Working on the notebooks.
This commit is contained in:
sforman
parent
7d8e2ae611
commit
387d9d4ed4
File diff suppressed because it is too large
Load Diff
|
|
@ -244,103 +244,160 @@ b [b+a b F]
|
|||
</code></pre>
|
||||
<p>Putting it all together:</p>
|
||||
<pre><code>F == + [popdd over] cons infra uncons
|
||||
fib_gen == [1 1 F]
|
||||
</code></pre>
|
||||
<p>Let's call <code>F</code> <code>fib_gen</code>:</p>
|
||||
<pre><code>[fib_gen + [popdd over] cons infra uncons] inscribe
|
||||
<h3><code>fib-gen</code></h3>
|
||||
<p>Let's call <code>F</code> <code>fib-gen</code>:</p>
|
||||
<pre><code>[fib-gen + [popdd over] cons infra uncons] inscribe
|
||||
</code></pre>
|
||||
<p>We can just write the initial quote and then "force" it with <code>x</code>:</p>
|
||||
<pre><code>joy? [1 1 fib_gen] 10 [x] times
|
||||
1 2 3 5 8 13 21 34 55 89 [144 89 fib_gen]
|
||||
<pre><code>joy? [1 1 fib-gen] 10 [x] times
|
||||
1 2 3 5 8 13 21 34 55 89 [144 89 fib-gen]
|
||||
</code></pre>
|
||||
<p>It skips the first term (1) but if that bothers you you can just prepend it to the program:</p>
|
||||
<pre><code>1 [1 1 fib_gen] 10 [x] times
|
||||
<pre><code>1 [1 1 fib-gen] 10 [x] times
|
||||
</code></pre>
|
||||
<h2>Project Euler Problem Two</h2>
|
||||
<blockquote>
|
||||
<p>By considering the terms in the Fibonacci sequence whose values do not exceed four million, find the sum of the even-valued terms.</p>
|
||||
</blockquote>
|
||||
<p>Now that we have a generator for the Fibonacci sequence, we need a function that adds a term in the sequence to a sum if it is even, and <code>pop</code>s it otherwise.</p>
|
||||
<p><code>python
|
||||
define('PE2.1 == dup 2 % [+] [pop] branch')</code></p>
|
||||
<p>Now that we have a generator for the Fibonacci sequence, we need a function that adds
|
||||
a term in the sequence to a sum if it is even, and <code>pop</code>s it otherwise.</p>
|
||||
<h3><code>even</code></h3>
|
||||
<pre><code>[even 2 % bool] inscribe
|
||||
</code></pre>
|
||||
<h3><code>PE2.1</code></h3>
|
||||
<pre><code>[PE2.1 dup even [+] [pop] branch] inscribe
|
||||
</code></pre>
|
||||
<p>And a predicate function that detects when the terms in the series "exceed four million".</p>
|
||||
<p><code>python
|
||||
define('>4M == 4000000 >')</code></p>
|
||||
<p>Now it's straightforward to define <code>PE2</code> as a recursive function that generates terms in the Fibonacci sequence until they exceed four million and sums the even ones.</p>
|
||||
<p><code>python
|
||||
define('PE2 == 0 fib_gen x [pop >4M] [popop] [[PE2.1] dip x] primrec')</code></p>
|
||||
<p><code>python
|
||||
J('PE2')</code></p>
|
||||
<pre><code>4613732
|
||||
<h3><code>>4M</code></h3>
|
||||
<pre><code>[>4M 4000000 >] inscribe
|
||||
</code></pre>
|
||||
<p>Here's the collected program definitions:</p>
|
||||
<pre><code>fib == + swons [popdd over] infra uncons
|
||||
fib_gen == [1 1 fib]
|
||||
|
||||
even == dup 2 %
|
||||
>4M == 4000000 >
|
||||
|
||||
PE2.1 == even [+] [pop] branch
|
||||
PE2 == 0 fib_gen x [pop >4M] [popop] [[PE2.1] dip x] primrec
|
||||
<p>Now it's straightforward to define <code>PE2</code> as a recursive function that generates terms
|
||||
in the Fibonacci sequence until they exceed four million and sums the even ones.</p>
|
||||
<pre><code>joy? 0 [1 1 fib-gen] x [pop >4M] [popop] [[PE2.1] dip x] tailrec
|
||||
4613732
|
||||
</code></pre>
|
||||
<h3>Even-valued Fibonacci Terms</h3>
|
||||
<h3><code>PE2</code></h3>
|
||||
<pre><code>[PE2 0 [1 1 fib-gen] x [pop >4M] [popop] [[PE2.1] dip x] tailrec] inscribe
|
||||
</code></pre>
|
||||
