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Update some of the docs.

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This commit is contained in:
Simon Forman
2020-05-20 19:15:47 -07:00
parent 6a6b63bf62
commit ffabda0407
60 changed files with 5182 additions and 5853 deletions
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docs/3._Developing_a_Program.md
+274 -281
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@@ -13,7 +13,7 @@ Let's create a predicate that returns `True` if a number is a multiple of 3 or 5
```python
define('P == [3 % not] dupdip 5 % not or')
define('P [3 % not] dupdip 5 % not or')
```
@@ -21,19 +21,19 @@ define('P == [3 % not] dupdip 5 % not or')
V('80 P')
```
. 80 P
80 . P
80 . [3 % not] dupdip 5 % not or
80 [3 % not] . dupdip 5 % not or
80 . 3 % not 80 5 % not or
80 3 . % not 80 5 % not or
2 . not 80 5 % not or
False . 80 5 % not or
False 80 . 5 % not or
False 80 5 . % not or
False 0 . not or
False True . or
True .
• 80 P
80 • P
80 • [3 % not] dupdip 5 % not or
80 [3 % not] • dupdip 5 % not or
80 • 3 % not 80 5 % not or
80 3 • % not 80 5 % not or
2 • not 80 5 % not or
False • 80 5 % not or
False 80 • 5 % not or
False 80 5 • % not or
False 0 • not or
False True • or
True •
Given the predicate function `P` a suitable program is:
@@ -86,7 +86,7 @@ counter to the running sum. This function will do that:
```python
define('PE1.1 == + [+] dupdip')
define('PE1.1 + [+] dupdip')
```
@@ -94,16 +94,16 @@ define('PE1.1 == + [+] dupdip')
V('0 0 3 PE1.1')
```
. 0 0 3 PE1.1
0 . 0 3 PE1.1
0 0 . 3 PE1.1
0 0 3 . PE1.1
0 0 3 . + [+] dupdip
0 3 . [+] dupdip
0 3 [+] . dupdip
0 3 . + 3
3 . 3
3 3 .
• 0 0 3 PE1.1
0 • 0 3 PE1.1
0 0 • 3 PE1.1
0 0 3 • PE1.1
0 0 3 • + [+] dupdip
0 3 • [+] dupdip
0 3 [+] • dupdip
0 3 • + 3
3 • 3
3 3 •
@@ -111,79 +111,79 @@ V('0 0 3 PE1.1')
V('0 0 [3 2 1 3 1 2 3] [PE1.1] step')
```
. 0 0 [3 2 1 3 1 2 3] [PE1.1] step
0 . 0 [3 2 1 3 1 2 3] [PE1.1] step
0 0 . [3 2 1 3 1 2 3] [PE1.1] step
0 0 [3 2 1 3 1 2 3] . [PE1.1] step
0 0 [3 2 1 3 1 2 3] [PE1.1] . step
0 0 3 [PE1.1] . i [2 1 3 1 2 3] [PE1.1] step
0 0 3 . PE1.1 [2 1 3 1 2 3] [PE1.1] step
0 0 3 . + [+] dupdip [2 1 3 1 2 3] [PE1.1] step
0 3 . [+] dupdip [2 1 3 1 2 3] [PE1.1] step
0 3 [+] . dupdip [2 1 3 1 2 3] [PE1.1] step
0 3 . + 3 [2 1 3 1 2 3] [PE1.1] step
3 . 3 [2 1 3 1 2 3] [PE1.1] step
3 3 . [2 1 3 1 2 3] [PE1.1] step
3 3 [2 1 3 1 2 3] . [PE1.1] step
3 3 [2 1 3 1 2 3] [PE1.1] . step
3 3 2 [PE1.1] . i [1 3 1 2 3] [PE1.1] step
3 3 2 . PE1.1 [1 3 1 2 3] [PE1.1] step
3 3 2 . + [+] dupdip [1 3 1 2 3] [PE1.1] step
3 5 . [+] dupdip [1 3 1 2 3] [PE1.1] step
