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utils.py
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utils.py
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#!/usr/bin/env python3.7
"""Tools for premise selection NN framework."""
# Built-in modules
import os
from datetime import timedelta
from random import sample
from time import time
# Third-party modules
import numpy as np
import pickle
from lark import Lark, Transformer
from tqdm import tqdm
# -- File info --
__version__ = '0.1.4'
__copyright__ = 'Andrzej Kucik 2019'
__author__ = 'Andrzej Kucik'
__maintainer__ = 'Andrzej Kucik'
__email__ = 'andrzej.kucik@gmail.com'
__date__ = '2019-08-23'
# TPTP parser
tptp_parser = Lark(r"""
?tptp_file : tptp_input*
?tptp_input : annotated_formula | include
?annotated_formula : thf_annotated | tfx_annotated | tff_annotated| tcf_annotated | fof_annotated | cnf_annotated
| tpi_annotated
tpi_annotated : "tpi(" name "," formula_role "," tpi_formula annotations* ")."
tpi_formula : fof_formula
thf_annotated : "thf(" name "," formula_role "," thf_formula annotations* ")."
tfx_annotated : "tfx(" name "," formula_role "," tfx_formula annotations* ")."
tff_annotated : "tff(" name "," formula_role "," tff_formula annotations* ")."
tcf_annotated : "tcf(" name "," formula_role "," tcf_formula annotations* ")."
fof_annotated : "fof(" name "," formula_role "," fof_formula annotations* ")."
cnf_annotated : "cnf(" name "," formula_role "," cnf_formula annotations* ")."
annotations : "," source (optional_info)*
formula_role : FORMULA_ROLE
FORMULA_ROLE : "axiom" | "hypothesis" | "definition" | "assumption" | "lemma" | "theorem" | "corollary"
| "conjecture" | "negated_conjecture" | "plain" | "type" | "fi_domain" | "fi_functors"
| "fi_predicates" | "unknown" | LOWER_WORD
thf_formula : thf_logic_formula | thf_sequent
thf_logic_formula : thf_binary_formula | thf_unitary_formula | thf_type_formula | thf_subtype
thf_binary_formula : thf_binary_pair | thf_binary_tuple | thf_binary_type
thf_binary_pair : thf_unitary_formula thf_pair_connective thf_unitary_formula
thf_binary_tuple : thf_or_formula | thf_and_formula | thf_apply_formula
thf_or_formula : thf_unitary_formula "|" thf_unitary_formula | thf_or_formula "|" thf_unitary_formula
thf_and_formula : thf_unitary_formula "&" thf_unitary_formula | thf_and_formula "&" thf_unitary_formula
thf_apply_formula: thf_unitary_formula "@" thf_unitary_formula | thf_apply_formula "@" thf_unitary_formula
thf_unitary_formula : thf_quantified_formula | thf_unary_formula | thf_atom | thf_conditional | thf_let | thf_tuple
| "(" thf_logic_formula ")"
thf_quantified_formula : thf_quantification thf_unitary_formula
thf_quantification : thf_quantifier "[" thf_variable_list "] :"
thf_variable_list : thf_variable ("," thf_variable)*
thf_variable : thf_typed_variable | variable
thf_typed_variable : variable ":" thf_top_level_type
thf_unary_formula : thf_unary_connective "(" thf_logic_formula ")"
thf_atom : thf_function | variable | defined_term | thf_conn_term
thf_function : atom | functor "(" thf_arguments ")" | defined_functor "(" thf_arguments ")"
| system_functor "(" thf_arguments ")"
thf_conn_term : thf_pair_connective | assoc_connective | thf_unary_connective
thf_conditional : "$ite(" thf_logic_formula "," thf_logic_formula "," thf_logic_formula ")"
thf_let : "$let(" thf_unitary_formula "," thf_formula ")" | "$let(" thf_let_defns "," thf_formula")"
thf_let_defns : thf_let_defn | "[" thf_let_defn_list "]"
thf_let_defn_list : thf_let_defn ("," thf_let_defn)*
thf_let_defn : thf_let_quantified_defn | thf_let_plain_defn
thf_let_quantified_defn: thf_quantification "(" thf_let_plain_defn ")"
thf_let_plain_defn: thf_let_defn_lhs ASSIGNMENT thf_formula
thf_let_defn_lhs : constant | functor "(" fof_arguments ")" | thf_tuple
