Mango
Provides interfaces for argument functions 0, 1, and 2. Uses Java generics. A good range of algorithms for working with functions.
Jga
Provides classes for 0, 1, 2 and an arbitrary number of argument functions. Subclass of subclass objects. Uses Java generics. A wide range of algorithms. Includes JFXG (Java Functor eXpression Grammar) - a parsed language designed to simplify the creation of arbitrarily complex functors. Provides several algorithms for working with functions.
Apocal commons functor
Provides interfaces for argument functions 0, 1, and 2, as well as argument procedures 0, 1, and 2 (which do not return a value). Uses Java generics. Good range of algorithms.
Google Guava (were Google collections)
Provides function and predicate interfaces for single argument functions. Uses Java generics. Provides only a layout method for combining functions. Pretty simple.
FunctionalJ
Provides interfaces and classes for 0, 1, 2 and an arbitrary number of argument functions. Uses Java generics. Existing methods can be turned into functions through function mapping classes.
tukushan
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