3 5 [+] . dupdip [1 3 1 2 3] [PE1.1] step
3 5 . + 5 [1 3 1 2 3] [PE1.1] step
8 . 5 [1 3 1 2 3] [PE1.1] step
8 5 . [1 3 1 2 3] [PE1.1] step
8 5 [1 3 1 2 3] . [PE1.1] step
8 5 [1 3 1 2 3] [PE1.1] . step
8 5 1 [PE1.1] . i [3 1 2 3] [PE1.1] step
8 5 1 . PE1.1 [3 1 2 3] [PE1.1] step
8 5 1 . + [+] dupdip [3 1 2 3] [PE1.1] step
8 6 . [+] dupdip [3 1 2 3] [PE1.1] step
8 6 [+] . dupdip [3 1 2 3] [PE1.1] step
8 6 . + 6 [3 1 2 3] [PE1.1] step
14 . 6 [3 1 2 3] [PE1.1] step
14 6 . [3 1 2 3] [PE1.1] step
14 6 [3 1 2 3] . [PE1.1] step
14 6 [3 1 2 3] [PE1.1] . step
14 6 3 [PE1.1] . i [1 2 3] [PE1.1] step
14 6 3 . PE1.1 [1 2 3] [PE1.1] step
14 6 3 . + [+] dupdip [1 2 3] [PE1.1] step
14 9 . [+] dupdip [1 2 3] [PE1.1] step
14 9 [+] . dupdip [1 2 3] [PE1.1] step
14 9 . + 9 [1 2 3] [PE1.1] step
23 . 9 [1 2 3] [PE1.1] step
23 9 . [1 2 3] [PE1.1] step
23 9 [1 2 3] . [PE1.1] step
23 9 [1 2 3] [PE1.1] . step
23 9 1 [PE1.1] . i [2 3] [PE1.1] step
23 9 1 . PE1.1 [2 3] [PE1.1] step
23 9 1 . + [+] dupdip [2 3] [PE1.1] step
23 10 . [+] dupdip [2 3] [PE1.1] step
23 10 [+] . dupdip [2 3] [PE1.1] step
23 10 . + 10 [2 3] [PE1.1] step
33 . 10 [2 3] [PE1.1] step
33 10 . [2 3] [PE1.1] step
33 10 [2 3] . [PE1.1] step
33 10 [2 3] [PE1.1] . step
33 10 2 [PE1.1] . i [3] [PE1.1] step
33 10 2 . PE1.1 [3] [PE1.1] step
33 10 2 . + [+] dupdip [3] [PE1.1] step
33 12 . [+] dupdip [3] [PE1.1] step
33 12 [+] . dupdip [3] [PE1.1] step
33 12 . + 12 [3] [PE1.1] step
45 . 12 [3] [PE1.1] step
45 12 . [3] [PE1.1] step
45 12 [3] . [PE1.1] step
45 12 [3] [PE1.1] . step
45 12 3 [PE1.1] . i
45 12 3 . PE1.1
45 12 3 . + [+] dupdip
45 15 . [+] dupdip
45 15 [+] . dupdip
45 15 . + 15
60 . 15
60 15 .
• 0 0 [3 2 1 3 1 2 3] [PE1.1] step
0 • 0 [3 2 1 3 1 2 3] [PE1.1] step
0 0 • [3 2 1 3 1 2 3] [PE1.1] step
0 0 [3 2 1 3 1 2 3] • [PE1.1] step
0 0 [3 2 1 3 1 2 3] [PE1.1] • step
0 0 3 [PE1.1] • i [2 1 3 1 2 3] [PE1.1] step
0 0 3 • PE1.1 [2 1 3 1 2 3] [PE1.1] step
0 0 3 • + [+] dupdip [2 1 3 1 2 3] [PE1.1] step
0 3 • [+] dupdip [2 1 3 1 2 3] [PE1.1] step
0 3 [+] • dupdip [2 1 3 1 2 3] [PE1.1] step
0 3 • + 3 [2 1 3 1 2 3] [PE1.1] step
3 • 3 [2 1 3 1 2 3] [PE1.1] step
3 3 • [2 1 3 1 2 3] [PE1.1] step
3 3 [2 1 3 1 2 3] • [PE1.1] step
3 3 [2 1 3 1 2 3] [PE1.1] • step
3 3 2 [PE1.1] • i [1 3 1 2 3] [PE1.1] step
3 3 2 • PE1.1 [1 3 1 2 3] [PE1.1] step
3 3 2 • + [+] dupdip [1 3 1 2 3] [PE1.1] step
3 5 • [+] dupdip [1 3 1 2 3] [PE1.1] step
3 5 [+] • dupdip [1 3 1 2 3] [PE1.1] step
3 5 • + 5 [1 3 1 2 3] [PE1.1] step
8 • 5 [1 3 1 2 3] [PE1.1] step
8 5 • [1 3 1 2 3] [PE1.1] step
8 5 [1 3 1 2 3] • [PE1.1] step
8 5 [1 3 1 2 3] [PE1.1] • step