<p>Here's the collected program definitions (with a little editorializing):</p>
|
||||
<pre><code>fib-gen + [popdd over] cons infra uncons
|
||||
even 2 % bool
|
||||
>4M 4000000 >
|
||||
PE2.1 dup even [+] [pop] branch
|
||||
PE2.2 [PE2.1] dip x
|
||||
PE2.init 0 [1 1 fib-gen] x
|
||||
PE2.rec [pop >4M] [popop] [PE2.2] tailrec
|
||||
PE2 PE2.init PE2.rec
|
||||
</code></pre>
|
||||
<h3>Hmm...</h3>
|
||||
<pre><code>fib-gen + swons [popdd over] infra uncons
|
||||
</code></pre>
|
||||
<h2>Even-valued Fibonacci Terms</h2>
|
||||
<p>Using <code>o</code> for odd and <code>e</code> for even:</p>
|
||||
<pre><code>o + o = e
|
||||
e + e = e
|
||||
o + e = o
|
||||
</code></pre>
|
||||
<p>So the Fibonacci sequence considered in terms of just parity would be:</p>
|
||||
<pre><code>o o e o o e o o e o o e o o e o o e
|
||||
1 1 2 3 5 8 . . .
|
||||
<pre><code>o o e o o e o o e o o e . . .
|
||||
1 1 2 3 5 8 13 21 34 55 89 144 . . .
|
||||
</code></pre>
|
||||
<p>Every third term is even.</p>
|
||||
<p><code>python
|
||||
J('[1 0 fib] x x x') # To start the sequence with 1 1 2 3 instead of 1 2 3.</code></p>
|
||||
<pre><code>1 1 2 [3 2 fib]
|
||||
<p>So what if we drive the generator three times and discard the odd terms?
|
||||
We would have to initialize our <code>fib</code> generator with 1 0:</p>
|
||||
<pre><code>[1 0 fib-gen]
|
||||
</code></pre>
|
||||
<p>Drive the generator three times and <code>popop</code> the two odd terms.</p>
|
||||
<p><code>python
|
||||
J('[1 0 fib] x x x [popop] dipd')</code></p>
|
||||
<pre><code>2 [3 2 fib]
|
||||
<h3><code>third-term</code></h3>
|
||||
<pre><code>[third-term x x x [popop] dipd] inscribe
|
||||
</code></pre>
|
||||
<p><code>python
|
||||
define('PE2.2 == x x x [popop] dipd')</code></p>
|
||||
<p><code>python
|
||||
J('[1 0 fib] 10 [PE2.2] times')</code></p>
|
||||
<pre><code>2 8 34 144 610 2584 10946 46368 196418 832040 [1346269 832040 fib]
|
||||
<p>So:</p>
|
||||
<pre><code>joy? [1 0 fib-gen]
|
||||
[1 0 fib-gen]
|
||||
|
||||
joy? third-term
|
||||
2 [3 2 fib-gen]
|
||||
|
||||
joy? third-term
|
||||
2 8 [13 8 fib-gen]
|
||||
|
||||
joy? third-term
|
||||
2 8 34 [55 34 fib-gen]
|
||||
|
||||
joy? third-term
|
||||
2 8 34 144 [233 144 fib-gen]
|
||||
</code></pre>
|
||||
<p>Replace <code>x</code> with our new driver function <code>PE2.2</code> and start our <code>fib</code> generator at <code>1 0</code>.</p>
|
||||
<p><code>python
|
||||
J('0 [1 0 fib] PE2.2 [pop >4M] [popop] [[PE2.1] dip PE2.2] primrec')</code></p>
|
||||
<pre><code>4613732
|
||||
<p>So now we need a sum:</p>
|
||||
<pre><code>joy? 0
|
||||
0
|
||||
</code></pre>
|
||||
<h2>How to compile these?</h2>
|
||||
<p>You would probably start with a special version of <code>G</code>, and perhaps modifications to the default <code>x</code>?</p>
|
||||
<h2>An Interesting Variation</h2>
|
||||
<p><code>python
|
||||
define('codireco == cons dip rest cons')</code></p>
|
||||
<p><code>python
|
||||
V('[0 [dup ++] codireco] x')</code></p>
|
||||
<pre><code> . [0 [dup ++] codireco] x
|
||||
[0 [dup ++] codireco] . x
|
||||
[0 [dup ++] codireco] . 0 [dup ++] codireco
|
||||
[0 [dup ++] codireco] 0 . [dup ++] codireco
|
||||
[0 [dup ++] codireco] 0 [dup ++] . codireco
|
||||
[0 [dup ++] codireco] 0 [dup ++] . cons dip rest cons
|
||||
[0 [dup ++] codireco] [0 dup ++] . dip rest cons
|
||||
. 0 dup ++ [0 [dup ++] codireco] rest cons
|
||||
0 . dup ++ [0 [dup ++] codireco] rest cons
|
||||
0 0 . ++ [0 [dup ++] codireco] rest cons
|
||||
0 1 . [0 [dup ++] codireco] rest cons
|
||||
0 1 [0 [dup ++] codireco] . rest cons
|
||||
0 1 [[dup ++] codireco] . cons
|
||||
0 [1 [dup ++] codireco] .
