TUF_LOGICTUF_LOGIC: Three-Value Logic for Pine Script v6
The TUF_LOGIC library implements a robust three-valued logic system (trilean logic) for Pine Script v6, providing a formal framework for reasoning about uncertain or incomplete information in financial markets. By extending beyond binary True/False states to include an explicit "Uncertain" state, this library enables more nuanced algorithmic decision-making, particularly valuable in environments characterized by imperfect information.
Core Architecture
TUF_LOGIC offers two complementary interfaces for working with trilean values:
Enum-Based API (Recommended): Leverages Pine Script v6's enum capabilities with Trilean.True , Trilean.Uncertain , and Trilean.False for improved type safety and performance.
Integer-Based API (Legacy Support): Maintains compatibility with existing code using integer values 1 (True), 0 (Uncertain), and -1 (False).
Fundamental Operations
The library provides type conversion methods for seamless interaction between integer representation and enum types ( to_trilean() , to_int() ), along with validation functions to maintain trilean invariants.
Logical Operators
TUF_LOGIC extends traditional boolean operators to the trilean domain with NOT , AND , OR , XOR , and EQUALITY functions that properly handle the Uncertain state according to the principles of three-valued logic.
The library implements three different implication operators providing flexibility for different logical requirements: IMP_K (Kleene's approach), IMP_L (Łukasiewicz's approach), and IMP_RM3 (Relevant implication under RM3 logic).
Inspired by Tarski-Łukasiewicz's modal logic formulations, TUF_LOGIC includes modal operators: MA (Modal Assertion) evaluates whether a state is possibly true; LA (Logical Assertion) determines if a state is necessarily true; and IA (Indeterminacy Assertion) identifies explicitly uncertain states.
The UNANIMOUS operator evaluates trilean values for complete agreement, returning the consensus value if one exists or Uncertain otherwise. This function is available for both pairs of values and arrays of trilean values.
Practical Applications
TUF_LOGIC excels in financial market scenarios where decision-making must account for uncertainty. It enables technical indicator consensus by combining signals with different confidence levels, supports multi-timeframe analysis by reconciling potentially contradictory signals, enhances risk management by explicitly modeling uncertainty, and handles partial information systems where some data sources may be unreliable.
By providing a mathematically sound framework for reasoning about uncertainty, TUF_LOGIC elevates trading system design beyond simplistic binary logic, allowing for more sophisticated decision-making that better reflects real-world market complexity.
Library "TUF_LOGIC"
Three-Value Logic (TUF: True, Uncertain, False) implementation for Pine Script.
This library provides a comprehensive set of logical operations supporting trilean logic systems,
including Kleene, Łukasiewicz, and RM3 implications. Compatible with Pine v6 enums.
method validate(self)
Ensures a valid trilean integer value by clamping to the appropriate range .
Namespace types: series int, simple int, input int, const int
Parameters:
self (int) : The integer value to validate.
Returns: An integer value guaranteed to be within the valid trilean range.
method to_trilean(self)
Converts an integer value to a Trilean enum value.
Namespace types: series int, simple int, input int, const int
Parameters:
self (int) : The integer to convert (typically -1, 0, or 1).
Returns: A Trilean enum value: True (1), Uncertain (0), or False (-1).
method to_int(self)
Converts a Trilean enum value to its corresponding integer representation.
Namespace types: series Trilean
Parameters:
self (series Trilean) : The Trilean enum value to convert.
Returns: Integer value: 1 (True), 0 (Uncertain), or -1 (False).
method NOT(self)
Negates a trilean integer value (NOT operation).
Namespace types: series int, simple int, input int, const int
Parameters:
self (int) : The integer value to negate.
Returns: Negated integer value: 1 -> -1, 0 -> 0, -1 -> 1.
method NOT(self)
Negates a Trilean enum value (NOT operation).
Namespace types: series Trilean
Parameters:
self (series Trilean) : The Trilean enum value to negate.
Returns: Negated Trilean: True -> False, Uncertain -> Uncertain, False -> True.
method AND(self, comparator)
Logical AND operation for trilean integer values.
Namespace types: series int, simple int, input int, const int
Parameters:
self (int) : The first integer value.
comparator (int) : The second integer value to compare with.