8 5 1 [PE1.1] • i [3 1 2 3] [PE1.1] step
8 5 1 • PE1.1 [3 1 2 3] [PE1.1] step
8 5 1 • + [+] dupdip [3 1 2 3] [PE1.1] step
8 6 • [+] dupdip [3 1 2 3] [PE1.1] step
8 6 [+] • dupdip [3 1 2 3] [PE1.1] step
8 6 • + 6 [3 1 2 3] [PE1.1] step
14 • 6 [3 1 2 3] [PE1.1] step
14 6 • [3 1 2 3] [PE1.1] step
14 6 [3 1 2 3] • [PE1.1] step
14 6 [3 1 2 3] [PE1.1] • step
14 6 3 [PE1.1] • i [1 2 3] [PE1.1] step
14 6 3 • PE1.1 [1 2 3] [PE1.1] step
14 6 3 • + [+] dupdip [1 2 3] [PE1.1] step
14 9 • [+] dupdip [1 2 3] [PE1.1] step
14 9 [+] • dupdip [1 2 3] [PE1.1] step
14 9 • + 9 [1 2 3] [PE1.1] step
23 • 9 [1 2 3] [PE1.1] step
23 9 • [1 2 3] [PE1.1] step
23 9 [1 2 3] • [PE1.1] step
23 9 [1 2 3] [PE1.1] • step
23 9 1 [PE1.1] • i [2 3] [PE1.1] step
23 9 1 • PE1.1 [2 3] [PE1.1] step
23 9 1 • + [+] dupdip [2 3] [PE1.1] step
23 10 • [+] dupdip [2 3] [PE1.1] step
23 10 [+] • dupdip [2 3] [PE1.1] step
23 10 • + 10 [2 3] [PE1.1] step
33 • 10 [2 3] [PE1.1] step
33 10 • [2 3] [PE1.1] step
33 10 [2 3] • [PE1.1] step
33 10 [2 3] [PE1.1] • step
33 10 2 [PE1.1] • i [3] [PE1.1] step
33 10 2 • PE1.1 [3] [PE1.1] step
33 10 2 • + [+] dupdip [3] [PE1.1] step
33 12 • [+] dupdip [3] [PE1.1] step
33 12 [+] • dupdip [3] [PE1.1] step
33 12 • + 12 [3] [PE1.1] step
45 • 12 [3] [PE1.1] step
45 12 • [3] [PE1.1] step
45 12 [3] • [PE1.1] step
45 12 [3] [PE1.1] • step
45 12 3 [PE1.1] • i
45 12 3 • PE1.1
45 12 3 • + [+] dupdip
45 15 • [+] dupdip
45 15 [+] • dupdip
45 15 • + 15
60 • 15
60 15 •
So one `step` through all seven terms brings the counter to 15 and the total to 60.
@@ -196,7 +196,7 @@ So one `step` through all seven terms brings the counter to 15 and the total to
66
66.66666666666667
@@ -242,7 +242,7 @@ That means we want to run the full list of numbers sixty-six times to get to 990
```python
define('PE1 == 0 0 66 [[3 2 1 3 1 2 3] [PE1.1] step] times [3 2 1 3] [PE1.1] step pop')
define('PE1 0 0 66 [[3 2 1 3 1 2 3] [PE1.1] step] times [3 2 1 3] [PE1.1] step pop')
```
@@ -278,7 +278,7 @@ integer terms from the list.
```python
define('PE1.2 == [3 & PE1.1] dupdip 2 >>')
define('PE1.2 [3 & PE1.1] dupdip 2 >>')
```
@@ -286,24 +286,24 @@ define('PE1.2 == [3 & PE1.1] dupdip 2 >>')
V('0 0 14811 PE1.2')
```
. 0 0 14811 PE1.2
0 . 0 14811 PE1.2
0 0 . 14811 PE1.2
0 0 14811 . PE1.2
0 0 14811 . [3 & PE1.1] dupdip 2 >>
0 0 14811 [3 & PE1.1] . dupdip 2 >>
0 0 14811 . 3 & PE1.1 14811 2 >>
0 0 14811 3 . & PE1.1 14811 2 >>
0 0 3 . PE1.1 14811 2 >>
0 0 3 . + [+] dupdip 14811 2 >>
0 3 . [+] dupdip 14811 2 >>
0 3 [+] . dupdip 14811 2 >>
0 3 . + 3 14811 2 >>
3 . 3 14811 2 >>
3 3 . 14811 2 >>
3 3 14811 . 2 >>
3 3 14811 2 . >>
3 3 3702 .
