Examples - HLola

Specifications

A Past-Linear Temporal Logic (PLTL) property for a sender/receiver model taken from Bounded Verification of Past LTL:

G (sender.state = waitForAck => Y (H sender.state != waitForAck))

which states that, it Globally holds that if the sender is waitingForAck, then Yesterday (i.e. at the previous instant), Historically it held that the sender state was not waitingForAck. In other words, the sender waits for acknowledgement at most once during the execution.

The only input stream is the state of the sender at each instant.

The only output stream is the value of the property at each instant.

format CSV
use library LTL

#HASKELL
data SenderState = Get | Send | WaitForAck deriving (Generic,Read,FromJSON,Eq)
#ENDOFHASKELL

input SenderState senderState

define Bool senderNotWaiting = senderState[now] /== 'WaitForAck

output Bool property = let
  senderWaitingAck   = senderState[now] === 'WaitForAck
  startedWaiting     = yesterday (historically senderNotWaiting)
  in senderWaitingAck `implies` startedWaiting[now]

senderState
senderNotWaiting,prop
False,False
False,False
False,False
False,False
False,False
False,False
False,False
False,False
False,False
False,False

format JSON
use library LTL

#HASKELL
data SenderState = Get | Send | WaitForAck deriving (Generic,Read,FromJSON,Eq)
#ENDOFHASKELL

input SenderState senderState

define Bool senderNotWaiting = senderState[now] /== 'WaitForAck

output Bool property = let
  senderWaitingAck   = senderState[now] === 'WaitForAck
  startedWaiting     = yesterday (historically senderNotWaiting)
  in senderWaitingAck `implies` startedWaiting[now]

{"senderState": "Get"}
{"senderState": "Get"}
{"senderState": "Get"}
{"senderState": "Send"}
{"senderState": "Send"}
{"senderState": "Send"}
{"senderState": "WaitForAck"}
{"senderState": "Get"}
{"senderState": "Get"}
{"senderState": "Get"}
{"senderState": "Send"}
{"senderState": "Send"}
{"senderState": "WaitForAck"}
{"senderState": "WaitForAck"}
{"senderState": "WaitForAck"}
{"senderState": "WaitForAck"}
{"senderState": "Send"}
{"senderState": "Send"}
{"senderState": "Send"}
{"senderState": "Send"}
{"senderState": "Get"}
{"senderState": "Get"}
{"senderState": "Get"}
{"senderState": "Send"}
{"senderState": "Send"}
{"senderState": "WaitForAck"}
{"senderState": "WaitForAck"}
{"senderState": "WaitForAck"}
{"senderState": "WaitForAck"}
{"senderState": "Get"}
{"senderState": "Get"}
{"senderState": "Get"}
{"senderState": "Get"}
{"senderState": "Get"}
{"senderState": "WaitForAck"}
{"senderState": "WaitForAck"}
{"property":true}
{"property":true}
{"property":true}
{"property":true}
{"property":true}
{"property":true}
{"property":true}
{"property":true}
{"property":true}
{"property":true}
{"property":true}
{"property":true}
{"property":false}
{"property":false}
{"property":false}
{"property":false}
{"property":true}
{"property":true}
{"property":true}
{"property":true}
{"property":true}
{"property":true}
{"property":true}
{"property":true}
{"property":true}
{"property":false}
{"property":false}
{"property":false}
{"property":false}
{"property":true}
{"property":true}
{"property":true}
{"property":true}
{"property":true}
{"property":false}
{"property":false}

A Metric Temporal Logic (MTL) property to establish deadlines between environment events and the corresponding system responses taken from Some Recent Results in Metric Temporal Logic:

G (alarm => (F[0,10] allclear || F[10,10] shutdown))

The property assesses that an alarm is followed by a shutdown event in exactly 10 time units unless all clear is sounded first.

The only input stream is the event happening at each instant.

The only output stream is the value of the property at each instant.

format CSV
use library MTL

#HASKELL
data Event
    = Alarm
    | AllClear
    | Shutdown
  deriving (Generic,Read,FromJSON,Eq)
#ENDOFHASKELL

input Event event

define Bool allClear = event [now] === 'AllClear
define Bool shutdown = event [now] === 'Shutdown
define Bool alarm = event [now] === 'Alarm

output Bool property = let
  willClear = eventually (0,10) allClear
  willShutdown = eventually (10,10) shutdown
  in alarm [now] `implies` (willClear [now] || willShutdown [now])

event

Alarm

AllClear

Alarm

AllClear

Alarm

property

True

False

format JSON
use library MTL

#HASKELL
data Event
    = Alarm
    | AllClear
    | Shutdown
  deriving (Generic,Read,FromJSON,Eq)
#ENDOFHASKELL

input Event event

define Bool allClear = event [now] === 'AllClear
define Bool shutdown = event [now] === 'Shutdown
define Bool alarm = event [now] === 'Alarm

output Bool property = let
  willClear = eventually (0,10) allClear
  willShutdown = eventually (10,10) shutdown
  in alarm [now] `implies` (willClear [now] || willShutdown [now])

