/**
 * Copyright (C) 2019, 2021, 2024, 2025 Adrien Hopkins
 *
 * This program is free software: you can redistribute it and/or modify
 * it under the terms of the GNU Affero General Public License as published by
 * the Free Software Foundation, either version 3 of the License, or
 * (at your option) any later version.
 *
 * This program is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 * GNU Affero General Public License for more details.
 *
 * You should have received a copy of the GNU Affero General Public License
 * along with this program.  If not, see <https://www.gnu.org/licenses/>.
 */
package sevenUnits.utils;

import java.util.ArrayDeque;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Deque;
import java.util.HashMap;
import java.util.List;
import java.util.Map;
import java.util.Objects;
import java.util.function.BiFunction;
import java.util.function.BinaryOperator;
import java.util.function.Function;
import java.util.function.UnaryOperator;

/**
 * An object that can parse expressions with unary or binary operators.
 * 
 * @author Adrien Hopkins
 * @param <T> type of object that exists in parsed expressions
 * @since 2019-03-14
 * @since v0.2.0
 */
public final class ExpressionParser<T> {
	/**
	 * A builder that can create {@code ExpressionParser<T>} instances.
	 * 
	 * @author Adrien Hopkins
	 * @param <T> type of object that exists in parsed expressions
	 * @since 2019-03-17
	 * @since v0.2.0
	 */
	public static final class Builder<T> {
		/**
		 * A function that obtains a parseable object from a string. For example,
		 * an integer {@code ExpressionParser} would use
		 * {@code Integer::parseInt}.
		 * 
		 * @since 2019-03-14
		 * @since v0.2.0
		 */
		private final Function<String, ? extends T> objectObtainer;
		
		/**
		 * The function of the space as an operator (like 3 x y)
		 * 
		 * @since 2019-03-22
		 * @since v0.2.0
		 */
		private String spaceFunction = null;
		
		/**
		 * A map mapping operator strings to operator functions, for unary
		 * operators.
		 * 
		 * @since 2019-03-14
		 * @since v0.2.0
		 */
		private final Map<String, PriorityUnaryOperator<T>> unaryOperators;
		
		/**
		 * A map mapping operator strings to operator functions, for binary
		 * operators.
		 * 
		 * @since 2019-03-14
		 * @since v0.2.0
		 */
		private final Map<String, PriorityBinaryOperator<T>> binaryOperators;
		
		/**
		 * A map mapping operator strings to numeric functions.
		 * 
		 * @since 2024-03-23
		 * @since v0.5.0
		 */
		private final Map<String, PriorityBiFunction<T, UncertainDouble, T>> numericOperators;
		
		/**
		 * Creates the {@code Builder}.
		 * 
		 * @param objectObtainer a function that can turn strings into objects of
		 *                       the type handled by the parser.
		 * @throws NullPointerException if {@code objectObtainer} is null
		 * @since 2019-03-17
		 * @since v0.2.0
		 */
		public Builder(final Function<String, ? extends T> objectObtainer) {
			this.objectObtainer = Objects.requireNonNull(objectObtainer,
					"objectObtainer must not be null.");
			this.unaryOperators = new HashMap<>();
			this.binaryOperators = new HashMap<>();
			this.numericOperators = new HashMap<>();
		}
		
		/**
		 * Adds a binary operator to the builder.
		 * 
		 * @param text     text used to reference the operator, like '+'
		 * @param operator operator to add
		 * @param priority operator's priority, which determines which operators
		 *                 are applied first
		 * @return this builder
		 * @throws NullPointerException if {@code text} or {@code operator} is
		 *                              null
		 * @since 2019-03-17
		 * @since v0.2.0
		 */
		public Builder<T> addBinaryOperator(final String text,
				final BinaryOperator<T> operator, final int priority) {
			Objects.requireNonNull(text, "text must not be null.");
			Objects.requireNonNull(operator, "operator must not be null.");
			
			// Unfortunately, I cannot use a lambda because the
			// PriorityBinaryOperator requires arguments.
			final PriorityBinaryOperator<T> priorityOperator = new PriorityBinaryOperator<>(
					priority) {
				@Override
				public T apply(final T t, final T u) {
					return operator.apply(t, u);
				}
				
