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Tests.hs
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Tests.hs
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{-# LANGUAGE DataKinds, GADTs #-}
module Tests where
import Syntax
import Helpers
import UserInterface
import Simplify
import Test.HUnit
-- import Debug.Trace
type Model a b = Term ('HMeasure ('HPair a b))
freeVarFail :: Model 'HReal 'HUnit
freeVarFail = Dirac (Pair (Var (V "x")) Unit)
plusFail :: Model 'HReal 'HUnit
plusFail = Do (x :<~ stdNormal)
(Dirac (Pair (Add (Var x) (Var x)) Unit))
where x = V "x"
normTest :: Model 'HReal 'HUnit
normTest = Do (n :<~ stdNormal)
(Dirac (Pair (Var n) Unit))
where n = V "n"
radius :: Model 'HReal 'HUnit
radius = do_ [ x :<~ stdNormal
, y :<~ stdNormal ]
(Dirac (Pair (Sqrt (Add (Square (Var x))
(Square (Var y))))
Unit))
where (x,y) = (V "x", V "y")
unitCircle :: Term ('HMeasure ('HPair 'HReal 'HReal))
unitCircle = do_ [ x :<~ Lebesgue
, y :<~ Lebesgue
, observe (Equal (Add (Square (Var x))
(Square (Var y)))
(Real 1)) ]
(Dirac (Pair (Var x) (Var y)))
where (x,y) = (V "x", V "y")
axch :: Model ('HPair 'HReal 'HReal) 'HUnit
axch = Do (xy :<~ unitCircle)
(Dirac (Pair (f (Var xy)) Unit))
where xy = V "xy"
f p = Pair (Mul (Real 2) (Fst p)) (Mul (Real 20) (Snd p))
gaussMix :: Model 'HReal ('HPair 'HReal 'HReal)
gaussMix = Do (mu1 :<~ stdNormal)
(Do (mu2 :<~ stdNormal)
(Do (x :<~ MPlus (Normal (Var mu1) (Real 1))
(Normal (Var mu2) (Real 1)))
(Dirac (Pair (Var x)
(Pair (Var mu1) (Var mu2))))))
where (mu1, mu2, x) = (V "mu1", V "mu2", V "x")
helloWorld :: Model 'HReal 'HReal
helloWorld = do_ [ mu :<~ stdNormal
, x :<~ Normal (Var mu) (Real 1) ]
(Dirac (Pair (Var x) (Var mu)))
where (mu, x) = (V "mu", V "x")
helloProposal :: Term 'HReal -> Term ('HMeasure 'HReal)
helloProposal x = Normal x (Real 0.5)
helloWorld2D :: Model ('HPair 'HReal 'HReal) 'HReal
helloWorld2D = do_ [ mu :<~ stdNormal
, x :<~ Normal (Var mu) (Real 1)
, y :<~ Normal (Var mu) (Real 1) ]
(Dirac (Pair (Pair (Var x) (Var y)) (Var mu)))
where (mu, x, y) = (V "mu", V "x", V "y")
density2D :: Model ('HPair 'HReal 'HReal) 'HUnit
density2D = do_ [ x :<~ Normal (Real 0) (Real 1)
, y :<~ Normal (Var x) (Real 1) ]
(Dirac (Pair (Pair (Var y) (Var x)) Unit))
where (x, y) = (V "x", V "y")
unclampedGPA :: Model 'HReal ('HEither 'HUnit 'HUnit)
unclampedGPA = MPlus (Do (x :<~ Normal (Real 2) (Real 3))
(Dirac (Pair (Var x) true_)))
(Do (y :<~ Normal (Real 5) (Real 6))
(Dirac (Pair (Var y) false_)))
where (x,y) = (V "x", V "y")
-- | Examples that produce base-constraints containing term-language variables
-------------------------------------------------------------------------------
lubAndMPlus :: Model 'HReal 'HUnit
lubAndMPlus = do_ [ x :<~ stdNormal
, y :<~ MPlus (Normal (Var x) (Real 1))
(Dirac (Real 0)) ]
(Dirac (Pair (Add (Var x) (Var y)) Unit))
where (x,y) = (V "x", V "y")
addAdd :: Model 'HReal 'HUnit
addAdd = do_ [ x :<~ stdNormal
, y :<~ stdNormal ]
(Dirac (Pair (Add (Var y) (Add (Var x) (Var x))) Unit))
where (x,y) = (V "x", V "y")
plus :: Model 'HReal 'HUnit
plus = Do (x :<~ stdNormal)
(Dirac (Pair (Add (Var x) (Var x)) Unit))
where x = (V "x")
-------------------------------------------------------------------------------
discrete2 :: Model 'HReal 'HUnit
discrete2 = msum_ [Dirac (Pair (Real r) Unit) | r <- [1..3]]
