module Probability.ProbabilityMeasure.Macro where

import           Types

import           Macro.Tuple

import           Functions.Application.Macro

import           Probability.Intro.Macro
import           Probability.SigmaAlgebra.Macro

-- * Probability space

-- | Probabilty space given a universe, sigma algebra and probability measure
prsp :: Note -> Note -> Note -> Note
prsp = triple

-- | Concrete probability space
prsp_ :: Note
prsp_ = prsp univ_ sa_ prm_

prbsp :: Note
prbsp = prsp reals boreals prm_


-- | Concrete probability measure
prm_ :: Note
prm_ = "Pr"

-- | Probability with given probability measure
prm :: Note -> Note -> Note
prm = fn -- probability with custom measure

-- | Probability
prob :: Note -> Note
prob = prm prm_