thf_arguments : thf_formula_list
thf_type_formula : thf_typeable_formula ":" thf_top_level_type | constant ":" thf_top_level_type
thf_typeable_formula : thf_atom | "(" thf_logic_formula ")"
thf_subtype : thf_atom "<<" thf_atom
thf_top_level_type : thf_unitary_type | thf_mapping_type | thf_apply_type
thf_unitary_type : thf_unitary_formula
thf_apply_type : thf_apply_formula
thf_binary_type : thf_mapping_type | thf_xprod_type | thf_union_type
thf_mapping_type : thf_unitary_type ">" thf_unitary_type | thf_unitary_type ">" thf_mapping_type
thf_xprod_type : thf_unitary_type "*" thf_unitary_type | thf_xprod_type "*" thf_unitary_type
thf_union_type : thf_unitary_type "+" thf_unitary_type | thf_union_type "+" thf_unitary_type
thf_sequent : thf_tuple "-->" thf_tuple | "(" thf_sequent ")"
thf_tuple : "[" thf_formula_list? "]" | "{" thf_formula_list? "}"
thf_formula_list : thf_logic_formula ("," thf_logic_formula)*
logic_defn_rule : logic_defn_lhs assignment logic_defn_rhs
logic_defn_lhs : logic_defn_value | thf_top_level_type | name | "$constants" | "$quantification" | "$consequence"
| "$modalities"
logic_defn_rhs : logic_defn_value | thf_unitary_formula
logic_defn_value : LOGIC_DEFN_VALUE
LOGIC_DEFN_VALUE : DEFINED_CONSTANT | "$rigid" | "$flexible" | "$constant" | "$varying" | "$cumulative"
| "$decreasing" | "$local" | "$global" | "$modal_system_K" | "$modal_system_T" | "$modal_system_D"
| "$modal_system_S4" | "$modal_system_S5" | "$modal_axiom_K" | "$modal_axiom_T" | "$modal_axiom_B"
| "$modal_axiom_D" | "$modal_axiom_4" | "$modal_axiom_5"
tfx_formula : tfx_logic_formula | thf_sequent
tfx_logic_formula : thf_logic_formula
tff_formula : tff_logic_formula | tff_typed_atom | tff_sequent
tff_logic_formula : tff_binary_formula | tff_unitary_formula | tff_subtype
tff_binary_formula : tff_binary_nonassoc | tff_binary_assoc
tff_binary_nonassoc : tff_unitary_formula binary_connective tff_unitary_formula
tff_binary_assoc : tff_or_formula | tff_and_formula
tff_or_formula : tff_unitary_formula "|" tff_unitary_formula | tff_or_formula "|" tff_unitary_formula
tff_and_formula : tff_unitary_formula "&" tff_unitary_formula | tff_and_formula "&" tff_unitary_formula
tff_unitary_formula : tff_quantified_formula | tff_unary_formula | tff_atomic_formula | tff_conditional | tff_let
| "(" tff_logic_formula ")"
tff_quantified_formula : fof_quantifier "[" tff_variable_list "] :" tff_unitary_formula
tff_variable_list : tff_variable ("," tff_variable)*
tff_variable : tff_typed_variable | variable
tff_typed_variable : variable ":" tff_atomic_type
tff_unary_formula : "~" tff_unitary_formula | fof_infix_unary
tff_atomic_formula : fof_atomic_formula
tff_conditional : "$ite_f(" tff_logic_formula "," tff_logic_formula "," tff_logic_formula ")"
tff_let : "$let_tf(" tff_let_term_defns "," tff_formula ")" | "$let_ff(" tff_let_formula_defns "," tff_formula ")"
tff_let_term_defns : tff_let_term_defn | "[" tff_let_term_list "]"
tff_let_term_list : tff_let_term_defn ("," tff_let_term_defn)*
tff_let_term_defn : "! [" tff_variable_list "] :" tff_let_term_defn | tff_let_term_binding
tff_let_term_binding : fof_plain_term "=" fof_term | "(" tff_let_term_binding ")"
tff_let_formula_defns : tff_let_formula_defn | "[" tff_let_formula_list "]"
tff_let_formula_list : tff_let_formula_defn ("," tff_let_formula_defn)*
tff_let_formula_defn : "! [ "tff_variable_list "] :" tff_let_formula_defn | tff_let_formula_binding
tff_let_formula_binding : fof_plain_atomic_formula "<=>" tff_unitary_formula | "(" tff_let_formula_binding ")"
tff_sequent : tff_formula_tuple "-->" tff_formula_tuple | "(" tff_sequent ")"
tff_formula_tuple : "[" [tff_formula_tuple_list] "]"
tff_formula_tuple_list : tff_logic_formula ("," tff_logic_formula)*
