ecsolticia.codeberg.page
Tiny expressions-based language for elementary cellular automata simulation
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# ecaxpr
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Tiny expressions-based language for elementary cellular automata simulation.
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---
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```
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l == ~(r | t)
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***************#*************** 16
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```
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becomes...
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```
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***************#***************
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**************###**************
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*************##**#*************
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************##*####************
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***********##**#***#***********
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**********##*####*###**********
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*********##**#****#**#*********
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********##*####**######********
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*******##**#***###*****#*******
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******##*####*##**#***###******
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*****##**#****#*####*##**#*****
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****##*####**##*#****#*####****
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***##**#***###**##**##*#***#***
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**##*####*##**###*###**##*###**
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*##**#****#*###***#**###**#**#*
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##*####**##*#**#*#####**#######
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```
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---
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- [Installation](./docs/install.md).
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- [Guide](./docs/guide.md).
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- [Language Reference](./docs/langrefs.md).
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# `ecaxpr` Guide
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`ecaxpr` is a domain-specific language. That domain here is elementary cellular automata.
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If you are unfamiliar with elementary cellular automata, and cellular automata in general, then this guide will not be able to help you. As such, you may consider resources like
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- [Cellular Automata (Wikipedia)](https://en.wikipedia.org/wiki/Cellular_automaton).
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- [Conway's Game of Life (Lifewiki)](https://conwaylife.com/wiki/Conway%27s_Game_of_Life).
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- [Wolfram Mathworld's entry on Elementary Cellular Automata](https://mathworld.wolfram.com/ElementaryCellularAutomaton.html).
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- [The "Rule 30" Wikipedia page - a particular ECA](https://en.wikipedia.org/wiki/Rule_30).
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This guide assumes that you have `ecaxpr` installed on your system. You may refer to the [Installation Instructions](./install.md) page if you have not already installed it.
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# in the works... look back again later
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# Language Reference
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Every `ecaxpr` file corresponds to an `ecaxpr` expression.
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An `ecaxpr` expression consists of three parts:
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1. `L-expr`: A predicate logic expression representing the rules.
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2. `State-expr`: An expression representing the initial state.
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3. `Steps-expr`: A non-negative integer representing the number of steps to simulate.
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These names are mostly neologisms given for convenience and precise reference.
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Each part of the `ecaxpr` expression must occur in order exactly as stated.
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Newlines, spaces, and tabs do not matter.
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## L-expr
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The following is a verbal description of the grammar of `L-expr`.
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For any operation that is mentioned as "taking in" `L-expr`, it should be assumed that what they produce are also `L-expr`. No exceptions arise.
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### Predicates
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> The simplest of `L-expr` are `l`, `t`, and `r`.
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Given any cell in our elementary cellular automaton, `l` is the value of the cell to the left, `t` the value of the present cell ("this" cell), and `r` the value of the cell to the right.
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These are called **predicates**, a fancy name for variables in logic.
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### Negation
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Given any `L-expr`, we can take its negation.
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To take the negation of a statement or predicate in logic means to invert its truth value. If it is true, then its negation is false, and vice versa.
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> If an `L-expr` predicate is writen as `X`, we take its negation as `~X` in an `L-expr`. Thus, if `X` is `t`, its negation is `~t`.
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### Conjunction ("AND")
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Given any set of at least two `L-expr`, we can take their conjunction.
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To take the conjunction in logic means to check if *all* the conjuncted statements or predicates are true. The conjunction statement/predicate itself is only true if all of them are true, and false otherwise.
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For two statements/predicates, this corresponds to stating that both of them are true. In general, it corresponds to stating that *all* of them are true.
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> Suppose that we have two `L-expr` predicates written as `A` and `B`, respectively. Then, their conjunction is written as `A & B`.
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> Suppose that we have a list of N `L-expr` predicates, where N is some non-negative integer greater than or equal to 2. Suppose that they are written as `L1`, `L2`, `L3`, ..., `LN`, respectively. Then, their conjunction is written out as `L1 & L2 & ... & LN`.
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### Disjunction ("OR")
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Given any set of at least two `L-expr`, we can take their disjunction.
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To take the disjunction in logic means to check if *at least one* of the disjuncted statements or predicates is true. The disjunction statement/predicate itself is only false if all of them are false, and true otherwise.
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> Suppose that we have two `L-expr` predicates written as `A` and `B`, respectively. Then, their disjunction is written as `A | B`.
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> Suppose that we have a list of N `L-expr` predicates, where N is some positive integer greater than or equal to 2. Suppose that they are written as `L1`, `L2`, `L3`, ..., `LN`, respectively. Then, their disjunction is written out as `L1 | L2 | ... | LN`.
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### Equality
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Given any two `L-expr`, we can take their equality.
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To "take the equality" here means to check if both of the operands are of the same truth values. If so, then the equality is true, and false otherwise.
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> Suppose that we have two `L-expr` predicates written as `A` and `B`, respectively. Then, their equality is written as `A == B`.
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## State-expr
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A `State-expr` consists of `*` and `#` in succession.
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- `*` represents white or `false` cells.
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- `#` represents black or `true` cells.
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Thus, `***#***` would correspond to an initial states configuration where the first three cells are `false`, followed by a `true` one, which is then followed by three more `false` cells.
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## Steps-expr
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A `Steps-expr` is simply a non-negative integer.