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"""
Classic cart-pole system implemented by Rich Sutton et al.
Copied from http://incompleteideas.net/sutton/book/code/pole.c
permalink: https://perma.cc/C9ZM-652R

Edit reset in order to change initial stae to down low


"""

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print("Success!")
import pickle
favorite_color = { "lion": "yellow", "kitty": "red" }
import os
os.mkdir("logs")
pickle.dump( favorite_color, open( "./logs/save.p", "wb" ) )
print("it good b")

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-- state of an oscillator
data SHOState = X | P deriving (Show, Enum, Bounded, Eq, Ord)
data Control = F  deriving (Show, Enum, Bounded, Eq, Ord)
-- Costate newtype wrapper
newtype Co a = Co a deriving (Show, Enum, Bounded, Eq, Ord)

type M = Matrix Double
dynamics :: forall x u. (BEnum x, BEnum u) =>  Matrix Double -> Matrix Double ->  
  HLinRel (Either x u) x

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type HLinRel2D u d l r = HLinRel (Either u l) (Either d r)


{-
A stencil  of 2d resistors for tiling


          u
          /
          \

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#direct from https://en.wikipedia.org/wiki/Batcher_odd%E2%80%93even_mergesort
def oddeven_merge(lo: int, hi: int, r: int):
    step = r * 2
    if step < hi - lo:
        yield from oddeven_merge(lo, hi, step)
        yield from oddeven_merge(lo + r, hi, step)
        yield from [(i, i + r) for i in range(lo + r, hi - r, step)]
    else:
        yield (lo, lo + r)

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def babylonian(x):
    res = 1
    for i in range(7):
        res = (x / res + res) / 2
    return res    

x, y = Reals("x y")
prove(Implies(And(y**2 == x, y >= 0, 0 <= x, x <= 10), babylonian(x) - y <= 0.01))

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import cvxpy as cvx
import numpy as np
import sos
import sympy as sy
import matplotlib.pyplot as plt
#raised chebyehve
t = sy.symbols("t")

N = 5
# seems like even N becomes infeasible.

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trivial = BoolVal(True)

def top1(x,y): # top is the full relation,
    return trivial
def bottom1(x,y):
    return BoolVal(False)

def top2(sorty):
    def res(x):
        y = FreshConst(sorty)

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#A*x = 0
using LinearAlgebra
struct HRep{T}
   n :: Int64 #input size
   A :: AbstractArray{T}
end
struct VRep{T}
   n :: Int64 #input size
   A :: AbstractArray{T}
end