Returns: Integer result of the AND operation (minimum value).
method AND(self, comparator)
Logical AND operation for Trilean enum values following three-valued logic.
Namespace types: series Trilean
Parameters:
self (series Trilean) : The first Trilean enum value.
comparator (series Trilean) : The second Trilean enum value to compare with.
Returns: Trilean result of the AND operation.
method OR(self, comparator)
Logical OR operation for trilean integer values.
Namespace types: series int, simple int, input int, const int
Parameters:
self (int) : The first integer value.
comparator (int) : The second integer value to compare with.
Returns: Integer result of the OR operation (maximum value).
method OR(self, comparator)
Logical OR operation for Trilean enum values following three-valued logic.
Namespace types: series Trilean
Parameters:
self (series Trilean) : The first Trilean enum value.
comparator (series Trilean) : The second Trilean enum value to compare with.
Returns: Trilean result of the OR operation.
method EQUALITY(self, comparator)
Logical EQUALITY operation for trilean integer values.
Namespace types: series int, simple int, input int, const int
Parameters:
self (int) : The first integer value.
comparator (int) : The second integer value to compare with.
Returns: Integer representation (1/-1) indicating if values are equal.
method EQUALITY(self, comparator)
Logical EQUALITY operation for Trilean enum values.
Namespace types: series Trilean
Parameters:
self (series Trilean) : The first Trilean enum value.
comparator (series Trilean) : The second Trilean enum value to compare with.
Returns: Trilean.True if both values are equal, Trilean.False otherwise.
method XOR(self, comparator)
Logical XOR (Exclusive OR) operation for trilean integer values.
Namespace types: series int, simple int, input int, const int
Parameters:
self (int) : The first integer value.
comparator (int) : The second integer value to compare with.
Returns: Integer result of the XOR operation.
method XOR(self, comparator)
Logical XOR (Exclusive OR) operation for Trilean enum values.
Namespace types: series Trilean
Parameters:
self (series Trilean) : The first Trilean enum value.
comparator (series Trilean) : The second Trilean enum value to compare with.
Returns: Trilean result of the XOR operation.
method IMP_K(self, comparator)
Material implication using Kleene's logic for trilean integer values.
Namespace types: series int, simple int, input int, const int
Parameters:
self (int) : The antecedent integer value.
comparator (int) : The consequent integer value.
Returns: Integer result of Kleene's implication operation.
method IMP_K(self, comparator)
Material implication using Kleene's logic for Trilean enum values.
Namespace types: series Trilean
Parameters:
self (series Trilean) : The antecedent Trilean enum value.
comparator (series Trilean) : The consequent Trilean enum value.
Returns: Trilean result of Kleene's implication operation.
method IMP_L(self, comparator)
Logical implication using Łukasiewicz's logic for trilean integer values.
Namespace types: series int, simple int, input int, const int
Parameters:
self (int) : The antecedent integer value.
comparator (int) : The consequent integer value.
Returns: Integer result of Łukasiewicz's implication operation.
method IMP_L(self, comparator)
Logical implication using Łukasiewicz's logic for Trilean enum values.
Namespace types: series Trilean
Parameters:
self (series Trilean) : The antecedent Trilean enum value.
comparator (series Trilean) : The consequent Trilean enum value.
Returns: Trilean result of Łukasiewicz's implication operation.
method IMP_RM3(self, comparator)
Logical implication using RM3 logic for trilean integer values.
Namespace types: series int, simple int, input int, const int
Parameters:
self (int) : The antecedent integer value.
comparator (int) : The consequent integer value.
Returns: Integer result of the RM3 implication operation.
method IMP_RM3(self, comparator)
Logical implication using RM3 logic for Trilean enum values.
Namespace types: series Trilean
Parameters:
self (series Trilean) : The antecedent Trilean enum value.
comparator (series Trilean) : The consequent Trilean enum value.
Returns: Trilean result of the RM3 implication operation.
method MA(self)
Modal Assertion (MA) operation for trilean integer values.
Namespace types: series int, simple int, input int, const int
Parameters:
self (int) : The integer value to evaluate.
