Pepper Constraints

A Quick Overview

Pepper constraints are functions that reduce domains for constraint satisfaction problems, such as the provided Pepper.allDiff (for the all different constraint) and Pepper.setVal (for any unary constraint). TableSalt allows you to write your own constraint functions, to allow flexibility in the problems you want to solve. Each pepper constraint is then passed in to the framework along with the variables it modifies before solving.

Writing Pepper Constraints

Declaring a new pepper constraint is easy:

function newConstraint(section, board, ...)

The TableSalt framework will always pass in the section and board for each constraint function. So be sure that these are the first two arguments declared when creating a new constraint function! The section is a table of id's corresponding to variables that that constraint will be modifying and the board is the current TableSalt instance that is being used. Pepper constraint functions also allow for multiple additional parameters to be passed in, hence the ... in the function decleration. Constraints should be designed to work in a variety of situations, they are applied to certain variables (called a section) when they are passed in to the framework.

The main thing about pepper constraints are that they should return a table of tables of the new domains that correspond to the section ids passed in to the constraint. While that sounds confusing let's break it down. Take the Pepper.setVal constraint for example:

function Pepper.setVal(section, board, val)
    local allValues = {}
    for i = 1, #section do
        allValues [ #allValues+1 ] = {val}
    end
    return allValues
end

It's important that the table that is returned, allValues, is the same length as section. The first element in allValues corresponds to the new domain (which is always given as a table) of the first element (which will be an id for a constraint) in section. Since this is the setVal constraint, each domain is reduced to exactly one value.

It's also worth noting that if a constraint fails on a specific id, the associated domain should be an empty table: {}. Ex: The section {1, 3, 4} fails the constraint on the third element, the table the constraint returns could look like this: { {1, 4, 3}, {2}, {} }.

Helpful functions when writing constraints

Since the pepper constraints pass in an instance of TableSalt , some of the functions available should be quite useful. Most particularly TableSalt:getValueByID() and TableSalt:getDomainByID(). Here's a quick example of how they could be used:

function newConstraint(section, board)
    for ind, id in ipairs(section) do
        local currentValue = board:getValueByID(id)
        local currentDomain = board:getDomainByID(id)
        -- some more stuff
    end
end

This will iterate through all the variables's ids that were passed in and do magical things with their associated values and domains!

Passing in Pepper Constraints

There are a multitude of functions that are used to pass in pepper constraints:

The first three (addConstraintByIDs , addConstraintByPairs , and addConstraintByNames ) in the list all follow a similar structure for passing in pepper constraints:

    --code
    addConstraintByX(section, pepperConstraint, ...)
    --more code

The section can be passed in through a variety of methods, check the documentation on those specific functions for more information on that. The pepperConstraint is simply the name of the pepperConstraint (be sure not to pass in any arguments here). The ... represents any additional arguments that are required to run the constraint.

The other three (addConstraintForEachRow , addConstraintForEachColumn , and addConstraintForAll ) only pass in the pepperConstraint and any additional arguments.

Here's a quick example on how to pass in Pepper.setVal(section, board, val) which takes in the additional parameter 'val':

    -- some crazy game that is played on 5 squares where each square have the values 1-5
    local crazyGame = TableSalt:new({1, 2, 3, 4, 5}, 5)
    -- squares 1, 3, and 5 all need to be set to 5 for some reason
    crazyGame:addConstraintByIDs({1, 3, 5}, Pepper.setVal, 5)

Any additional parameters can just be appended and TableSalt should take care of the rest!

TableSalt

Contents

Manual

Modules

Pepper Constraints

A Quick Overview

Writing Pepper Constraints

Helpful functions when writing constraints

Passing in Pepper Constraints