gazprea-fuzzer-python/ast_generator/ast_generator.py

import random
import string
import xml.etree.ElementTree as ET

from english_words import get_english_words_set

from ast_generator.utils import Variable, Argument, Routine, Scope, build_xml_element
from constants import *

import keyword


class AstGenerator:
    """
    Generates an AST from a grammar based on given settings

    Originally the intention was to use the ISLa library to generate
    the AST, however I found that ISLa is like taking a buldozer to
    a sledgehammer's job, so I decided to write a procedural generator
    instead.

    The way we select elements is we take all the settings in their
    category and assign them a range on a number line. Then we
    pick a random number in that range and whichever category it
    falls into will be selected.
    """

    def __init__(self, settings: dict):
        """
        This class is designed to get  the settings from some wrapper class that
        better defines the precise constraints of the language being generated

        the necessary settings are in the .yaml file and #TODO this is not generalizable yet

        @param settings: settings for weights and probabilities and lengths
        """
        self.settings = settings

        self.symbol_table = []
        global_scope = Scope(None, None)
        self.symbol_table.append(global_scope)  # NOTE for debug
        self.current_scope = global_scope

        names = get_english_words_set(['web2'], alpha=True)
        possible_names = filter(lambda x: self.settings['properties']['id-length']['max'] <= len(x) <=
                                          self.settings['properties']['id-length']['max'] and not keyword.iskeyword(x), names)

        var_name_list = list(possible_names)
        var_name_len = len(var_name_list)
        self.variable_names = var_name_list[0:var_name_len // 2]
        self.routine_names = var_name_list[var_name_len // 2:var_name_len]

        self.ast: ET.Element or None = None
        self.current_ast_element: ET.Element or None = None
        self.current_nesting_depth = 0
        self.current_control_flow_nesting_depth = 0

        # Numberlines - For computing probabilities
        self.int_op_options, self.int_op_cutoffs, self.int_op_numline = (
            self.get_numberlines('expression-weights',
                                 ['brackets', 'arithmetic', 'unary'],
                                 [[], [], ['not']]))
        self.int_unary = ['negation', 'noop']

        self.bool_op_options, self.bool_op_cutoffs, self.bool_op_numline = (
            self.get_numberlines('expression-weights',
                                 ['brackets', 'comparison', 'logical', 'unary'],
                                 excluded_values=[[], ['less-than-or-equal', 'greater-than-or-equal', 'less-than',
                                                       'greater-than'], [], ['noop', 'negation']]))
        self.bool_unary = ['not']

        self.float_op_options, self.float_op_cutoffs, self.float_op_numline = (
            self.get_numberlines('expression-weights',
                                 ['brackets', 'arithmetic', 'unary'],
                                 [[], [], ['not']]))
        self.float_unary = ['negation', 'noop']

        self.char_op_options, self.char_op_cutoffs, self.char_op_numline = (
            self.get_numberlines('expression-weights',
                                 ['brackets', 'comparison'],
                                 [[], ['less-than', 'greater-than', 'less-than-or-equal', 'greater-than-or-equal']]))

        self.comp_op_options, self.comp_op_cutoffs, self.comp_op_numline = (
            self.get_numberlines('expression-weights',
                                 ['brackets', 'comparison'],
                                 [[], []]))

    def get_numberlines(self, settings_section: str, subsettings: list[str], excluded_values):
        assert len(subsettings) == len(excluded_values)

        number_line = 0
        cutoffs = []
        cutoff = 0
        options = {}
        option = 0

        settings = []

        for key, value in self.settings[settings_section].items():
            if key in subsettings and key not in excluded_values:  # this check needs to be done recursively
                if isinstance(value, int):
                    t = {
                        key: value
                    }
                    settings.append(t)
                elif isinstance(value, dict):
                    settings.append(value)
                else:
                    raise TypeError("invalid setting type. Found " + str(value) + " instead of expected int or dict")

        for v in range(len(settings)):
            for i in excluded_values:
                for j in i:
                    if j in settings[v]:
                        settings[v].pop(j)

        for v in settings:
            if isinstance(v, dict):
                for key, value in v.items():
                    number_line += value
                    cutoffs.append(cutoff + value)
                    cutoff += value
                    options[option] = key
                    option += 1
            elif isinstance(v, int):
                number_line += v
                cutoffs.append(cutoff + v)
                cutoff += v
                options[option] = v
                option += 1
            else:
                raise TypeError("invalid setting type. Found " + str(v) + " instead of expected int")