• 0 0 14811 PE1.2
0 • 0 14811 PE1.2
0 0 • 14811 PE1.2
0 0 14811 • PE1.2
0 0 14811 • [3 & PE1.1] dupdip 2 >>
0 0 14811 [3 & PE1.1] • dupdip 2 >>
0 0 14811 • 3 & PE1.1 14811 2 >>
0 0 14811 3 • & PE1.1 14811 2 >>
0 0 3 • PE1.1 14811 2 >>
0 0 3 • + [+] dupdip 14811 2 >>
0 3 • [+] dupdip 14811 2 >>
0 3 [+] • dupdip 14811 2 >>
0 3 • + 3 14811 2 >>
3 • 3 14811 2 >>
3 3 • 14811 2 >>
3 3 14811 • 2 >>
3 3 14811 2 • >>
3 3 3702 •
@@ -311,24 +311,24 @@ V('0 0 14811 PE1.2')
V('3 3 3702 PE1.2')
```
. 3 3 3702 PE1.2
3 . 3 3702 PE1.2
3 3 . 3702 PE1.2
3 3 3702 . PE1.2
3 3 3702 . [3 & PE1.1] dupdip 2 >>
3 3 3702 [3 & PE1.1] . dupdip 2 >>
3 3 3702 . 3 & PE1.1 3702 2 >>
3 3 3702 3 . & PE1.1 3702 2 >>
3 3 2 . PE1.1 3702 2 >>
3 3 2 . + [+] dupdip 3702 2 >>
3 5 . [+] dupdip 3702 2 >>
3 5 [+] . dupdip 3702 2 >>
3 5 . + 5 3702 2 >>
8 . 5 3702 2 >>
8 5 . 3702 2 >>
8 5 3702 . 2 >>
8 5 3702 2 . >>
8 5 925 .
• 3 3 3702 PE1.2
3 • 3 3702 PE1.2
3 3 • 3702 PE1.2
3 3 3702 • PE1.2
3 3 3702 • [3 & PE1.1] dupdip 2 >>
3 3 3702 [3 & PE1.1] • dupdip 2 >>
3 3 3702 • 3 & PE1.1 3702 2 >>
3 3 3702 3 • & PE1.1 3702 2 >>
3 3 2 • PE1.1 3702 2 >>
3 3 2 • + [+] dupdip 3702 2 >>
3 5 • [+] dupdip 3702 2 >>
3 5 [+] • dupdip 3702 2 >>
3 5 • + 5 3702 2 >>
8 • 5 3702 2 >>
8 5 • 3702 2 >>
8 5 3702 • 2 >>
8 5 3702 2 • >>
8 5 925 •
@@ -336,144 +336,137 @@ V('3 3 3702 PE1.2')
V('0 0 14811 7 [PE1.2] times pop')
```
. 0 0 14811 7 [PE1.2] times pop
0 . 0 14811 7 [PE1.2] times pop
0 0 . 14811 7 [PE1.2] times pop
0 0 14811 . 7 [PE1.2] times pop
0 0 14811 7 . [PE1.2] times pop
0 0 14811 7 [PE1.2] . times pop
0 0 14811 [PE1.2] . i 6 [PE1.2] times pop
0 0 14811 . PE1.2 6 [PE1.2] times pop
0 0 14811 . [3 & PE1.1] dupdip 2 >> 6 [PE1.2] times pop
0 0 14811 [3 & PE1.1] . dupdip 2 >> 6 [PE1.2] times pop
0 0 14811 . 3 & PE1.1 14811 2 >> 6 [PE1.2] times pop
0 0 14811 3 . & PE1.1 14811 2 >> 6 [PE1.2] times pop
0 0 3 . PE1.1 14811 2 >> 6 [PE1.2] times pop
0 0 3 . + [+] dupdip 14811 2 >> 6 [PE1.2] times pop
0 3 . [+] dupdip 14811 2 >> 6 [PE1.2] times pop
0 3 [+] . dupdip 14811 2 >> 6 [PE1.2] times pop
0 3 . + 3 14811 2 >> 6 [PE1.2] times pop
3 . 3 14811 2 >> 6 [PE1.2] times pop
3 3 . 14811 2 >> 6 [PE1.2] times pop
3 3 14811 . 2 >> 6 [PE1.2] times pop
3 3 14811 2 . >> 6 [PE1.2] times pop
3 3 3702 . 6 [PE1.2] times pop
3 3 3702 6 . [PE1.2] times pop
3 3 3702 6 [PE1.2] . times pop
3 3 3702 [PE1.2] . i 5 [PE1.2] times pop
3 3 3702 . PE1.2 5 [PE1.2] times pop
3 3 3702 . [3 & PE1.1] dupdip 2 >> 5 [PE1.2] times pop
3 3 3702 [3 & PE1.1] . dupdip 2 >> 5 [PE1.2] times pop
