grammar.py

# -*- coding: utf-8 -*-
"""
GSC Software: Grammar class
Author: Nick Becker
Department of Cognitive Science, Johns Hopkins University
Summer 2015
"""

import os.path
import re
import sys
import numpy as np
from collections import OrderedDict
from itertools import product
from tree import Tree

class Grammar(object):
    """
    The last grammar class you will ever need. Currently under development. 
    """

    # -------------------------------------------------------------------------
    # Constructor and supporting functions

    def __init__(self, rules, isPcfg=False, isHnf=False):
        """
        Create a grammar object from a grammar specification.

        If grammar rules are being passed in a file, they must be written in the form
            A -> B C | D E
            F -> G H
        ... etc. Separate rules must be written on separate lines.

        If grammar rules are being passed as an argument, they must be written in the form
            "A -> B C | D E; F -> G H"
        ... etc. Separate rules must be separated by a semicolon (;).

        In both cases, rules with multiple right-hand sides can use a vertical bar ('|') to
        separate different right-hand sides, or every rule can just be written on a separate line.
        All sister symbols must be separated by a space (' '). The first node of the first
        rule will be treated as the root node internally. For now, all rules must be binary
        branching at most; this is enforced within the program.

        By default, this function accepts rules in (approximately) CNF form and converts them to HNF. 
        If you want to enter HNF rules using the standard bracketing practice, you must set the hnf
        parameter to True by passing this as a value to the function.

        Rules can be entered in HNF; if they are, the flag 'isHnf' must be set to 'True.'
        PCFG functionality is on its way. For now, best not to use this functionality.
        Some features (i.e. 'toString' methods) may not work if you do.

        This function is based on one originally written by Colin Wilson.
        """
        self.isPcfg = isPcfg

        listOfRules = []

        if os.path.isfile(rules):
            f = open(rules, 'r')
            for line in f:
                listOfRules.append(line)
            f.close()
        else:
            listOfRules = rules.split(';')

        # check that all rules approximately conform to prescribed format
        ruleForm = re.compile(r'.+->.+')
        for i in range(len(listOfRules)):
            listOfRules[i] = listOfRules[i].strip()
            if re.match(ruleForm, listOfRules[i]) == None:
                sys.exit('Error: input ' + listOfRules[i] + ' is not formatted correctly.')

        # this is a bit sloppy right now, but the order in which these lines are executed does matter;
        # there is a different form depending on whether we received HNF rules (and need to convert
        # to CNF) or received CNF (and need to convert to HNF)
        if not isHnf: # default
            self.cnfRules = self.createRules(listOfRules)
            self.hnfRules, self.branchSyms = self.cnfToHnf()
        else:
            self.hnfRules = self.createRules(listOfRules)
            self.cnfRules, self.branchSyms = self.hnfToCnf()

        if self.isPcfg:
            self.cnfRules, self.hnfRules = self.setRemainingProbabilities()

        self.hgRulesAreSet = False
        self.networkInfoIsSet = False
        self.allGridpointsAreSet = False
        self.zIsSet = False
        self.allHarmoniesAreSet = False

    def createRules(self, listOfRules):
        """
        Create the internal representation of the CFG passed as parameter listOfRules.
        """
        maxN = 2

        fl = re.compile(r'^0*1?\.?\d+?$')

        rules = OrderedDict()
        for rule in listOfRules:
            splitRule = rule.split('->')        # split ruleInput into rhs and lhs
            lhs = splitRule[0].strip()          # rule[0] is the first piece (lhs)
            wholeRhs = splitRule[1].split('|')  # rule[1] is the second piece (rhs)

            for rhs in wholeRhs:
                rhsList = rhs.split()
                nChildren = len(rhsList)
                if self.isPcfg and re.match(fl, rhsList[0]) != None:
                    rhsList[0] = float(rhsList[0]) # this is a probability
                    nChildren -= 1
                if nChildren > maxN:
                    sys.exit('Seriously? Do you really need ' + str(len(rhsList))  + \
                        '-ary trees? Chomsky was satisfied with binary trees; ' + \
                        'they should be sufficient for you too.')
                rules.setdefault(lhs, []).append(rhsList)

        return rules

    def cnfToHnf(self):
        """
        Convert rules in "Conventional Normal Form" to Harmonic Normal Form. (In other
        words, add intermediate bracketed symbols.) Must be called after self.cnfRules has
        been created.