{"event": "Alarm"}
{"event": "Alarm"}
{"event": "Alarm"}
{"event": "Alarm"}
{"event": "AllClear"}
{"event": "Alarm"}
{"event": "Alarm"}
{"event": "Alarm"}
{"event": "Alarm"}
{"event": "Alarm"}
{"event": "Alarm"}
{"event": "Alarm"}
{"event": "Alarm"}
{"event": "AllClear"}
{"event": "AllClear"}
{"event": "AllClear"}
{"event": "AllClear"}
{"event": "AllClear"}
{"event": "Alarm"}
{"event": "Alarm"}
{"event": "Alarm"}
{"event": "Alarm"}
{"event": "Alarm"}
{"event": "Alarm"}
{"event": "Alarm"}
{"event": "Alarm"}
{"event": "Alarm"}
{"event": "Alarm"}
{"event": "Alarm"}
{"event": "Alarm"}
{"event": "Alarm"}
{"property":true}
{"property":true}
{"property":true}
{"property":true}
{"property":true}
{"property":true}
{"property":true}
{"property":true}
{"property":true}
{"property":true}
{"property":true}
{"property":true}
{"property":true}
{"property":true}
{"property":true}
{"property":true}
{"property":true}
{"property":true}
{"property":false}
{"property":false}
{"property":false}
{"property":false}
{"property":false}
{"property":false}
{"property":false}
{"property":false}
{"property":false}
{"property":false}
{"property":false}
{"property":false}
{"property":false}

TradingView is an online charting platform for stock exchange, which offers a series-oriented language to create customized studies and signals (called Pinescript) and run them in the company servers.

We have implemented the indicators of Pinescript in HLola as a library, and we show the implementation of a trading strategy using the HLola Pinescript library.

The input streams are the close and high values of a stock at each day.

The output streams indicate how much stock to buy or sell every day.

format CSV
use library Pinescript

#HASKELL
buy_size  = 10
sell_size = 10
#ENDOFHASKELL

input Double close
input Double high

define Bool buy = ema18 [now] < high [now] && macd_buy_sig [now]
define Bool sell = not (macd_buy_sig [-1|'False]) && macd_sell_sig [now] && positionsize [-1|0] > 0

output Double positionsize = positionsize [-1|0] +
  if buy [now]  then buy_size  else 0 -
  if sell [now] then sell_size else 0

define Double ema18 = ema close 18 [now]
define Double signalLine = macd_signal close [now]
define Double macdLine = macd close [now]
define Bool macd_sell_sig = crossover signalLine macdLine [now]
define Bool macd_buy_sig = crossover macdLine signalLine [now]

00,129.04
44,124.81
49,125.01
99,126.52
18,124.82
79,125.86
87,124.37
39,118.28
16,115.71
00,115.56
09,114.61
00,114.91
04,115.01
28,113.01
48,109.38
78,112.73
68,111.11
41,113.90
39,110.06
79,109.67
64,108.94
42,106.26
30,96.19
23,95.04
55,93.25
90,94.81
97,92.61
08,92.85
97,97.27
25,97.00
50,98.36
15,96.33
40,96.52
25,97.72
25,97.06
96,95.48
98,95.92
32,95.75
38,95.34
65,93.17
94,93.46
62,91.03
84,91.03
50,91.20
54,90.44
33,88.41
25,91.21
20,90.01
10,91.63
86,89.72
14,87.43
36,87.93
85,87.90
30,88.02
42,85.75
95,84.70
76,83.97
69,88.21
40,86.00
40,83.36
94,82.88
40,80.58
55,81.28
86,80.83
59,80.46
29,79.49
86,79.56
68,79.53
06,79.18
81,79.72
22,79.21
88,79.81
63,78.29
13,78.74
97,76.93
45,77.39
99,76.91
92,77.85
26,78.75
59,77.53
29,75.93
81,75.16
25,74.39
42,73.29
75,72.27
63,73.45
42,71.93
46,69.64
14,70.79
75,70.74
44,68.76
47,69.03
31,67.09
42,69.23
74,70.70
05,71.67
58,71.11
06,71.76
43,68.31
52,67.00
84,66.52
93,64.86
78,65.62
42,60.35
29,61.23
18,60.23
62,63.57
88,63.70
97,61.94
67,64.61
56,61.38
92,61.72
13,56.09
96,57.31
21,61.19
50,61.67
40,63.22
77,60.55
98,69.49
50,62.06
31,68.86
61,71.33
52,66.54
71,72.26
89,73.23
85,75.68
00,72.33
36,74.70
60,68.34
50,68.38
47,73.16
63,72.02
04,74.54
11,78.26
16,80.07
14,80.90
94,79.75
50,81.24
56,81.22
81,81.80
97,79.90
39,80.39
85,80.01
31,81.30
19,80.36
91,79.71
37,77.17
67,77.38
02,80.97
96,81.08
60,79.42
94,77.24
83,79.58
89,79.81
00,79.43
75,79.14
68,79.68
93,78.81
88,77.83
39,78.17
27,79.24
17,77.58
61,77.41
11,75.80
22,74.60
99,74.95
14,74.36
15,75.09
positionsize

format JSON
use library Pinescript

#HASKELL
buy_size  = 10
sell_size = 10
#ENDOFHASKELL

input Double close
input Double high

define Bool buy = ema18 [now] < high [now] && macd_buy_sig [now]
define Bool sell = not (macd_buy_sig [-1|'False]) && macd_sell_sig [now] && positionsize [-1|0] > 0

output Double positionsize = positionsize [-1|0] +
  if buy [now]  then buy_size  else 0 -
  if sell [now] then sell_size else 0

define Double ema18 = ema close 18 [now]
define Double signalLine = macd_signal close [now]
define Double macdLine = macd close [now]
define Bool macd_sell_sig = crossover signalLine macdLine [now]
define Bool macd_buy_sig = crossover macdLine signalLine [now]

