(* Title: HOL/TPTP/TPTP_Parser/tptp_syntax.ML
Author: Nik Sultana, Cambridge University Computer Laboratory
TPTP abstract syntax and parser-related definitions.
*)
signature TPTP_SYNTAX =
sig
exception TPTP_SYNTAX of string
val debug: ('a -> unit) -> 'a -> unit
(*Note that in THF "^ [X] : ^ [Y] : f @ g" should parse
as "(^ [X] : (^ [Y] : f)) @ g"
*)
datatype number_kind = Int_num | Real_num | Rat_num
datatype 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
type name = string
type atomic_word = string
type inference_rule = atomic_word
type file_info = name option
type single_quoted = string
type file_name = single_quoted
type creator_name = atomic_word
type variable = string
type upper_word = string
datatype language = FOF | CNF | TFF | THF | FOT | TFF_with_arithmetic
and role =
Role_Axiom | Role_Hypothesis | Role_Definition | Role_Assumption |
Role_Lemma | Role_Theorem | Role_Conjecture | Role_Negated_Conjecture |
Role_Plain | Role_Fi_Domain | Role_Fi_Functors | Role_Fi_Predicates |
Role_Type | Role_Unknown
and general_data = (*Bind of variable * formula_data*)
Atomic_Word of string
| Application of string * general_term list (*general_function*)
| V of upper_word (*variable*)
| Number of number_kind * string
| Distinct_Object of string
| (*formula_data*) Formula_Data of language * tptp_formula (* $thf(<thf_formula>) *)
| (*formula_data*) Term_Data of tptp_term
and interpreted_symbol =
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 |
(*these should be in defined_pred, but that's not being used in TPTP*)
Less | LessEq | Greater | GreaterEq | EvalEq | Is_Int | Is_Rat |
Apply (*this is just a matter of convenience*)
and logic_symbol = Equals | NEquals | Or | And | Iff | If | Fi | Xor |
Nor | Nand | Not | Op_Forall | Op_Exists |
(*these should be in defined_pred, but that's not being used in TPTP*)
True | False
and quantifier = (*interpreted binders*)
Forall | Exists | Epsilon | Iota | Lambda | Dep_Prod | Dep_Sum
and tptp_base_type =
Type_Ind | Type_Bool | Type_Type | Type_Int | Type_Rat | Type_Real
and symbol =
Uninterpreted of string
| Interpreted_ExtraLogic of interpreted_symbol
| Interpreted_Logic of logic_symbol
| TypeSymbol of tptp_base_type
| System of string
and general_term =
General_Data of general_data (*general_data*)
| General_Term of general_data * general_term (*general_data : general_term*)
| General_List of general_term list
and tptp_term =
Term_Func of symbol * tptp_term list
| Term_Var of string
| Term_Conditional of tptp_formula * tptp_term * tptp_term
| Term_Num of number_kind * string
| Term_Distinct_Object of string
and tptp_atom =
TFF_Typed_Atom of symbol * tptp_type option (*only TFF*)
| THF_Atom_term of tptp_term (*from here on, only THF*)
| THF_Atom_conn_term of symbol
and tptp_formula =
Pred of symbol * tptp_term list
| Fmla of symbol * tptp_formula list
| Sequent of tptp_formula list * tptp_formula list
| Quant of quantifier * (string * tptp_type option) list * tptp_formula
| Conditional of tptp_formula * tptp_formula * tptp_formula
| Let of tptp_let list * tptp_formula
| Atom of tptp_atom
| THF_type of tptp_type
| THF_typing of tptp_formula * tptp_type (*only THF*)
and tptp_let =
Let_fmla of (string * tptp_type option) * tptp_formula
| Let_term of (string * tptp_type option) * tptp_term (*only TFF*)
and tptp_type =
Prod_type of tptp_type * tptp_type
| Fn_type of tptp_type * tptp_type
| Atom_type of string
| Defined_type of tptp_base_type
| Sum_type of tptp_type * tptp_type (*only THF*)
| Fmla_type of tptp_formula (*only THF*)
| Subtype of symbol * symbol (*only THF*)
type general_list = general_term list
type parent_details = general_list
type useful_info = general_term list
type info = useful_info
type annotation = general_term * general_term list
exception DEQUOTE of string
type position = string * int * int
datatype tptp_line =
Annotated_Formula of position * language * string * role * tptp_formula * annotation option
| Include of string * string list
type tptp_problem = tptp_line list
val dequote : single_quoted -> single_quoted
val role_to_string : role -> string
val status_to_string : status_value -> string
val nameof_tff_atom_type : tptp_type -> string
(*Returns the list of all files included in a directory and its