3 3 3702 . 3 & PE1.1 3702 2 >> 5 [PE1.2] times pop
3 3 3702 3 . & PE1.1 3702 2 >> 5 [PE1.2] times pop
3 3 2 . PE1.1 3702 2 >> 5 [PE1.2] times pop
3 3 2 . + [+] dupdip 3702 2 >> 5 [PE1.2] times pop
3 5 . [+] dupdip 3702 2 >> 5 [PE1.2] times pop
3 5 [+] . dupdip 3702 2 >> 5 [PE1.2] times pop
3 5 . + 5 3702 2 >> 5 [PE1.2] times pop
8 . 5 3702 2 >> 5 [PE1.2] times pop
8 5 . 3702 2 >> 5 [PE1.2] times pop
8 5 3702 . 2 >> 5 [PE1.2] times pop
8 5 3702 2 . >> 5 [PE1.2] times pop
8 5 925 . 5 [PE1.2] times pop
8 5 925 5 . [PE1.2] times pop
8 5 925 5 [PE1.2] . times pop
8 5 925 [PE1.2] . i 4 [PE1.2] times pop
8 5 925 . PE1.2 4 [PE1.2] times pop
8 5 925 . [3 & PE1.1] dupdip 2 >> 4 [PE1.2] times pop
8 5 925 [3 & PE1.1] . dupdip 2 >> 4 [PE1.2] times pop
8 5 925 . 3 & PE1.1 925 2 >> 4 [PE1.2] times pop
8 5 925 3 . & PE1.1 925 2 >> 4 [PE1.2] times pop
8 5 1 . PE1.1 925 2 >> 4 [PE1.2] times pop
8 5 1 . + [+] dupdip 925 2 >> 4 [PE1.2] times pop
8 6 . [+] dupdip 925 2 >> 4 [PE1.2] times pop
8 6 [+] . dupdip 925 2 >> 4 [PE1.2] times pop
8 6 . + 6 925 2 >> 4 [PE1.2] times pop
14 . 6 925 2 >> 4 [PE1.2] times pop
14 6 . 925 2 >> 4 [PE1.2] times pop
14 6 925 . 2 >> 4 [PE1.2] times pop
14 6 925 2 . >> 4 [PE1.2] times pop
14 6 231 . 4 [PE1.2] times pop
14 6 231 4 . [PE1.2] times pop
14 6 231 4 [PE1.2] . times pop
14 6 231 [PE1.2] . i 3 [PE1.2] times pop
14 6 231 . PE1.2 3 [PE1.2] times pop
14 6 231 . [3 & PE1.1] dupdip 2 >> 3 [PE1.2] times pop
14 6 231 [3 & PE1.1] . dupdip 2 >> 3 [PE1.2] times pop
14 6 231 . 3 & PE1.1 231 2 >> 3 [PE1.2] times pop
14 6 231 3 . & PE1.1 231 2 >> 3 [PE1.2] times pop
14 6 3 . PE1.1 231 2 >> 3 [PE1.2] times pop
14 6 3 . + [+] dupdip 231 2 >> 3 [PE1.2] times pop
14 9 . [+] dupdip 231 2 >> 3 [PE1.2] times pop
14 9 [+] . dupdip 231 2 >> 3 [PE1.2] times pop
14 9 . + 9 231 2 >> 3 [PE1.2] times pop
23 . 9 231 2 >> 3 [PE1.2] times pop
23 9 . 231 2 >> 3 [PE1.2] times pop
23 9 231 . 2 >> 3 [PE1.2] times pop
23 9 231 2 . >> 3 [PE1.2] times pop
23 9 57 . 3 [PE1.2] times pop
23 9 57 3 . [PE1.2] times pop
23 9 57 3 [PE1.2] . times pop
23 9 57 [PE1.2] . i 2 [PE1.2] times pop
23 9 57 . PE1.2 2 [PE1.2] times pop
23 9 57 . [3 & PE1.1] dupdip 2 >> 2 [PE1.2] times pop
23 9 57 [3 & PE1.1] . dupdip 2 >> 2 [PE1.2] times pop
23 9 57 . 3 & PE1.1 57 2 >> 2 [PE1.2] times pop
23 9 57 3 . & PE1.1 57 2 >> 2 [PE1.2] times pop
23 9 1 . PE1.1 57 2 >> 2 [PE1.2] times pop
23 9 1 . + [+] dupdip 57 2 >> 2 [PE1.2] times pop
23 10 . [+] dupdip 57 2 >> 2 [PE1.2] times pop
23 10 [+] . dupdip 57 2 >> 2 [PE1.2] times pop
23 10 . + 10 57 2 >> 2 [PE1.2] times pop