        return options, cutoffs, number_line

    def generate_ast(self):
        """
        @brief generates an AST from a grammar
        """
        self.generate_top_level_block()

    def generate_top_level_block(self):  # TODO add constant generation into this block
        i = 0

        element = build_xml_element([], name=GAZ_BLOCK_TAG)
        self.current_ast_element = element

        self.ast = element

        # optional constants here too

        self.generate_main()
        while i < self.settings['generation-options']['max-number-of-routines']:
            if random.random() < self.settings['block-termination-probability']:
                break
            self.generate_routine()
            i += 1

    def generate_main(self):
        parent = self.current_ast_element
        self.push_scope()
        main_args = [  # TODO refactor these into constants
            ("name", "main"),
            ("return_type", GAZ_INT_KEY),
            ("args", "()"),
        ]
        element = build_xml_element(main_args, name=GAZ_PROCEDURE_TAG)
        self.current_ast_element.append(element)
        self.current_ast_element = element
        self.generate_block(return_stmt=True, return_value="0", return_type=GAZ_INT_KEY)
        self.pop_scope()
        self.current_ast_element = parent

    def generate_block(self, tag=None, return_stmt=False, return_value=None, return_type=None, block_type=None,
                       loop_var=None):
        # TODO this should be broken into many functions depending on the block requirements

        if tag is None:
            tag = []
        parent = self.current_ast_element
        self.push_scope()
        element = build_xml_element(tag, name=GAZ_BLOCK_TAG)
        self.current_ast_element.append(element)
        self.current_ast_element = element

        # Generate the loop condition increment if we are in a loop
        if block_type == GAZ_LOOP_TAG:
            self.generate_loop_condition_check(loop_var)
            self.generate_loop_condition_increment(loop_var)

        self.generate_statements()
        if return_stmt:
            self.generate_return(return_type=return_type, return_value=return_value)
        if self.settings['generation-options']['generate-dead-code']:
            self.generate_statements()
        self.pop_scope()
        self.current_ast_element = parent

    def generate_loop_condition_check(self, loop_var: Variable):
        """
        @brief generates the loop condition check

        Ensures that the loop does not iterate more than max-loop-iterations times

        @param loop_var:
        @return:
        """
        # loop var is always an int
        assert loop_var.type == GAZ_INT_KEY

        # create a conditional xml tag
        if_stmt = build_xml_element([], name=GAZ_IF_TAG)
        self.current_ast_element.append(if_stmt)
        parent = self.current_ast_element
        self.current_ast_element = if_stmt

        # add the check 'if loop_var >= self.settings['generation_options']['max-loop-iterations']: break'
        operation = build_xml_element([("op", ">=")], name=GAZ_OPERATOR_TAG)
        self.current_ast_element.append(operation)
        self.current_ast_element = operation

        lhs = build_xml_element([], name=GAZ_LHS_TAG)
        operation.append(lhs)

        var = build_xml_element([("name", loop_var.name), ("type", loop_var.type)], name=GAZ_VAR_TAG)
        lhs.append(var)

        rhs = build_xml_element([], name=GAZ_RHS_TAG)
        operation.append(rhs)
        rhs.append(self.make_literal(GAZ_INT_KEY, "'" + str(self.settings['generation-options']['max-loop-iterations']) + "'"))

        true_block = build_xml_element([], name=GAZ_BLOCK_TAG)
        if_stmt.append(true_block)
        self.current_ast_element = true_block
        break_stmt = build_xml_element([], name=GAZ_BREAK_TAG)
        true_block.append(break_stmt)

        # return everything to normalcy
        self.current_ast_element = parent

    def generate_loop_condition_increment(self, loop_var):
        assert loop_var.type == GAZ_INT_KEY

        parent = self.current_ast_element
        assignment = build_xml_element([], name=GAZ_ASSIGNMENT_TAG)
        self.current_ast_element.append(assignment)
        self.current_ast_element = assignment