{"high": 131.00, "close":129.04}
{"high": 126.44, "close":124.81}
{"high": 127.49, "close":125.01}
{"high": 126.99, "close":126.52}
{"high": 125.18, "close":124.82}
{"high": 128.79, "close":125.86}
{"high": 124.87, "close":124.37}
{"high": 118.39, "close":118.28}
{"high": 117.16, "close":115.71}
{"high": 116.00, "close":115.56}
{"high": 116.09, "close":114.61}
{"high": 115.00, "close":114.91}
{"high": 116.04, "close":115.01}
{"high": 113.28, "close":113.01}
{"high": 112.48, "close":109.38}
{"high": 113.78, "close":112.73}
{"high": 113.68, "close":111.11}
{"high": 114.41, "close":113.90}
{"high": 110.39, "close":110.06}
{"high": 110.79, "close":109.67}
{"high": 111.64, "close":108.94}
{"high": 106.42, "close":106.26}
{"high": 96.30, "close":96.19}
{"high": 95.23, "close":95.04}
{"high": 94.55, "close":93.25}
{"high": 94.90, "close":94.81}
{"high": 92.97, "close":92.61}
{"high": 97.08, "close":92.85}
{"high": 97.97, "close":97.27}
{"high": 99.25, "close":97.00}
{"high": 98.50, "close":98.36}
{"high": 97.15, "close":96.33}
{"high": 97.40, "close":96.52}
{"high": 99.25, "close":97.72}
{"high": 97.25, "close":97.06}
{"high": 99.96, "close":95.48}
{"high": 95.98, "close":95.92}
{"high": 96.32, "close":95.75}
{"high": 95.38, "close":95.34}
{"high": 94.65, "close":93.17}
{"high": 93.94, "close":93.46}
{"high": 92.62, "close":91.03}
{"high": 91.84, "close":91.03}
{"high": 91.50, "close":91.20}
{"high": 90.54, "close":90.44}
{"high": 91.33, "close":88.41}
{"high": 91.25, "close":91.21}
{"high": 92.20, "close":90.01}
{"high": 93.10, "close":91.63}
{"high": 89.86, "close":89.72}
{"high": 89.14, "close":87.43}
{"high": 88.36, "close":87.93}
{"high": 88.85, "close":87.90}
{"high": 88.30, "close":88.02}
{"high": 86.42, "close":85.75}
{"high": 86.95, "close":84.70}
{"high": 87.76, "close":83.97}
{"high": 88.69, "close":88.21}
{"high": 86.40, "close":86.00}
{"high": 83.40, "close":83.36}
{"high": 82.94, "close":82.88}
{"high": 81.40, "close":80.58}
{"high": 81.55, "close":81.28}
{"high": 80.86, "close":80.83}
{"high": 80.59, "close":80.46}
{"high": 80.29, "close":79.49}
{"high": 80.86, "close":79.56}
{"high": 79.68, "close":79.53}
{"high": 81.06, "close":79.18}
{"high": 79.81, "close":79.72}
{"high": 80.22, "close":79.21}
{"high": 79.88, "close":79.81}
{"high": 79.63, "close":78.29}
{"high": 79.13, "close":78.74}
{"high": 76.97, "close":76.93}
{"high": 77.45, "close":77.39}
{"high": 78.99, "close":76.91}
{"high": 79.92, "close":77.85}
{"high": 79.26, "close":78.75}
{"high": 77.59, "close":77.53}
{"high": 76.29, "close":75.93}
{"high": 75.81, "close":75.16}
{"high": 75.25, "close":74.39}
{"high": 73.42, "close":73.29}
{"high": 74.75, "close":72.27}
{"high": 73.63, "close":73.45}
{"high": 72.42, "close":71.93}
{"high": 71.46, "close":69.64}
{"high": 71.14, "close":70.79}
{"high": 70.75, "close":70.74}
{"high": 70.44, "close":68.76}
{"high": 69.47, "close":69.03}
{"high": 69.31, "close":67.09}
{"high": 70.42, "close":69.23}
{"high": 71.74, "close":70.70}
{"high": 72.05, "close":71.67}
{"high": 71.58, "close":71.11}
{"high": 72.06, "close":71.76}
{"high": 68.43, "close":68.31}
{"high": 67.52, "close":67.00}
{"high": 66.84, "close":66.52}
{"high": 67.93, "close":64.86}
{"high": 65.78, "close":65.62}
{"high": 61.42, "close":60.35}
{"high": 61.29, "close":61.23}
{"high": 62.18, "close":60.23}
{"high": 65.62, "close":63.57}
{"high": 63.88, "close":63.70}
{"high": 63.97, "close":61.94}
{"high": 64.67, "close":64.61}
{"high": 64.56, "close":61.38}
{"high": 61.92, "close":61.72}
{"high": 57.13, "close":56.09}
{"high": 62.96, "close":57.31}
{"high": 63.21, "close":61.19}
{"high": 62.50, "close":61.67}
{"high": 64.40, "close":63.22}
{"high": 64.77, "close":60.55}
{"high": 69.98, "close":69.49}
{"high": 67.50, "close":62.06}
{"high": 70.31, "close":68.86}
{"high": 71.61, "close":71.33}
{"high": 69.52, "close":66.54}
{"high": 72.71, "close":72.26}
{"high": 74.89, "close":73.23}
{"high": 75.85, "close":75.68}
{"high": 76.00, "close":72.33}
{"high": 75.36, "close":74.70}
{"high": 69.60, "close":68.34}
{"high": 71.50, "close":68.38}
{"high": 74.47, "close":73.16}
{"high": 75.63, "close":72.02}
{"high": 76.04, "close":74.54}
{"high": 80.11, "close":78.26}
{"high": 81.16, "close":80.07}
{"high": 81.14, "close":80.90}
{"high": 79.94, "close":79.75}
{"high": 81.50, "close":81.24}
{"high": 81.56, "close":81.22}
{"high": 81.81, "close":81.80}
{"high": 80.97, "close":79.90}
{"high": 80.39, "close":80.39}
{"high": 80.85, "close":80.01}
{"high": 81.31, "close":81.30}
{"high": 81.19, "close":80.36}
{"high": 79.91, "close":79.71}
{"high": 78.37, "close":77.17}
{"high": 80.67, "close":77.38}
{"high": 81.02, "close":80.97}
{"high": 81.96, "close":81.08}
{"high": 79.60, "close":79.42}
{"high": 77.94, "close":77.24}
{"high": 80.83, "close":79.58}
{"high": 79.89, "close":79.81}
{"high": 80.00, "close":79.43}
{"high": 79.75, "close":79.14}
{"high": 79.68, "close":79.68}
{"high": 78.93, "close":78.81}
{"high": 78.88, "close":77.83}
{"high": 79.39, "close":78.17}
{"high": 79.27, "close":79.24}
{"high": 78.17, "close":77.58}
{"high": 77.61, "close":77.41}
{"high": 76.11, "close":75.80}
{"high": 75.22, "close":74.60}
{"high": 74.99, "close":74.95}
{"high": 75.14, "close":74.36}
{"high": 75.15, "close":75.09}
{"positionsize":0}
{"positionsize":10}
{"positionsize":20}
{"positionsize":30}
{"positionsize":30}
{"positionsize":40}
{"positionsize":40}
{"positionsize":40}
{"positionsize":40}
{"positionsize":40}
{"positionsize":40}
{"positionsize":40}
{"positionsize":40}
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{"positionsize":40}
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{"positionsize":30}
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{"positionsize":20}
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{"positionsize":10}
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{"positionsize":0}
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{"positionsize":0}