gpa :: Model 'HReal ('HEither 'HUnit 'HUnit)
gpa = Do (n :<~ Normal (Real 2) (Real 3))
(MPlus (if_ (Less (Var n) (Real 4))
(if_ (leq (Var n) (Real 0))
(Dirac (Pair (Real 0) true_))
(Dirac (Pair (Var n) true_)))
(Dirac (Pair (Real 4) true_)))
(if_ (Less (Var n) (Real 10))
(if_ (leq (Var n) (Real 0))
(Dirac (Pair (Real 0) false_))
(Dirac (Pair (Var n) false_)))
(Dirac (Pair (Real 10) false_))))
where n = V "n"
gpaWu :: CH (Model 'HReal ('HEither 'HUnit 'HUnit))
gpaWu = uniform (Real 0) (Real 4) >>= \usaDist ->
uniform (Real 0) (Real 10) >>= \indiaDist ->
return $
mplus_ (Do (g :<~ mplus_ (weight (Real 0.01) (Dirac (Real 4)))
(weight (Real 0.99) usaDist))
(Dirac (Pair (Var g) true_)))
(Do (g :<~ mplus_ (weight (Real 0.01) (Dirac (Real 10)))
(weight (Real 0.99) indiaDist))
(Dirac (Pair (Var g) false_)))
where g = V "g"
-- | 2D Gaussian Mixture Model with 2 clusters
-- We want to do unsupervised learning, i.e., having observed two points
-- we want to infer a distribution over their cluster labels and the cluster means
type R2 = 'HPair 'HReal 'HReal
type B2 = 'HPair HBool HBool
gmm :: CH (Model R2 ('HPair B2 R2))
gmm = bind meandist $ \mu1 ->
bind meandist $ \mu2 ->
bind faircoin $ \b1 ->
bind faircoin $ \b2 ->
bind (mixture b1 mu1 mu2) $ \p1 ->
bind (mixture b2 mu1 mu2) $ \p2 ->
dirac $ Pair (Pair p1 p2) (Pair (Pair b1 b2) (Pair mu1 mu2))
where meandist = Normal (Real 2) (Real 3)
faircoin = bern_ (Real 0.5)
mixture b c1 c2 = if_ b (Normal c1 (Real 1)) (Normal c2 (Real 1))
clampNorm :: Model 'HReal 'HReal
clampNorm = Do (n :<~ Normal (Real 2) (Real 3))
(if_ (Less (Var n) (Real 0))
(Dirac (Pair (Real 0) (Var n)))
(Dirac (Pair (Var n) (Var n))))
where n = V "n"
truncatedNorm :: Model 'HReal 'HReal
truncatedNorm = do_ [ n :<~ Normal (Real 0) (Real 1)
, observe (Less (Var n) (Real 0)) ]
(Dirac (Pair (Var n) (Var n)))
where n = V "n"
sqrNorm :: Model 'HReal 'HUnit
sqrNorm = Do (n :<~ Normal (Sqrt (Real 2.6)) (Sqrt (Real 0.1)))
(Dirac (Pair (Square (Var n)) Unit))
where n = V "n"
eitherTest :: Model ('HEither 'HUnit 'HUnit) 'HUnit
eitherTest = Dirac (Pair (Inl Unit) Unit)
sometimesPerturb :: Model ('HPair 'HReal 'HReal) 'HUnit
sometimesPerturb = do_ [ x :<~ Normal (Real 0) (Real 1)
, y :<~ mplus_ (Normal (Var x) (Real 1))
(Dirac (Var x)) ]
(Dirac (Pair (Pair (Var x) (Var y)) Unit))
where (x, y) = (V "x", V "y")
sometimesDouble :: Model ('HPair 'HReal 'HReal) 'HUnit
sometimesDouble = do_ [ x :<~ Normal (Real 0) (Real 1)
, y :<~ mplus_ (Dirac (double (Var x)))
(Dirac (Var x)) ]
(Dirac (Pair (Pair (Var x) (Var y)) Unit))
where (x, y) = (V "x", V "y")
-- | MCMC
--------------------------------------------------------------------------------
singleSiteProposal :: Model ('HPair ('HPair 'HReal 'HReal) ('HPair 'HReal 'HReal)) 'HUnit
singleSiteProposal = do_ [ x :<~ stdNormal
, y :<~ stdNormal
, p :<~ MPlus (Do (x' :<~ Normal (Var x) (Real 0.1))
(Dirac (Pair (Var x' :: Term 'HReal) (Var y :: Term 'HReal))))
(Do (y' :<~ Normal (Var y) (Real 0.1))
(Dirac (Pair (Var x) (Var y')))) ]
(Dirac (Pair (Pair (Pair (Var x) (Var y))
(Var p))
Unit))
where (x,y,x',y',p) = (V "x", V "y", V "x'", V "y'", V "p")
singleSiteBase :: Base ('HPair ('HPair 'HReal 'HReal) ('HPair 'HReal 'HReal))
singleSiteBase = Bindx (Bindx Lebesgue_ (const Lebesgue_))
(\p -> Bindx (Mixture True [frst p])
(const $ Mixture True [scnd p]))