			};
			this.binaryOperators.put(text, priorityOperator);
			return this;
		}
		
		/**
		 * Adds a two-argument operator where the second operator is a number.
		 * This is used for operations like vector scaling and exponentation.
		 * 
		 * @param text     text used to reference the operator, like '^'
		 * @param operator operator to add
		 * @param priority operator's priority, which determines which operators
		 *                 are applied first
		 * @return this builder
		 */
		public Builder<T> addNumericOperator(final String text,
				final BiFunction<T, UncertainDouble, T> operator,
				final int priority) {
			Objects.requireNonNull(text, "text must not be null.");
			Objects.requireNonNull(operator, "operator must not be null.");
			
			// Unfortunately, I cannot use a lambda because the
			// PriorityBinaryOperator requires arguments.
			final PriorityBiFunction<T, UncertainDouble, T> priorityOperator = new PriorityBiFunction<>(
					priority) {
				@Override
				public T apply(final T t, final UncertainDouble u) {
					return operator.apply(t, u);
				}
				
			};
			this.numericOperators.put(text, priorityOperator);
			return this;
		}
		
		/**
		 * Adds a function for spaces. You must use the text of an existing binary
		 * operator.
		 * 
		 * @param operator text of operator to use
		 * @return this builder
		 * @since 2019-03-22
		 * @since v0.2.0
		 */
		public Builder<T> addSpaceFunction(final String operator) {
			Objects.requireNonNull(operator, "operator must not be null.");
			
			if (!this.binaryOperators.containsKey(operator))
				throw new IllegalArgumentException(String
						.format("Could not find binary operator '%s'", operator));
			
			this.spaceFunction = operator;
			return this;
		}
		
		/**
		 * Adds a unary operator to the builder.
		 * 
		 * @param text     text used to reference the operator, like '-'
		 * @param operator operator to add
		 * @param priority operator's priority, which determines which operators
		 *                 are applied first
		 * @return this builder
		 * @throws NullPointerException if {@code text} or {@code operator} is
		 *                              null
		 * @since 2019-03-17
		 * @since v0.2.0
		 */
		public Builder<T> addUnaryOperator(final String text,
				final UnaryOperator<T> operator, final int priority) {
			Objects.requireNonNull(text, "text must not be null.");
			Objects.requireNonNull(operator, "operator must not be null.");
			
			// Unfortunately, I cannot use a lambda because the
			// PriorityUnaryOperator requires arguments.
			final PriorityUnaryOperator<T> priorityOperator = new PriorityUnaryOperator<>(
					priority) {
				@Override
				public T apply(final T t) {
					return operator.apply(t);
				}
			};
			this.unaryOperators.put(text, priorityOperator);
			return this;
		}
		
		/**
		 * @return an {@code ExpressionParser<T>} instance with the properties
		 *         given to this builder
		 * @since 2019-03-17
		 * @since v0.2.0
		 */
		public ExpressionParser<T> build() {
			return new ExpressionParser<>(this.objectObtainer, this.unaryOperators,
					this.binaryOperators, this.numericOperators, this.spaceFunction);
		}
	}
	
	/**
	 * A binary operator with a priority field that determines which operators
	 * apply first.
	 * 
	 * @author Adrien Hopkins
	 * @param <T> type of operand and result
	 * @since 2019-03-17
	 * @since v0.2.0
	 */
	private static abstract class PriorityBiFunction<T, U, R> implements
			BiFunction<T, U, R>, Comparable<PriorityBiFunction<T, U, R>> {
		/**
		 * The operator's priority. Higher-priority operators are applied before
		 * lower-priority operators
		 * 
		 * @since 2019-03-17
		 * @since v0.2.0
		 */
		private final int priority;
		
		/**
		 * Creates the {@code PriorityBinaryOperator}.
		 * 
		 * @param priority operator's priority
		 * @since 2019-03-17
		 * @since v0.2.0
		 */
		public PriorityBiFunction(final int priority) {
			this.priority = priority;
		}
		
		/**
		 * Compares this object to another by priority.
		 * 
		 * <p>
		 * {@inheritDoc}
		 * </p>
		 * 
		 * @since 2019-03-17
		 * @since v0.2.0
		 */
		@Override
		public int compareTo(final PriorityBiFunction<T, U, R> o) {
			if (this.priority < o.priority)
				return -1;
			else if (this.priority > o.priority)
				return 1;
			else
				return 0;
		}
		
		/**
		 * @return priority
		 * @since 2019-03-22
		 * @since v0.2.0
		 */
		public final int getPriority() {
			return this.priority;
		}
	}
	