33 . 10 57 2 >> 2 [PE1.2] times pop
33 10 . 57 2 >> 2 [PE1.2] times pop
33 10 57 . 2 >> 2 [PE1.2] times pop
33 10 57 2 . >> 2 [PE1.2] times pop
33 10 14 . 2 [PE1.2] times pop
33 10 14 2 . [PE1.2] times pop
33 10 14 2 [PE1.2] . times pop
33 10 14 [PE1.2] . i 1 [PE1.2] times pop
33 10 14 . PE1.2 1 [PE1.2] times pop
33 10 14 . [3 & PE1.1] dupdip 2 >> 1 [PE1.2] times pop
33 10 14 [3 & PE1.1] . dupdip 2 >> 1 [PE1.2] times pop
33 10 14 . 3 & PE1.1 14 2 >> 1 [PE1.2] times pop
33 10 14 3 . & PE1.1 14 2 >> 1 [PE1.2] times pop
33 10 2 . PE1.1 14 2 >> 1 [PE1.2] times pop
33 10 2 . + [+] dupdip 14 2 >> 1 [PE1.2] times pop
33 12 . [+] dupdip 14 2 >> 1 [PE1.2] times pop
33 12 [+] . dupdip 14 2 >> 1 [PE1.2] times pop
33 12 . + 12 14 2 >> 1 [PE1.2] times pop
45 . 12 14 2 >> 1 [PE1.2] times pop
45 12 . 14 2 >> 1 [PE1.2] times pop
45 12 14 . 2 >> 1 [PE1.2] times pop
45 12 14 2 . >> 1 [PE1.2] times pop
45 12 3 . 1 [PE1.2] times pop
45 12 3 1 . [PE1.2] times pop
45 12 3 1 [PE1.2] . times pop
45 12 3 [PE1.2] . i pop
45 12 3 . PE1.2 pop
45 12 3 . [3 & PE1.1] dupdip 2 >> pop
45 12 3 [3 & PE1.1] . dupdip 2 >> pop
45 12 3 . 3 & PE1.1 3 2 >> pop
45 12 3 3 . & PE1.1 3 2 >> pop
45 12 3 . PE1.1 3 2 >> pop
45 12 3 . + [+] dupdip 3 2 >> pop
45 15 . [+] dupdip 3 2 >> pop
45 15 [+] . dupdip 3 2 >> pop
45 15 . + 15 3 2 >> pop
60 . 15 3 2 >> pop
60 15 . 3 2 >> pop
60 15 3 . 2 >> pop
60 15 3 2 . >> pop
60 15 0 . pop
60 15 .
• 0 0 14811 7 [PE1.2] times pop
0 • 0 14811 7 [PE1.2] times pop
0 0 • 14811 7 [PE1.2] times pop
0 0 14811 • 7 [PE1.2] times pop
0 0 14811 7 • [PE1.2] times pop
0 0 14811 7 [PE1.2] • times pop
0 0 14811 • PE1.2 6 [PE1.2] times pop
0 0 14811 • [3 & PE1.1] dupdip 2 >> 6 [PE1.2] times pop
0 0 14811 [3 & PE1.1] • dupdip 2 >> 6 [PE1.2] times pop
0 0 14811 • 3 & PE1.1 14811 2 >> 6 [PE1.2] times pop
0 0 14811 3 • & PE1.1 14811 2 >> 6 [PE1.2] times pop
0 0 3 • PE1.1 14811 2 >> 6 [PE1.2] times pop
0 0 3 • + [+] dupdip 14811 2 >> 6 [PE1.2] times pop
0 3 • [+] dupdip 14811 2 >> 6 [PE1.2] times pop
0 3 [+] • dupdip 14811 2 >> 6 [PE1.2] times pop
0 3 • + 3 14811 2 >> 6 [PE1.2] times pop
3 • 3 14811 2 >> 6 [PE1.2] times pop
3 3 • 14811 2 >> 6 [PE1.2] times pop
3 3 14811 • 2 >> 6 [PE1.2] times pop
3 3 14811 2 • >> 6 [PE1.2] times pop
3 3 3702 • 6 [PE1.2] times pop
3 3 3702 6 • [PE1.2] times pop
3 3 3702 6 [PE1.2] • times pop
3 3 3702 • PE1.2 5 [PE1.2] times pop
3 3 3702 • [3 & PE1.1] dupdip 2 >> 5 [PE1.2] times pop
3 3 3702 [3 & PE1.1] • dupdip 2 >> 5 [PE1.2] times pop
3 3 3702 • 3 & PE1.1 3702 2 >> 5 [PE1.2] times pop
