-- |
-- Module      : Conjure.Engine
-- Copyright   : (c) 2021 Rudy Matela
-- License     : 3-Clause BSD  (see the file LICENSE)
-- Maintainer  : Rudy Matela <rudy@matela.com.br>
--
-- An internal module of 'Conjure',
-- a library for Conjuring function implementations
-- from tests or partial definitions.
-- (a.k.a.: functional inductive programming)
{-# LANGUAGE CPP, RecordWildCards, TupleSections #-}
module Conjure.Engine
  ( module Data.Express
  , module Data.Express.Fixtures
  , module Test.Speculate.Engine
  , module Test.Speculate.Reason
  , Args(..)
  , args
  , conjure
  , conjureWith
  , conjureWithMaxSize
  , conjpure
  , conjpureWith
  , candidateExprs
  )
where

import Data.Express
import Data.Express.Fixtures hiding ((-==-))
import qualified Data.Ratio
import Test.LeanCheck.Error (errorToTrue, errorToFalse, errorToNothing)
import Test.Speculate hiding ((===), Args(..), args)
import Test.Speculate.Reason
import Test.Speculate.Engine
import Test.Speculate.Expr
import System.IO

import Conjure.Expr
import Conjure.Conjurable

-- | Arguments to be passed to 'conjureWith' or 'conjpureWith'.
--   See 'args' for the defaults.
data Args = Args
  { Args -> Int
maxTests          :: Int  -- ^ defaults to 60
  , Args -> Int
maxSize           :: Int  -- ^ defaults to 9, keep greater than maxEquationSize
  , Args -> Int
maxRecursiveCalls :: Int  -- ^ defaults to 1
  , Args -> Int
maxEquationSize   :: Int  -- ^ defaults to 5, keep smaller than maxSize
  , Args -> Int
maxRecursionSize  :: Int  -- ^ defaults to 60
  }

-- | Default arguments to conjure.
--
-- * 60 tests
-- * functions of up to 9 symbols
-- * maximum of 1 recursive call
-- * pruning with equations up to size 5
-- * recursion up to 60 symbols.
args :: Args
args :: Args
args = Args :: Int -> Int -> Int -> Int -> Int -> Args
Args
  { maxTests :: Int
maxTests           =  Int
60
  , maxSize :: Int
maxSize            =  Int
12
  , maxRecursiveCalls :: Int
maxRecursiveCalls  =   Int
1
  , maxEquationSize :: Int
maxEquationSize    =   Int
5
  , maxRecursionSize :: Int
maxRecursionSize   =  Int
60
  }

-- | Like 'conjure' but in the pure world.
--
-- Returns a triple with:
--
-- 1. tiers of implementations
-- 2. tiers of candidate bodies
-- 3. a list of tests
conjpure :: Conjurable f => String -> f -> [Expr] -> ([[Expr]], [[Expr]], [Expr])
conjpure :: String -> f -> [Expr] -> ([[Expr]], [[Expr]], [Expr])
conjpure =  Args -> String -> f -> [Expr] -> ([[Expr]], [[Expr]], [Expr])
forall f.
Conjurable f =>
Args -> String -> f -> [Expr] -> ([[Expr]], [[Expr]], [Expr])
conjpureWith Args
args