        This function is based on one originally written by Colin Wilson.
        """
        hnfRules = OrderedDict()
        branchSyms = []

        # for each left hand side
        b = re.compile(r'.*\[\d+\]')
        goodInput = True
        for lhs in self.cnfRules.keys():
            if re.match(b, lhs) != None:
                goodInput = False
            bracketIndex = 1
            for rhs in self.cnfRules[lhs]:
                # get degree of of rule (# of nonterminals)
                degree = len(rhs)
                # if there is more than one nonterminal
                if degree >= 1:
                    # create bracket symbol
                    newSym = lhs +'['+ str(bracketIndex) +']'
                    # add unique branching lhs to list
                    if not newSym in branchSyms:
                        branchSyms.append(newSym)

                    # add rules (lhs --> new and new --> rhs)
                    if self.isPcfg and isinstance(rhs[0], float):
                        hnfRules.setdefault(lhs, []).append([rhs[0], newSym])
                        hnfRules.setdefault(newSym, []).append(rhs[1:])
                    else:
                        hnfRules.setdefault(lhs, []).append([newSym])
                        hnfRules.setdefault(newSym, []).append(rhs[:])

                    bracketIndex += 1

                # if it's a terminal, just add original rule
                else:
                    hnfRules[lhs].append(rhs)

        # issue warning if no bracketed symbols were found
        if not goodInput:
            sys.exit('Error: HNF-style bracketing detected. If you meant to enter your rules in HNF, ' + \
            'you must pass parameter \'True\' to setRules(); otherwise, you should avoid using HNF-style ' + \
            'bracketing structure in your nodes.')

        # return converted rules
        return hnfRules, branchSyms

    def hnfToCnf(self):
        """
        Convert rules in Harmonic Normal Form to "Conventional Normal Form." (In other
        words, remove intermediate bracketed symbols.) Must be called after self.hnfRules
        has been created.
        """
        cnfRules = OrderedDict()
        branchSyms = []

        # for each left hand side
        b = re.compile(r'.*\[\d+\]')
        goodInput = False
        for lhs in self.hnfRules.keys():
            if re.match(b, lhs) != None:
                branchSyms.append(lhs)
                newLhs = lhs.split('[')[0]
                for rhs in self.hnfRules[lhs]:
                    cnfRules.setdefault(newLhs, []).append(rhs[:])
                goodInput = True

        if not goodInput:
            sys.exit('Error: HNF not detected. If you did not intend to use HNF, do not pass parameter ' + \
            '\'True\' to setRules().')

        # return converted rules
        return cnfRules, branchSyms

    def hnfTreeToState(self, inputString):
        """
        Use grammar to convert a tree in HNF (input as text) to a state based on the current
        network settings.
        """
        if not self.networkInfoIsSet:
            self.setNetworkInfo()

        currentTree = Tree(inputString)
        frBindings = currentTree.getFRbindings()

        byRole = {}
        for binding in frBindings:
            if binding[0] not in self.fillerNames:
                sys.exit('Error: Invalid filler (' + binding[0] + ').')
            if binding[1] not in self.roleNames:
                sys.exit('Error: Invalid role (' + binding[1] + ').')
            byRole[binding[1]] = binding[0]