Returns: 1 if the value is 1 or 0, -1 if the value is -1.
method MA(self)
Modal Assertion (MA) operation for Trilean enum values.
Namespace types: series Trilean
Parameters:
self (series Trilean) : The Trilean enum value to evaluate.
Returns: Trilean.True if value is True or Uncertain, Trilean.False if value is False.
method LA(self)
Logical Assertion (LA) operation for trilean integer values.
Namespace types: series int, simple int, input int, const int
Parameters:
self (int) : The integer value to evaluate.
Returns: 1 if the value is 1, -1 otherwise.
method LA(self)
Logical Assertion (LA) operation for Trilean enum values.
Namespace types: series Trilean
Parameters:
self (series Trilean) : The Trilean enum value to evaluate.
Returns: Trilean.True if value is True, Trilean.False otherwise.
method IA(self)
Indeterminacy Assertion (IA) operation for trilean integer values.
Namespace types: series int, simple int, input int, const int
Parameters:
self (int) : The integer value to evaluate.
Returns: 1 if the value is 0, -1 otherwise.
method IA(self)
Indeterminacy Assertion (IA) operation for Trilean enum values.
Namespace types: series Trilean
Parameters:
self (series Trilean) : The Trilean enum value to evaluate.
Returns: Trilean.True if value is Uncertain, Trilean.False otherwise.
method UNANIMOUS(self, comparator)
Evaluates the unanimity between two trilean integer values.
Namespace types: series int, simple int, input int, const int
Parameters:
self (int) : The first integer value.
comparator (int) : The second integer value.
Returns: Integer value of self if both values are equal, 0 (Uncertain) otherwise.
method UNANIMOUS(self, comparator)
Evaluates the unanimity between two Trilean enum values.
Namespace types: series Trilean
Parameters:
self (series Trilean) : The first Trilean enum value.
comparator (series Trilean) : The second Trilean enum value.
Returns: Value of self if both values are equal, Trilean.Uncertain otherwise.
method UNANIMOUS(self)
Evaluates the unanimity among an array of trilean integer values.
Namespace types: array
Parameters:
self (array) : The array of integer values.
Returns: First value if all values are identical, 0 (Uncertain) otherwise.
method UNANIMOUS(self)
Evaluates the unanimity among an array of Trilean enum values.
Namespace types: array
Parameters:
self (array) : The array of Trilean enum values.
Returns: First value if all values are identical, Trilean.Uncertain otherwise.
Logic
Advanced Multi-Timeframe Trading System (Risk Managed)Description:
This strategy is an original approach that combines two main analytical components to identify potential trade opportunities while simulating realistic trading conditions:
1. Market Trend Analysis via an Approximate Hurst Exponent
• What It Does:
The strategy computes a rough measure of market trending using an approximate Hurst exponent. A value above 0.5 suggests persistent, trending behavior, while a value below 0.5 indicates a tendency toward mean-reversion.
• How It’s Used:
The Hurst exponent is calculated on both the chart’s current timeframe and a higher timeframe (default: Daily) to capture both local and broader market dynamics.
2. Fibonacci Retracement Levels
• What It Does:
Using daily high and low data from a selected timeframe (default: Daily), the script computes key Fibonacci retracement levels.
• How It’s Used:
• The 61.8% level (Golden Ratio) serves as a key threshold:
• A long entry is signaled when the price crosses above this level if the daily Hurst exponent confirms a trending market.
• The 38.2% level is used to identify short-entry opportunities when the price crosses below it and the daily Hurst indicates non-trending conditions.
Signal Logic:
• Long Entry:
When the price crosses above the 61.8% Fibonacci level (Golden Ratio) and the daily Hurst exponent is greater than 0.5, suggesting a trending market.
• Short Entry:
When the price crosses below the 38.2% Fibonacci level and the daily Hurst exponent is less than 0.5, indicating a less trending or potentially reversing market.
Risk Management & Trade Execution:
• Stop-Loss:
Each trade is risk-managed with a stop-loss set at 2% below (for longs) or above (for shorts) the entry price. This ensures that no single trade risks more than a small, sustainable portion of the account.
• Take Profit:
A take profit order targets a risk-reward ratio of 1:2 (i.e., the target profit is twice the amount risked).