|
||||
<p>And our Fibonacci generator:</p>
|
||||
<pre><code>joy? [1 0 fib-gen]
|
||||
0 [1 0 fib-gen]
|
||||
</code></pre>
|
||||
<p><code>python
|
||||
define('G == [codireco] cons cons')</code></p>
|
||||
<p><code>python
|
||||
J('230 [dup ++] G 5 [x] times pop')</code></p>
|
||||
<pre><code>230 231 232 233 234
|
||||
<p>We want to generate the initial term:</p>
|
||||
<pre><code>joy? third-term
|
||||
0 2 [3 2 fib-gen]
|
||||
</code></pre>
|
||||
<p>Now we check if the term is less than four million,
|
||||
if so we add it and recur,
|
||||
otherwise we discard the term and the generator leaving the sum on the stack:</p>
|
||||
<pre><code>joy? [pop >4M] [popop] [[PE2.1] dip third-term] tailrec
|
||||
4613732
|
||||
</code></pre>
|
||||
<h2>Math</h2>
|
||||
<pre><code>a b
|
||||
b a+b
|
||||
a+b a+b+b
|
||||
a+b+b a+a+b+b+b
|
||||
</code></pre>
|
||||
<p>So if (a,b) and a is even then the next even term pair is (a+2b, 2a+3b)</p>
|
||||
<p>Reconsider:</p>
|
||||
<pre><code>[b a F] x
|
||||
[b a F] b a F
|
||||
</code></pre>
|
||||
<p>From here we want to arrive at:</p>
|
||||
<pre><code>(a+2b) [(2a+3b) (a+2b) F]
|
||||
|
||||
b a F
|
||||
b a [F0] [F1] fork
|
||||
|
||||
b a over [+] ii
|
||||
---------------------
|
||||
a+2b
|
||||
</code></pre>
|
||||
<p>And:</p>
|
||||
<pre><code> b a over [dup + +] ii
|
||||
---------------------------
|
||||
2a+3b
|
||||
|
||||
|
||||
[over [dup + +] ii] [over [+] ii] clop
|
||||
roll< rrest [tuck] dip ccons
|
||||
|
||||
|
||||
[b a F] b a F
|
||||
|
||||
[b a F] (2a+3b) (a+2b) roll<
|
||||
(2a+3b) (a+2b) [b a F] rrest
|
||||
(2a+3b) (a+2b) [F] [tuck] dip ccons
|
||||
|
||||
|
||||
joy? [1 0 [over [dup + +] ii] [over [+] ii] clop roll< rrest [tuck] dip ccons]
|
||||
[1 0 [over [dup + +] ii] [over [+] ii] clop roll< rrest [tuck] dip ccons]
|
||||
|
||||
joy? x
|
||||
2 [3 2 [over [dup + +] ii] [over [+] ii] clop roll< rrest [tuck] dip ccons]
|
||||
|
||||
joy? x
|
||||
2 8 [13 8 [over [dup + +] ii] [over [+] ii] clop roll< rrest [tuck] dip ccons]
|
||||
|
||||
joy? x
|
||||
2 8 34 [55 34 [over [dup + +] ii] [over [+] ii] clop roll< rrest [tuck] dip ccons]
|
||||
|
||||
joy? x
|
||||
2 8 34 144 [233 144 [over [dup + +] ii] [over [+] ii] clop roll< rrest [tuck] dip ccons]
|
||||
</code></pre>
|
||||
<p>And so it goes...</p>
|
||||
</body>
|
||||
</html>
|
||||
|
|
|
|||
|
|
@ -93,3 +93,43 @@ them in host language for greater efficiency if you like.)