        state = []
        for role in self.roleNames:
            if role not in byRole:
                if self.padWithNulls:
                    sys.exit('Error: Role ' + role + ' not in tree. Check that \n(a) you entered ' + \
                    'your tree in HNF, \n(b) null elements in the tree are explicitly represented with ' + \
                    'the null symbol (' + self.nullSymbol + '), and \n(b) your tree is licensed by the ' + \
                    'following grammar:\n\n' + self.hnfRulesToString())
                else:
                    sys.exit('Error: Role ' + role + ' not in tree. Check that \n(a) you entered ' + \
                    'your tree in HNF, and \n(b) your tree is licensed by the following grammar:\n\n' + \
                    self.hnfRulesToString())
            thisRole = [0] * len(self.fillerNames)
            thisRole[self.fillerNames.index(byRole[role])] = 1
            state += thisRole

        return np.transpose(np.array(state))

    def stateToString(self, state):
        """
        Convert state stored as a column vector to a string of 1s and 0s.
        """
        returnString = np.array_str(state)           # convert array to string
        returnString = returnString[1:-1]            # strip off leading and trailing brackets
        returnString = returnString.replace(' ','')  # remove spaces...
        returnString = returnString.replace('.','')  # ... and remove periods...
        returnString = returnString.replace('\n','') # ... and remove newlines so we are left with a binary string

        return returnString

    # -------------------------------------------------------------------------
    # Probability-related functions (these are only called in the case of a PCFG)

    def setRemainingProbabilities(self):
        """
        Fix rules such that if this is a PCFG, all rules that can expand to more than
        one right-hand side are given an equal probability to expand to each of those right-hand
        sides. Make sense?
        """
        rulesSet = [self.cnfRules, self.hnfRules]
        for rules in rulesSet:
            for lhs in rules.keys():
                wholeRhs = rules[lhs] # a list of right-hand sides (list of lists)
                currentProbValues = []
                noProbIndices = []
                probToDistribute = 0
                for rhs in wholeRhs:
                    if isinstance(rhs[0], float):
                        if rhs[0] < 0 or rhs[0] > 1:
                            sys.exit('Error: Invalid probability (' + str(rules[lhs][0]) + ').')
                        else:
                            currentProbValues.append(rhs[0])
                    else:
                        noProbIndices.append(wholeRhs.index(rhs))
                if len(noProbIndices) != 0:
                    probToDivide = 1 - sum(currentProbValues)
                    probToDistribute = probToDivide / len(noProbIndices)
                    for index in noProbIndices:
                        wholeRhs[index].insert(0, probToDistribute)
                if np.abs(1 - (len(noProbIndices) * probToDistribute + sum(currentProbValues))) > 0.02:
                    sys.exit('Error: Probabilities do not sum to 1 (check rules beginning with ' + lhs + ')')

        return rulesSet[0], rulesSet[1]

    def adjustBiases(self):
        """
        Adds values from self.biasAdjustments to self.biasVector to influence probability.
        Here, the probability difference is simply added to the most likely structure.
        """
        inf = float('Inf')
        for adjustment in self.biasAdjustments:
            if adjustment[1] > 0 and adjustment[1] < inf:
                frBinding = adjustment[0][0] + '/' + adjustment[0][1]
                self.biasVector[self.allFRbindings.index(frBinding)] += adjustment[1]

    def computeProb(self, tree, T=1):
        """
        Compute probability of tree (input as text), using all gridpoints as the sample
        space and T = 1 by default.
        """
        if not self.zIsSet:
            self.computeZ()

        return np.exp(self.getHarmony(tree) / T) / self.z

    def computeZ(self, T=1):
        """
        Computes sum_i (exp(H(tree_i)/T)) for T = 1
        """
        if not self.allHarmoniesAreSet:
            self.setAllHarmonies()

        allHarmonies = np.array(list(self.allHarmonies.values()))

        self.z = np.exp(allHarmonies / T).sum()
        self.zIsSet = True


    # -------------------------------------------------------------------------
    # Setters and supporting functions

    def setAllGridpoints(self):
        """
        Generate all gridpoints and evaluate their Harmony.
        """
        if not self.networkInfoIsSet:
            self.setNetworkInfo()

        nR = len(self.roleNames)
        nF = len(self.fillerNames)