This specification is an online monitor to assess two properties over the flight of an UAV in real time:

That the UAV does not fly over forbidden regions, and
That the UAV is in good position when it takes a picture.

The input streams of this specification consist of the state of the UAV at every instant and the onboard camera events to detect when a picture is being captured.

The output streams are the values of properties 1. and 2.

format JSON
use theory Geometry2D
use library Utils
use haskell Data.Maybe
use haskell Data.List

#HASKELL
data Attitude = Attitude {yaw :: Double, roll :: Double, pitch :: Double} deriving (Show,Generic,Read,FromJSON,ToJSON)
data Target   = Target {x :: Double, y :: Double, mutex :: Double, num_wp :: Double} deriving (Show,Generic,Read,FromJSON,ToJSON)
data Position = Position {x :: Double, y :: Double, alt :: Double, zone :: Double} deriving (Show,Generic,Read,FromJSON,ToJSON)
#ENDOFHASKELL

-- Input streams

input     Attitude attitude

input      Vector2 velocity

input     Position position

input       Double altitude

input       Target target

input [[[Double]]] nofly

input     [String] events_within

-- Output streams

output Bool all_ok_capturing = capturing [now] `implies`
  (height_ok [now] && near [now] && roll_ok [now] && pitch_ok [now])

output Bool flying_in_safe_zones = 'isNothing (flying_in_poly [now])

output (Maybe Double) depth_into_poly = let
  mSides = '(fmap polygonSides) (flying_in_poly [now])
  distance_from_pos = 'shortestDist (filtered_pos [now])
  in 2'fmap distance_from_pos mSides
  where
  shortestDist x = minimum.map (distancePointSegment x)

-- Intermediate streams

define Bool capturing = let
  has_capture = '(elem "capture") (events_within [now])
  in has_capture || open_capture [-1|'False]

define Bool open_capture = let
  relevant_events = '(filter isrelevant) (events_within [now])
  in 2'lastIsCapture (open_capture [-1|'False]) relevant_events
  where
  lastIsCapture dflt [] = dflt
  lastIsCapture _ xs = last xs == "capture"
  isrelevant = flip elem ["capture", "yes_person", "no_person"]

-- x_filt[i] = ( x[i] + tau * ( - x_filt[i-2] / 2 + 2 * x_filt[i-1] ) ) / (1.5* tau + 1)
define Double filtered_pos_component <(Position -> Double) accessor> <String nm> = let
  dt      = 0.1
  tau     = 6*dt
  _this   = filtered_pos_component accessor nm
  nowcomp = 'accessor (position [now])
  in if instantN [now] < 3 then nowcomp else (nowcomp + tau * (2 * _this [-1|0] - _this [-2|0] / 2)) / (1.5 * tau + 1)

define Double filtered_pos_x = filtered_pos_component x "x" [now]

define Double filtered_pos_y = filtered_pos_component y "y" [now]

define Double filtered_pos_alt = filtered_pos_component alt "alt" [now]

define Point2 filtered_pos = 'P (filtered_pos_x [now]) (filtered_pos_y [now])

define Bool near = let
  target_pos = 'targetToPoint (target [now])
  in 2'distance (filtered_pos [now]) target_pos < 1
  where
  targetToPoint (Target x y _ _) = P x y

define Bool height_ok = filtered_pos_alt [now] > 0

define Bool roll_ok = '(abs.roll) (attitude [now]) < 0.0523

define Bool pitch_ok = '(abs.pitch) (attitude [now]) < 0.0523

define [Polygon] no_fly_polys = no_fly_polys [-1|'(map.map$createPoint) (nofly [now])]
  where
  createPoint [x,y] = P x y

-- We assume that no-fly zones are non-overlapping
define (Maybe Polygon) flying_in_poly = let
  position_in_poly = 'pointInPoly (filtered_pos [now])
  in
  2'find position_in_poly (no_fly_polys [now])