-- | Like 'conjpure' but allows setting options through 'Args' and 'args'.
conjpureWith :: Conjurable f => Args -> String -> f -> [Expr] -> ([[Expr]], [[Expr]], [Expr])
conjpureWith :: Args -> String -> f -> [Expr] -> ([[Expr]], [[Expr]], [Expr])
conjpureWith Args{Int
maxRecursionSize :: Int
maxEquationSize :: Int
maxRecursiveCalls :: Int
maxSize :: Int
maxTests :: Int
maxRecursionSize :: Args -> Int
maxEquationSize :: Args -> Int
maxRecursiveCalls :: Args -> Int
maxSize :: Args -> Int
maxTests :: Args -> Int
..} String
nm f
f [Expr]
es  =  ([[Expr]]
implementationsT, [[Expr]]
candidatesT, [Expr]
tests)
  where
  tests :: [Expr]
tests  =  [Expr
ffxx Expr -> [(Expr, Expr)] -> Expr
//- [(Expr, Expr)]
bs | [(Expr, Expr)]
bs <- [[(Expr, Expr)]]
dbss]
  implementationsT :: [[Expr]]
implementationsT  =  (Expr -> Expr) -> [[Expr]] -> [[Expr]]
forall a b. (a -> b) -> [[a]] -> [[b]]
mapT (Expr
vffxx Expr -> Expr -> Expr
-==-) ([[Expr]] -> [[Expr]]) -> [[Expr]] -> [[Expr]]
forall a b. (a -> b) -> a -> b
$ (Expr -> Bool) -> [[Expr]] -> [[Expr]]
forall a. (a -> Bool) -> [[a]] -> [[a]]
filterT Expr -> Bool
implements [[Expr]]
candidatesT
  implements :: Expr -> Bool
implements Expr
e  =  Expr -> Expr -> Bool
apparentlyTerminates Expr
rrff Expr
e
                Bool -> Bool -> Bool
&& Expr
ffxx Expr -> Expr -> Bool
?=? Int -> Expr -> Expr -> Expr
recursexpr Int
maxRecursionSize Expr
vffxx Expr
e
  candidatesT :: [[Expr]]
candidatesT  =  (Expr -> Bool) -> [[Expr]] -> [[Expr]]
forall a. (a -> Bool) -> [[a]] -> [[a]]
filterT (\Expr
e -> Expr -> TypeRep
typ Expr
e TypeRep -> TypeRep -> Bool
forall a. Eq a => a -> a -> Bool
== Expr -> TypeRep
typ Expr
ffxx)
               ([[Expr]] -> [[Expr]])
-> ([[Expr]] -> [[Expr]]) -> [[Expr]] -> [[Expr]]
forall b c a. (b -> c) -> (a -> b) -> a -> c
.  Int -> [[Expr]] -> [[Expr]]
forall a. Int -> [a] -> [a]
take Int
maxSize
               ([[Expr]] -> [[Expr]]) -> [[Expr]] -> [[Expr]]
forall a b. (a -> b) -> a -> b
$  String
-> f -> Int -> Int -> (Expr -> Expr -> Bool) -> [Expr] -> [[Expr]]
forall f.
Conjurable f =>
String
-> f -> Int -> Int -> (Expr -> Expr -> Bool) -> [Expr] -> [[Expr]]
candidateExprs String
nm f
f Int
maxEquationSize Int
maxRecursiveCalls Expr -> Expr -> Bool
(===) [Expr]
es
  ffxx :: Expr
ffxx   =  String -> f -> Expr
forall f. Conjurable f => String -> f -> Expr
canonicalApplication String
nm f
f
  vffxx :: Expr
vffxx  =  String -> f -> Expr
forall f. Conjurable f => String -> f -> Expr
canonicalVarApplication String
nm f
f
  (Expr
rrff:[Expr]
_)   =  Expr -> [Expr]
unfoldApp Expr
vffxx

  Expr
e1 === :: Expr -> Expr -> Bool
=== Expr
e2  =  Expr -> Bool
isReallyTrue (Expr
e1 Expr -> Expr -> Expr
-==- Expr
e2)
  Expr
e1 ?=? :: Expr -> Expr -> Bool
?=? Expr
e2  =  Expr -> Bool
isTrueWhenDefined (Expr
e1 Expr -> Expr -> Expr
-==- Expr
e2)
  -==- :: Expr -> Expr -> Expr
(-==-)  =  f -> Expr -> Expr -> Expr
forall f. Conjurable f => f -> Expr -> Expr -> Expr
conjureMkEquation f
f

