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(* Title: HOL/TPTP/TPTP_Parser/tptp_syntax.ML
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Author: Nik Sultana, Cambridge University Computer Laboratory
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TPTP abstract syntax and parser-related definitions.
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*)
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signature TPTP_SYNTAX =
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sig
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exception TPTP_SYNTAX of string
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val debug: ('a -> unit) -> 'a -> unit
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(*Note that in THF "^ [X] : ^ [Y] : f @ g" should parse
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as "(^ [X] : (^ [Y] : f)) @ g"
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*)
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datatype number_kind = Int_num | Real_num | Rat_num
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datatype status_value =
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Suc | Unp | Sap | Esa | Sat | Fsa
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| Thm | Eqv | Tac | Wec | Eth | Tau
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| Wtc | Wth | Cax | Sca | Tca | Wca
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| Cup | Csp | Ecs | Csa | Cth | Ceq
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| Unc | Wcc | Ect | Fun | Uns | Wuc
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| Wct | Scc | Uca | Noc
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type name = string
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type atomic_word = string
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type inference_rule = atomic_word
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type file_info = name option
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type single_quoted = string
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type file_name = single_quoted
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type creator_name = atomic_word
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type variable = string
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type upper_word = string
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datatype language = FOF | CNF | TFF | THF | FOT | TFF_with_arithmetic
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and role =
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Role_Axiom | Role_Hypothesis | Role_Definition | Role_Assumption |
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Role_Lemma | Role_Theorem | Role_Conjecture | Role_Negated_Conjecture |
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Role_Plain | Role_Fi_Domain | Role_Fi_Functors | Role_Fi_Predicates |
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Role_Type | Role_Unknown
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and general_data = (*Bind of variable * formula_data*)
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Atomic_Word of string
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| Application of string * general_term list (*general_function*)
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| V of upper_word (*variable*)
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| Number of number_kind * string
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| Distinct_Object of string
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| (*formula_data*) Formula_Data of language * tptp_formula (* $thf(<thf_formula>) *)
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| (*formula_data*) Term_Data of tptp_term
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and interpreted_symbol =
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UMinus | Sum | Difference | Product | Quotient | Quotient_E |
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Quotient_T | Quotient_F | Remainder_E | Remainder_T | Remainder_F |
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Floor | Ceiling | Truncate | Round | To_Int | To_Rat | To_Real |
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(*these should be in defined_pred, but that's not being used in TPTP*)
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Less | LessEq | Greater | GreaterEq | EvalEq | Is_Int | Is_Rat |
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Apply (*this is just a matter of convenience*)
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and logic_symbol = Equals | NEquals | Or | And | Iff | If | Fi | Xor |
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Nor | Nand | Not | Op_Forall | Op_Exists |
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(*these should be in defined_pred, but that's not being used in TPTP*)
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True | False
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and quantifier = (*interpreted binders*)
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Forall | Exists | Epsilon | Iota | Lambda | Dep_Prod | Dep_Sum
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and tptp_base_type =
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Type_Ind | Type_Bool | Type_Type | Type_Int | Type_Rat | Type_Real
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and symbol =
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Uninterpreted of string
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| Interpreted_ExtraLogic of interpreted_symbol
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| Interpreted_Logic of logic_symbol
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| TypeSymbol of tptp_base_type
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| System of string
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and general_term =
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General_Data of general_data (*general_data*)
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| General_Term of general_data * general_term (*general_data : general_term*)
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| General_List of general_term list
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and tptp_term =
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Term_Func of symbol * tptp_term list
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| Term_Var of string
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| Term_Conditional of tptp_formula * tptp_term * tptp_term
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| Term_Num of number_kind * string
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| Term_Distinct_Object of string
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and tptp_atom =
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TFF_Typed_Atom of symbol * tptp_type option (*only TFF*)
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| THF_Atom_term of tptp_term (*from here on, only THF*)
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| THF_Atom_conn_term of symbol
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and tptp_formula =
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Pred of symbol * tptp_term list
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| Fmla of symbol * tptp_formula list
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| Sequent of tptp_formula list * tptp_formula list
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| Quant of quantifier * (string * tptp_type option) list * tptp_formula
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| Conditional of tptp_formula * tptp_formula * tptp_formula
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| Let of tptp_let list * tptp_formula
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| Atom of tptp_atom
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| THF_type of tptp_type
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| THF_typing of tptp_formula * tptp_type (*only THF*)
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and tptp_let =
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Let_fmla of (string * tptp_type option) * tptp_formula
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| Let_term of (string * tptp_type option) * tptp_term (*only TFF*)
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and tptp_type =
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Prod_type of tptp_type * tptp_type
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| Fn_type of tptp_type * tptp_type
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| Atom_type of string
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| Defined_type of tptp_base_type
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| Sum_type of tptp_type * tptp_type (*only THF*)
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| Fmla_type of tptp_formula (*only THF*)
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| Subtype of symbol * symbol (*only THF*)
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type general_list = general_term list
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type parent_details = general_list
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type useful_info = general_term list
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type info = useful_info
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type annotation = general_term * general_term list
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exception DEQUOTE of string
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type position = string * int * int