subdirectories. This is only used for testing the parser/interpreter against
all THF problems.*)
val get_file_list : Path.T -> Path.T list
val string_of_tptp_term : tptp_term -> string
val string_of_tptp_formula : tptp_formula -> string
end
structure TPTP_Syntax : TPTP_SYNTAX =
struct
exception TPTP_SYNTAX of string
datatype number_kind = Int_num | Real_num | Rat_num
datatype 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
type name = string
type atomic_word = string
type inference_rule = atomic_word
type file_info = name option
type single_quoted = string
type file_name = single_quoted
type creator_name = atomic_word
type variable = string
type upper_word = string
datatype language = FOF | CNF | TFF | THF | FOT | TFF_with_arithmetic
and role =
Role_Axiom | Role_Hypothesis | Role_Definition | Role_Assumption |
Role_Lemma | Role_Theorem | Role_Conjecture | Role_Negated_Conjecture |
Role_Plain | Role_Fi_Domain | Role_Fi_Functors | Role_Fi_Predicates |
Role_Type | Role_Unknown
and general_data = (*Bind of variable * formula_data*)
Atomic_Word of string
| Application of string * (general_term list)
| V of upper_word (*variable*)
| Number of number_kind * string
| Distinct_Object of string
| (*formula_data*) Formula_Data of language * tptp_formula (* $thf(<thf_formula>) *)
| (*formula_data*) Term_Data of tptp_term
and interpreted_symbol =
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 |
(*these should be in defined_pred, but that's not being used in TPTP*)
Less | LessEq | Greater | GreaterEq | EvalEq | Is_Int | Is_Rat |
Apply (*this is just a matter of convenience*)
and logic_symbol = Equals | NEquals | Or | And | Iff | If | Fi | Xor |
Nor | Nand | Not | Op_Forall | Op_Exists |
(*these should be in defined_pred, but that's not being used in TPTP*)
True | False
and quantifier = (*interpreted binders*)
Forall | Exists | Epsilon | Iota | Lambda | Dep_Prod | Dep_Sum
and tptp_base_type =
Type_Ind | Type_Bool | Type_Type | Type_Int | Type_Rat | Type_Real
and symbol =
Uninterpreted of string
| Interpreted_ExtraLogic of interpreted_symbol
| Interpreted_Logic of logic_symbol
| TypeSymbol of tptp_base_type
| System of string
and general_term =
General_Data of general_data (*general_data*)
| General_Term of general_data * general_term (*general_data : general_term*)
| General_List of general_term list
and tptp_term =
Term_Func of symbol * tptp_term list
| Term_Var of string
| Term_Conditional of tptp_formula * tptp_term * tptp_term
| Term_Num of number_kind * string
| Term_Distinct_Object of string
and tptp_atom =
TFF_Typed_Atom of symbol * tptp_type option (*only TFF*)
| THF_Atom_term of tptp_term (*from here on, only THF*)
| THF_Atom_conn_term of symbol
and tptp_formula =
Pred of symbol * tptp_term list
| Fmla of symbol * tptp_formula list
| Sequent of tptp_formula list * tptp_formula list
| Quant of quantifier * (string * tptp_type option) list * tptp_formula
| Conditional of tptp_formula * tptp_formula * tptp_formula
| Let of tptp_let list * tptp_formula
| Atom of tptp_atom
| THF_type of tptp_type
| THF_typing of tptp_formula * tptp_type
and tptp_let =
Let_fmla of (string * tptp_type option) * tptp_formula (*both TFF and THF*)
| Let_term of (string * tptp_type option) * tptp_term (*only TFF*)
and tptp_type =
Prod_type of tptp_type * tptp_type
| Fn_type of tptp_type * tptp_type
| Atom_type of string
| Defined_type of tptp_base_type
| Sum_type of tptp_type * tptp_type (*only THF*)
| Fmla_type of tptp_formula (*only THF*)
| Subtype of symbol * symbol (*only THF*)
type general_list = general_term list
type parent_details = general_list
type useful_info = general_term list
type info = useful_info
(*type annotation = (source * info option)*)
type annotation = general_term * general_term list
exception DEQUOTE of string
(*
datatype defined_functor =
ITE_T | 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
*)
type position = string * int * int
datatype tptp_line =
Annotated_Formula of position * language * string * role * tptp_formula * annotation option
| Include of string * string list
type tptp_problem = tptp_line list
fun debug f x = if !Runtime.debug then (f x; ()) else ()
fun nameof_tff_atom_type (Atom_type str) = str
| nameof_tff_atom_type _ = raise TPTP_SYNTAX "nameof_tff_atom_type called on non-atom type"