        # append the variable
        self.current_ast_element.append(loop_var.xml)

        # add the increment 'loop_var += 1'
        assn_rhs = build_xml_element([], name=GAZ_RHS_TAG)
        self.current_ast_element.append(assn_rhs)
        self.current_ast_element = assn_rhs

        operation = build_xml_element([("op", "+")], name=GAZ_OPERATOR_TAG)
        self.current_ast_element.append(operation)
        self.current_ast_element = operation

        lhs = build_xml_element([], name=GAZ_LHS_TAG)
        operation.append(lhs)

        var = build_xml_element([("name", loop_var.name), ("type", loop_var.type)], name=GAZ_VAR_TAG)
        lhs.append(var)

        rhs = build_xml_element([], name=GAZ_RHS_TAG)
        operation.append(rhs)
        rhs.append(self.make_literal(GAZ_INT_KEY, '1'))

        # return everything to normalcy
        self.current_ast_element = parent

    def generate_return(self, return_type=None, return_value=None):
        if return_type is None or return_type == GAZ_VOID_TYPE:
            self.current_ast_element.append(build_xml_element([], name=GAZ_RETURN_TAG))
            return
        else:
            if return_value is None:
                xml_element = build_xml_element([("type", return_type)], name=GAZ_RETURN_TAG)
                self.current_ast_element.append(xml_element)
                parent = self.current_ast_element
                self.current_ast_element = xml_element
                self.generate_expression(return_type)
                self.current_ast_element = parent
                return
            else:
                xml_element = build_xml_element([("type", return_type)], name=GAZ_RETURN_TAG)
                self.current_ast_element.append(xml_element)
                parent = self.current_ast_element
                self.current_ast_element = xml_element
                self.current_ast_element.append(self.make_literal(return_type, return_value))
                self.current_ast_element = parent
                return

    def generate_routine(self, routine_type=None):
        if routine_type is None:
            routine_type = self.get_routine_type()
        else:
            routine_type = routine_type

        args = self.generate_routine_args()

        name = self.get_name(routine_type)
        return_type = self.get_type(routine_type)

        routine = Routine(name, routine_type, return_type, args)

        routine_args = [
            ("name", routine.name),
            ("return_type", routine.return_type),
        ]

        element = build_xml_element(routine_args, name=routine.type)
        self.current_ast_element.append(element)
        parent = self.current_ast_element
        self.current_ast_element = element
        self.push_scope()

        self.define_args(routine.arguments)

        self.generate_block(return_stmt=True, return_type=routine.return_type)
        self.pop_scope()

        self.current_ast_element = parent

    def define_args(self, args):
        for arg in args:
            self.current_ast_element.append(arg.xml)
            self.current_scope.append(arg.name, arg)

    def generate_statements(self):
        # Number line
        number_line = 180  # TODO fix the numberline stuff to reflect the settings
        cutoffs = [10, 30, 50, 80, 100, 140, 180]
        options = {
            0: self.generate_declaration,
            1: self.generate_routine_call,
            2: self.generate_conditional,
            3: self.generate_loop,
            4: self.generate_assignment,
            5: self.generate_out_stream,
            6: self.generate_in_stream,
        }

        while True:
            if random.random() < self.settings['block-termination-probability']:
                break

            a = random.randint(0, number_line)
            i = 0
            for i in range(len(cutoffs) - 1):
                if cutoffs[i] < a < cutoffs[i + 1]:
                    try:
                        options[i]()
                    except ValueError:
                        break
                    break

    def generate_int_expr(self):
        self._generate_expression([GAZ_INT_KEY],
                                  self.int_op_numline,
                                  self.int_op_cutoffs,
                                  self.int_op_options,
                                  self.int_unary)

    def generate_float_expr(self):
        self._generate_expression([GAZ_FLOAT_KEY, GAZ_INT_KEY],
                                  self.float_op_numline,
                                  self.float_op_cutoffs,
                                  self.float_op_options,
                                  self.float_unary)

    def generate_bool_expr(self):
        self._generate_expression([GAZ_BOOL_KEY],
                                  self.bool_op_numline,
                                  self.bool_op_cutoffs,
                                  self.bool_op_options,
                                  self.bool_unary)

    def generate_char_expr(self):
        self._generate_expression([GAZ_CHAR_KEY],
                                  self.char_op_numline,
                                  self.char_op_cutoffs,
                                  self.char_op_options)

    def generate_comp_expr(self):
        self._generate_expression([GAZ_BOOL_KEY],
                                  self.comp_op_numline,
                                  self.comp_op_cutoffs,
                                  self.comp_op_options,
                                  comparison=True)