|
|||
| NOT | `not` | | |
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
## An Interesting Variation
|
||||
|
||||
|
||||
codireco == cons dip rest cons')
|
||||
|
||||
|
||||
[0 [dup ++] codireco] x
|
||||
|
||||
|
||||
. [0 [dup ++] codireco] x
|
||||
[0 [dup ++] codireco] . x
|
||||
[0 [dup ++] codireco] . 0 [dup ++] codireco
|
||||
[0 [dup ++] codireco] 0 . [dup ++] codireco
|
||||
[0 [dup ++] codireco] 0 [dup ++] . codireco
|
||||
[0 [dup ++] codireco] 0 [dup ++] . cons dip rest cons
|
||||
[0 [dup ++] codireco] [0 dup ++] . dip rest cons
|
||||
. 0 dup ++ [0 [dup ++] codireco] rest cons
|
||||
0 . dup ++ [0 [dup ++] codireco] rest cons
|
||||
0 0 . ++ [0 [dup ++] codireco] rest cons
|
||||
0 1 . [0 [dup ++] codireco] rest cons
|
||||
0 1 [0 [dup ++] codireco] . rest cons
|
||||
0 1 [[dup ++] codireco] . cons
|
||||
0 [1 [dup ++] codireco] .
|
||||
|
||||
|
||||
|
||||
```python
|
||||
define('G == [codireco] cons cons')
|
||||
```
|
||||
|
||||
|
||||
```python
|
||||
J('230 [dup ++] G 5 [x] times pop')
|
||||
```
|
||||
|
||||
230 231 232 233 234
|
||||
|
||||
|
|
|
|||
File diff suppressed because it is too large
Load Diff
|
|
@ -294,66 +294,72 @@ Lastly:
|
|||
Putting it all together:
|
||||
|
||||
F == + [popdd over] cons infra uncons
|
||||
fib_gen == [1 1 F]
|
||||
|
||||
Let's call `F` `fib_gen`:
|
||||
### `fib-gen`
|
||||
|
||||
[fib_gen + [popdd over] cons infra uncons] inscribe
|
||||
Let's call `F` `fib-gen`:
|
||||
|
||||
[fib-gen + [popdd over] cons infra uncons] inscribe
|
||||
|
||||
We can just write the initial quote and then "force" it with `x`:
|
||||
|
||||
joy? [1 1 fib_gen] 10 [x] times
|
||||
1 2 3 5 8 13 21 34 55 89 [144 89 fib_gen]
|
||||
joy? [1 1 fib-gen] 10 [x] times
|
||||
1 2 3 5 8 13 21 34 55 89 [144 89 fib-gen]
|
||||
|
||||
It skips the first term (1) but if that bothers you you can just prepend it to the program:
|
||||
|
||||
1 [1 1 fib_gen] 10 [x] times
|
||||
1 [1 1 fib-gen] 10 [x] times
|
||||
|
||||
|
||||
## Project Euler Problem Two
|
||||
|
||||
> By considering the terms in the Fibonacci sequence whose values do not exceed four million, find the sum of the even-valued terms.
|
||||
|
||||
Now that we have a generator for the Fibonacci sequence, we need a function that adds a term in the sequence to a sum if it is even, and `pop`s it otherwise.
|
||||
Now that we have a generator for the Fibonacci sequence, we need a function that adds
|
||||
a term in the sequence to a sum if it is even, and `pop`s it otherwise.
|
||||
|
||||
### `even`
|
||||
|
||||
```python
|
||||
define('PE2.1 == dup 2 % [+] [pop] branch')
|
||||
```
|
||||
[even 2 % bool] inscribe
|
||||
|
||||
### `PE2.1`
|
||||
|
||||
[PE2.1 dup even [+] [pop] branch] inscribe
|
||||
|
||||
And a predicate function that detects when the terms in the series "exceed four million".
|
||||
|
||||
### `>4M`
|
||||
|
||||
```python
|
||||
define('>4M == 4000000 >')
|
||||
```
|
||||
[>4M 4000000 >] inscribe
|
||||
|
||||
Now it's straightforward to define `PE2` as a recursive function that generates terms in the Fibonacci sequence until they exceed four million and sums the even ones.