	/**
	 * A binary operator with a priority field that determines which operators
	 * apply first.
	 * 
	 * @author Adrien Hopkins
	 * @param <T> type of operand and result
	 * @since 2019-03-17
	 * @since v0.2.0
	 */
	private static abstract class PriorityBinaryOperator<T>
			implements BinaryOperator<T>, Comparable<PriorityBinaryOperator<T>> {
		/**
		 * The operator's priority. Higher-priority operators are applied before
		 * lower-priority operators
		 * 
		 * @since 2019-03-17
		 * @since v0.2.0
		 */
		private final int priority;
		
		/**
		 * Creates the {@code PriorityBinaryOperator}.
		 * 
		 * @param priority operator's priority
		 * @since 2019-03-17
		 * @since v0.2.0
		 */
		public PriorityBinaryOperator(final int priority) {
			this.priority = priority;
		}
		
		/**
		 * Compares this object to another by priority.
		 * 
		 * <p>
		 * {@inheritDoc}
		 * </p>
		 * 
		 * @since 2019-03-17
		 * @since v0.2.0
		 */
		@Override
		public int compareTo(final PriorityBinaryOperator<T> o) {
			if (this.priority < o.priority)
				return -1;
			else if (this.priority > o.priority)
				return 1;
			else
				return 0;
		}
		
		/**
		 * @return priority
		 * @since 2019-03-22
		 * @since v0.2.0
		 */
		public final int getPriority() {
			return this.priority;
		}
	}
	
	/**
	 * A unary operator with a priority field that determines which operators
	 * apply first.
	 * 
	 * @author Adrien Hopkins
	 * @param <T> type of operand and result
	 * @since 2019-03-17
	 * @since v0.2.0
	 */
	private static abstract class PriorityUnaryOperator<T>
			implements UnaryOperator<T>, Comparable<PriorityUnaryOperator<T>> {
		/**
		 * The operator's priority. Higher-priority operators are applied before
		 * lower-priority operators
		 * 
		 * @since 2019-03-17
		 * @since v0.2.0
		 */
		private final int priority;
		
		/**
		 * Creates the {@code PriorityUnaryOperator}.
		 * 
		 * @param priority operator's priority
		 * @since 2019-03-17
		 * @since v0.2.0
		 */
		public PriorityUnaryOperator(final int priority) {
			this.priority = priority;
		}
		
		/**
		 * Compares this object to another by priority.
		 * 
		 * <p>
		 * {@inheritDoc}
		 * </p>
		 * 
		 * @since 2019-03-17
		 * @since v0.2.0
		 */
		@Override
		public int compareTo(final PriorityUnaryOperator<T> o) {
			if (this.priority < o.priority)
				return -1;
			else if (this.priority > o.priority)
				return 1;
			else
				return 0;
		}
		
		/**
		 * @return priority
		 * @since 2019-03-22
		 * @since v0.2.0
		 */
		public final int getPriority() {
			return this.priority;
		}
	}
	
	/**
	 * The types of tokens that are available.
	 * 
	 * @author Adrien Hopkins
	 * @since 2019-03-14
	 * @since v0.2.0
	 */
	private static enum TokenType {
		OBJECT, UNARY_OPERATOR, BINARY_OPERATOR, NUMERIC_OPERATOR;
	}
	
	/**
	 * The opening bracket.
	 * 
	 * @since 2019-03-22
	 * @since v0.2.0
	 */
	public static final char OPENING_BRACKET = '(';
	
	/**
	 * The closing bracket.
	 * 
	 * @since 2019-03-22
	 * @since v0.2.0
	 */
	public static final char CLOSING_BRACKET = ')';
	
	/**
	 * Finds the other bracket in a pair of brackets, given the position of one.
	 * 
	 * @param string          string that contains brackets
	 * @param bracketPosition position of first bracket
	 * @return position of matching bracket
	 * @throws NullPointerException if string is null
	 * @since 2019-03-22
	 * @since v0.2.0
	 */
	private static int findBracketPair(final String string,
			final int bracketPosition) {
		Objects.requireNonNull(string, "string must not be null.");
		
		final char openingBracket = string.charAt(bracketPosition);
		
		// figure out what closing bracket to look for
		final char closingBracket;
		switch (openingBracket) {
		case '(':
			closingBracket = ')';
			break;
		case '[':
			closingBracket = ']';
			break;
		case '{':
			closingBracket = '}';
			break;
		default:
			throw new IllegalArgumentException(
					String.format("Invalid bracket '%s'", openingBracket));
		}
		
		// level of brackets. every opening bracket increments this; every closing
		// bracket decrements it
		int bracketLevel = 0;
		