• Position Sizing:
Trades are executed with a fixed position size equal to 10% of account equity.
• Trade Frequency Limits:
• Daily Limit: A maximum of 5 trades per day
• Overall Limit: No more than 510 trades during the backtesting period (e.g., since 2019)
These limits are imposed to simulate realistic trading frequency and to avoid overtrading in backtest results.
Backtesting Parameters:
• Initial Capital: $10,000
• Commission: 0.1% per trade
• Slippage: 1 tick per bar
These settings aim to reflect the conditions faced by the average trader and help ensure that the backtesting results are realistic and not misleading.
Chart Overlays & Visual Aids:
• Fibonacci Levels:
The key Fibonacci retracement levels are plotted on the chart, and the zone between the 61.8% and 38.2% levels is highlighted to show a key retracement area.
• Market Trend Background:
The chart background is tinted green when the daily Hurst exponent indicates a trending market (value > 0.5) and red otherwise.
• Information Table:
An on-chart table displays key parameters such as the current Hurst exponent, daily Hurst value, the number of trades executed today, and the global trade count.
Disclaimer:
Past performance is not indicative of future results. This strategy is experimental and provided solely for educational purposes. It is essential that you backtest and paper trade using your own settings before considering any live deployment. The Hurst exponent calculation is an approximation and should be interpreted as a rough gauge of market behavior. Adjust the parameters and risk management settings according to your personal risk tolerance and market conditions.
Additional Notes:
• Originality & Usefulness:
This script is an original mashup that combines trend analysis with Fibonacci retracement methods. The description above explains how these components work together to provide trading signals.
• Realistic Results:
The strategy uses realistic account sizes, commission rates, slippage, and risk management rules to generate backtesting results that are representative of real-world trading.
• Educational Purpose:
This script is intended to support the TradingView community by offering insights into combining multiple analysis techniques in one strategy. It is not a “get-rich-quick” system but rather an educational tool to help traders understand risk management and trade signal logic.
By using this script, you acknowledge that trading involves risk and that you are responsible for testing and adjusting the strategy to fit your own trading environment. This publication is fully open source, and any modifications should include proper attribution if significant portions of the code are reused.
MathOperatorLibrary "MathOperator"
Methods to handle operators.
method add(value_a, value_b)
Add value a to b.
Namespace types: series float, simple float, input float, const float
Parameters:
value_a (float) : float, value a.
value_b (float) : float, value b.
Returns: float.
method subtract(value_a, value_b)
subtract value b from a.
Namespace types: series float, simple float, input float, const float
Parameters:
value_a (float) : float, value a.
value_b (float) : float, value b.
Returns: float.
method multiply(value_a, value_b)
multiply value a with b.
Namespace types: series float, simple float, input float, const float
Parameters:
value_a (float) : float, value a.
value_b (float) : float, value b.
Returns: float.
method divide(value_a, value_b)
divide value a with b.
Namespace types: series float, simple float, input float, const float
Parameters:
value_a (float) : float, value a.
value_b (float) : float, value b.
Returns: float.
method remainder(value_a, value_b)
remainder of a with b.
Namespace types: series float, simple float, input float, const float
Parameters:
value_a (float) : float, value a.
value_b (float) : float, value b.
Returns: float.
method equal(value_a, value_b)
equality of value a with b.
Namespace types: series float, simple float, input float, const float
Parameters:
value_a (float) : float, value a.
value_b (float) : float, value b.
Returns: bool.
method not_equal(value_a, value_b)
inequality of value a with b.
Namespace types: series float, simple float, input float, const float
Parameters:
value_a (float) : float, value a.
value_b (float) : float, value b.
Returns: bool.
method over(value_a, value_b)
value a is over b.
Namespace types: series float, simple float, input float, const float
Parameters:
value_a (float) : float, value a.
value_b (float) : float, value b.
Returns: bool.
method under(value_a, value_b)
value a is under b.
Namespace types: series float, simple float, input float, const float
Parameters:
value_a (float) : float, value a.
value_b (float) : float, value b.
Returns: bool.
method over_equal(value_a, value_b)
value a is over equal b.
