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LaMa4J (“Lattice Manipulation for Java”) is a set of Java classes
    that implement a number of lattices and lattice operations. It is free software
	 distributed under the GNU 
	 General Public License.
	
    
History and Motivation

    
MG4J uses
	 minimal-interval semantics to express the semantics of a query.
	 A single-index query is turned into an element of a
	 {@linkplain it.unimi.dsi.lama4j.IntervalAntichains interval-antichain lattice}; the element
	 expresses the regions of the documents that satisfy the query. Queries involving
	 more than one index are turned into elements of a
	 {@linkplain it.unimi.dsi.lama4j.Sum sum} of such lattices.
	 
	 
Manipulating the above lattices is not always trivial, so we decided to write a full Java package
	 that could manipulate easily any kind of lattice. Marco Rosa wrote the first
	 implementation, under Sebastiano Vigna's 
	 supervision, as part of his degree thesis.
	 
	 
Roadmap

	 
First of all, have a look at the {@link it.unimi.dsi.lama4j.Lattice}
	 and {@link it.unimi.dsi.lama4j.Element} interfaces to see which operations
	 are supported. The main idea is that by playing with an interactive environment such as
	 the BeanShell you can create lattices, create elements,
	 and use Java variables and syntactic constructs as if you were using an ad hoc computational
	 algebra package. The  {@link it.unimi.dsi.lama4j.Lattices} static container
	 provides methods that do nice things such as 
	 {@linkplain it.unimi.dsi.lama4j.Lattices#generateDot(Lattice,Map,PrintWriter,boolean) emitting a representation
	 of the covering relation} in the Graphviz language, that
	 can be automatically drawn into a Hasse diagram, as shown on the right for the free
	 lattice on three generators (actually, the {@linkplain it.unimi.dsi.lama4j.Sum sum} of three 3-{@linkplain it.unimi.dsi.lama4j.Chain chains}).
	 
	 
There are two ways you can use LaMa4J: you can enrich the existing set of lattices (see,
	 e.g., {@link it.unimi.dsi.lama4j.Chain}, {@link it.unimi.dsi.lama4j.Parts}, and
	 so on), or you can build new lattices using operators such as
	 {@link it.unimi.dsi.lama4j.Product}, {@link it.unimi.dsi.lama4j.Sum} (just
	 for distributive lattices) and {@linkplain it.unimi.dsi.lama4j.Op dualisation}.