		// iterate over the string to find the closing bracket
		for (int currentPosition = bracketPosition; currentPosition < string
				.length(); currentPosition++) {
			final char currentCharacter = string.charAt(currentPosition);
			
			if (currentCharacter == openingBracket) {
				bracketLevel++;
			} else if (currentCharacter == closingBracket) {
				bracketLevel--;
				if (bracketLevel == 0)
					return currentPosition;
			}
		}
		
		throw new IllegalArgumentException("No matching bracket found.");
	}
	
	/**
	 * A function that obtains a parseable object from a string. For example, an
	 * integer {@code ExpressionParser} would use {@code Integer::parseInt}.
	 * 
	 * @since 2019-03-14
	 * @since v0.2.0
	 */
	private final Function<String, ? extends T> objectObtainer;
	
	/**
	 * A map mapping operator strings to operator functions, for unary operators.
	 * 
	 * @since 2019-03-14
	 * @since v0.2.0
	 */
	private final Map<String, PriorityUnaryOperator<T>> unaryOperators;
	
	/**
	 * A map mapping operator strings to operator functions, for binary
	 * operators.
	 * 
	 * @since 2019-03-14
	 * @since v0.2.0
	 */
	private final Map<String, PriorityBinaryOperator<T>> binaryOperators;
	
	/**
	 * A map mapping operator strings to numeric functions.
	 * 
	 * @since 2024-03-23
	 * @since v0.5.0
	 */
	private final Map<String, PriorityBiFunction<T, UncertainDouble, T>> numericOperators;
	
	/**
	 * The operator for space, or null if spaces have no function.
	 * 
	 * @since 2019-03-22
	 * @since v0.2.0
	 */
	private final String spaceOperator;
	
	/**
	 * Creates the {@code ExpressionParser}.
	 * 
	 * @param objectObtainer   function to get objects from strings
	 * @param unaryOperators   unary operators available to the parser
	 * @param binaryOperators  binary operators available to the parser
	 * @param numericOperators numeric operators available to the parser
	 * @param spaceOperator    operator used by spaces
	 * @since 2019-03-14
	 * @since v0.2.0
	 */
	private ExpressionParser(final Function<String, ? extends T> objectObtainer,
			final Map<String, PriorityUnaryOperator<T>> unaryOperators,
			final Map<String, PriorityBinaryOperator<T>> binaryOperators,
			final Map<String, PriorityBiFunction<T, UncertainDouble, T>> numericOperators,
			final String spaceOperator) {
		this.objectObtainer = objectObtainer;
		this.unaryOperators = unaryOperators;
		this.binaryOperators = binaryOperators;
		this.numericOperators = numericOperators;
		this.spaceOperator = spaceOperator;
	}
	
	/**
	 * Converts a given mathematical expression to reverse Polish notation
	 * (operators after operands).
	 * <p>
	 * For example,<br>
	 * {@code 2 * (3 + 4)}<br>
	 * becomes<br>
	 * {@code 2 3 4 + *}.
	 * 
	 * @param expression expression
	 * @return expression in RPN
	 * @throws IllegalArgumentException if expression is invalid (e.g.
	 *                                  "{@code 3 *}")
	 * @since 2019-03-17
	 * @since v0.2.0
	 */
	String convertExpressionToReversePolish(final String expression) {
		Objects.requireNonNull(expression, "expression must not be null.");
		
		final List<String> components = new ArrayList<>();
		
		// the part of the expression remaining to parse
		String partialExpression = expression;
		
		// find and deal with brackets
		while (partialExpression.indexOf(OPENING_BRACKET) != -1) {
			final int openingBracketPosition = partialExpression
					.indexOf(OPENING_BRACKET);
			final int closingBracketPosition = findBracketPair(partialExpression,
					openingBracketPosition);
			
			// check for function
			if (openingBracketPosition > 0
					&& partialExpression.charAt(openingBracketPosition - 1) != ' ') {
				// function like sin(2) or tempF(32)
				// find the position of the last space
				int spacePosition = openingBracketPosition;
				while (spacePosition >= 0
						&& partialExpression.charAt(spacePosition) != ' ') {
					spacePosition--;
				}
				// then split the function into pre-function and function, using the
				// space position
				components.addAll(Arrays.asList(partialExpression
						.substring(0, spacePosition + 1).split(" ")));
				components.add(partialExpression.substring(spacePosition + 1,
						closingBracketPosition + 1));
				partialExpression = partialExpression
						.substring(closingBracketPosition + 1);
			} else {
				// normal brackets like (1 + 2) * (3 / 5)
				components.addAll(Arrays.asList(partialExpression
						.substring(0, openingBracketPosition).split(" ")));
				components.add(this.convertExpressionToReversePolish(
						partialExpression.substring(openingBracketPosition + 1,
								closingBracketPosition)));
				partialExpression = partialExpression
						.substring(closingBracketPosition + 1);
			}
		}
		