tff_typed_atom : untyped_atom ":" tff_top_level_type | "(" tff_typed_atom ")"
tff_subtype : untyped_atom "<<" atom
tff_top_level_type : tff_atomic_type | tff_mapping_type | tf1_quantified_type | "(" tff_top_level_type ")"
tf1_quantified_type : "!> [" tff_variable_list "] :" tff_monotype
tff_monotype : tff_atomic_type | "(" tff_mapping_type ")"
tff_unitary_type : tff_atomic_type | "(" tff_xprod_type ")"
tff_atomic_type : type_constant | defined_type | type_functor "(" tff_type_arguments ")" | variable
tff_type_arguments : tff_atomic_type ("," tff_atomic_type)*
tff_mapping_type : tff_unitary_type ">" tff_atomic_type
tff_xprod_type : tff_unitary_type "*" tff_atomic_type | tff_xprod_type "*" tff_atomic_type
tcf_formula : tcf_logic_formula | tff_typed_atom
tcf_logic_formula : tcf_quantified_formula | cnf_formula
tcf_quantified_formula : "! [" tff_variable_list "] :" cnf_formula
?fof_formula : fof_logic_formula | fof_sequent
?fof_logic_formula : fof_binary_formula | fof_unitary_formula
?fof_binary_formula : fof_binary_nonassoc | fof_binary_assoc
?fof_binary_nonassoc : fof_unitary_formula binary_connective fof_unitary_formula
?fof_binary_assoc : fof_or_formula | fof_and_formula
fof_or_formula : fof_unitary_formula "|" fof_unitary_formula | fof_or_formula "|" fof_unitary_formula
fof_and_formula : fof_unitary_formula "&" fof_unitary_formula | fof_and_formula "&" fof_unitary_formula
?fof_unitary_formula : fof_quantified_formula | fof_unary_formula | fof_atomic_formula | "(" fof_logic_formula ")"
?fof_quantified_formula : fof_quantifier "[" fof_variable_list "] :" fof_unitary_formula
?fof_variable_list : variable ("," variable)*
fof_unary_formula : "~" fof_unitary_formula | fof_infix_unary
fof_infix_unary : fof_term infix_inequality fof_term
?fof_atomic_formula : fof_plain_atomic_formula | fof_defined_atomic_formula | fof_system_atomic_formula
?fof_plain_atomic_formula : fof_plain_term
?fof_defined_atomic_formula : fof_defined_plain_formula | fof_defined_infix_formula
?fof_defined_plain_formula : fof_defined_plain_term | defined_proposition | defined_predicate "(" fof_arguments ")"
?fof_defined_infix_formula : fof_term defined_infix_pred fof_term
?fof_system_atomic_formula : fof_system_term
?fof_plain_term : constant | functor "(" fof_arguments ")"
?fof_defined_term : defined_term | fof_defined_atomic_term
?fof_defined_atomic_term : fof_defined_plain_term
?fof_defined_plain_term : defined_constant | defined_functor "(" fof_arguments ")"
?fof_system_term : system_constant | system_functor "(" fof_arguments ")"
?fof_arguments : fof_term ("," fof_term)*
?fof_term : fof_function_term | variable | tff_conditional_term | tff_let_term | tff_tuple_term
?fof_function_term : fof_plain_term | fof_defined_term | fof_system_term
tff_conditional_term : "$ite_t(" tff_logic_formula "," fof_term "," fof_term ")"
tff_let_term : "let_ft(" tff_let_formula_defns "," fof_term ")" | "$let_tt(" tff_let_term_defns ","fof_term ")"
tff_tuple_term : "{" [fof_arguments] "}"
fof_sequent : fof_formula_tuple "-->" fof_formula_tuple | "(" fof_sequent ")"
?fof_formula_tuple : "[" [fof_formula_tuple_list] "]"
?fof_formula_tuple_list : fof_logic_formula ("," fof_logic_formula)*
cnf_formula : disjunction | "(" disjunction ")"
disjunction : literal ("|" literal)*
literal : fof_atomic_formula | "~" fof_atomic_formula | fof_infix_unary
thf_quantifier : fof_quantifier | th0_quantifier | th1_quantifier
th1_quantifier : TH1_QUANTIFIER
TH1_QUANTIFIER : "!>" | "?*"
th0_quantifier : TH0_QUANTIFIER
TH0_QUANTIFIER : "^" | "@+" | "@-"
thf_pair_connective : infix_equality | infix_inequality | binary_connective | assignment
thf_unary_connective : "~" | TH1_UNARY_CONNECTIVE
TH1_UNARY_CONNECTIVE : "!!" | "??" | "@@+" | "@@-" | "@="
fof_quantifier : FOF_QUANTIFIER
FOF_QUANTIFIER : "!" | "?"