  isTrueWhenDefined :: Expr -> Bool
isTrueWhenDefined Expr
e  =  (Expr -> Bool) -> [Expr] -> Bool
forall (t :: * -> *) a. Foldable t => (a -> Bool) -> t a -> Bool
all (Bool -> Bool
errorToFalse (Bool -> Bool) -> (Expr -> Bool) -> Expr -> Bool
forall b c a. (b -> c) -> (a -> b) -> a -> c
. Bool -> Expr -> Bool
forall a. Typeable a => a -> Expr -> a
eval Bool
False) ([Expr] -> Bool) -> [Expr] -> Bool
forall a b. (a -> b) -> a -> b
$ ([(Expr, Expr)] -> Expr) -> [[(Expr, Expr)]] -> [Expr]
forall a b. (a -> b) -> [a] -> [b]
map (Expr
e Expr -> [(Expr, Expr)] -> Expr
//-) [[(Expr, Expr)]]
dbss
  isReallyTrue :: Expr -> Bool
isReallyTrue  =  (Expr -> Bool) -> [Expr] -> Bool
forall (t :: * -> *) a. Foldable t => (a -> Bool) -> t a -> Bool
all (Bool -> Bool
errorToFalse (Bool -> Bool) -> (Expr -> Bool) -> Expr -> Bool
forall b c a. (b -> c) -> (a -> b) -> a -> c
. Bool -> Expr -> Bool
forall a. Typeable a => a -> Expr -> a
eval Bool
False) ([Expr] -> Bool) -> (Expr -> [Expr]) -> Expr -> Bool
forall b c a. (b -> c) -> (a -> b) -> a -> c
. Expr -> [Expr]
gs

  gs :: Expr -> [Expr]
  gs :: Expr -> [Expr]
gs  =  Int -> [Expr] -> [Expr]
forall a. Int -> [a] -> [a]
take Int
maxTests ([Expr] -> [Expr]) -> (Expr -> [Expr]) -> Expr -> [Expr]
forall b c a. (b -> c) -> (a -> b) -> a -> c
. (Expr -> [[Expr]]) -> Expr -> [Expr]
grounds (f -> Expr -> [[Expr]]
forall f. Conjurable f => f -> Expr -> [[Expr]]
conjureTiersFor f
f)

  bss, dbss :: [[(Expr,Expr)]]
  bss :: [[(Expr, Expr)]]
bss  =  Int -> [[(Expr, Expr)]] -> [[(Expr, Expr)]]
forall a. Int -> [a] -> [a]
take Int
maxTests ([[(Expr, Expr)]] -> [[(Expr, Expr)]])
-> [[(Expr, Expr)]] -> [[(Expr, Expr)]]
forall a b. (a -> b) -> a -> b
$ (Expr -> [[Expr]]) -> Expr -> [[(Expr, Expr)]]
groundBinds (f -> Expr -> [[Expr]]
forall f. Conjurable f => f -> Expr -> [[Expr]]
conjureTiersFor f
f) Expr
ffxx
  dbss :: [[(Expr, Expr)]]
dbss  =  [[(Expr, Expr)]
bs | [(Expr, Expr)]
bs <- [[(Expr, Expr)]]
bss, Bool -> Bool
errorToFalse (Bool -> Bool) -> (Expr -> Bool) -> Expr -> Bool
forall b c a. (b -> c) -> (a -> b) -> a -> c
. Bool -> Expr -> Bool
forall a. Typeable a => a -> Expr -> a
eval Bool
False (Expr -> Bool) -> Expr -> Bool
forall a b. (a -> b) -> a -> b
$ Expr
e Expr -> [(Expr, Expr)] -> Expr
//- [(Expr, Expr)]
bs]
    where
    e :: Expr
e  =  Expr
ffxx Expr -> Expr -> Expr
-==- Expr
ffxx