|
||||
|
||||
|
||||
```python
|
||||
define('PE2 == 0 fib_gen x [pop >4M] [popop] [[PE2.1] dip x] primrec')
|
||||
```
|
||||
|
||||
|
||||
```python
|
||||
J('PE2')
|
||||
```
|
||||
Now it's straightforward to define `PE2` as a recursive function that generates terms
|
||||
in the Fibonacci sequence until they exceed four million and sums the even ones.
|
||||
|
||||
joy? 0 [1 1 fib-gen] x [pop >4M] [popop] [[PE2.1] dip x] tailrec
|
||||
4613732
|
||||
|
||||
### `PE2`
|
||||
|
||||
Here's the collected program definitions:
|
||||
[PE2 0 [1 1 fib-gen] x [pop >4M] [popop] [[PE2.1] dip x] tailrec] inscribe
|
||||
|
||||
fib == + swons [popdd over] infra uncons
|
||||
fib_gen == [1 1 fib]
|
||||
Here's the collected program definitions (with a little editorializing):
|
||||
|
||||
even == dup 2 %
|
||||
>4M == 4000000 >
|
||||
fib-gen + [popdd over] cons infra uncons
|
||||
even 2 % bool
|
||||
>4M 4000000 >
|
||||
PE2.1 dup even [+] [pop] branch
|
||||
PE2.2 [PE2.1] dip x
|
||||
PE2.init 0 [1 1 fib-gen] x
|
||||
PE2.rec [pop >4M] [popop] [PE2.2] tailrec
|
||||
PE2 PE2.init PE2.rec
|
||||
|
||||
PE2.1 == even [+] [pop] branch
|
||||
PE2 == 0 fib_gen x [pop >4M] [popop] [[PE2.1] dip x] primrec
|
||||
|
||||
### Even-valued Fibonacci Terms
|
||||
### Hmm...
|
||||
|
||||
fib-gen + swons [popdd over] infra uncons
|
||||
|
||||
|
||||
## Even-valued Fibonacci Terms
|
||||
|
||||
Using `o` for odd and `e` for even:
|
||||
|
||||
|
|
@ -363,93 +369,116 @@ Using `o` for odd and `e` for even:
|
|||
|
||||
So the Fibonacci sequence considered in terms of just parity would be:
|
||||
|
||||
o o e o o e o o e o o e o o e o o e
|
||||
1 1 2 3 5 8 . . .
|
||||
o o e o o e o o e o o e . . .
|
||||
1 1 2 3 5 8 13 21 34 55 89 144 . . .
|
||||
|
||||
Every third term is even.
|
||||
|
||||
So what if we drive the generator three times and discard the odd terms?
|
||||
We would have to initialize our `fib` generator with 1 0:
|
||||
|
||||
[1 0 fib-gen]
|
||||
|
||||
```python
|
||||
J('[1 0 fib] x x x') # To start the sequence with 1 1 2 3 instead of 1 2 3.
|
||||
```
|
||||
### `third-term`
|
||||
|
||||
1 1 2 [3 2 fib]
|
||||
[third-term x x x [popop] dipd] inscribe
|
||||
|
||||
So:
|
||||
|
||||
Drive the generator three times and `popop` the two odd terms.
|
||||
joy? [1 0 fib-gen]
|
||||
[1 0 fib-gen]
|
||||
|
||||
joy? third-term
|
||||
2 [3 2 fib-gen]
|
||||
|
||||
```python
|
||||
J('[1 0 fib] x x x [popop] dipd')
|
||||
```
|
||||
joy? third-term
|
||||
2 8 [13 8 fib-gen]
|
||||
|
||||
2 [3 2 fib]
|
||||
joy? third-term
|
||||
2 8 34 [55 34 fib-gen]
|
||||
|
||||
joy? third-term
|
||||
2 8 34 144 [233 144 fib-gen]
|
||||
|
||||
So now we need a sum:
|
||||
|
||||
```python
|
||||
define('PE2.2 == x x x [popop] dipd')
|
||||
```
|
||||
joy? 0
|
||||
0
|
||||
|
||||
And our Fibonacci generator:
|
||||
|
||||
```python
|
||||
J('[1 0 fib] 10 [PE2.2] times')
|
||||
```
|
||||
joy? [1 0 fib-gen]
|
||||
0 [1 0 fib-gen]
|
||||
|
||||
2 8 34 144 610 2584 10946 46368 196418 832040 [1346269 832040 fib]
|
||||
We want to generate the initial term:
|
||||
|
||||
joy? third-term
|
||||
0 2 [3 2 fib-gen]
|
||||
|
||||
Replace `x` with our new driver function `PE2.2` and start our `fib` generator at `1 0`.