{"events_within": ["initial_config", "takeoff", "sort_locations", "takeoff_ended", "has_next", "yes_next", "go_next", "sort_locations"], "attitude": {"yaw": 0.17313674092292786, "roll": 0.007439206819981337, "pitch": 0.13648805022239685}, "target": {"y": 5438008.23911845, "x": 322870.52179215587, "mutex": 1.0, "num_wp": 0.0}, "timestamp": 1601912482, "velocity": {"y": 23.22, "x": 4.46}, "target_dir": {"y": 14.161232273443602, "x": 26.55765673518181}, "position": {"y": 5438034.7967751855, "x": 322856.3605598824, "alt": 39.958, "zone": 19.0}, "altitude": 39.958, "nofly": [[[322796.16375333746, 5438250.825848085], [322678.1268212263, 5437956.05416451], [323075.4336759561, 5437889.640751129], [323001.00459137175, 5438272.032294986], [322796.16375333746, 5438250.825848085]]], "wind": {"speed_z": 0.0, "direction": 16.148731231689453, "speed": 1.8658108711242676}}
{"events_within": [], "attitude": {"yaw": 0.17313674092292786, "roll": 0.007439206819981337, "pitch": 0.13648805022239685}, "target": {"y": 5438008.23911845, "x": 322870.52179215587, "mutex": 1.0, "num_wp": 0.0}, "timestamp": 1601912482, "velocity": {"y": 23.22, "x": 4.46}, "target_dir": {"y": 14.161232273443602, "x": 26.55765673518181}, "position": {"y": 5438034.7967751855, "x": 322856.3605598824, "alt": 39.958, "zone": 19.0}, "altitude": 39.958, "nofly": [[[322796.16375333746, 5438250.825848085], [322678.1268212263, 5437956.05416451], [323075.4336759561, 5437889.640751129], [323001.00459137175, 5438272.032294986], [322796.16375333746, 5438250.825848085]]], "wind": {"speed_z": 0.0, "direction": 16.148731231689453, "speed": 1.8658108711242676}}
{"events_within": [], "attitude": {"yaw": 0.16149266064167023, "roll": -0.13158294558525085, "pitch": 0.06372390687465668}, "target": {"y": 5438008.23911845, "x": 322870.52179215587, "mutex": 1.0, "num_wp": 0.0}, "timestamp": 1601912482, "velocity": {"y": 23.77, "x": 4.37}, "target_dir": {"y": 14.161232273443602, "x": 26.55765673518181}, "position": {"y": 5438047.914024658, "x": 322858.55107034865, "alt": 42.688, "zone": 19.0}, "altitude": 42.688, "nofly": [[[322796.16375333746, 5438250.825848085], [322678.1268212263, 5437956.05416451], [323075.4336759561, 5437889.640751129], [323001.00459137175, 5438272.032294986], [322796.16375333746, 5438250.825848085]]], "wind": {"speed_z": 0.0, "direction": 16.148731231689453, "speed": 1.8658108711242676}}
{"events_within": [], "attitude": {"yaw": 0.16149266064167023, "roll": -0.13158294558525085, "pitch": 0.06372390687465668}, "target": {"y": 5438008.23911845, "x": 322870.52179215587, "mutex": 1.0, "num_wp": 0.0}, "timestamp": 1601912482, "velocity": {"y": 23.77, "x": 4.37}, "target_dir": {"y": 14.161232273443602, "x": 26.55765673518181}, "position": {"y": 5438047.914024658, "x": 322858.55107034865, "alt": 42.688, "zone": 19.0}, "altitude": 42.688, "nofly": [[[322796.16375333746, 5438250.825848085], [322678.1268212263, 5437956.05416451], [323075.4336759561, 5437889.640751129], [323001.00459137175, 5438272.032294986], [322796.16375333746, 5438250.825848085]]], "wind": {"speed_z": 0.0, "direction": 16.591218948364258, "speed": 1.880706548690796}}
{"events_within": [], "attitude": {"yaw": 0.1702425479888916, "roll": -0.16701115667819977, "pitch": 0.05536281690001488}, "target": {"y": 5438008.23911845, "x": 322870.52179215587, "mutex": 1.0, "num_wp": 0.0}, "timestamp": 1601912482, "velocity": {"y": 23.84, "x": 4.04}, "target_dir": {"y": 14.161232273443602, "x": 26.55765673518181}, "position": {"y": 5438052.652885669, "x": 322859.2751392252, "alt": 43.44, "zone": 19.0}, "altitude": 43.44, "nofly": [[[322796.16375333746, 5438250.825848085], [322678.1268212263, 5437956.05416451], [323075.4336759561, 5437889.640751129], [323001.00459137175, 5438272.032294986], [322796.16375333746, 5438250.825848085]]], "wind": {"speed_z": 0.0, "direction": 16.591218948364258, "speed": 1.880706548690796}}
{"events_within": [], "attitude": {"yaw": 0.1702425479888916, "roll": -0.16701115667819977, "pitch": 0.05536281690001488}, "target": {"y": 5438008.23911845, "x": 322870.52179215587, "mutex": 1.0, "num_wp": 0.0}, "timestamp": 1601912482, "velocity": {"y": 23.84, "x": 4.04}, "target_dir": {"y": 14.161232273443602, "x": 26.55765673518181}, "position": {"y": 5438052.652885669, "x": 322859.2751392252, "alt": 43.44, "zone": 19.0}, "altitude": 43.44, "nofly": [[[322796.16375333746, 5438250.825848085], [322678.1268212263, 5437956.05416451], [323075.4336759561, 5437889.640751129], [323001.00459137175, 5438272.032294986], [322796.16375333746, 5438250.825848085]]], "wind": {"speed_z": 0.0, "direction": 16.88837432861328, "speed": 1.892228126525879}}
{"events_within": [], "attitude": {"yaw": 0.1702425479888916, "roll": -0.16701115667819977, "pitch": 0.05536281690001488}, "target": {"y": 5438008.23911845, "x": 322870.52179215587, "mutex": 1.0, "num_wp": 1.0}, "timestamp": 1601912482, "velocity": {"y": 23.84, "x": 4.04}, "target_dir": {"y": 14.161232273443602, "x": 26.55765673518181}, "position": {"y": 5438052.652885669, "x": 322859.2751392252, "alt": 43.44, "zone": 19.0}, "altitude": 43.44, "nofly": [[[322796.16375333746, 5438250.825848085], [322678.1268212263, 5437956.05416451], [323075.4336759561, 5437889.640751129], [323001.00459137175, 5438272.032294986], [322796.16375333746, 5438250.825848085]]], "wind": {"speed_z": 0.0, "direction": 16.88837432861328, "speed": 1.892228126525879}}