binary_connective : BINARY_CONNECTIVE
BINARY_CONNECTIVE : "<=>" | "=>" | "<=" | "<~>" | "~|" | "~&"
assoc_connective : ASSOC_CONNECTIVE
ASSOC_CONNECTIVE : "&" | "|"
assignment : ASSIGNMENT
ASSIGNMENT : ":="
type_constant : TYPE_CONSTANT
TYPE_CONSTANT : TYPE_FUNCTOR
type_functor : TYPE_FUNCTOR
TYPE_FUNCTOR : ATOMIC_WORD
defined_type : DEFINED_TYPE
DEFINED_TYPE : ATOMIC_DEFINED_WORD | "$oType" | "$o" | "$iType" | "$i" | "$tType" | "$real" | "$rat" | "$int"
system_type : SYSTEM_TYPE
SYSTEM_TYPE : ATOMIC_SYSTEM_WORD
atom : ATOM
ATOM : UNTYPED_ATOM | DEFINED_CONSTANT
untyped_atom : UNTYPED_ATOM
UNTYPED_ATOM : CONSTANT | SYSTEM_CONSTANT
defined_proposition : DEFINED_PROPOSITION
DEFINED_PROPOSITION : ATOMIC_DEFINED_WORD | "$true" | "$false"
defined_predicate : DEFINED_PREDICATE
DEFINED_PREDICATE : ATOMIC_DEFINED_WORD | "$distinct" | "$less" | "$lesseq" | "$greater" | "$greatereq" | "$is_int"
| "$is_rat" | "$box_P" | "$box_i" | "$box_int" | "$box" | "$dia_P" | "$dia_i" | "$dia_int"
| "$dia"
defined_infix_pred : infix_equality | assignment
infix_equality : INFIX_EQUALITY
INFIX_EQUALITY : "="
infix_inequality : INFIX_INEQUALITY
INFIX_INEQUALITY : "!="
constant : CONSTANT
CONSTANT : FUNCTOR
functor : FUNCTOR
FUNCTOR : ATOMIC_WORD
system_constant : SYSTEM_CONSTANT
SYSTEM_CONSTANT : SYSTEM_FUNCTOR
system_functor : SYSTEM_FUNCTOR
SYSTEM_FUNCTOR : ATOMIC_SYSTEM_WORD
defined_constant : DEFINED_CONSTANT
DEFINED_CONSTANT : DEFINED_FUNCTOR
defined_functor : DEFINED_FUNCTOR
DEFINED_FUNCTOR : ATOMIC_DEFINED_WORD |"$uminus" | "$sum" | "$difference" | "$product" | "$quotient" | "$quotient_e"
| "$quotient_t" | "$quotient_f" | "$remainder_e" | "$remainder_t" | "$remainder_f" | "$floor"
| "$ceiling" | "$truncate" | "$round" | "$to_int" | "$to_rat" | "$to_real"
?defined_term : number | DISTINCT_OBJECT
variable : VARIABLE
VARIABLE : UPPER_WORD
source : general_term | dag_source | internal_source | external_source | "[" sources "]"
sources : source ("," source)*
dag_source : name | inference_record
inference_record : "inference(" inference_rule "," useful_info "," inference_parents ")"
inference_rule : INFERENCE_RULE
INFERENCE_RULE : ATOMIC_WORD
inference_parents : "[" parent_list* "]"
parent_list : parent_info ("," parent_info)*
parent_info : source parent_details*
parent_details : general_list
internal_source : "introduced(" intro_type optional_info* ")"
intro_type : "definition" | "axiom_of_choice" | "tautology" | "assumption"
external_source : file_source | theory | creator_source
file_source : "file(" FILE_NAME FILE_INFO* ")"
FILE_INFO : "," NAME
theory : "theory(" THEORY_NAME optional_info* ")"
THEORY_NAME : "equality" | "ac"
creator_source : "creator(" CREATOR_NAME optional_info* ")"
CREATOR_NAME : ATOMIC_WORD
optional_info : "," useful_info
useful_info : general_list | "[" info_items* "]"
info_items : info_item ("," info_item)*
info_item : formula_item | inference_item | general_function
formula_item : DESCRIPTION_ITEM | IQUOTE_ITEM
DESCRIPTION_ITEM : "description(" ATOMIC_WORD ")"
IQUOTE_ITEM : "iquote(" ATOMIC_WORD ")"
inference_item : inference_status | assumptions_record | new_symbol_record | refutation
inference_status : "status(" STATUS_VALUE ")" | inference_info
STATUS_VALUE : "suc" | "unp" | "sap" | "esa" | "sat" | "fsa" | "thm" | "eqv" | "tac" | "wec" | "eth" | "tau"
| "wtc" | "wth" | "cax" | "sca" | "tca" | "wca" | "cup" | "csp" | "ecs" | "csa" | "cth" | "ceq"
| "unc" | "wcc" | "ect" | "fun" | "uns" | "wuc" | "wct" | "scc" | "uca" | "noc"
inference_info : inference_rule "(" ATOMIC_WORD "," general_list ")"
assumptions_record : "assumptions([" name_list "])"
refutation : "refutation(" file_source ")"
new_symbol_record : "new_symbols(" ATOMIC_WORD ", [" new_symbol_list "])"
new_symbol_list : principal_symbol ("," principal_symbol)*
principal_symbol : functor | variable
include : "include(" FILE_NAME formula_selection* ")."