    def _generate_expression(self, expr_type: list[str], number_line,
                             cutoffs, options, unary=None, comparison: bool = False):
        if unary is None:
            unary = []

        parent = self.current_ast_element
        self.current_nesting_depth += 1

        if self.current_nesting_depth > self.settings['generation-options']['max-nesting-depth'] or random.random() < \
                self.settings['block-termination-probability']:
            self.generate_literal(random.choice(expr_type))
            self.current_nesting_depth -= 1
            return

        op = ""
        a = random.randint(0, number_line - 1)
        i = 0
        for i in range(len(cutoffs) - 1):
            if i == 0:
                if a < cutoffs[i]:
                    op = options[i]
                    break
            if cutoffs[i] <= a < cutoffs[i + 1]:
                op = options[i]
                break

        if op in unary:
            self.generate_unary(op, random.choice(expr_type))
        elif op == GAZ_BRACKET_TAG:
            self.generate_bracket(random.choice(expr_type))
        elif comparison:
            if op in ['equality', 'inequality']:
                self.generate_binary(op, random.choice([GAZ_INT_KEY, GAZ_FLOAT_KEY, GAZ_CHAR_KEY]))
            else:
                self.generate_binary(op, random.choice([GAZ_INT_KEY, GAZ_FLOAT_KEY]))
        else:
            self.generate_binary(op, random.choice(expr_type))

        self.current_nesting_depth -= 1
        self.current_ast_element = parent

    def generate_declaration(self, mut=None):
        parent = self.current_ast_element
        decl_type = self.get_type(GAZ_VAR_TAG)
        decl_args = [
            ("type", decl_type),
        ]
        element = build_xml_element(decl_args, name=GAZ_DECLARATION_TAG)
        self.current_ast_element.append(element)
        self.current_ast_element = element

        variable = self.generate_variable(decl_type, mut=mut)
        self.current_ast_element.append(variable.xml)
        self.current_scope.append(variable.name, variable)

        self.generate_xhs(GAZ_RHS_TAG, decl_type)  # TODO add real type (decl_type)
        self.current_ast_element = parent

    def generate_binary(self, op, op_type):
        parent = self.current_ast_element
        if op == "":
            raise ValueError("op is empty!")
        args = [
            ("op", op),
            ("type", op_type),
        ]
        element = build_xml_element(args, name=GAZ_OPERATOR_TAG)
        self.current_ast_element.append(element)
        self.current_ast_element = element

        self.generate_xhs(GAZ_LHS_TAG, op_type)
        self.generate_xhs(GAZ_RHS_TAG, op_type)

        self.current_ast_element = parent

    def generate_bracket(self, op_type):
        parent = self.current_ast_element
        args = [
            ("type", op_type),
        ]
        element = build_xml_element(args, name=GAZ_BRACKET_TAG)
        self.current_ast_element.append(element)
        self.current_ast_element = element

        self.generate_xhs(GAZ_RHS_TAG, op_type)

        self.current_ast_element = parent

    def generate_xhs(self, handedness, op_type, is_zero=False):
        element = build_xml_element([], name=handedness)
        parent = self.current_ast_element
        self.current_ast_element.append(element)
        self.current_ast_element = element

        self.generate_expression(op_type, is_zero=is_zero)

        self.current_ast_element = parent

    def generate_unary(self, op, op_type=ANY_TYPE):
        parent = self.current_ast_element
        args = [
            ("op", op),
            ("type", op_type),
        ]
        element = build_xml_element(args, name=GAZ_UNARY_OPERATOR_TAG)
        self.current_ast_element.append(element)
        self.current_ast_element = element

        self.generate_xhs(GAZ_RHS_TAG, op_type)

        self.current_ast_element = parent

    def generate_routine_call(self):
        pass

    def generate_conditional(self):
        if self.current_control_flow_nesting_depth >= self.settings['generation-options']['max-nesting-depth']:
            return

        if self.current_control_flow_nesting_depth > 0 and random.random() < self.settings[
            'block-termination-probability']:
            return

        element = build_xml_element([], name=GAZ_IF_TAG)
        self.current_ast_element.append(element)
        parent = self.current_ast_element
        self.current_ast_element = element