3 3 3702 3 • & PE1.1 3702 2 >> 5 [PE1.2] times pop
3 3 2 • PE1.1 3702 2 >> 5 [PE1.2] times pop
3 3 2 • + [+] dupdip 3702 2 >> 5 [PE1.2] times pop
3 5 • [+] dupdip 3702 2 >> 5 [PE1.2] times pop
3 5 [+] • dupdip 3702 2 >> 5 [PE1.2] times pop
3 5 • + 5 3702 2 >> 5 [PE1.2] times pop
8 • 5 3702 2 >> 5 [PE1.2] times pop
8 5 • 3702 2 >> 5 [PE1.2] times pop
8 5 3702 • 2 >> 5 [PE1.2] times pop
8 5 3702 2 • >> 5 [PE1.2] times pop
8 5 925 • 5 [PE1.2] times pop
8 5 925 5 • [PE1.2] times pop
8 5 925 5 [PE1.2] • times pop
8 5 925 • PE1.2 4 [PE1.2] times pop
8 5 925 • [3 & PE1.1] dupdip 2 >> 4 [PE1.2] times pop
8 5 925 [3 & PE1.1] • dupdip 2 >> 4 [PE1.2] times pop
8 5 925 • 3 & PE1.1 925 2 >> 4 [PE1.2] times pop
8 5 925 3 • & PE1.1 925 2 >> 4 [PE1.2] times pop
8 5 1 • PE1.1 925 2 >> 4 [PE1.2] times pop
8 5 1 • + [+] dupdip 925 2 >> 4 [PE1.2] times pop
8 6 • [+] dupdip 925 2 >> 4 [PE1.2] times pop
8 6 [+] • dupdip 925 2 >> 4 [PE1.2] times pop
8 6 • + 6 925 2 >> 4 [PE1.2] times pop
14 • 6 925 2 >> 4 [PE1.2] times pop
14 6 • 925 2 >> 4 [PE1.2] times pop
14 6 925 • 2 >> 4 [PE1.2] times pop
14 6 925 2 • >> 4 [PE1.2] times pop
14 6 231 • 4 [PE1.2] times pop
14 6 231 4 • [PE1.2] times pop
14 6 231 4 [PE1.2] • times pop
14 6 231 • PE1.2 3 [PE1.2] times pop
14 6 231 • [3 & PE1.1] dupdip 2 >> 3 [PE1.2] times pop
14 6 231 [3 & PE1.1] • dupdip 2 >> 3 [PE1.2] times pop
14 6 231 • 3 & PE1.1 231 2 >> 3 [PE1.2] times pop
14 6 231 3 • & PE1.1 231 2 >> 3 [PE1.2] times pop
14 6 3 • PE1.1 231 2 >> 3 [PE1.2] times pop
14 6 3 • + [+] dupdip 231 2 >> 3 [PE1.2] times pop
14 9 • [+] dupdip 231 2 >> 3 [PE1.2] times pop
14 9 [+] • dupdip 231 2 >> 3 [PE1.2] times pop
14 9 • + 9 231 2 >> 3 [PE1.2] times pop
23 • 9 231 2 >> 3 [PE1.2] times pop
23 9 • 231 2 >> 3 [PE1.2] times pop
23 9 231 • 2 >> 3 [PE1.2] times pop
23 9 231 2 • >> 3 [PE1.2] times pop
23 9 57 • 3 [PE1.2] times pop
23 9 57 3 • [PE1.2] times pop
23 9 57 3 [PE1.2] • times pop
23 9 57 • PE1.2 2 [PE1.2] times pop
23 9 57 • [3 & PE1.1] dupdip 2 >> 2 [PE1.2] times pop
23 9 57 [3 & PE1.1] • dupdip 2 >> 2 [PE1.2] times pop
23 9 57 • 3 & PE1.1 57 2 >> 2 [PE1.2] times pop
23 9 57 3 • & PE1.1 57 2 >> 2 [PE1.2] times pop
23 9 1 • PE1.1 57 2 >> 2 [PE1.2] times pop
23 9 1 • + [+] dupdip 57 2 >> 2 [PE1.2] times pop
23 10 • [+] dupdip 57 2 >> 2 [PE1.2] times pop
23 10 [+] • dupdip 57 2 >> 2 [PE1.2] times pop
23 10 • + 10 57 2 >> 2 [PE1.2] times pop
33 • 10 57 2 >> 2 [PE1.2] times pop
33 10 • 57 2 >> 2 [PE1.2] times pop
33 10 57 • 2 >> 2 [PE1.2] times pop
33 10 57 2 • >> 2 [PE1.2] times pop