Namespace types: series float, simple float, input float, const float
Parameters:
value_a (float) : float, value a.
value_b (float) : float, value b.
Returns: bool.
method under_equal(value_a, value_b)
value a is under equal b.
Namespace types: series float, simple float, input float, const float
Parameters:
value_a (float) : float, value a.
value_b (float) : float, value b.
Returns: bool.
method and_(value_a, value_b)
logical and of a with b
Namespace types: series bool, simple bool, input bool, const bool
Parameters:
value_a (bool) : bool, value a.
value_b (bool) : bool, value b.
Returns: bool.
method or_(value_a, value_b)
logical or of a with b.
Namespace types: series bool, simple bool, input bool, const bool
Parameters:
value_a (bool) : bool, value a.
value_b (bool) : bool, value b.
Returns: bool.
method not_(value_a)
logical not of a.
Namespace types: series bool, simple bool, input bool, const bool
Parameters:
value_a (bool) : bool, value a.
Returns: bool.
method xor_(value_a, value_b)
logical xor of a with b.
Namespace types: series bool, simple bool, input bool, const bool
Parameters:
value_a (bool) : bool, value a.
value_b (bool) : bool, value b.
Returns: bool.
method xnor_(value_a, value_b)
logical xnor of a with b.
Namespace types: series bool, simple bool, input bool, const bool
Parameters:
value_a (bool) : bool, value a.
value_b (bool) : bool, value b.
Returns: bool.
method nand_(value_a, value_b)
logical nand of a with b.
Namespace types: series bool, simple bool, input bool, const bool
Parameters:
value_a (bool) : bool, value a.
value_b (bool) : bool, value b.
Returns: bool.
method nor_(value_a, value_b)
logical nor of a with b.
Namespace types: series bool, simple bool, input bool, const bool
Parameters:
value_a (bool) : bool, value a.
value_b (bool) : bool, value b.
Returns: bool.
TUF_LOGICThe TUF_LOGIC library incorporates three-valued logic (also known as trilean logic) into Pine Script, enabling the representation of states beyond the binary True and False to include an 'Uncertain' state. This addition is particularly apt for financial market contexts where information may not always be black or white, accommodating scenarios of partial or ambiguous data.
Key Features:
Trilean Data Type: Defines a tri type, facilitating the representation of True (1), Uncertain (0), and False (-1) states, thus accommodating a more nuanced approach to logical evaluation.
Validation and Conversion: Includes methods like validate, to ensure trilean variables conform to expected states, and to_bool, for converting trilean to boolean values, enhancing interoperability with binary logic systems.
Core Logical Operations: Extends traditional logical operators (AND, OR, NOT, XOR, EQUALITY) to work within the trilean domain, enabling complex conditionals that reflect real-world uncertainties.
Specialized Logical Operations:
Implication Operators: Features IMP_K (Kleene's), IMP_L (Łukasiewicz's), and IMP_RM3, offering varied approaches to logical implication within the trilean framework.
Possibility, Necessity, and Contingency Operators: Implements MA ("it is possible that..."), LA ("it is necessary that..."), and IA ("it is unknown/contingent that..."), derived from Tarski-Łukasiewicz's modal logic attempts, enriching the library with modal logic capabilities.
Unanimity Functions: The UNANIMOUS operator assesses complete agreement among trilean values, useful for scenarios requiring consensus or uniformity across multiple indicators or conditions.
This library is developed to support scenarios in financial trading and analysis where decisions might hinge on more than binary outcomes. By incorporating modal logic aspects and providing a framework for handling uncertainty through the MA, LA, and IA operations, TUF_LOGIC bridges the gap between classical binary logic and the realities of uncertain information, making it a valuable tool for developing sophisticated trading strategies and analytical models.
Library "TUF_LOGIC"
3VL Implementation (TUF stands for True, Uncertain, False.)
method validate(self)
Ensures a valid trilean variable. This works by clamping the variable to the range associated with the trilean type.
Namespace types: tri
Parameters:
self (tri)
Returns: Validated trilean object.
method to_bool(self)
Converts a trilean object into a boolean object. True -> True, Uncertain -> na, False -> False.