-- | Conjures an implementation of a partially defined function.
--
-- Takes a 'String' with the name of a function,
-- a partially-defined function from a conjurable type,
-- and a list of building blocks encoded as 'Expr's.
--
-- For example, given:
--
-- > square :: Int -> Int
-- > square 0  =  0
-- > square 1  =  1
-- > square 2  =  4
-- >
-- > primitives :: [Expr]
-- > primitives =
-- >   [ val (0::Int)
-- >   , val (1::Int)
-- >   , value "+" ((+) :: Int -> Int -> Int)
-- >   , value "*" ((*) :: Int -> Int -> Int)
-- > ]
--
-- The conjure function does the following:
--
-- > > conjure "square" square primitives
-- > square :: Int -> Int
-- > -- testing 3 combinations of argument values
-- > -- looking through 3 candidates of size 1
-- > -- looking through 3 candidates of size 2
-- > -- looking through 5 candidates of size 3
-- > square x  =  x * x
--
-- The primitives list is defined with 'val' and 'value'.
conjure :: Conjurable f => String -> f -> [Expr] -> IO ()
conjure :: String -> f -> [Expr] -> IO ()
conjure  =  Args -> String -> f -> [Expr] -> IO ()
forall f. Conjurable f => Args -> String -> f -> [Expr] -> IO ()
conjureWith Args
args

-- | Like 'conjure' but allows setting the maximum size of considered expressions
--   instead of the default value of 9.
--
-- > conjureWithMaxSize 10 "function" function [...]
conjureWithMaxSize :: Conjurable f => Int -> String -> f -> [Expr] -> IO ()
conjureWithMaxSize :: Int -> String -> f -> [Expr] -> IO ()
conjureWithMaxSize Int
sz  =  Args -> String -> f -> [Expr] -> IO ()
forall f. Conjurable f => Args -> String -> f -> [Expr] -> IO ()
conjureWith Args
args
                       {  maxSize :: Int
maxSize = Int
sz
                       ,  maxEquationSize :: Int
maxEquationSize = Int -> Int -> Int
forall a. Ord a => a -> a -> a
min Int
sz (Args -> Int
maxEquationSize Args
args)
                       }

-- | Like 'conjure' but allows setting options through 'Args'/'args'.
--
-- > conjureWith args{maxSize = 11} "function" function [...]
conjureWith :: Conjurable f => Args -> String -> f -> [Expr] -> IO ()
conjureWith :: Args -> String -> f -> [Expr] -> IO ()
conjureWith Args
args String
nm f
f [Expr]
es  =  do
  Expr -> IO ()
forall a. Show a => a -> IO ()
print (String -> f -> Expr
forall a. Typeable a => String -> a -> Expr
var ([String] -> String
forall a. [a] -> a
head ([String] -> String) -> [String] -> String
forall a b. (a -> b) -> a -> b
$ String -> [String]
words String
nm) f
f)
  String -> IO ()
putStrLn (String -> IO ()) -> String -> IO ()
forall a b. (a -> b) -> a -> b
$ String
"-- testing " String -> String -> String
forall a. [a] -> [a] -> [a]
++ Int -> String
forall a. Show a => a -> String
show ([Expr] -> Int
forall (t :: * -> *) a. Foldable t => t a -> Int
length [Expr]
ts) String -> String -> String
forall a. [a] -> [a] -> [a]
++ String
" combinations of argument values"
  Integer -> [([Expr], [Expr])] -> IO ()
forall (t :: * -> *) t a.
(Foldable t, Show t, Num t) =>
t -> [([Expr], t a)] -> IO ()
pr Integer
1 [([Expr], [Expr])]
rs
  where
  pr :: t -> [([Expr], t a)] -> IO ()
pr t
n []  =  String -> IO ()
putStrLn (String -> IO ()) -> String -> IO ()
forall a b. (a -> b) -> a -> b
$ String
"cannot conjure"
  pr t
n (([Expr]
is,t a
es):[([Expr], t a)]
rs)  =  do
    String -> IO ()
putStrLn (String -> IO ()) -> String -> IO ()
forall a b. (a -> b) -> a -> b
$ String
"-- looking through " String -> String -> String
forall a. [a] -> [a] -> [a]
++ Int -> String
forall a. Show a => a -> String
show (t a -> Int
forall (t :: * -> *) a. Foldable t => t a -> Int
length t a
es) String -> String -> String
forall a. [a] -> [a] -> [a]
++ String
" candidates of size " String -> String -> String
forall a. [a] -> [a] -> [a]
++ t -> String
forall a. Show a => a -> String
show t
n
    case [Expr]
is of
      []     ->  t -> [([Expr], t a)] -> IO ()
pr (t
nt -> t -> t
forall a. Num a => a -> a -> a
+t
1) [([Expr], t a)]
rs
      (Expr
i:[Expr]
_)  ->  do String -> IO ()
putStrLn (String -> IO ()) -> String -> IO ()
forall a b. (a -> b) -> a -> b
$ Expr -> String
showEq Expr
i
                    String -> IO ()
putStrLn String
""
  rs :: [([Expr], [Expr])]
rs  =  [[Expr]] -> [[Expr]] -> [([Expr], [Expr])]
forall a b. [a] -> [b] -> [(a, b)]
zip [[Expr]]
iss [[Expr]]
css
  ([[Expr]]
iss, [[Expr]]
css, [Expr]
ts)  =  Args -> String -> f -> [Expr] -> ([[Expr]], [[Expr]], [Expr])
forall f.
Conjurable f =>
Args -> String -> f -> [Expr] -> ([[Expr]], [[Expr]], [Expr])
conjpureWith Args
args String
nm f
f [Expr]
es
  showEq :: Expr -> String
showEq Expr
eq  =  Expr -> String
showExpr (Expr -> Expr
lhs Expr
eq) String -> String -> String
forall a. [a] -> [a] -> [a]
++ String
"  =  " String -> String -> String
forall a. [a] -> [a] -> [a]
++ Expr -> String
showExpr (Expr -> Expr
rhs Expr
eq)