{"events_within": [], "attitude": {"yaw": 0.1676052063703537, "roll": -0.10290601849555969, "pitch": 0.05071267858147621}, "target": {"y": 5438008.23911845, "x": 322870.52179215587, "mutex": 1.0, "num_wp": 1.0}, "timestamp": 1601912482, "velocity": {"y": 23.78, "x": 3.91}, "target_dir": {"y": 14.161232273443602, "x": 26.55765673518181}, "position": {"y": 5438058.3829094805, "x": 322860.10101082723, "alt": 44.287, "zone": 19.0}, "altitude": 44.287, "nofly": [[[322796.16375333746, 5438250.825848085], [322678.1268212263, 5437956.05416451], [323075.4336759561, 5437889.640751129], [323001.00459137175, 5438272.032294986], [322796.16375333746, 5438250.825848085]]], "wind": {"speed_z": 0.0, "direction": 16.88837432861328, "speed": 1.892228126525879}}
{"events_within": [], "attitude": {"yaw": 0.16742002964019775, "roll": 0.008988788351416588, "pitch": 0.04925258830189705}, "target": {"y": 5438008.23911845, "x": 322870.52179215587, "mutex": 1.0, "num_wp": 1.0}, "timestamp": 1601912482, "velocity": {"y": 23.79, "x": 3.79}, "target_dir": {"y": 14.161232273443602, "x": 26.55765673518181}, "position": {"y": 5438058.3829094805, "x": 322860.10101082723, "alt": 45.164, "zone": 19.0}, "altitude": 45.164, "nofly": [[[322796.16375333746, 5438250.825848085], [322678.1268212263, 5437956.05416451], [323075.4336759561, 5437889.640751129], [323001.00459137175, 5438272.032294986], [322796.16375333746, 5438250.825848085]]], "wind": {"speed_z": 0.0, "direction": 16.88837432861328, "speed": 1.892228126525879}}
{"events_within": [], "attitude": {"yaw": 0.16742002964019775, "roll": 0.008988788351416588, "pitch": 0.04925258830189705}, "target": {"y": 5438008.23911845, "x": 322870.52179215587, "mutex": 1.0, "num_wp": 1.0}, "timestamp": 1601912482, "velocity": {"y": 23.79, "x": 3.79}, "target_dir": {"y": 14.161232273443602, "x": 26.55765673518181}, "position": {"y": 5438064.536043862, "x": 322860.9669576193, "alt": 45.164, "zone": 19.0}, "altitude": 45.164, "nofly": [[[322796.16375333746, 5438250.825848085], [322678.1268212263, 5437956.05416451], [323075.4336759561, 5437889.640751129], [323001.00459137175, 5438272.032294986], [322796.16375333746, 5438250.825848085]]], "wind": {"speed_z": 0.0, "direction": 16.98767852783203, "speed": 1.8991962671279907}}
{"events_within": [], "attitude": {"yaw": 0.16742002964019775, "roll": 0.008988788351416588, "pitch": 0.04925258830189705}, "target": {"y": 5438008.23911845, "x": 322870.52179215587, "mutex": 1.0, "num_wp": 1.0}, "timestamp": 1601912482, "velocity": {"y": 23.79, "x": 3.79}, "target_dir": {"y": 14.161232273443602, "x": 26.55765673518181}, "position": {"y": 5438064.536043862, "x": 322860.9669576193, "alt": 45.164, "zone": 19.0}, "altitude": 45.164, "nofly": [[[322796.16375333746, 5438250.825848085], [322678.1268212263, 5437956.05416451], [323075.4336759561, 5437889.640751129], [323001.00459137175, 5438272.032294986], [322796.16375333746, 5438250.825848085]]], "wind": {"speed_z": 0.0, "direction": 17.054811477661133, "speed": 1.9020949602127075}}
{"events_within": [], "attitude": {"yaw": 0.18850252032279968, "roll": 0.36402449011802673, "pitch": 0.04924868419766426}, "target": {"y": 5438008.23911845, "x": 322870.52179215587, "mutex": 1.0, "num_wp": 1.0}, "timestamp": 1601912482, "velocity": {"y": 23.76, "x": 4.73}, "target_dir": {"y": 14.161232273443602, "x": 26.55765673518181}, "position": {"y": 5438070.233778837, "x": 322861.8355756351, "alt": 45.99, "zone": 19.0}, "altitude": 45.99, "nofly": [[[322796.16375333746, 5438250.825848085], [322678.1268212263, 5437956.05416451], [323075.4336759561, 5437889.640751129], [323001.00459137175, 5438272.032294986], [322796.16375333746, 5438250.825848085]]], "wind": {"speed_z": 0.0, "direction": 17.054811477661133, "speed": 1.9020949602127075}}
{"events_within": [], "attitude": {"yaw": 0.1818120777606964, "roll": 0.39427152276039124, "pitch": 0.09566180408000946}, "target": {"y": 5438008.23911845, "x": 322870.52179215587, "mutex": 1.0, "num_wp": 1.0}, "timestamp": 1601912483, "velocity": {"y": 23.71, "x": 6.17}, "target_dir": {"y": 14.161232273443602, "x": 26.55765673518181}, "position": {"y": 5438076.374485949, "x": 322863.1046322796, "alt": 46.92, "zone": 19.0}, "altitude": 46.92, "nofly": [[[322796.16375333746, 5438250.825848085], [322678.1268212263, 5437956.05416451], [323075.4336759561, 5437889.640751129], [323001.00459137175, 5438272.032294986], [322796.16375333746, 5438250.825848085]]], "wind": {"speed_z": 0.0, "direction": 16.8132266998291, "speed": 1.914101481437683}}
{"events_within": [], "attitude": {"yaw": 0.1818120777606964, "roll": 0.39427152276039124, "pitch": 0.09566180408000946}, "target": {"y": 5438008.23911845, "x": 322870.52179215587, "mutex": 1.0, "num_wp": 1.0}, "timestamp": 1601912483, "velocity": {"y": 23.71, "x": 6.17}, "target_dir": {"y": 14.161232273443602, "x": 26.55765673518181}, "position": {"y": 5438076.374485949, "x": 322863.1046322796, "alt": 46.92, "zone": 19.0}, "altitude": 47.968, "nofly": [[[322796.16375333746, 5438250.825848085], [322678.1268212263, 5437956.05416451], [323075.4336759561, 5437889.640751129], [323001.00459137175, 5438272.032294986], [322796.16375333746, 5438250.825848085]]], "wind": {"speed_z": 0.0, "direction": 16.8132266998291, "speed": 1.914101481437683}}
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This specification estimates the trajectory of a flying UAV to assess if it will reach its target destination.

