---
title: "Extending fcaR: Equivalence Rules for Implications"
output: rmarkdown::html_vignette
vignette: >
  %\VignetteIndexEntry{Extending fcaR: Equivalence Rules for Implications}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

```{r, include = FALSE}
knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>",
  fig.width = 7,
  fig.height = 5,
  warning = FALSE
)
```

# Introduction

In this vignette, we present a way to extend the functionalities provided in the `fcaR` package: define new operations on an `ImplicationSet`.

First, we load the `fcaR` package by:
```{r setup}
library(fcaR)
```

Let us use the `planets` dataset included in the package:
```{r}
fc <- FormalContext$new(planets)
fc$find_implications()
```

# The Registry

In `fcaR`, we have decided to use a `registry` from the `registry` package to store the operations that can be performed on an `ImplicationSet`. Currently, its purpose is to store equivalence rules, that is, methods that obtain equivalent `ImplicationSet`s from one given.

This registry is called `equivalencesRegistry` and one can inspect its contents by:
```{r}
equivalencesRegistry$get_entry_names()
```

These names correspond to the methods that are added to the registry by default, and are used to index those methods. Every method is accompanied by a description, so we can see its definition:
```{r}
equivalencesRegistry$get_entry("Composition")
```

We can even use abbreviated names to refer to the method:
```{r}
equivalencesRegistry$get_entry("comp")
```

# Use of the Rules

As explained in the vignette corresponding to `ImplicationSet`s, we can use any of these methods by using the `apply_rules()` method in the `ImplicationSet`:

```{r eval = FALSE}
fc$implications$apply_rules(c("comp", "simp"))
```

# Definition of New Equivalence Rules

The way to extend the functionality in `fcaR` is to define new equivalence operators and include them in the registry.

In order to add a new method, we use:
```{r eval = FALSE}
equivalencesRegistry$set_entry(method = "Method name",
                               fun = method_function,
                               description = "Method description")
```
where `method_function()` must be a function with the following scheme:
```{r eval = FALSE}
method_function <- function(LHS, RHS, attributes) {
  
  # LHS and RHS are the sparse matrices of the left-hand and
  # right-hand sides of the implications
  # attributes is the vector of attribute names
  # The three arguments are mandatory
  
  # Perform operations on LHS and RHS
  # ...
  
  # Must return a list with two components: lhs and rhs
  return(list(lhs = LHS,
              rhs = RHS))
  
}
```

The `method_function()` function must be defined before adding the method to the registry. Once the method is added, it can be executed by using the corresponding call to `apply_rules()`.

# An Example
Let us define an operator which randomly reorders the implications. Evidently, this operation provides an equivalent `ImplicationSet`.

In this case, we begin by defining the method function:
```{r}
random_reorder <- function(LHS, RHS, attributes) {
  
  # Remember: attributes are in rows, implications are
  # in columns.
  # Random order for columns:
  o <- sample(ncol(LHS), ncol(LHS))
  
  # Return the reordered implications
  return(list(lhs = LHS[, o],
              rhs = RHS[, o]))
  
}
```

Once we have defined the function, we add the method to the registry:
```{r}
equivalencesRegistry$set_entry(method = "Randomize",
                               fun = random_reorder,
                               description = "Randomize the order of the implications.")
```

If we inspect the registry, we obtain the list of the methods, including the one we have just inserted:
```{r}
equivalencesRegistry$get_entry_names()
```

We can apply the new method:
```{r}
# Original implications
fc$implications
```
```{r}
# Apply the randomize method
fc$implications$apply_rules("randomize")
```
```{r}
# Reordered implications
fc$implications
```