candidateExprs :: Conjurable f
               => String -> f
               -> Int
               -> Int
               -> (Expr -> Expr -> Bool)
               -> [Expr]
               -> [[Expr]]
candidateExprs :: String
-> f -> Int -> Int -> (Expr -> Expr -> Bool) -> [Expr] -> [[Expr]]
candidateExprs String
nm f
f Int
sz Int
mc Expr -> Expr -> Bool
(===) [Expr]
es  =
  String
-> f
-> Int
-> Int
-> (Expr -> Expr -> Bool)
-> [[Expr]]
-> [[Expr]]
forall f.
Conjurable f =>
String
-> f
-> Int
-> Int
-> (Expr -> Expr -> Bool)
-> [[Expr]]
-> [[Expr]]
candidateExprsT String
nm f
f Int
sz Int
mc Expr -> Expr -> Bool
(===)
    [[Expr] -> [Expr]
forall a. Eq a => [a] -> [a]
nub ([Expr] -> [Expr]) -> [Expr] -> [Expr]
forall a b. (a -> b) -> a -> b
$ [Bool -> Expr
forall a. (Typeable a, Show a) => a -> Expr
val Bool
False, Bool -> Expr
forall a. (Typeable a, Show a) => a -> Expr
val Bool
True] [Expr] -> [Expr] -> [Expr]
forall a. [a] -> [a] -> [a]
++ [Expr]
es [Expr] -> [Expr] -> [Expr]
forall a. [a] -> [a] -> [a]
++ f -> [Expr]
forall f. Conjurable f => f -> [Expr]
conjureIfs f
f]

