{-# LANGUAGE NoImplicitPrelude #-} -- | A DSL for describing and computing with combinatorial species. -- This module re-exports the most generally useful functionality; -- for more specialized functionality (for example, computing -- directly with cycle index series), see the various sub-modules. -- -- Note that this library makes extensive use of the numeric-prelude -- library; to use it you will want to use -XNoImplicitPrelude, and -- import NumericPrelude and PreludeBase. -- -- For a friendly introduction to combinatorial species in general -- and this library in particular, see my series of blog posts: -- -- * -- -- * -- -- * -- -- For a good reference (really, the -- only English-language reference!) on combinatorial species, see -- Bergeron, Labelle, and Leroux, \"Combinatorial Species and -- Tree-Like Structures\", Vol. 67 of the Encyclopedia of -- Mathematics and its Applications, Gian-Carlo Rota, ed., Cambridge -- University Press, 1998. module Math.Combinatorics.Species ( -- * The combinatorial species DSL -- \$DSL -- Explicitly export methods of the Species class since -- we don't want to export all of them Species ( singleton, set, cycle, linOrd , subset, ksubset, element , o, (><), (@@) , ofSize, ofSizeExactly, nonEmpty , rec ) -- ** Convenience methods -- \$synonyms , oneHole , x, sets, cycles , linOrds , subsets , ksubsets , elements -- ** Derived operations , pointed -- ** Derived species , octopus, octopi , partition, partitions , permutation, permutations , ballot, ballots , simpleGraph, simpleGraphs , directedGraph, directedGraphs -- * Counting species structures -- \$counting , labeled, labelled , unlabeled, unlabelled -- * Enumerating species structures -- \$enum , Enumerable(..) , structureType , enumerate , enumerateL , enumerateU , enumerateM , enumerateAll, enumerateAllU -- ** Types used for generation -- \$types , Void, Unit(..) , Id(..), Const(..) , Sum(..), Prod(..), Comp(..) , Star(..), Cycle(..), Set(..) -- * Species AST -- \$ast , SpeciesAST , reify , reflect , TSpeciesAST , ESpeciesAST , wrap, unwrap , erase, erase', annotate -- * Species simplification , simplify , sumOfProducts -- * Recursive species -- \$rec , ASTFunctor(..) , Interp , newtonRaphsonRec , newtonRaphson -- * Template Haskell , deriveDefaultSpecies , deriveSpecies ) where import Math.Combinatorics.Species.Class import Math.Combinatorics.Species.Labeled import Math.Combinatorics.Species.Unlabeled import Math.Combinatorics.Species.Structures import Math.Combinatorics.Species.Enumerate import Math.Combinatorics.Species.AST import Math.Combinatorics.Species.AST.Instances import Math.Combinatorics.Species.TH import Math.Combinatorics.Species.Simplify import Math.Combinatorics.Species.NewtonRaphson -- \$DSL -- The combinatorial species DSL consists of the 'Species' type class, -- which defines some primitive species and species operations. -- Expressions of type @Species s => s@ can then be interpreted at -- various instance types in order to compute with species in various -- ways. -- \$synonyms -- Some synonyms are provided for convenience. In particular, -- gramatically it can often be convenient to have both the singular -- and plural versions of species, for example, @set \`o\` nonEmpty -- sets@. -- \$counting -- \$enum -- \$types -- Many of these functors are already defined elsewhere, in other -- packages; but to avoid a plethora of imports, inconsistent -- naming/instance schemes, etc., we just redefine them here. -- \$ast -- Species expressions can be reified into one of several AST types. -- \$rec -- Tools for dealing with recursive species.