singleSiteProposalSwap :: Model ('HPair ('HPair 'HReal 'HReal) ('HPair 'HReal 'HReal)) 'HUnit
singleSiteProposalSwap = do_ [ x :<~ stdNormal
, y :<~ stdNormal
, p :<~ MPlus (Do (x' :<~ Normal (Var x) (Real 0.1))
(Dirac (Pair (Var x' :: Term 'HReal) (Var y :: Term 'HReal))))
(Do (y' :<~ Normal (Var y) (Real 0.1))
(Dirac (Pair (Var x) (Var y')))) ]
(Dirac (Pair (Pair (Var p)
(Pair (Var x) (Var y)))
Unit))
where (x,y,x',y',p) = (V "x", V "y", V "x'", V "y'", V "p")
-- singleSiteBaseSwap :: Base ('HPair ('HPair 'HReal 'HReal) ('HPair 'HReal 'HReal))
-- singleSiteBaseSwap = Bindx
proposal1 :: Model ('HPair 'HReal 'HReal) 'HUnit
proposal1 = do_ [ x :<~ stdNormal
, y :<~ MPlus (Normal (Var x) (Real 0.1))
(Dirac (Var x)) ]
(Dirac (Pair (Pair (Var x) (Var y)) Unit))
where (x,y) = (V "x", V "y")
proposal1Swap :: Model ('HPair 'HReal 'HReal) 'HUnit
proposal1Swap = do_ [ x :<~ stdNormal
, y :<~ MPlus (Normal (Var x) (Real 0.1))
(Dirac (Var x)) ]
(Dirac (Pair (Pair (Var y) (Var x)) Unit))
where (x,y) = (V "x", V "y")
base1 :: Base ('HPair 'HReal 'HReal)
base1 = Bindx Lebesgue_ (\x -> Mixture True [x])
test2 :: Model 'HReal 'HReal
test2 = do_ [ x :<~ stdNormal
, y :<~ MPlus (Normal (Var x) (Real 0.1))
(Dirac (Var x)) ]
(Dirac (Pair (Var y) (Var x)))
where (x,y) = (V "x", V "y")
test3 :: Model ('HPair 'HReal 'HReal) 'HUnit
test3 = do_ [ x :<~ stdNormal
, x' :<~ stdNormal
, y :<~ MPlus (Normal (Var x) (Real 0.1))
(Dirac (Var x')) ]
(Dirac (Pair (Pair (Var x) (Var y)) Unit))
where (x,x',y) = (V "x", V "x'", V "y")
detCorr :: Model ('HPair 'HReal 'HReal) 'HUnit
detCorr = do_ [ x :<~ stdNormal
, y :<~ Dirac (Exp (Var x)) ]
(Dirac (Pair (Pair (Var x) (Var y)) Unit))
where (x,y) = (V "x", V "y")
-- This is essentially helloWorld2D
noisyCorr :: Model ('HPair 'HReal 'HReal) 'HUnit
noisyCorr = do_ [ x :<~ stdNormal
, y :<~ Normal (Var x) (Real 1) ]
(Dirac (Pair (Pair (Var x) (Var y)) Unit))
where (x,y) = (V "x", V "y")
-- | Boolean example
----------------------------------------------------------------------
burglarAlarm :: Model ('HEither 'HUnit 'HUnit)
('HEither 'HUnit 'HUnit)
burglarAlarm = do_ [ b :<~ bern_ (Real 0.0001)
, a :<~ bern_ (If (Var b) (Real 0.95) (Real 0.01)) ]
(Dirac (Pair (Var a) (Var b)))
where (a,b) = (V "a", V "b")
boolBase :: Base ('HEither 'HUnit 'HUnit)
boolBase = Either (Dirac_ Unit) (Dirac_ Unit)
diracPlus :: Model 'HReal 'HUnit
diracPlus = Do (x :<~ (Dirac (Real 5)))
(Dirac (Pair (Add (Var x) (Var x)) Unit))
where x = V "x"
twoDice :: Model 'HReal 'HReal
twoDice = do_ [ x :<~ msum_ [Dirac (Real 1), Dirac (Real 2), Dirac (Real 3)]
, y :<~ msum_ [Dirac (Real 2), Dirac (Real 3), Dirac (Real 4)]
, d :<~ bern_ (Real 0.5)
, r :<~ Dirac (If (Var d) (Var x :: Term 'HReal) (Var y)) ]
(Dirac (Pair (Var r) (Var d)))
where (x,y,r,d) = (V "x", V "y", V "r", V "d")
-- | Testing equality on Hakaru terms
----------------------------------------------------------------------
eqTests :: Test
eqTests =
TestList
[
"1+4 == 1+4" ~: termEq (Add (Real 1) (Real 4)) (Add (Real 1) (Real 4)) ~?= yes
,"1+4 == 4+1" ~: termEq (Add (Real 1) (Real 4)) (Add (Real 4) (Real 1)) ~?= yes
,"--1 =?= 1" ~: termEq (Neg (Neg (Real 1))) (Real 1) ~?= unknown
,"4*3 == 2*6" ~: termEq (Mul (Real 4) (Real 3)) (Mul (Real 2) (Real 6)) ~?= yes
, "-1 =/= --1" ~: termEq (Neg (Real 1)) (Neg (Real (-1))) ~?= no
]