        # generate a tuple for every possible gridpoint, storing all of them in allGrids
        allPoints = []
        for i in range(len(self.fillerNames)):
            currentPoint = [0] * len(self.fillerNames)
            currentPoint[i] = 1
            allPoints.append(currentPoint)

        allGridsList = list(product(allPoints, repeat=len(self.roleNames)))

        allGridsMat = np.zeros(shape=(nR * nF, len(allGridsList)))
        for i in range(len(allGridsList)):
            # the following line creates a matrix from the current tuple, reshapes it into a
            # single row, then transposes it to a single colum that represents this gridpoint
            gridCol = np.transpose(np.reshape(np.array(allGridsList[i]), (nR * nF, 1)))
            allGridsMat[:,i] = gridCol

        self.allGridpoints = allGridsMat
        self.allGridpointsAreSet = True

    def setAllHarmonies(self):
        """
        Store the harmony for every gridpoint because, why not? This may take a while to run,
        but will only need to be run once per grammar.
        """
        if not self.allGridpointsAreSet:
            self.setAllGridpoints()

        nGrids = self.allGridpoints.shape[1]
        allHarmonies = {}
        for i in range(nGrids):
            stateKey = self.stateToString(self.allGridpoints[:,i])
            allHarmonies[stateKey] = self.getHarmony(self.allGridpoints[:,i])

        self.allHarmonies = allHarmonies
        self.allHarmoniesAreSet = True

    def setHarmonicGrammarRules(self, maxDepth=6, useHnf=True, addNullFillers=True, nullSymbol='_'):
        """
        Create Harmonic Grammar rules based on the CFG passed as parameter
        ruleDictionary.
        """
        self.maxDepth = maxDepth
        self.useHnf = useHnf

        if self.useHnf:
            ruleSet = self.hnfRules
        else:
            ruleSet = self.cnfRules

        start = (self.getRootNode(ruleSet), 'r')

        if addNullFillers:
            self.needNullFiller = addNullFillers
            self.nullSymbol = nullSymbol
            self.nullPaddedRules = self.padWithNulls(ruleSet, self.nullSymbol)
            ruleSet = self.nullPaddedRules

        hgWeights = []
        hgBiases = []
        self.biasAdjustments = []

        self.hgWeights, self.hgBiases = self.expandHGrules(start, ruleSet, hgWeights, hgBiases)
        self.hgWeights, self.hgBiases = self.sortHGrules(self.hgWeights, self.hgBiases)
        self.hgRulesAreSet = True

    def padWithNulls(self, ruleSet, nullSymbol):
        """
        "Symmetrizes" the CFG grammar in ruleSet by padding projections with null symbols.
        For example, given the grammar
            S -> A; S -> B B,
        this function creates
            S -> A _; S -> B B
        Note that after this function is run, all parent nodes have the same number of children.
        """
        # get max number of children (max 'n')
        maxN = 0
        for lhs in ruleSet.keys():
            for rhs in ruleSet[lhs]:
                currentN = len(rhs)
                if currentN > maxN:
                    maxN = currentN

        # fill each branching rule up to n children with fillers
        for lhs in ruleSet.keys():
            if lhs in self.branchSyms:
                for rhs in ruleSet[lhs]:
                    while len(rhs) < maxN:
                        rhs.append(self.nullSymbol)

        return ruleSet

    def expandHGrules(self, parent, ruleSet, hgWeights, hgBiases):
        """
        Recursive function to find Harmonic Grammar rules. Stops when all possible
        paths through the CFG are explored, or the maximum depth is reached.