		// add everything else
		components.addAll(Arrays.asList(partialExpression.split(" ")));
		
		// remove empty entries
		while (components.contains("")) {
			components.remove("");
		}
		
		// deal with space multiplication (x y)
		if (this.spaceOperator != null) {
			for (int i = 0; i < components.size() - 1; i++) {
				if (this.getTokenType(components.get(i)) == TokenType.OBJECT && this
						.getTokenType(components.get(i + 1)) == TokenType.OBJECT) {
					components.add(++i, this.spaceOperator);
				}
			}
		}
		
		// turn the expression into reverse Polish
		while (true) {
			final int highestPriorityOperatorPosition = this
					.findHighestPriorityOperatorPosition(components);
			if (highestPriorityOperatorPosition == -1) {
				break;
			}
			
			// swap components based on what kind of operator there is
			// 1 + 2 becomes 2 1 +
			// - 1 becomes 1 -
			switch (this
					.getTokenType(components.get(highestPriorityOperatorPosition))) {
			case UNARY_OPERATOR:
				if (components.size() < 2)
					throw new IllegalArgumentException(
							"Invalid expression \"" + expression + "\"");
				final String unaryOperator = components
						.remove(highestPriorityOperatorPosition);
				final String operand = components
						.remove(highestPriorityOperatorPosition);
				components.add(highestPriorityOperatorPosition,
						operand + " " + unaryOperator);
				break;
			case BINARY_OPERATOR:
			case NUMERIC_OPERATOR:
				if (components.size() < 3)
					throw new IllegalArgumentException(
							"Invalid expression \"" + expression + "\"");
				final String binaryOperator = components
						.remove(highestPriorityOperatorPosition);
				final String operand1 = components
						.remove(highestPriorityOperatorPosition - 1);
				final String operand2 = components
						.remove(highestPriorityOperatorPosition - 1);
				components.add(highestPriorityOperatorPosition - 1,
						operand1 + " " + operand2 + " " + binaryOperator);
				break;
			default:
				throw new AssertionError("Expected operator, found non-operator.");
			}
		}
		
		// join all of the components together, then ensure there is only one
		// space in a row
		if (components.size() != 1)
			throw new IllegalArgumentException(
					"Invalid expression \"" + expression + "\".");
		return components.get(0).replaceAll(" +", " ").trim();
	}
	
	/**
	 * Finds the position of the highest-priority operator in a list
	 * 
	 * @param components components to test
	 * @param blacklist  positions of operators that should be ignored
	 * @return position of highest priority, or -1 if the list contains no
	 *         operators
	 * @throws NullPointerException if components is null
	 * @since 2019-03-22
	 * @since v0.2.0
	 */
	private int findHighestPriorityOperatorPosition(
			final List<String> components) {
		Objects.requireNonNull(components, "components must not be null.");
		// find highest priority
		int maxPriority = Integer.MIN_VALUE;
		int maxPriorityPosition = -1;
		
		// go over components one by one
		// if it is an operator, test its priority to see if it's max
		// if it is, update maxPriority and maxPriorityPosition
		for (int i = 0; i < components.size(); i++) {
			
			switch (this.getTokenType(components.get(i))) {
			case UNARY_OPERATOR:
				final PriorityUnaryOperator<T> unaryOperator = this.unaryOperators
						.get(components.get(i));
				final int unaryPriority = unaryOperator.getPriority();
				
				if (unaryPriority > maxPriority) {
					maxPriority = unaryPriority;
					maxPriorityPosition = i;
				}
				break;
			case BINARY_OPERATOR:
				final PriorityBinaryOperator<T> binaryOperator = this.binaryOperators
						.get(components.get(i));
				final int binaryPriority = binaryOperator.getPriority();
				
				if (binaryPriority > maxPriority) {
					maxPriority = binaryPriority;
					maxPriorityPosition = i;
				}
				break;
			case NUMERIC_OPERATOR:
				final PriorityBiFunction<T, UncertainDouble, T> numericOperator = this.numericOperators
						.get(components.get(i));
				final int numericPriority = numericOperator.getPriority();
				
				if (numericPriority > maxPriority) {
					maxPriority = numericPriority;
					maxPriorityPosition = i;
				}
				break;
			default:
				break;
			}
		}
		