(*Used for debugging. Returns all files contained within a directory or its
subdirectories. Follows symbolic links, filters away directories.*)
fun get_file_list path =
let
fun check_file_entry f rest =
let
(*NOTE needed since no File.is_link and File.read_link*)
val f_str = Path.implode f
in
if File.is_dir f then
rest @ get_file_list f
else if OS.FileSys.isLink f_str then
(*follow links -- NOTE this breaks if links are relative paths*)
check_file_entry (Path.explode (OS.FileSys.readLink f_str)) rest
else f :: rest
end
in
File.read_dir path
|> map
(Path.explode
#> Path.append path)
|> (fn l => fold check_file_entry l [])
end
fun role_to_string role =
case role of
Role_Axiom => "axiom"
| Role_Hypothesis => "hypothesis"
| Role_Definition => "definition"
| Role_Assumption => "assumption"
| Role_Lemma => "lemma"
| Role_Theorem => "theorem"
| Role_Conjecture => "conjecture"
| Role_Negated_Conjecture => "negated_conjecture"
| Role_Plain => "plain"
| Role_Fi_Domain => "fi_domain"
| Role_Fi_Functors => "fi_functors"
| Role_Fi_Predicates => "fi_predicates"
| Role_Type => "type"
| Role_Unknown => "unknown"
(*accepts a string "'abc'" and returns "abc"*)
fun dequote str : single_quoted =
if str = "" then
raise (DEQUOTE "empty string")
else
(unprefix "'" str
|> unsuffix "'"
handle (Fail str) =>
if str = "unprefix" then
raise DEQUOTE ("string doesn't open with quote:" ^ str)
else if str = "unsuffix" then
raise DEQUOTE ("string doesn't close with quote:" ^ str)
else raise Fail str)
(* Printing parsed TPTP formulas *)
(*FIXME this is not pretty-printing, just printing*)
fun status_to_string status_value =
case status_value of
Suc => "suc" | Unp => "unp"
| Sap => "sap" | Esa => "esa"
| Sat => "sat" | Fsa => "fsa"
| Thm => "thm" | Wuc => "wuc"
| Eqv => "eqv" | Tac => "tac"
| Wec => "wec" | Eth => "eth"
| Tau => "tau" | Wtc => "wtc"
| Wth => "wth" | Cax => "cax"
| Sca => "sca" | Tca => "tca"
| Wca => "wca" | Cup => "cup"
| Csp => "csp" | Ecs => "ecs"
| Csa => "csa" | Cth => "cth"
| Ceq => "ceq" | Unc => "unc"
| Wcc => "wcc" | Ect => "ect"
| Fun => "fun" | Uns => "uns"
| Wct => "wct" | Scc => "scc"
| Uca => "uca" | Noc => "noc"
fun string_of_tptp_term x =
case x of
Term_Func (symbol, tptp_term_list) =>
"(" ^ string_of_symbol symbol ^ " " ^
String.concatWith " " (map string_of_tptp_term tptp_term_list) ^ ")"
| Term_Var str => str
| Term_Conditional (tptp_formula, tptp_term1, tptp_term2) => "" (*FIXME*)
| Term_Num (_, str) => str
| Term_Distinct_Object str => str
and string_of_symbol (Uninterpreted str) = str
| string_of_symbol (Interpreted_ExtraLogic interpreted_symbol) = string_of_interpreted_symbol interpreted_symbol
| string_of_symbol (Interpreted_Logic logic_symbol) = string_of_logic_symbol logic_symbol
| string_of_symbol (TypeSymbol tptp_base_type) = string_of_tptp_base_type tptp_base_type
| string_of_symbol (System str) = str
and string_of_tptp_base_type Type_Ind = "$i"
| string_of_tptp_base_type Type_Bool = "$o"
| string_of_tptp_base_type Type_Type = "$tType"
| string_of_tptp_base_type Type_Int = "$int"
| string_of_tptp_base_type Type_Rat = "$rat"
| string_of_tptp_base_type Type_Real = "$real"
and string_of_interpreted_symbol x =
case x of
UMinus => "$uminus"
| Sum => "$sum"
| Difference => "$difference"
| Product => "$product"
| Quotient => "$quotient"
| Quotient_E => "$quotient_e"
| Quotient_T => "$quotient_t"
| Quotient_F => "$quotient_f"
| Remainder_E => "$remainder_e"
| Remainder_T => "$remainder_t"
| Remainder_F => "$remainder_f"
| Floor => "$floor"
| Ceiling => "$ceiling"
| Truncate => "$truncate"
| Round => "$round"
| To_Int => "$to_int"
| To_Rat => "$to_rat"
| To_Real => "$to_real"
| Less => "$less"
| LessEq => "$lesseq"
| Greater => "$greater"
| GreaterEq => "$greatereq"
| EvalEq => "$evaleq"
| Is_Int => "$is_int"
| Is_Rat => "$is_rat"
| Apply => "@"
and string_of_logic_symbol Equals = "="
| string_of_logic_symbol NEquals = "!="
| string_of_logic_symbol Or = "|"
| string_of_logic_symbol And = "&"
| string_of_logic_symbol Iff = "<=>"
| string_of_logic_symbol If = "=>"
| string_of_logic_symbol Fi = "<="
| string_of_logic_symbol Xor = "<~>"
| string_of_logic_symbol Nor = "~|"
| string_of_logic_symbol Nand = "~&"
| string_of_logic_symbol Not = "~"
| string_of_logic_symbol Op_Forall = "!!"