        Right now, biases are added to roles only, not filler/role bindings.
        """
        if len(parent[1]) < self.maxDepth:
            if parent[0] in ruleSet.keys():
                for rhs in ruleSet[parent[0]]:
                    harmonyDiff = 0
                    if self.isPcfg:
                        temp = rhs[1:]
                        # this currently only works for binary-branching trees
                        harmonyDiff = np.log(rhs[0]) - np.log(1 - rhs[0])
                    else:
                        temp = rhs[:]
                    if parent[1] == 'r':
                        hgBiases.append([parent[1], -(len(temp))])
                    else:
                        hgBiases.append([parent[1], -(len(temp) + 1)])
                    childLevel = '0' + parent[1]
                    for childSymbol in temp:
                        # format for hgRules: [[(S, r), (S[1], 0), 2], [...], ...]
                        self.biasAdjustments.append([[childSymbol, childLevel], harmonyDiff])
                        hgWeights.append([(parent[0], parent[1]), (childSymbol, childLevel), 2])
                        hgWeights, hgBiases = \
                            self.expandHGrules((childSymbol, childLevel), ruleSet, hgWeights, hgBiases)
                        childLevel = str(int(childLevel[0]) + 1) + childLevel[1:]
            else:
                # handles case where we are at a terminal node (at bottom of tree)
                hgBiases.append([parent[1], -1])
        else:
            # handles case where max depth was reached at a non-terminal symbol (at bottom of tree)
            hgBiases.append([parent[1], -1])

        return hgWeights, hgBiases

    def sortHGrules(self, hgWeights, hgBiases):
        """
        This is pretty sloppy. So it will remain until we come up with a a more
        clever data structure to store the HG rules (low priority right now).
        """
        # sort hgWeights
        needSwapped = True
        while needSwapped:
            needSwapped = False
            for i in range(len(hgWeights) - 1):
                if len(hgWeights[i][0][1]) > len(hgWeights[i+1][0][1]):
                    # swap
                    temp = hgWeights[i]
                    hgWeights[i] = hgWeights[i+1]
                    hgWeights[i+1] = temp
                    needSwapped = True

        # use sets to remove duplicates
        hgWeightsNoDuplicates = []
        seen = set()
        for weight in hgWeights:
            # strings are hashable, lists are not, so we must convert to add to set
            stringWeight = ''.join([weight[0][0], weight[0][1], weight[1][0], weight[1][1]])
            if stringWeight not in seen:
                hgWeightsNoDuplicates.append(weight)
                seen.add(stringWeight)

        # sort hgBiases; remember, hgBiases are currently in the form [role, bias]
        needSwapped = True
        while needSwapped:
            needSwapped = False
            for i in range(len(hgBiases) - 1):
                if len(hgBiases[i][0]) > len(hgBiases[i+1][0]):
                    # swap
                    temp = hgBiases[i]
                    hgBiases[i] = hgBiases[i+1]
                    hgBiases[i+1] = temp
                    needSwapped = True

        # use sets to remove duplicates again
        hgBiasesNoDuplicates = []
        seen = set()
        for biasPair in hgBiases:
            # strings are hashable, lists are not, so we must convert to add to set
            if biasPair[0] not in seen:
                hgBiasesNoDuplicates.append(biasPair)
                seen.add(biasPair[0])

        return hgWeightsNoDuplicates, hgBiasesNoDuplicates

    def setNetworkInfo(self):
        """
        Set the role names, filler names, weight matrix, and bias vector for
        this HNF grammar.
        """
        if not self.hgRulesAreSet:
            self.setHarmonicGrammarRules()

        roleNames = []
        for i in range(len(self.hgBiases)):
            if self.hgBiases[i][0] not in roleNames:
                roleNames.append(self.hgBiases[i][0])

        fillerNames = []
        for i in range(len(self.hgWeights)):
            if self.hgWeights[i][0][0] not in fillerNames:
                fillerNames.append(self.hgWeights[i][0][0])
            if self.hgWeights[i][1][0] not in fillerNames:
                fillerNames.append(self.hgWeights[i][1][0])

        if self.needNullFiller and self.nullSymbol not in fillerNames:
            fillerNames.append(self.nullSymbol)