        self.current_control_flow_nesting_depth += 1

        self.push_scope()

        self.generate_expression(GAZ_BOOL_KEY)

        self.generate_block(tag=[("type", GAZ_TRUE_BLOCK_TAG)])
        self.generate_block(tag=[("type", GAZ_FALSE_BLOCK_TAG)])

        self.pop_scope()
        self.current_ast_element = parent

    def generate_loop(self):  # fixme generation of infinite loops happens too often...
        # FIXME make sure that loop conditions are evaluated at least once (assert true or make a config param)
        if self.current_control_flow_nesting_depth >= self.settings['generation-options']['max-nesting-depth']:
            return

        if self.current_control_flow_nesting_depth > 0 and random.random() < self.settings[
            'block-termination-probability']:
            return

        init_var = self.generate_zero_declaration()
        parent = self.current_ast_element
        element = build_xml_element([], name=GAZ_LOOP_TAG)
        self.current_ast_element.append(element)
        self.current_ast_element = element

        self.current_control_flow_nesting_depth += 1
        self.push_scope()
        self.generate_expression(GAZ_BOOL_KEY)
        self.generate_block(block_type=GAZ_LOOP_TAG,
                            loop_var=init_var)  # append a variable increment and prepend a break statement if var is > max loop iterations
        self.pop_scope()
        self.current_ast_element = parent

    def generate_zero_declaration(self):
        parent = self.current_ast_element
        element = build_xml_element([], name=GAZ_DECLARATION_TAG)

        self.current_ast_element.append(element)
        self.current_ast_element = element

        variable = self.generate_variable(GAZ_INT_KEY, 'var')
        self.current_ast_element.append(variable.xml)
        self.current_scope.append(variable.name, variable)

        self.generate_xhs(GAZ_RHS_TAG, variable.type, is_zero=True)
        self.current_ast_element = parent

        return variable

    def generate_assignment(self):
        possible_vars = self.current_scope.get_all_defined_mutable_vars()
        if len(possible_vars) == 0:
            raise ValueError("No possible variables to assign to!")

        # same structure as a declaration
        parent = self.current_ast_element

        element = build_xml_element([], name=GAZ_ASSIGNMENT_TAG)
        self.current_ast_element.append(element)
        self.current_ast_element = element

        variable = random.choice(possible_vars)

        self.current_ast_element.append(variable.xml)
        self.generate_xhs(GAZ_RHS_TAG, variable.type)

        self.current_ast_element = parent

    def generate_out_stream(self):
        self.generate_stream(GAZ_OUT_STREAM)

    def generate_in_stream(self):
        self.generate_stream(GAZ_IN_STREAM)

    def generate_stream(self, stream_type):
        parent = self.current_ast_element
        args = [
            ("type", stream_type),
        ]
        element = build_xml_element(args, name=GAZ_STREAM_TAG)
        self.current_ast_element.append(element)
        self.current_ast_element = element

        self.generate_expression(ANY_TYPE)

        self.current_ast_element = parent

    def generate_variable(self, var_type: str, mut=None):
        if mut is None:
            return Variable(self.get_name(GAZ_VAR_TAG), var_type, self.get_qualifier())
        else:
            return Variable(self.get_name(GAZ_VAR_TAG), var_type, mut)

    def generate_literal(self, var_type: str, value=None):
        if value is None:
            value = self.get_value(var_type)
        else:
            value = value
        args = [
            ("type", var_type),
            ("value", str(value)),
        ]
        element = build_xml_element(args, name=GAZ_LIT_TAG)
        self.current_ast_element.append(element)

    def make_literal(self, type, value):
        args = [
            ("type", type),
            ("value", value),
        ]
        element = build_xml_element(args, name=GAZ_LIT_TAG)
        return element

    def generate_global(self):
        current_scope = self.current_scope
        current_element = self.current_ast_element

        self.current_scope = self.current_scope.get_top_scope()
        self.current_ast_element = self.ast

        self.generate_declaration(mut='const')

        self.current_scope = current_scope
        self.current_ast_element = current_element