Namespace types: tri
Parameters:
self (tri)
Returns: A boolean variable.
method NOT(self)
Negates the trilean object. True -> False, Uncertain -> Uncertain, False -> True
Namespace types: tri
Parameters:
self (tri)
Returns: Negated trilean object.
method AND(self, comparator)
Logical AND operation for trilean objects.
Namespace types: tri
Parameters:
self (tri) : The first trilean object.
comparator (tri) : The second trilean object to compare with.
Returns: `tri` Result of the AND operation as a trilean object.
method OR(self, comparator)
Logical OR operation for trilean objects.
Namespace types: tri
Parameters:
self (tri) : The first trilean object.
comparator (tri) : The second trilean object to compare with.
Returns: `tri` Result of the OR operation as a trilean object.
method EQUALITY(self, comparator)
Logical EQUALITY operation for trilean objects.
Namespace types: tri
Parameters:
self (tri) : The first trilean object.
comparator (tri) : The second trilean object to compare with.
Returns: `tri` Result of the EQUALITY operation as a trilean object, True if both are equal, False otherwise.
method XOR(self, comparator)
Logical XOR (Exclusive OR) operation for trilean objects.
Namespace types: tri
Parameters:
self (tri) : The first trilean object.
comparator (tri) : The second trilean object to compare with.
Returns: `tri` Result of the XOR operation as a trilean object.
method IMP_K(self, comparator)
Material implication using Kleene's logic for trilean objects.
Namespace types: tri
Parameters:
self (tri) : The antecedent trilean object.
comparator (tri) : The consequent trilean object.
Returns: `tri` Result of the implication operation as a trilean object.
method IMP_L(self, comparator)
Logical implication using Łukasiewicz's logic for trilean objects.
Namespace types: tri
Parameters:
self (tri) : The antecedent trilean object.
comparator (tri) : The consequent trilean object.
Returns: `tri` Result of the implication operation as a trilean object.
method IMP_RM3(self, comparator)
Logical implication using RM3 logic for trilean objects.
Namespace types: tri
Parameters:
self (tri) : The antecedent trilean object.
comparator (tri) : The consequent trilean object.
Returns: `tri` Result of the RM3 implication as a trilean object.
method MA(self)
Evaluates to True if the trilean object is either True or Uncertain, False otherwise.
Namespace types: tri
Parameters:
self (tri) : The trilean object to evaluate.
Returns: `tri` Result of the operation as a trilean object.
method LA(self)
Evaluates to True if the trilean object is True, False otherwise.
Namespace types: tri
Parameters:
self (tri) : The trilean object to evaluate.
Returns: `tri` Result of the operation as a trilean object.
method IA(self)
Evaluates to True if the trilean object is Uncertain, False otherwise.
Namespace types: tri
Parameters:
self (tri) : The trilean object to evaluate.
Returns: `tri` Result of the operation as a trilean object.
UNANIMOUS(self, comparator)
Evaluates the unanimity between two trilean values.
Parameters:
self (tri) : The first trilean value.
comparator (tri) : The second trilean value.
Returns: `tri` Returns True if both values are True, False if both are False, and Uncertain otherwise.
method UNANIMOUS(self)
Evaluates the unanimity among an array of trilean values.
Namespace types: array
Parameters:
self (array) : The array of trilean values.
Returns: `tri` Returns True if all values are True, False if all are False, and Uncertain otherwise.
tri
Three Value Logic (T.U.F.), or trilean. Can be True (1), Uncertain (0), or False (-1).
Fields:
v (series int) : Value of the trilean variable. Can be True (1), Uncertain (0), or False (-1).
xor logical operatorLibrary "xor"
xor(a, b)
xor: Exclusive or, or exclusive disjunction is a logical operation that is true if and only if its arguments differ (one is true, the other is false).
Parameters:
a : first argument
b : second argument
Returns: returns xor (true only if a and b are true, but not both)
Example:
true xor true = false
true xor false = true
false xor true = true
false xor false = false
Example - Switching LineExample of manipulating a float series to:
• switch from one source to another
• maintain a level by referencing itself
This script publication is intended for:
• Educational Purposes
Who is it for?
Anyone who wants to learn how to change the position or state of an active float series.