formula_selection : ",[" name_list "]"
name_list : name ("," name)*
general_term : general_data | general_data ":" general_term | general_list
general_data : ATOMIC_WORD | general_function | variable | number | DISTINCT_OBJECT | formula_data
| "bind(" variable "," formula_data ")"
general_function : ATOMIC_WORD "(" general_terms ")"
formula_data : "$thf(" thf_formula ")" | "$tff(" tff_formula ")" | "$fof(" fof_formula ")" | "$cnf(" cnf_formula ")"
| "$fot(" fof_term ")"
general_list : "[" general_terms? "]"
general_terms : general_term ("," general_term)*
name : NAME
NAME : ATOMIC_WORD | INTEGER
ATOMIC_WORD : LOWER_WORD | SINGLE_QUOTED
ATOMIC_DEFINED_WORD : "$" LOWER_WORD
ATOMIC_SYSTEM_WORD : "$$" LOWER_WORD
number : INTEGER | RATIONAL | REAL
FILE_NAME : SINGLE_QUOTED
COMMENT : COMMENT_LINE | COMMENT_BLOCK
COMMENT_LINE : "%" PRINTABLE_CHAR*
COMMENT_BLOCK : "/*" NOT_STAR_SLASH? "*"+ "/"
NOT_STAR_SLASH : ("^*"* "*"+ "^/*") ("^*")*
SINGLE_QUOTED : "'" SQ_CHAR+ "'"
DISTINCT_OBJECT : "\"" DO_CHAR* "\""
UPPER_WORD : UPPER_ALPHA ALPHA_NUMERIC*
LOWER_WORD : LOWER_ALPHA ALPHA_NUMERIC*
REAL : SIGN? DECIMAL_FRACTION | SIGN? DECIMAL_EXPONENT
RATIONAL : SIGN? DECIMAL "/" POSITIVE_DECIMAL
INTEGER : SIGN? DECIMAL
DECIMAL : ZERO_NUMERIC | POSITIVE_DECIMAL
POSITIVE_DECIMAL : NON_ZERO_NUMERIC NUMERIC*
DECIMAL_EXPONENT : DECIMAL EXPONENT EXP_INTEGER | DECIMAL_FRACTION EXPONENT EXP_INTEGER
DECIMAL_FRACTION : DECIMAL DOT_DECIMAL
DOT_DECIMAL : "." NUMERIC+
EXP_INTEGER : SIGN? NUMERIC+
DO_CHAR : (/["\40"-"\41", "\43"-"\133", "\135"-"\176"]/ | "\\\\ \" \\\\")
SQ_CHAR : (/["\40"-"\46", "\50"-"\133", "\135"-"\176"]/ | "\\\\ ' \\\\")
SIGN : "+" | "-"
EXPONENT : "E" | "e"
ZERO_NUMERIC : "0"
NON_ZERO_NUMERIC : "1" .. "9"
NUMERIC : "0" .. "9"
LOWER_ALPHA : "a" .. "z"
UPPER_ALPHA : "A" .. "Z"
ALPHA_NUMERIC : LOWER_ALPHA | UPPER_ALPHA | NUMERIC | "_"
PRINTABLE_CHAR : /["\32"-"\126"]/
VIEWABLE_CHAR : "\n"
%import common.WS
%ignore WS
%ignore COMMENT
""", start='tptp_file')
# TPTP transformer
class list_of_functions(Transformer):
fof_annotated = lambda self, a: tuple([a[0], a[2]])
fof_formula = lambda self, a: a
fof_logic_formula = lambda self, a: a
fof_binary_formula = lambda self, a: a
fof_binary_nonassoc = lambda self, a: a
fof_binary_assoc = lambda self, a: a
fof_or_formula = lambda self, a: a
fof_and_formula = lambda self, a: a
fof_unitary_formula = lambda self, a: a
fof_quantified_formula = lambda self, a: a
fof_variable_list = lambda self, a: a
fof_unary_formula = lambda self, a: a
fof_infix_unary = lambda self, a: a
fof_atomic_formula = lambda self, a: a
fof_plain_atomic_formula = lambda self, a: a
fof_defined_atomic_formula = lambda self, a: a
fof_defined_plain_formula = lambda self, a: a
fof_defined_infix_formula = lambda self, a: a
fof_system_atomic_formula = lambda self, a: a
fof_plain_term = lambda self, a: a
fof_defined_term = lambda self, a: a
fof_defined_atomic_term = lambda self, a: a
fof_defined_plain_term = lambda self, a: a
fof_system_term = lambda self, a: a
fof_arguments = lambda self, a: a
fof_term = lambda self, a: a
fof_function_term = lambda self, a: a
tff_conditional_term = lambda self, a: a
tff_let_term = lambda self, a: a
tff_tuple_term = lambda self, a: a
fof_sequent = lambda self, a: a
fof_formula_tuple = lambda self, a: a
fof_formula_tuple_list = lambda self, a: a
fof_quantifier = lambda self, a: []
binary_connective = lambda self, a: []
assoc_connective = lambda self, a: []
assignment = lambda self, a: []
type_constant = lambda self, a: a[0][:]
type_functor = lambda self, a: a[0][:]
defined_type = lambda self, a: a[0][:]
system_type = lambda self, a: a[0][:]
atom = lambda self, a: a
untyped_atom = lambda self, a: a
defined_proposition = lambda self, a: []
defined_predicate = lambda self, a: a[0][:]
defined_infix_pred = lambda self, a: []
infix_equality = lambda self, a: []
infix_inequality = lambda self, a: []
constant = lambda self, a: a[0][:]
functor = lambda self, a: a[0][:]
system_constant = lambda self, a: a[0][:]
system_functor = lambda self, a: a[0][:]
defined_constant = lambda self, a: a[0][:]
defined_functor = lambda self, a: a[0][:]
defined_term = lambda self, a: a
variable = lambda self, a: []
name = lambda self, a: a[0][:]
number = lambda self, a: []
def flatten_list(lst):
"""Function flattening list of lists.
