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docs/src/constraints/constraint_commons.md

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## Extensions
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We extended some operations for `Nothing` and `Symbol`.
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We extend some operations for `Nothing` and `Symbol`.
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```@docs; canonical=false
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symcon
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## Sampling
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During our constraint learning processes, we use sampling to efficiently make partial exploration of search spaces. Follows some sampling utilities.
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During our constraint learning processes, we use sampling to efficiently make partial exploration of search spaces. The following are some examples of sampling utilities.
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```@docs; canonical=false
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oversample
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δ_extrema
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```
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### Performances
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```@raw html
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<div style="display: flex; justify-content: space-between;">
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<img src="https://github.com/JuliaConstraints/Benchmarks/blob/main/ConstraintCommons/visuals/bench_evolution_extrema.png?raw=true" alt="Bench Evolution" style="width:48%;"/>
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<img src="https://github.com/JuliaConstraints/Benchmarks/blob/main/ConstraintCommons/visuals/chair_evolution_extrema.png?raw=true" alt="Chair Evolution" style="width:48%;"/>
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</div>
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```
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### Performances
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## Dictionaries
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We provide the everuseful `incsert!` function for dictionaries.
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We provide the ever-useful `incsert!` function for dictionaries.
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```@docs; canonical=false
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<img src="https://github.com/JuliaConstraints/Benchmarks/blob/main/ConstraintCommons/visuals/bench_evolution_dictionaries.png?raw=true" alt="Bench Evolution" style="width:48%;"/>
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<img src="https://github.com/JuliaConstraints/Benchmarks/blob/main/ConstraintCommons/visuals/chair_evolution_dictionaries.png?raw=true" alt="Chair Evolution" style="width:48%;"/>
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</div>
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```
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```
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docs/src/constraints/generic_constraints.md

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We provide a straightforward example through the `:dist_different` constraint on how to define and add such a constraint in the `USUAL_CONSTRAINTS` collection.
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Higher level modeling language such as `JuMP` should provide a `Intention` interface.
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Higher level modeling languages such as `JuMP` should provide a `Intention` interface.
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### Defining an intention constraint in JC-API
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## Extension Constraints
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These are constraints that are defined by explicitly listing all the tuples of values that satisfy the constraint. They are called extensional because they are defined by the set of values they allow. For example, a binary constraint that specifies that a variable X must be either 1 or 2 and a variable Y must be either 3 or 4 could be defined extensionally by the set of tuples {(1,3), (1,4), (2,3), (2,4)}.
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These are constraints that are defined by explicitly listing all the tuples of values that satisfy the constraint. They are called extensional because they are defined by the set of values they allow. For example, a binary constraint that specifies that a variable X must be either 1 or 2 and a variable Y must be either 3 or 4 could be defined extensionally by the set of tuples `{(1,3), (1,4), (2,3), (2,4)}`.
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These two types of constraints provide a flexible way to define complex relationships between variables in constraint programming.
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docs/src/constraints/variables_and_domains.md

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### `RangeDomain`
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A range domain allows for minimal storage and more efficient operation on discrete sets defined as `Range` in Julia. It is not recommended for dynamic domains (it will be replaced with `SetDomain` as soon non-extremal element is removed).
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A range domain allows for minimal storage and more efficient operation on discrete sets defined as `Range` in Julia. It is not recommended for dynamic domains (it will be replaced with `SetDomain` as soon as a non-extremal element is removed).
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::: code-group
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