-- Hoogle documentation, generated by Haddock
-- See Hoogle, http://www.haskell.org/hoogle/


-- | Connection-set algebra (CSA) library
--   
--   Library for algebraic connection-set expressions, built on M.
--   Djurfeldt's idea of connection-set algebra [1].
--   
--   1: Mikael Djurfeldt. The Connection-set Algebra: a formalism for the
--   representation of connectivity structure in neuronal network models,
--   implementations in Python and C++, and their use in simulators, BMC
--   Neuroscience, 2011. <a>https://doi.org/10.1186/1471-2202-12-S1-P80</a>
@package csa
@version 0.1.0


-- | This module uses connection-set algebra to describe connectivity
--   between two entities with a scalar (<a>Double</a>) value. The library
--   build on the concept of M. Djurfeldt's Connection-Set Algebar [1]. The
--   connection expressions can be compiled to a dependently typed
--   <a>AdjacencyMatrix</a> from the <a>Numeric.LinearAlgebra.Static</a>
--   package. Such a matrix can be used and exported as a regular
--   n-dimensional vector.
--   
--   Usage:
--   
--   <pre>
--   &gt;&gt;&gt; toAdjacencyMatrix None :: L 2 2
--   (matrix
--    [ 0.0, 0.0
--    , 0.0, 0.0 ] :: L 2 2)
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; toAdjacencyMatrix $ Minus (AllToAll 2) (OneToOne 1) :: L 2 2
--   (matrix
--    [ 1.0, 2.0
--    , 2.0, 1.0 ] :: L 2 2)
--   </pre>
--   
--   1: Mikael Djurfeldt. The Connection-set Algebra: a formalism for the
--   representation of connectivity structure in neuronal network models,
--   implementations in Python and C++, and their use in simulators, BMC
--   Neuroscience, 2011. <a>https://doi.org/10.1186/1471-2202-12-S1-P80</a>
module CSA

-- | An adjacency matrix describing connections in a directed graph
type AdjacencyMatrix = L

-- | An expression algebra tree (AST) that describes connections between
--   two elements
data Expr

-- | An empty connection (only 0s)
None :: Expr

-- | Full connectivity with the given value
AllToAll :: ℝ -> Expr

-- | One-to-one (diagonally) connectivity
OneToOne :: ℝ -> Expr

-- | A masked connectivity given by a function
Mask :: (ℝ -> ℝ -> ℝ) -> Expr

-- | Addition of two connectivity expressions
Plus :: Expr -> Expr -> Expr

-- | Subtraction of two connectivity expressions
Minus :: Expr -> Expr -> Expr

-- | Converts an expression to an adjacency matrix by unrolling the
--   expression tree from left to right
toAdjacencyMatrix :: (KnownNat m, KnownNat n) => Expr -> AdjacencyMatrix m n