33 10 14 • 2 [PE1.2] times pop
33 10 14 2 • [PE1.2] times pop
33 10 14 2 [PE1.2] • times pop
33 10 14 • PE1.2 1 [PE1.2] times pop
33 10 14 • [3 & PE1.1] dupdip 2 >> 1 [PE1.2] times pop
33 10 14 [3 & PE1.1] • dupdip 2 >> 1 [PE1.2] times pop
33 10 14 • 3 & PE1.1 14 2 >> 1 [PE1.2] times pop
33 10 14 3 • & PE1.1 14 2 >> 1 [PE1.2] times pop
33 10 2 • PE1.1 14 2 >> 1 [PE1.2] times pop
33 10 2 • + [+] dupdip 14 2 >> 1 [PE1.2] times pop
33 12 • [+] dupdip 14 2 >> 1 [PE1.2] times pop
33 12 [+] • dupdip 14 2 >> 1 [PE1.2] times pop
33 12 • + 12 14 2 >> 1 [PE1.2] times pop
45 • 12 14 2 >> 1 [PE1.2] times pop
45 12 • 14 2 >> 1 [PE1.2] times pop
45 12 14 • 2 >> 1 [PE1.2] times pop
45 12 14 2 • >> 1 [PE1.2] times pop
45 12 3 • 1 [PE1.2] times pop
45 12 3 1 • [PE1.2] times pop
45 12 3 1 [PE1.2] • times pop
45 12 3 • PE1.2 pop
45 12 3 • [3 & PE1.1] dupdip 2 >> pop
45 12 3 [3 & PE1.1] • dupdip 2 >> pop
45 12 3 • 3 & PE1.1 3 2 >> pop
45 12 3 3 • & PE1.1 3 2 >> pop
45 12 3 • PE1.1 3 2 >> pop
45 12 3 • + [+] dupdip 3 2 >> pop
45 15 • [+] dupdip 3 2 >> pop
45 15 [+] • dupdip 3 2 >> pop
45 15 • + 15 3 2 >> pop
60 • 15 3 2 >> pop
60 15 • 3 2 >> pop
60 15 3 • 2 >> pop
60 15 3 2 • >> pop
60 15 0 • pop
60 15 •
And so we have at last:
```python
define('PE1 == 0 0 66 [14811 7 [PE1.2] times pop] times 14811 4 [PE1.2] times popop')
define('PE1 0 0 66 [14811 7 [PE1.2] times pop] times 14811 4 [PE1.2] times popop')
```
@@ -493,14 +486,14 @@ Let's refactor.
```python
define('PE1.3 == 14811 swap [PE1.2] times pop')
define('PE1.3 14811 swap [PE1.2] times pop')
```
Now we can simplify the definition above:
```python
define('PE1 == 0 0 66 [7 PE1.3] times 4 PE1.3 pop')
define('PE1 0 0 66 [7 PE1.3] times 4 PE1.3 pop')
```
@@ -523,7 +516,7 @@ It's a little clunky iterating sixty-six times though the seven numbers then fou
```python
define('PE1.terms == [0 swap [dup [pop 14811] [] branch [3 &] dupdip 2 >>] dip rest cons]')
define('PE1.terms [0 swap [dup [pop 14811] [] branch [3 &] dupdip 2 >>] dip rest cons]')
```
@@ -602,7 +595,7 @@ From the above example we can deduce that the sum of the first N positive intege
```python
define('F == dup ++ * 2 floordiv')
define('F dup ++ * 2 floordiv')
```
@@ -610,14 +603,14 @@ define('F == dup ++ * 2 floordiv')
V('10 F')
```
. 10 F
10 . F
10 . dup ++ * 2 floordiv
10 10 . ++ * 2 floordiv
10 11 . * 2 floordiv
110 . 2 floordiv
110 2 . floordiv
55 .
• 10 F
10 • F
10 • dup ++ * 2 floordiv
10 10 • ++ * 2 floordiv
10 11 • * 2 floordiv
110 • 2 floordiv
110 2 • floordiv
55 •
## Generalizing to Blocks of Terms