Arguments:
lst - list (of lists).
Returns:
flattened - flattened list."""
flattened = []
for l in lst:
if isinstance(l, list):
flattened += flatten_list(l)
else:
flattened.append(l)
return flattened
def extract_functions(tptp_file):
"""Function extracting functional symbols from a TPTP FOF formula.
Arguments:
tptp_file - TPTP file, that can be parsed by a TPTP parser.
Returns:
premise_name - name of the TPTP FOF formula,
premise_functions - list of functional symbols (expressed as strings) within the scope of the TPTP FOF formula.
"""
# Parse TPTP file
tree = tptp_parser.parse(tptp_file)
# Transform it into a list of functions
list_of_fun = list_of_functions().transform(tree)
# The first element on the list is the name of the TPTP formula
premise_name = list_of_fun[0]
# The second element is a list (of lists) of functional symbols, which we flatten to be a list of strings.
premise_functions = flatten_list(list_of_fun[1])
return premise_name, premise_functions
def extract_premises(path_to_premises, save_dir):
"""Function converting nndata from https://github.com/JUrban/deepmath to dictionaries.
Arguments:
path_to_premises - path to where nndata is saved,
save_dir - path to where to save the dictionaries.
Returns:
conjecture_signatures - dictionary with conjectures as keys and their functional signatures as values,
axiom_signatures - dictionary with axioms as keys and their functional signatures as values,
useful_axioms - dictionary with conjectures as keys and useful axioms as values,
useless_axioms - dictionary with conjectures as keys and useless axioms as values.
"""
# Record time
start_time = time()
# Create placeholders
conjecture_signatures = {}
axiom_signatures = {}
useful_axioms = {}
useless_axioms = {}
# Loop through premise files
for file in tqdm(os.listdir(path_to_premises)):
# Open file
with open(os.path.join(path_to_premises, file), 'r') as current_file:
problem = current_file.read()
# Split file into premises
premises = problem.split('\n')[:-1]
# The first line is a conjecture
conjecture = premises[0][2:]
# Get conjecture name and its functional signature and save in a dictionary
conjecture_name, conjecture_functions = extract_functions(conjecture)
conjecture_signatures[conjecture_name] = conjecture_functions
# Get conjecture's axioms
useful_axioms[conjecture_name] = []
useless_axioms[conjecture_name] = []
for axiom in premises[1:]:
# Get axiom name
axiom_name = axiom[6:].split(', axiom, ')[0]
# Check axiom's usefulness
if axiom.startswith('+'):
useful_axioms[conjecture_name].append(axiom_name)
elif axiom.startswith('-'):
useless_axioms[conjecture_name].append(axiom_name)
# If axiom was not seen before, we need to add its signature to axiom_signatures
if axiom_name not in axiom_signatures.keys():
axiom_signatures[axiom_name] = extract_functions(axiom[2:])[1]
# Rec ord end time
end_time = time()
# Save the data as dictionaries
with open(os.path.join(save_dir, 'conjecture_signatures.pickle'), 'wb') as dictionary:
pickle.dump(conjecture_signatures, dictionary, protocol=pickle.HIGHEST_PROTOCOL)
with open(os.path.join(save_dir, 'axiom_signatures.pickle'), 'wb') as dictionary:
pickle.dump(axiom_signatures, dictionary, protocol=pickle.HIGHEST_PROTOCOL)
with open(os.path.join(save_dir, 'useful_axioms.pickle'), 'wb') as dictionary:
pickle.dump(useful_axioms, dictionary, protocol=pickle.HIGHEST_PROTOCOL)
with open(os.path.join(save_dir, 'useless_axioms.pickle'), 'wb') as dictionary:
pickle.dump(useless_axioms, dictionary, protocol=pickle.HIGHEST_PROTOCOL)
# Print some statistics
print('Formatting time:', str(timedelta(seconds=end_time - start_time)), 'hours.')
print('Total number of conjectures:', len(conjecture_signatures))
print('Total number of axioms:', len(axiom_signatures))
def get_all_used_functions(paths_to_signatures):
"""Function returning the list of all functional signatures (expressed as strings) within the scope of some FOF
formulae.
