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https://github.com/abrudz/stencil

Thin cover for Dyalog APL's ⌺
https://github.com/abrudz/stencil

apl cellular-automata cellular-automaton code-golf codegolf dyalog-apl dyalog-library dyalogapl game-of-life gameoflife moore-neighborhoods neighbourhood stencil tio

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Thin cover for Dyalog APL's ⌺

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README 

        
# Stencil



## Introduction

Stencil is a thin cover for [Dyalog APL](https://www.dyalog.com/)'s ⌺ [Stencil operator](http://help.dyalog.com/16.0/Content/Language/Primitive%20Operators/Stencil.htm) and is intended as golfing language and an easy interface for common tasks involving `⌺`. Stencil code can in fact easily be rewritten as normal Dyalog APL code.



Feel free to contact me, [Adám](https://stackexchange.com/users/3114363/ad%C3%A1m), in Stack Exchange's [APL chat room](https://chat.stackexchange.com/rooms/52405/apl) to learn more about Stencil and Dyalog APL.



## In-APL Usage



Execute `2⎕FIX'file://path/Stencil.dyalog` to load the operator.



The syntax is `result←opts (code Stencil specs) input`, but `opts` is optional.



For the specifics of [`opts`](https://github.com/abrudz/Stencil/blob/master/README.md#command-line-options), [`code`](https://github.com/abrudz/Stencil/blob/master/README.md#code), and [`specs`](https://github.com/abrudz/Stencil/blob/master/README.md#arguments), see the linked guidance for the corresponding TIO fields.



Input is an array specifying the initial state.



| `opts` | `result` |

| :---: | --- |

| none | final state or last state before going to a previously encountered state |

| `∊` | vector of states |

| `≢` | scalar non-negative integer |

| `≡` | 0-by-0 numeric matrix |

| number | a state |



If code is a function, then identifiers may be both single- and multi-letter, and spaces are needed to separate them, i.e. `me` is *not* equivalent to `m e`, and `⎕IO` is *not* set to `0` either. However, the predefined values listed [`below`](https://github.com/abrudz/Stencil/blob/master/README.md#code) *are* available.



## TIO User guide



[Try It Online](https://tio.run/#home) is a code testing website for many programming languages, both practical and recreational ones, made by Stack Exchange user [Dennis](https://codegolf.stackexchange.com/users/12012). The following describes the relevant fields when using [Stencil on TIO](https://tio.run/#stencil). 



### Command-line options

This may be any one of the following options:



| opt | Effect |

| :---: | --- |

| none | return final state or last state before going to a previously encountered state |

| `∊` | return list of states from input to final state or last state before going to a previously encountered state |

| `≢` | return the number of states in the above |

| `≡` | output states until stable, or forever if cyclic |

| number | return the state after that many states |



combined with any of the following options:



| opt | Effect |

| :---: | --- |

| `P` | `┌───┐` Plane:
 `│   │` left and right disconnected
 `└───┘` lower and upper disconnected |

| `C` | `┌───┐` Cylinder:
 `↑   ↑` left and right joined
 `└───┘` lower and upper disconnected |

| `T` | `┌─→─┐` Torus:
 `↑   ↑` left and right joined
 `└─→─┘` lower and upper joined |

| `M` | `┌─→─┐` Möbius strip:
 `│   │` left and right disconnected
 `└─←─┘` lower and upper twist-joined |

| `K` | `┌─→─┐` Klein bottle:
 `↑   ↑` left and right joined
 `└─←─┘` lower and upper twist-joined |

| `R` | `┌─→─┐` Real projective plane:
 `↑   ↓` left and right twist-joined
 `└─←─┘` lower and upper twist-joined |

| `I` | `┌   ┐` Infinite:
 `     ` left and right expand and shrink as needed
 `└   ┘` lower and upper expand and shrink as needed |



### Code

This describes what shall be returned for each neighbourhood. It may be a function, or one or more character vectors.



If a single character vector, then this forms the body (i.e. without outer curly braces) of a dfn left operand to 

`⌺`. For more information about the `⌺` operator, see [its documentation](http://help.dyalog.com/16.0/Content/Language/Primitive%20Operators/Stencil.htm).



If two character vectors, then the first will be used as a dfn snippet ( ⍵ is appended to its right) to post-process the result(s).



If three or more character vectors, then the last will additionally be used as a dfn snippet ( ⍵ is appended to its right) to pre-process the input(s).



Stencil provides some shortcuts not available to with the original `⌺`.  All identifiers are expected to be single-letter, and no spaces are needed to separate them, i.e. `me` is equivalent to `m e`. The following values are pre-defined:



Note that all code runs with `⎕IO←0` (0-based **I**ndex **O**rigin).



Examples:



`3 5` will use 3-row, 5-column neighbourhoods



`⍪3 3` will use neighbourhoods of size 3 in every dimension, and step size 



| name | Description |

| :---: | ------- |

| `⍵` | multi-dimensional Moore neighbourhood with self |

| `M` | vector of Moore neighbourhood with self |

| `m` | count of non-empty cells in the above | 

| `E` | vector of moorE neighbourhood without self | 

| `e` | count of non-empty cells in the above | 

| `V` | vector of Von neumann neighbourhood with self | 

| `v` | count of non-empty cells in the above |

| `N` | vector of von neumanN neighbourhood without self |

| `n` | count of non-empty cells in the above |

| `S` | scalar self  |

| `s` | Boolean (1 or 0) for whether above is non-empty    |

| `P` | vector of Booleans for each dimension whether it has been padded or not  |

| `p` | number of dimensions which have been padded |

| `⍺` | vector of amounts of padding for each dimension |

| `W` | original input |

| `w` | flattened original input |

| `Y` | preprocessed input |

| `y` | flattened preprocessed input |



In the above table, *Moore neighbordhood* means the entire n×m neighbourhood, while *von Neumann neighbourhood* means cells orthogonal to the self.



### Input

Each line is an APL expression for an initial state. Each will be processed separately.

 

### Arguments

This allows specifying the neighbourhood and step size. The arguments will be joined with spaces and executed as an APL expression to be used as right operand for `⌺`. Stencil provides two shortcuts not available to with original `⌺`. If a single size is given, it will be used for every dimension. If no size is given, size 3 will be used in every dimension.



Examples:



`3 5` will use 3-row, 5-column neighbourhoods



`⍪5 3` will use  neighbourhoods of size 5 in every dimension with a step size of 3 in every dimension



## Examples



### Hello, World!



Code: `S`



Input `Hello, World!`



Every character will be replaced by it**S**elf.



### Game of Life



Code: `3∊me`



A cell will be alive in the next genration if there are 3 live cells either counting itself or not.



To get just the next generation, add the command-line option `1`.



To list all generations, add the command-line options `∊`.



To calculate the period of a cyclic pattern (an [oscillator](https://en.wikipedia.org/wiki/Oscillator_(cellular_automaton)) or a [spaceship](https://en.wikipedia.org/wiki/Spaceship_(cellular_automaton)), add the command-line options `≢I`



To check whether a patter is a [still life](https://en.wikipedia.org/wiki/Still_life_(cellular_automaton)), add the command-line options `≢I` and let code be `1=` `3∊me`.



### Primality checker



Command-line option: `1`



Code: `~S∊1,∘.×⍨2+⍳S`



Input has one or more lists of integers. For each such **S**elf, it generates the integers from 0 to **S**elf-1 (`⍳S`), adds 2 (`2+`), giving from 2 to Self+1, creates a multiplication table (`∘.×⍨`), prepends a column of ones (`1,`), and asks whether the **S**elf is a member thereof (`S∊`), and then negates that (`~`).