    def generate_expression(self, expr_type: str, is_zero=False):
        if is_zero:
            self.generate_literal(expr_type, value=0)
            return
        elif expr_type == GAZ_INT_KEY or expr_type == GAZ_FLOAT_KEY:
            self.generate_int_expr()
        elif expr_type == GAZ_BOOL_KEY:
            if random.random() < 0.5:
                self.generate_bool_expr()
            else:
                self.generate_comp_expr()
        elif expr_type == GAZ_CHAR_KEY:
            self.generate_char_expr()
        elif expr_type == ANY_TYPE:  # TODO implement the choice of any type
            self.generate_int_expr()
        else:
            raise NotImplementedError(f"Expression type {expr_type} not implemented")

    def generate_routine_args(self):
        number = random.randint(self.settings['properties']['number-of-arguments']['min'],
                                self.settings['properties']['number-of-arguments']['max'])
        args = []
        for i in range(number):
            arg = self.generate_arg()
            args.append(arg)
            self.current_scope.append(arg.name, arg)
        return args

    def generate_arg(self):
        return Argument(self.get_name(GAZ_VAR_TAG), self.get_type(GAZ_VAR_TAG))

    def push_scope(self, xml_element: ET.Element = None):
        scope = Scope(self.current_scope)
        self.symbol_table.append(scope)
        self.current_scope = scope

    def pop_scope(self):
        self.current_scope = self.current_scope.enclosing_scope

    # TODO revamp the random value generations
    def get_qualifier(self):
        """
        @brief get a random qualifier from the list of possible qualifiers

        @return a qualifier as a string
        """
        number_line = (self.settings["misc-weights"]["type-qualifier-weights"]["const"] +
                       self.settings["misc-weights"]["type-qualifier-weights"]["var"] - 1)

        res = random.randint(0, number_line)
        if res in range(0, self.settings["misc-weights"]["type-qualifier-weights"]["const"]):
            return 'const'
        elif res in range(self.settings["misc-weights"]["type-qualifier-weights"]["const"],
                          self.settings["misc-weights"]["type-qualifier-weights"]["const"] +
                          self.settings["misc-weights"]["type-qualifier-weights"]["var"]):
            return 'var'
        else:
            raise ValueError("Internal Error, please report the stack trace to me")

    def get_routine_type(self):
        cutoffs = []
        values = []
        ops = []
        for key, value in self.settings["routine-weights"].items():
            cutoffs.append(value + sum(cutoffs))
            values.append(value)
            ops.append(key)

        res = random.randint(0, sum(values))
        for i in range(len(cutoffs)):
            if res < cutoffs[i]:
                return ops[i]  # TODO everything should be fast faied

    def get_value(self, type):
        if type == GAZ_INT_KEY:
            if self.settings["properties"]["generate-max-int"]:
                return random.randint(-2147483648, 2147483647)
            else:
                return random.randint(-1000, 1000)
        elif type == GAZ_FLOAT_KEY:
            return random.uniform(-1000, 1000)
        elif type == GAZ_BOOL_KEY:
            return random.choice([True, False])
        elif type == GAZ_CHAR_KEY:
            return "'" + random.choice(string.ascii_letters) + "'"
        else:
            raise TypeError("Unimplemented generator for type: " + type)

    def get_name(self, name_type):
        """
        @brief get a random name from the list of possible names and add it to the current scope

        @param name_type:
        @return:
        """
        if not self.settings['properties']['use-english-words']:
            length = random.randint(self.settings['properties']['id-length']['min'],
                                    self.settings['properties']['id-length']['max'])
            name = ''.join(random.choices(string.ascii_letters, k=length))
            return name
        else:
            if name_type == GAZ_VAR_TAG:
                choice = random.choice(self.variable_names)
                self.variable_names.remove(choice)
                return choice
            else:
                choice = random.choice(self.routine_names)
                self.routine_names.remove(choice)
                return choice

    def get_type(self, tag):  # TODO Add support for composite types
        return 'int'  # TODO Add support for all types
        if tag in [GAZ_PROCEDURE_TAG, GAZ_FUNCTION_TAG, GAZ_VAR_TAG]:
            cutoffs = []
            values = []
            types = []
            for key, value in self.settings["type-weights"]["value-types"].items():
                if key == GAZ_VOID_TYPE and tag != GAZ_PROCEDURE_TAG:
                    continue
                cutoffs.append(value + sum(cutoffs))
                values.append(value)
                types.append(key)

            res = random.randint(0, sum(values))
            for i in range(len(cutoffs)):
                if res < cutoffs[i]:
                    return types[i]