Arguments:
paths_to_signatures - list of paths or a path to a signature file.
Return:
all_used_functions - alphabetically sorted list of all functional signatures (strings) within files stored at
paths_to_signatures.
"""
if not isinstance(paths_to_signatures, list):
paths_to_signatures = [paths_to_signatures]
# Functional symbols are collected in the form of a set, to avoid repetitions
all_used_functions = set()
for path in paths_to_signatures:
with open(path, 'rb') as dictionary:
signatures = pickle.load(dictionary)
for signature in signatures.values():
all_used_functions |= set(signature)
print('Total number of used functional symbols:', len(all_used_functions))
return sorted(list(all_used_functions))
def convert_to_integers(paths_to_signatures):
"""Function converting list of functions expressed as strings to a list of functions expressed as integers.
Arguments:
path_to_signatures - list of paths or a path to dictionary/-ies with FOF formulae names as keys and list of
functional symbols (expressed as strings) as values.
"""
if not isinstance(paths_to_signatures, list):
paths_to_signatures = [paths_to_signatures]
# Get all used functions to know how many integers are needed to label the functional symbols.
all_used_functions = get_all_used_functions(paths_to_signatures)
for path in paths_to_signatures:
new_signatures = {}
with open(path, 'rb') as dictionary:
signatures = pickle.load(dictionary)
for key, value in tqdm(signatures.items()):
new_signatures[key] = [all_used_functions.index(v) for v in value]
new_path = '_int.'.join(path.split('.'))
with open(new_path, 'wb') as dictionary:
pickle.dump(new_signatures, dictionary, protocol=pickle.HIGHEST_PROTOCOL)
def count_functions(signature, functions):
"""Function counting occurrences of a given functional symbol within the scope of a functional signature.
Arguments:
signature - list of functional symbols (expressed as strings),
functions - list of all available functional symbols (also as strings).
"""
return [signature.count(functions[n]) for n in range(len(functions))]
def convert_to_count_signatures(paths_to_signatures):
if not isinstance(paths_to_signatures, list):
paths_to_signatures = [paths_to_signatures]
all_used_functions = get_all_used_functions(paths_to_signatures)
for path in paths_to_signatures:
with open(path, 'rb') as dictionary:
signatures = pickle.load(dictionary)
signatures = dict([(key, count_functions(value, all_used_functions)) for key, value in signatures.items()])
new_path = '_count.'.join(path.split('.'))
with open(new_path, 'wb') as dictionary:
pickle.dump(signatures, dictionary, protocol=pickle.HIGHEST_PROTOCOL)
def calculate_context_distribution(path_to_context):
with open(path_to_context, 'rb') as dictionary:
context = pickle.load(dictionary)
context = np.array(list(context.values()), dtype='uint16')
num_context, num_fun = context.shape
print('Number of context premises: {}, number of functions: {}.'.format(num_context, num_fun))
# Create network output placeholder
output_data = np.zeros((num_fun, num_fun), dtype='float32')
# Calculate probability distribution of functions which are in scope of the same premises
for n in tqdm(range(num_fun)):
output = np.array([context[m] for m in range(num_context) if context[m, n] != 0], dtype='float32')
numerator = np.sum(output, axis=0)
denominator = np.sum(numerator)
if denominator == 0:
output_data[n, n] = 1
else:
output_data[n] = numerator / denominator
new_path = path_to_context.split('.')[0] + '_context_distribution.npy'
np.save(new_path, output_data)
def embed_integers(path_to_signatures, weight):
new_signatures = {}
with open(path_to_signatures, 'rb') as dictionary:
signatures = pickle.load(dictionary)
for key, value in tqdm(signatures.items()):
new_signatures[key] = np.array([weight[n] for n in value], dtype='float32')
new_path = '_embed.'.join(path_to_signatures.split('.'))
with open(new_path, 'wb') as dictionary:
pickle.dump(new_signatures, dictionary, protocol=pickle.HIGHEST_PROTOCOL)
def embed_count(path_to_signatures, weight):
with open(path_to_signatures, 'rb') as dictionary:
signatures = pickle.load(dictionary)
for key in tqdm(signatures.keys()):
value = np.array(signatures[key], dtype='float32')
signatures[key] = np.matmul(value, weight) / np.max(value)
new_path = '_embed.'.join(path_to_signatures.split('.'))