		// max priority position found
		return maxPriorityPosition;
	}
	
	/**
	 * Determines whether an inputted string is an object or an operator
	 * 
	 * @param token string to input
	 * @return type of token it is
	 * @throws NullPointerException if {@code expression} is null
	 * @since 2019-03-14
	 * @since v0.2.0
	 */
	private TokenType getTokenType(final String token) {
		Objects.requireNonNull(token, "token must not be null.");
		
		if (this.unaryOperators.containsKey(token))
			return TokenType.UNARY_OPERATOR;
		else if (this.binaryOperators.containsKey(token))
			return TokenType.BINARY_OPERATOR;
		else if (this.numericOperators.containsKey(token))
			return TokenType.NUMERIC_OPERATOR;
		else
			return TokenType.OBJECT;
	}
	
	/**
	 * Parses an expression.
	 * 
	 * @param expression expression to parse
	 * @return result
	 * @throws NullPointerException if {@code expression} is null
	 * @since 2019-03-14
	 * @since v0.2.0
	 */
	public T parseExpression(final String expression) {
		return this.parseReversePolishExpression(
				this.convertExpressionToReversePolish(expression));
	}
	
	/**
	 * Parses an expression expressed in reverse Polish notation.
	 * 
	 * @param expression expression to parse
	 * @return result
	 * @throws NullPointerException if {@code expression} is null
	 * @since 2019-03-14
	 * @since v0.2.0
	 */
	T parseReversePolishExpression(final String expression) {
		Objects.requireNonNull(expression, "expression must not be null.");
		
		final Deque<T> stack = new ArrayDeque<>();
		final Deque<UncertainDouble> doubleStack = new ArrayDeque<>();
		
		// iterate over every item in the expression, then
		for (final String item : expression.split(" ")) {
			// choose a path based on what kind of thing was just read
			switch (this.getTokenType(item)) {
			
			case BINARY_OPERATOR:
				if (stack.size() < 2)
					throw new IllegalStateException(String.format(
							"Attempted to call binary operator %s with only %d arguments.",
							item, stack.size()));
				
				// get two arguments and operator, then apply!
				final T o1 = stack.pop();
				final T o2 = stack.pop();
				final BinaryOperator<T> binaryOperator = this.binaryOperators
						.get(item);
				
				stack.push(binaryOperator.apply(o2, o1));
				break;
			
			case NUMERIC_OPERATOR:
				if (stack.size() < 1 || doubleStack.size() < 1)
					throw new IllegalStateException(String.format(
							"Attempted to call binary operator %s with insufficient arguments.",
							item));
				
				final T ot = stack.pop();
				final UncertainDouble on = doubleStack.pop();
				final BiFunction<T, UncertainDouble, T> op = this.numericOperators
						.get(item);
				stack.push(op.apply(ot, on));
				break;
			
			case OBJECT:
				// just add it to the stack
				// these try-catch statements are necessary
				// to make the code as generalizable as possible
				// also they're required for number formatting code because
				// that's the only way to tell if an expression is a number or not.
				try {
					stack.push(this.objectObtainer.apply(item));
				} catch (final Exception e) {
					try {
						doubleStack.push(UncertainDouble.fromString(item));
					} catch (final IllegalArgumentException e2) {
						try {
							doubleStack.push(
									UncertainDouble.of(Double.parseDouble(item), 0));
						} catch (final NumberFormatException e3) {
							throw e;
						}
					}
				}
				break;
			
			case UNARY_OPERATOR:
				if (stack.size() < 1)
					throw new IllegalStateException(String.format(
							"Attempted to call unary operator %s with only %d arguments.",
							item, stack.size()));
				
				// get one argument and operator, then apply!
				final T o = stack.pop();
				final UnaryOperator<T> unaryOperator = this.unaryOperators
						.get(item);
				
				stack.push(unaryOperator.apply(o));
				break;
			default:
				throw new AssertionError(
						String.format("Internal error: Invalid token type %s.",
								this.getTokenType(item)));
			
			}
		}
		
		// return answer, or throw an exception if I can't
		if (stack.size() > 1)
			throw new IllegalStateException(
					"Computation ended up with more than one answer.");
		else if (stack.size() == 0)
			throw new IllegalStateException(
					"Computation ended up without an answer.");
		return stack.pop();
	}
}