|
||||
|
||||
|
||||
```python
|
||||
J('0 [1 0 fib] PE2.2 [pop >4M] [popop] [[PE2.1] dip PE2.2] primrec')
|
||||
```
|
||||
Now we check if the term is less than four million,
|
||||
if so we add it and recur,
|
||||
otherwise we discard the term and the generator leaving the sum on the stack:
|
||||
|
||||
joy? [pop >4M] [popop] [[PE2.1] dip third-term] tailrec
|
||||
4613732
|
||||
|
||||
## Math
|
||||
|
||||
## How to compile these?
|
||||
You would probably start with a special version of `G`, and perhaps modifications to the default `x`?
|
||||
a b
|
||||
b a+b
|
||||
a+b a+b+b
|
||||
a+b+b a+a+b+b+b
|
||||
|
||||
## An Interesting Variation
|
||||
So if (a,b) and a is even then the next even term pair is (a+2b, 2a+3b)
|
||||
|
||||
Reconsider:
|
||||
|
||||
[b a F] x
|
||||
[b a F] b a F
|
||||
|
||||
From here we want to arrive at:
|
||||
|
||||
(a+2b) [(2a+3b) (a+2b) F]
|
||||
|
||||
b a F
|
||||
b a [F0] [F1] fork
|
||||
|
||||
b a over [+] ii
|
||||
---------------------
|
||||
a+2b
|
||||
|
||||
And:
|
||||
|
||||
b a over [dup + +] ii
|
||||
---------------------------
|
||||
2a+3b
|
||||
|
||||
|
||||
```python
|
||||
define('codireco == cons dip rest cons')
|
||||
```
|
||||
[over [dup + +] ii] [over [+] ii] clop
|
||||
roll< rrest [tuck] dip ccons
|
||||
|
||||
|
||||
```python
|
||||
V('[0 [dup ++] codireco] x')
|
||||
```
|
||||
[b a F] b a F
|
||||
|
||||
. [0 [dup ++] codireco] x
|
||||
[0 [dup ++] codireco] . x
|
||||
[0 [dup ++] codireco] . 0 [dup ++] codireco
|
||||
[0 [dup ++] codireco] 0 . [dup ++] codireco
|
||||
[0 [dup ++] codireco] 0 [dup ++] . codireco
|
||||
[0 [dup ++] codireco] 0 [dup ++] . cons dip rest cons
|
||||
[0 [dup ++] codireco] [0 dup ++] . dip rest cons
|
||||
. 0 dup ++ [0 [dup ++] codireco] rest cons
|
||||
0 . dup ++ [0 [dup ++] codireco] rest cons
|
||||
0 0 . ++ [0 [dup ++] codireco] rest cons
|
||||
0 1 . [0 [dup ++] codireco] rest cons
|
||||
0 1 [0 [dup ++] codireco] . rest cons
|
||||
0 1 [[dup ++] codireco] . cons
|
||||
0 [1 [dup ++] codireco] .
|
||||
[b a F] (2a+3b) (a+2b) roll<
|
||||
(2a+3b) (a+2b) [b a F] rrest
|
||||
(2a+3b) (a+2b) [F] [tuck] dip ccons
|
||||
|
||||
|
||||
joy? [1 0 [over [dup + +] ii] [over [+] ii] clop roll< rrest [tuck] dip ccons]
|
||||
[1 0 [over [dup + +] ii] [over [+] ii] clop roll< rrest [tuck] dip ccons]
|
||||
|
||||
```python
|
||||
define('G == [codireco] cons cons')
|
||||
```
|
||||
joy? x
|
||||
2 [3 2 [over [dup + +] ii] [over [+] ii] clop roll< rrest [tuck] dip ccons]
|
||||
|
||||
joy? x
|
||||
2 8 [13 8 [over [dup + +] ii] [over [+] ii] clop roll< rrest [tuck] dip ccons]
|
||||
|
||||
```python
|
||||
J('230 [dup ++] G 5 [x] times pop')
|
||||
```
|
||||
joy? x
|
||||
2 8 34 [55 34 [over [dup + +] ii] [over [+] ii] clop roll< rrest [tuck] dip ccons]
|
||||
|
||||
230 231 232 233 234
|
||||
joy? x
|
||||
2 8 34 144 [233 144 [over [dup + +] ii] [over [+] ii] clop roll< rrest [tuck] dip ccons]
|
||||
|
||||
And so it goes...
|
||||
|
||||
|
|
|
|||
Loading…
Reference in New Issue