The input streams are data on the state of the vehicle at every instant and its target destination.

The output stream shows how close to the target destination will the vehicle fly.

format JSON
use theory Geometry2D
use theory SimulatedGuidance
use theory GuidanceTheory
use haskell Data.Either

#HASKELL
fst3 (x,_,_) = x
snd3 (_,y,_) = y
thd3 (_,_,z) = z

fst5 (x,_,_,_,_) = x
#ENDOFHASKELL

input NonLinearData navigation_data
input        Point2 target
input       Vector2 target_dir
input       Vector2 velocity
input        Point2 position

output Double intersDistance = let
  r0 = '(,) (position [now]) (velocity [now])
  r1 = '(,) (target [now])   (target_dir [now])
  in '(fromRight (-1)) (2'intersectionDistance r0 r1)

define (Matrix, Double, Double) kfuStream = let
  inroll            = 'initial_roll (navigation_data [now])
  prev_initial_roll = 'initial_roll (navigation_data [-1|navigation_data [now]])
  dt                = 0.05
  kfp               = 3'kalman_filter_predict (navigation_data [now]) 1 (tau [-1|0.5])
  roll_pred         = 'fst kfp
  tau_pred          = 'snd kfp
  dfltM             = '(M [[0.01,0],[0,0.01]])
  in
  7'kalman_filter_update (matrix_kfiltered [-1| dfltM]) prev_initial_roll (tau [-1|0.5]) inroll roll_pred tau_pred dt

define Matrix matrix_kfiltered = 'fst3 (kfuStream [now])

define Double tau = 'thd3 (kfuStream [now])

define ([Point2], Double, Bool, Double, Double) simulated_guidance = 3'simulate_guidance_logic (navigation_data [now]) (tau [now]) 200

define [Point2] simulated_guidance_wps = 'fst5 (simulated_guidance [now])

define (Double, Double) speed_integral = 'getVelIntegral (set_speed [-1|21]) (integral_for_speed [-1|0]) (simulated_guidance [now])

define Double set_speed = 'fst (speed_integral [now])

define Double integral_for_speed = 'snd (speed_integral [now])

define Estimation estim_data = 'simulate_guidance (tau [now]) (navigation_data [now])

define Double err = 21 - 'dist (estim_data [now]) / 'time (estim_data [now])

define Double err_int = if 3'isSaturated (pi_controller [-1|21]) 15 30 then
  err_int [-1|0] else err_int [-1|0] + err [now] * 0.03

define Double pi_controller = 3'saturate (21 + err [now] * 0.5 + err_int [now]) 15 30

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This specification is ECG.

The input streams of this specification consist of the timestamp and the measurement.

The output streams are the timestamp and if it is a peak.

format CSV
use theory ECG
use library Utils
use library Lola
use innerspec headismax

input Double ecg_measurement
input Int timestamp

define (Double, (D2, D2)) bandpassed_all = let
  butterargs = ((0.16020035, 0, -0.16020035), (1, -1.6795993, 0.6795993))
  in '(iir_df1 butterargs) bp_st [-1|'((0,0),(0,0))] ecg_measurement[now]
define Double bandpassed = 'fst bandpassed_all[now]
define (D2, D2) bp_st = 'snd bandpassed_all[now]

define Double stompedbandpassed = if instantN[now] <= 5 then stompedbandpassed [-1|bandpassed [5| 'undefined]] else bandpassed[now]

define Double differentiated = stompedbandpassed [1| stompedbandpassed[now]] - stompedbandpassed[now]
define Double squared = '(^2) differentiated[now]
define Double convolved = convolved [-1|0] + squared[now] - squared [-15|0]

define [Double] rprev50 = 'shift rprev50 [-1| '(replicate 50 (-1e-6))] convolved[now]
  where shift r x = x:init r
define Bool peak_candidate = let
  nextm50 = convolved [:50]
  in convolved[now]>0.35 && 'headisspike rprev50[now] && 'headisspike nextm50
  where
  headisspike = runSpec.headismax