        allFRbindings = []
        for i in range(len(roleNames)):
            for j in range(len(fillerNames)):
                allFRbindings.append(fillerNames[j] + '/'+ roleNames[i])

        weightMatrix = np.zeros((len(allFRbindings), len(allFRbindings)))
        for i in range(len(self.hgWeights)):
            index1 = allFRbindings.index(self.hgWeights[i][0][0] + '/' + self.hgWeights[i][0][1])
            index2 = allFRbindings.index(self.hgWeights[i][1][0] + '/' + self.hgWeights[i][1][1])
            weightMatrix[index1, index2] = self.hgWeights[i][2]
            weightMatrix[index2, index1] = self.hgWeights[i][2]

        biasVector = np.zeros((len(allFRbindings), 1))
        for i in range(len(self.hgBiases)):
            currentRole = self.hgBiases[i][0]
            currentBias = self.hgBiases[i][1]
            for j in range(len(allFRbindings)):
                if allFRbindings[j][-len(currentRole):] == currentRole:
                    biasVector[j, 0] = currentBias

        self.roleNames = roleNames
        self.fillerNames = fillerNames
        self.weightMatrix = weightMatrix
        self.biasVector = biasVector
        self.allFRbindings = allFRbindings
        self.networkInfoIsSet = True

        if self.isPcfg:
            self.adjustBiases()


    # -------------------------------------------------------------------------
    # Getters and supporting functions

    def getHarmony(self, state):
        """
        Calculate harmony of state input as column vector.
        """
        if isinstance(state, str):
            stateVector = self.hnfTreeToState(state)
        else:
            stateVector = state

        hWeight = np.dot(np.dot(np.transpose(stateVector), self.weightMatrix), stateVector)
        hBias = np.dot(np.transpose(stateVector), self.biasVector)

        return sum((0.5 * hWeight) + hBias)

    def getRootNode(self, ruleSet):
        """
        Given a dictionary of rules, find the first possible root node.
        """
        return list(ruleSet.keys())[0] # first key in ruleSet is root node

    def getTerminalNodes(self, ruleSet):
        """
        Given a dictionary of rules, find all terminal symbols.
        """
        terminals = []
        rhSides = []

        rhSides = ruleSet.keys()

        terminals = []
        for rhs in rhSides:
            for lhs in ruleSet[rhs]:
                for node in lhs:
                    if node not in rhSides and node not in terminals:
                        terminals.append(node) # must be a terminal

        return terminals

    def getNetworkInfo(self):
        """
        Get the information needed to create a weight matrix for use in neural network
        computation.
        """
        if not self.networkInfoIsSet:
            self.setNetworkInfo()

        return self.roleNames, self.fillerNames, self.weightMatrix, self.biasVector

    def getWeight(self, binding1, binding2):
        """
        Get specific weight from weight matrix.
        """
        binding1_isValid = binding1 in self.allFRbindings
        binding2_isValid = binding2 in self.allFRbindings
        if not binding1_isValid and not binding2_isValid:
            sys.exit('Error: \'' + binding1 + '\' and \'' + binding2 + '\' are not valid filler/role bindings.')
        elif not binding1_isValid:
            sys.exit('Error: \'' + binding1 + '\' is not a valid filler/role binding.')
        elif not binding2_isValid:
            sys.exit('Error: \'' + binding2 + '\' is not a valid filler/role binding.')
        else:
            return self.weightMatrix[self.allFRbindings.index(binding1), self.allFRbindings.index(binding2)]

    def getBias(self, binding):
        """
        Get specific bias from bias vector.
        """
        bindingIsValid = binding in self.allFRbindings
        if not bindingIsValid:
            sys.exit('Error: \'' + binding + '\' is not a valid filler/role binding.')
        else:
            return self.biasVector[self.allFRbindings.index(binding), 0]


