−Produces
24+#### Produces
31A constant atom.
26A constant atom.
36− ++ cap :: tree head
30+ ++ cap
39 ^- ?($2 $3)
33 ^- ?($2 $3)
@@ -43,10 +37,9 @@ Source
43 ?(%0 %1) !!
37 ?(%0 %1) !!
44 * $(a (div a 2))
38 * $(a (div a 2))
48−Examples
42+#### Examples
@@ -77,52 +70,19 @@ Examples
77Address within head/tail
70Address within head/tail
79Computes the tree address of atom `a` within either the head (`+2`) or tail
72Computes the tree address of atom `a` within either the head (`+2`) or tail
80−(`+3`) of a noun. In other words, `++mas` returns the relative address of `a`
73+(`+3`) of a noun.
81−with respect to the head or the tail subtrees, depending on which one `a`
87− 2 3 <--here are the head (`+2`) and the tail (`+3`)
93−Running `(mas 7)` in the Dojo will return `3`, because address `+3` is what
94−`+7` now occupies. The tree below helps illustrate the relationship. With
95−parentheses are `a` values (if `a` is in subtree `+3`), and without parentheses
96−are the values returned with `(mas a)`.
98− 1(3) ::new/(old) addresses
109−Notice how the old values in the head (subtree `+2`) were not illustrated in
110−this case, because `+7` is within the tail (subtree `+3`).
112−Accepts
75+#### Accepts
115`a` is an atom.
77`a` is an atom.
117−Produces
79+#### Produces
125− ++ mas :: tree body
85+ ++ mas
@@ -132,10 +92,9 @@ Source
133 * (add (mod a 2) (mul $(a (div a 2)) 2))
93 * (add (mod a 2) (mul $(a (div a 2)) 2))
137−Examples
97+#### Examples
140 > (mas 3)
99 > (mas 3)
@@ -159,12 +118,8 @@ Examples
159 > (mas (mas 11))
118 > (mas (mas 11))
167− > (cap (mas 5))
121+ > (cap (mas 6))
169 > (mas 0)
124 > (mas 0)
170 ! exit ::address `0` is in neither the head nor the tail
125 ! exit ::address `0` is in neither the head nor the tail
@@ -173,75 +128,62 @@ Examples
173 ! exit ::address `1` is in neither the head nor the tail
128 ! exit ::address `1` is in neither the head nor the tail
180−Address within address
182−Computes the absolute address of `b`, a relative address within the subtree
185−In other words, the subtree at address `a` is treated as a tree in its own
186−right (starting with root `+1`, head `+2`, and tail `+3`). Relative address
187−`b` is found with respect to `a`, and then its absolute address, within the
188−greater tree, is returned.
190−Running `(peg 3 4)` in the Dojo, for example, will return `12`. Looking at
191−a tree diagram makes it easy to see why.
197− 2 3 <- here is the subtree `+3`. The subtree address is `a` in `(peg a b)`
202− 8 9 10 11 12 13 14 15
203− /\ /\ /\ /\ /\ /\ /\ /\
137+ 2 3 <--here are the head (`+2`) and the tail (`+3`)
207−When we consider subtree at address `+3` by itself, it has relative addresses
143+Running `(mas 7)` in the Dojo will return `3`, because address `+3` is what
208−that are structured in the same way as its parent tree's absolute addresses.
144+`+7` now occupies. The tree below helps illustrate the relationship. With
209−The absolute addresses are given in parentheses in the diagram below.
145+parentheses are `a` values (if `a` is in subtree `+3`), and without parentheses
210−Notice how relative address `+4` is at the same position as absolute address
146+are the values returned with `(mas a)`.
213− 1(3) ::new/(old) addresses
148+ 1(3) ::new/(old) addresses
220− (12) (13) (14) (15)
155+ (12) (13) (14) (15)
221 / \ / \ / \ / \
156 / \ / \ / \ / \
222 (continues...)
157 (continues...)
159+Notice how the old values in the head (subtree `+2`) were not illustrated in
160+this case, because `+7` is within the tail (subtree `+3`).
165+Address within address
167+Computes the absolute address of `b`, a relative address within the subtree
225−Accepts
170+#### Accepts
228`a` is an atom.
172`a` is an atom.
230`b` is an atom.
174`b` is an atom.
232−Produces
176+#### Produces
237−Source
180+#### Source
240− ++ peg :: tree connect
182+ ++ peg
242− |= [a=@ b=@] :: creates a gate
184+ |= [a=@ b=@]
243− ?< =(0 a) :: branches if there is no equality
185+ ?< =(0 a)
244− ^- @ :: casts to type @
186+ ^- @
247 $2 (mul a 2)
189 $2 (mul a 2)
@@ -249,8 +191,7 @@ Source
249 * (add (mod b 2) (mul $(b (div b 2)) 2))
191 * (add (mod b 2) (mul $(b (div b 2)) 2))
252−Examples
194+#### Examples
255 > (peg 4 1)
196 > (peg 4 1)
@@ -270,24 +211,50 @@ Examples
270 > (peg 8 45)
211 > (peg 8 45)
285 > (cap (peg 4 2)) ::`(cap a)` computes whether address `a` is in the head or the tail
214 > (cap (peg 4 2)) ::`(cap a)` computes whether address `a` is in the head or the tail
220+In other words, the subtree at address `a` is treated as a tree in its own
221+right (starting with root `+1`, head `+2`, and tail `+3`). Relative address
222+`b` is found with respect to `a`, and then its absolute address, within the
223+greater tree, is returned.
225+Running `(peg 3 4)` in the Dojo, for example, will return `12`. Looking at
226+a tree diagram makes it easy to see why.
232+ 2 3 <- here is the subtree `+3`. The subtree address is `a` in `(peg a b)`
237+ 8 9 10 11 12 13 14 15
238+ /\ /\ /\ /\ /\ /\ /\ /\
242+When we consider subtree at address `+3` by itself, it has relative addresses
243+that are structured in the same way as its parent tree's absolute addresses.
244+The absolute addresses are given in parentheses in the diagram below.
245+Notice how relative address `+4` is at the same position as absolute address
248+ 1(3) ::new/(old) addresses