define Bool ispeak = peak_candidate[now] && instantN[now] - last_qrs_index[now] > 120
define Bool isqrs = convolved[now] > threshold_value[now]
output Bool is_qrs_peak = isqrs[now] && ispeak[now]
define Double qrs_peak_value = let
  qrs_peak_filtering_factor = 0.125
  in if ispeak[now] && isqrs[now] then qrs_peak_filtering_factor * convolved[now] + (1 - qrs_peak_filtering_factor) * qrs_peak_value [-1|0] else qrs_peak_value [-1|0]
define Double noise_peak_value = let
  noise_peak_filtering_factor = 0.125
  in if ispeak[now] && not isqrs[now] then noise_peak_filtering_factor * convolved[now] + (1 - noise_peak_filtering_factor) * noise_peak_value [-1|0] else noise_peak_value [-1|0]
define Double next_threshold_value = if ispeak[now] then noise_peak_value[now] + 0.25 * (qrs_peak_value[now] - noise_peak_value[now]) else threshold_value [-1|0]
define Double threshold_value = next_threshold_value [-1|0]
define Int last_qrs_index = next_last_qrs_index [-1|-120]
define Int next_last_qrs_index = if ispeak[now] && isqrs[now] then instantN[now] else last_qrs_index[now]

output Int ts = timestamp[now]

innerspec here

timestamp,ecg_measurement
is_qrs_peak,ts
False,6034140
False,6038012
False,6041904
False,6045784
False,6049652
False,6053532
False,6057412
False,6061296
False,6065180
False,6069064
False,6072948
False,6076836
False,6080708
False,6084572
False,6088452
False,6092320
False,6096192
False,6100064
False,6103940
False,6107816
False,6111688
False,6115568
False,6119444
False,6123312
False,6127200
False,6131088
False,6134964
False,6138820
False,6142692
False,6146548
False,6150412
False,6154280
False,6158148
False,6162020
False,6165892
False,6169772
False,6173636
False,6177516
False,6181396
False,6185276
False,6189156
False,6193036
False,6196924
False,6200804
False,6204692
False,6208572
False,6212452
False,6216324
False,6220196
False,6224076
False,6227948
False,6231828
False,6235700
False,6239580
False,6243460
False,6247324
False,6251196
False,6255084
False,6258964
False,6262832
False,6266700
False,6270580
False,6274456
False,6278328
False,6282196
False,6286084
False,6289972
False,6293856
False,6297740
False,6301620
False,6305504
False,6309364
False,6313248
False,6317116
False,6320996
False,6324888
False,6328772
False,6332652
False,6336532
False,6340404
False,6344292
False,6348184
False,6352068
False,6355948
False,6359832
False,6363720
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Libraries

library LTL
use library Utils

output Bool historically <Stream Bool p> = p[now] && historically p [-1|'True]

output Bool once <Stream Bool p> = p[now] || once p[-1|'False]

output Bool since <Stream Bool p> <Stream Bool q> = q[now] || (p[now] && p `since` q [-1|'False])

output Bool yesterday <Stream Bool p> = p[-1|'False]
output Bool zesterday <Stream Bool p> = p[-1|'True]

output Int nViolations <Stream Bool p> = nViolations p[-1|0] + if p[now] then 1 else 0

output Double percentViolations <Stream Bool p> = nViolations p [now] `intdivide` (instantN [now])

library MTL

output Bool until <(Int, Int) (a,b)> <Stream Bool phi> <Stream Bool psi> = until' a
  where
  until' a
    | a == b = psi[b| 'False]
    | otherwise = psi[a| 'False] || (phi[a| 'True] && until' (a+1))

output Bool eventually <(Int, Int) (a,b)> <Stream Bool phi> = foldl (||) 'False [phi[i|'False] | i <- [a..b]]

output Bool historically <Int k> <Stream Bool p> = consecutiveTrue p [now] > 'k

output Int consecutiveTrue <Stream Bool p> = if not (p[now]) then 0 else consecutiveTrue p[-1|0] + 1

library QMTL

use library Utils

output (Eq a, Fractional a, Streamable a) => a meanLast <Int k> <Stream a str> = let
  denom = '(fromIntegral.min k) (instantN[now])
  numerator = foldl (+) 0 [str [i|0] | i <- [(1-k)..0]]
  in numerator / denom

library Pinescript
use library Utils

output (Num a, Eq a, Streamable a) => a sumLast <Stream a str> <Int n> = sumLast str n [-1|0] + str[now] - str[-n|0]

output (Fractional a, Eq a, Streamable a) => a sma <Stream a str> <Int n> = let
  denominator = '(fromIntegral.min n) (instantN[now])
  in sumLast str n [now] / denominator

output (Fractional a, Eq a, Streamable a) => a wma <Stream a str> <Int n> = let
  slots = '(min n) (instantN[now])
  sumFirstN = 'fromIntegral (2'div (slots * (slots + 1)) 2)
  in foldl (+) 0 [str [-i|0] * '(fromIntegral (n-i)) | i<-[0..n-1]] / sumFirstN

output (Fractional a, Eq a, Streamable a) => a ema <Stream a str> <Int n> = let
  emaprev = ema str n [-1|0]
  multiplier = '((2 P./).fromIntegral.min n) (instantN[now])
  in (str[now] - emaprev) * multiplier + emaprev

output (Fractional a, Eq a, Streamable a) => a macd <Stream a str> = ema str 12[now] - ema str 26 [now]

output (Fractional a, Eq a, Streamable a) => a macd_signal <Stream a str> = ema (macd str) 9 [now]

output (Num a, Ord a, Eq a, Streamable a) => Bool crossover <Stream a str0> <Stream a str1> = str1[now] <= str0[now] && str0[-1|0] <= str1 [-1|0]