with open(new_path, 'wb') as dictionary:
pickle.dump(signatures, dictionary, protocol=pickle.HIGHEST_PROTOCOL)
def form_train_sets(path_to_data, split=10, rnn=False, embedding_len=256, max_len=64, concat=True):
if rnn:
name = '_int_embed.pickle'
else:
name = '_count_embed.pickle'
with open(os.path.join(path_to_data, 'conjecture_signatures' + name), 'rb') as dictionary:
conjecture_signatures = pickle.load(dictionary)
with open(os.path.join(path_to_data, 'axiom_signatures' + name), 'rb') as dictionary:
axiom_signatures = pickle.load(dictionary)
with open(os.path.join(path_to_data, 'useful_axioms.pickle'), 'rb') as dictionary:
useful_axioms = pickle.load(dictionary)
with open(os.path.join(path_to_data, 'useless_axioms.pickle'), 'rb') as dictionary:
useless_axioms = pickle.load(dictionary)
conjecture_names = sorted(list(conjecture_signatures.keys()))
chunk_size = len(conjecture_names) / split
for n in range(split):
selected_conjectures = conjecture_names[int(n * chunk_size): int((n + 1) * chunk_size)]
if rnn:
x_chunk = np.zeros((1, 2, max_len, embedding_len), dtype='float32')
else:
x_chunk = np.zeros((1, 2, embedding_len), dtype='float32')
y_chunk = np.zeros((1,), dtype='bool_')
print('Chunk {}/{}'.format(n + 1, split))
for conjecture_name in tqdm(selected_conjectures):
conjecture = conjecture_signatures[conjecture_name]
if rnn:
conjecture = conjecture[:max_len]
conjecture = np.pad(conjecture, ((0, max_len - conjecture.shape[0]), (0, 0)), mode='constant',
constant_values=0)
for axiom_name in useful_axioms[conjecture_name]:
axiom = axiom_signatures[axiom_name]
if rnn:
axiom = axiom[:max_len]
axiom = np.pad(axiom, ((0, max_len - axiom.shape[0]), (0, 0)), mode='constant', constant_values=0)
x = np.expand_dims(np.stack([conjecture, axiom], axis=0), axis=0)
x_chunk = np.concatenate([x_chunk, x], axis=0)
for axiom_name in useless_axioms[conjecture_name]:
axiom = axiom_signatures[axiom_name]
if rnn:
axiom = axiom[:max_len]
axiom = np.pad(axiom, ((0, max_len - axiom.shape[0]), (0, 0)), mode='constant', constant_values=0)
x = np.expand_dims(np.stack([conjecture, axiom], axis=0), axis=0)
x_chunk = np.concatenate([x_chunk, x], axis=0)
y_chunk = np.concatenate([y_chunk,
np.ones((len(useful_axioms[conjecture_name]),), dtype='bool_'),
np.zeros((len(useless_axioms[conjecture_name]),), dtype='bool_')])
if rnn:
name = '_rnn'
else:
name = ''
if concat:
try:
x = np.load('data/x{}.npy'.format(name), mmap_mode='r')
np.save('data/x{}.npy'.format(name), np.concatenate([x, x_chunk[1:]]))
y = np.load('data/y{}.npy'.format(name), mmap_mode='r')
np.save('data/y{}.npy'.format(name), np.concatenate([y, y_chunk[1:]]))
except FileNotFoundError:
np.save('data/x{}.npy'.format(name), x_chunk[1:])
np.save('data/y{}.npy'.format(name), y_chunk[1:])
else:
np.save('data/x{}_{}.npy'.format(name, n), x_chunk[1:])
np.save('data/y{}_{}.npy'.format(name, n), y_chunk[1:])
def get_test_indices(path_to_data, split=10):
with open(os.path.join(path_to_data, 'conjecture_signatures.pickle'), 'rb') as dictionary:
conjecture_signatures = pickle.load(dictionary)
with open(os.path.join(path_to_data, 'useful_axioms.pickle'), 'rb') as dictionary:
useful_axioms = pickle.load(dictionary)
with open(os.path.join(path_to_data, 'useless_axioms.pickle'), 'rb') as dictionary:
useless_axioms = pickle.load(dictionary)
conjecture_names = sorted(list(conjecture_signatures.keys()))
test_conjectures = sorted(sample(conjecture_names, len(conjecture_names)//split))
test_indices = []
for conjecture in test_conjectures:
start = conjecture_names.index(conjecture)
stop = start + 1
stop += len(useful_axioms[conjecture])
stop += len(useless_axioms[conjecture])
test_indices += list(range(start, stop))
return test_indices