    # -------------------------------------------------------------------------
    # Pretty 'toString' methods

    def cnfRulesToString(self):
        """
        Gets a pretty string for the CNF rules.
        """
        nRules = 0
        for lhs in self.cnfRules.keys():
            nRules += len(self.cnfRules[lhs])

        nStringified = 0
        returnString = '{'
        for lhs in self.cnfRules.keys():
            for rhs in self.cnfRules[lhs]:
                if nStringified != 0:
                    returnString += ' '
                returnString += lhs + ' -> '
                for i in range(len(rhs)):
                    if self.isPcfg and i == 0:
                        returnString += str(rhs[i])
                    else:
                        returnString += rhs[i]
                    if i != len(rhs) - 1:
                        returnString += ' '
                if nStringified != nRules - 1:
                    returnString += '; \n'
                nStringified += 1
        returnString += '}'

        return returnString

    def hnfRulesToString(self):
        """
        Gets a pretty string for the HNF rules.
        """
        nRules = 0
        for lhs in self.hnfRules.keys():
            nRules += len(self.hnfRules[lhs])

        nStringified = 0
        returnString = '{'
        for lhs in self.hnfRules.keys():
            for rhs in self.hnfRules[lhs]:
                if nStringified != 0:
                    returnString += ' '
                returnString += lhs + ' -> '
                for i in range(len(rhs)):
                    if self.isPcfg and i == 0:
                        returnString += str(rhs[i])
                    else:
                        returnString += rhs[i]
                    if i != len(rhs) - 1:
                        returnString += ' '
                if nStringified != nRules - 1:
                    returnString += '; \n'
                nStringified += 1
        returnString += '}'

        return returnString

    def hgWeightsToString(self):
        """
        Gets a pretty string for the HG weights.
        """
        if not self.hgRulesAreSet:
            self.setHarmonicGrammarRules()

        returnString = '{'
        for i in range(len(self.hgWeights)):
            if i != 0:
                returnString += ' '
            returnString += '[(' + self.hgWeights[i][0][0] + '/'+ self.hgWeights[i][0][1] \
                + ', ' + self.hgWeights[i][1][0] + '/' + self.hgWeights[i][1][1] \
                + '), ' + str(self.hgWeights[i][-1]) + ']'
            if i != len(self.hgWeights) - 1:
                returnString += '; \n'
        returnString += '}'

        return returnString

    def hgBiasesToString(self):
        """
        Gets a pretty string for the HG biases.
        """
        if not self.hgRulesAreSet:
            self.setHarmonicGrammarRules()

        returnString = '{'
        for i in range(len(self.hgBiases)):
            if i != 0:
                returnString += ' '
            returnString += '[' + self.hgBiases[i][0] + ', ' + str(self.hgBiases[i][1]) + ']'
            if i != len(self.hgBiases) - 1:
                returnString += '; \n'
        returnString += '}'

        return returnString

    def hgRulesToString(self):
        """
        Concatenates the HG weights and biases and gets a pretty string for them.
        """
        if not self.hgRulesAreSet:
            self.setHarmonicGrammarRules()

        returnString = '{'
        for i in range(len(self.hgWeights)):
            if i != 0:
                returnString += ' '
            returnString += '[(' + self.hgWeights[i][0][0] + '/'+ self.hgWeights[i][0][1] \
                + ', ' + self.hgWeights[i][1][0] + '/' + self.hgWeights[i][1][1] \
                + '), ' + str(self.hgWeights[i][-1]) + '];\n'
        for i in range(len(self.hgBiases)):
            returnString += ' [' + self.hgBiases[i][0] + ', ' + str(self.hgBiases[i][1]) + ']'
            if i != len(self.hgBiases) - 1:
                returnString += '; \n'
        returnString += '}'

        return returnString

    def biasVectorToString(self):
        """
        Gets a pretty string for the bias vector.
        """
        returnString = ''
        for i in range(len(self.allFRbindings)):
            returnString += self.allFRbindings[i] + ', ' + str(self.biasVector[i]) + '\n'

        return returnString