| string_of_logic_symbol Op_Exists = "??"
| string_of_logic_symbol True = "$true"
| string_of_logic_symbol False = "$false"
and string_of_quantifier Forall = "!"
| string_of_quantifier Exists = "?"
| string_of_quantifier Epsilon = "@+"
| string_of_quantifier Iota = "@-"
| string_of_quantifier Lambda = "^"
| string_of_quantifier Dep_Prod = "!>"
| string_of_quantifier Dep_Sum = "?*"
and string_of_tptp_atom (TFF_Typed_Atom (symbol, tptp_type_option)) =
(case tptp_type_option of
NONE => string_of_symbol symbol
| SOME tptp_type =>
string_of_symbol symbol ^ " : " ^ string_of_tptp_type tptp_type)
| string_of_tptp_atom (THF_Atom_term tptp_term) = string_of_tptp_term tptp_term
| string_of_tptp_atom (THF_Atom_conn_term symbol) = string_of_symbol symbol
and string_of_tptp_formula (Pred (symbol, tptp_term_list)) =
"(" ^ string_of_symbol symbol ^
String.concatWith " " (map string_of_tptp_term tptp_term_list) ^ ")"
| string_of_tptp_formula (Fmla (symbol, tptp_formula_list)) =
"(" ^
string_of_symbol symbol ^
String.concatWith " " (map string_of_tptp_formula tptp_formula_list) ^ ")"
| string_of_tptp_formula (Sequent (tptp_formula_list1, tptp_formula_list2)) = "" (*FIXME*)
| string_of_tptp_formula (Quant (quantifier, varlist, tptp_formula)) =
string_of_quantifier quantifier ^ "[" ^
String.concatWith ", " (map (fn (n, ty) =>
case ty of
NONE => n
| SOME ty => n ^ " : " ^ string_of_tptp_type ty) varlist) ^ "] : (" ^
string_of_tptp_formula tptp_formula ^ ")"
| string_of_tptp_formula (Conditional _) = "" (*FIXME*)
| string_of_tptp_formula (Let _) = "" (*FIXME*)
| string_of_tptp_formula (Atom tptp_atom) = string_of_tptp_atom tptp_atom
| string_of_tptp_formula (THF_type tptp_type) = string_of_tptp_type tptp_type
| string_of_tptp_formula (THF_typing (tptp_formula, tptp_type)) =
string_of_tptp_formula tptp_formula ^ " : " ^ string_of_tptp_type tptp_type
and string_of_tptp_type (Prod_type (tptp_type1, tptp_type2)) =
string_of_tptp_type tptp_type1 ^ " * " ^ string_of_tptp_type tptp_type2
| string_of_tptp_type (Fn_type (tptp_type1, tptp_type2)) =
string_of_tptp_type tptp_type1 ^ " > " ^ string_of_tptp_type tptp_type2
| string_of_tptp_type (Atom_type str) = str
| string_of_tptp_type (Defined_type tptp_base_type) =
string_of_tptp_base_type tptp_base_type
| string_of_tptp_type (Sum_type (tptp_type1, tptp_type2)) = ""
| string_of_tptp_type (Fmla_type tptp_formula) = string_of_tptp_formula tptp_formula
| string_of_tptp_type (Subtype (symbol1, symbol2)) =
string_of_symbol symbol1 ^ " << " ^ string_of_symbol symbol2
end