candidateExprsT :: Conjurable f
                => String -> f
                -> Int
                -> Int
                -> (Expr -> Expr -> Bool)
                -> [[Expr]]
                -> [[Expr]]
candidateExprsT :: String
-> f
-> Int
-> Int
-> (Expr -> Expr -> Bool)
-> [[Expr]]
-> [[Expr]]
candidateExprsT String
nm f
f Int
sz Int
mc Expr -> Expr -> Bool
(===) [[Expr]]
ess  =  [[Expr]] -> [[Expr]]
expressionsT ([[Expr]] -> [[Expr]]) -> [[Expr]] -> [[Expr]]
forall a b. (a -> b) -> a -> b
$ [Expr
efExpr -> [Expr] -> [Expr]
forall a. a -> [a] -> [a]
:[Expr]
exs] [[Expr]] -> [[Expr]] -> [[Expr]]
forall a. [[a]] -> [[a]] -> [[a]]
\/ [[Expr]]
ess
  where
  (Expr
ef:[Expr]
exs)  =  Expr -> [Expr]
unfoldApp (Expr -> [Expr]) -> Expr -> [Expr]
forall a b. (a -> b) -> a -> b
$ String -> f -> Expr
forall f. Conjurable f => String -> f -> Expr
canonicalVarApplication String
nm f
f
  thy :: Thy
thy  =  (Expr -> Expr -> Bool) -> Int -> [[Expr]] -> Thy
theoryFromAtoms Expr -> Expr -> Bool
(===) Int
sz ([[Expr]] -> Thy) -> [[Expr]] -> Thy
forall a b. (a -> b) -> a -> b
$ [f -> [Expr]
forall f. Conjurable f => f -> [Expr]
conjureHoles f
f] [[Expr]] -> [[Expr]] -> [[Expr]]
forall a. [[a]] -> [[a]] -> [[a]]
\/ [[Expr]]
ess
  expressionsT :: [[Expr]] -> [[Expr]]
expressionsT [[Expr]]
ds  =  (Expr -> Bool) -> [[Expr]] -> [[Expr]]
forall a. (a -> Bool) -> [[a]] -> [[a]]
filterT (\Expr
e -> (Expr -> Bool) -> [Expr] -> Int
forall a. (a -> Bool) -> [a] -> Int
count (Expr -> Expr -> Bool
forall a. Eq a => a -> a -> Bool
== Expr
ef) (Expr -> [Expr]
vars Expr
e) Int -> Int -> Bool
forall a. Ord a => a -> a -> Bool
<= Int
mc)
                   ([[Expr]] -> [[Expr]]) -> [[Expr]] -> [[Expr]]
forall a b. (a -> b) -> a -> b
$  (Expr -> Bool) -> [[Expr]] -> [[Expr]]
forall a. (a -> Bool) -> [[a]] -> [[a]]
filterT (Thy -> Expr -> Bool
isRootNormalE Thy
thy)
                   ([[Expr]] -> [[Expr]]) -> [[Expr]] -> [[Expr]]
forall a b. (a -> b) -> a -> b
$  [[Expr]]
ds [[Expr]] -> [[Expr]] -> [[Expr]]
forall a. [[a]] -> [[a]] -> [[a]]
\/ ([[Expr]] -> [[Expr]]
forall a. [[a]] -> [[a]]
delay ([[Expr]] -> [[Expr]]) -> [[Expr]] -> [[Expr]]
forall a b. (a -> b) -> a -> b
$ (Expr -> Expr -> Maybe Expr) -> [[Expr]] -> [[Expr]] -> [[Expr]]
forall a b c. (a -> b -> Maybe c) -> [[a]] -> [[b]] -> [[c]]
productMaybeWith Expr -> Expr -> Maybe Expr
($$) [[Expr]]
es [[Expr]]
es)
    where
    es :: [[Expr]]
es = [[Expr]] -> [[Expr]]
expressionsT [[Expr]]
ds

lhs, rhs :: Expr -> Expr
lhs :: Expr -> Expr
lhs (((Value String
"==" Dynamic
_) :$ Expr
e) :$ Expr
_)  =  Expr
e
rhs :: Expr -> Expr
rhs (((Value String
"==" Dynamic
_) :$ Expr
_) :$ Expr
e)  =  Expr
e

compareResult :: (Int,Expr) -> (Int,Expr) -> Ordering
compareResult :: (Int, Expr) -> (Int, Expr) -> Ordering
compareResult (Int
n1,Expr
e1) (Int
n2,Expr
e2)  =  Int
n2 Int -> Int -> Ordering
forall a. Ord a => a -> a -> Ordering
`compare` Int
n1
                               Ordering -> Ordering -> Ordering
forall a. Semigroup a => a -> a -> a
<> Expr
e1 Expr -> Expr -> Ordering
`compareSimplicity` Expr
e2

(%) :: Int -> Int -> Int
Int
x % :: Int -> Int -> Int
% Int
y  =  Int
x Int -> Int -> Int
forall a. Num a => a -> a -> a
* Int
100 Int -> Int -> Int
forall a. Integral a => a -> a -> a
`div` Int
y