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datatype tptp_line =
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Annotated_Formula of position * language * string * role * tptp_formula * annotation option
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| Include of string * string list
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type tptp_problem = tptp_line list
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val dequote : single_quoted -> single_quoted
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val role_to_string : role -> string
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val status_to_string : status_value -> string
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val nameof_tff_atom_type : tptp_type -> string
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(*Returns the list of all files included in a directory and its
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subdirectories. This is only used for testing the parser/interpreter against
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all THF problems.*)
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val get_file_list : Path.T -> Path.T list
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val string_of_tptp_term : tptp_term -> string
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val string_of_tptp_formula : tptp_formula -> string
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end
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structure TPTP_Syntax : TPTP_SYNTAX =
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struct
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exception TPTP_SYNTAX of string
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datatype number_kind = Int_num | Real_num | Rat_num
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datatype status_value =
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Suc | Unp | Sap | Esa | Sat | Fsa
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| Thm | Eqv | Tac | Wec | Eth | Tau
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| Wtc | Wth | Cax | Sca | Tca | Wca
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| Cup | Csp | Ecs | Csa | Cth | Ceq
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| Unc | Wcc | Ect | Fun | Uns | Wuc
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| Wct | Scc | Uca | Noc
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type name = string
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type atomic_word = string
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type inference_rule = atomic_word
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type file_info = name option
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type single_quoted = string
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type file_name = single_quoted
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type creator_name = atomic_word
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type variable = string
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type upper_word = string
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datatype language = FOF | CNF | TFF | THF | FOT | TFF_with_arithmetic
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and role =
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Role_Axiom | Role_Hypothesis | Role_Definition | Role_Assumption |
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Role_Lemma | Role_Theorem | Role_Conjecture | Role_Negated_Conjecture |
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Role_Plain | Role_Fi_Domain | Role_Fi_Functors | Role_Fi_Predicates |
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Role_Type | Role_Unknown
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and general_data = (*Bind of variable * formula_data*)
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Atomic_Word of string
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| Application of string * (general_term list)
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| V of upper_word (*variable*)
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| Number of number_kind * string
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| Distinct_Object of string
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| (*formula_data*) Formula_Data of language * tptp_formula (* $thf(<thf_formula>) *)
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| (*formula_data*) Term_Data of tptp_term
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and interpreted_symbol =
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UMinus | Sum | Difference | Product | Quotient | Quotient_E |
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Quotient_T | Quotient_F | Remainder_E | Remainder_T | Remainder_F |
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Floor | Ceiling | Truncate | Round | To_Int | To_Rat | To_Real |
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(*these should be in defined_pred, but that's not being used in TPTP*)
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Less | LessEq | Greater | GreaterEq | EvalEq | Is_Int | Is_Rat |
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Apply (*this is just a matter of convenience*)
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and logic_symbol = Equals | NEquals | Or | And | Iff | If | Fi | Xor |
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Nor | Nand | Not | Op_Forall | Op_Exists |
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(*these should be in defined_pred, but that's not being used in TPTP*)
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True | False
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and quantifier = (*interpreted binders*)
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Forall | Exists | Epsilon | Iota | Lambda | Dep_Prod | Dep_Sum
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and tptp_base_type =
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Type_Ind | Type_Bool | Type_Type | Type_Int | Type_Rat | Type_Real
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and symbol =
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Uninterpreted of string
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| Interpreted_ExtraLogic of interpreted_symbol
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| Interpreted_Logic of logic_symbol
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| TypeSymbol of tptp_base_type
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| System of string
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and general_term =
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General_Data of general_data (*general_data*)
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| General_Term of general_data * general_term (*general_data : general_term*)
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| General_List of general_term list
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and tptp_term =
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Term_Func of symbol * tptp_term list
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| Term_Var of string
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| Term_Conditional of tptp_formula * tptp_term * tptp_term
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| Term_Num of number_kind * string
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| Term_Distinct_Object of string
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and tptp_atom =
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TFF_Typed_Atom of symbol * tptp_type option (*only TFF*)
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| THF_Atom_term of tptp_term (*from here on, only THF*)
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| THF_Atom_conn_term of symbol
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and tptp_formula =
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Pred of symbol * tptp_term list
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| Fmla of symbol * tptp_formula list
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| Sequent of tptp_formula list * tptp_formula list
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| Quant of quantifier * (string * tptp_type option) list * tptp_formula
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| Conditional of tptp_formula * tptp_formula * tptp_formula
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| Let of tptp_let list * tptp_formula
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| Atom of tptp_atom
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| THF_type of tptp_type
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| THF_typing of tptp_formula * tptp_type
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and tptp_let =
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Let_fmla of (string * tptp_type option) * tptp_formula (*both TFF and THF*)
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| Let_term of (string * tptp_type option) * tptp_term (*only TFF*)
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and tptp_type =
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Prod_type of tptp_type * tptp_type
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| Fn_type of tptp_type * tptp_type
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| Atom_type of string
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| Defined_type of tptp_base_type
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| Sum_type of tptp_type * tptp_type (*only THF*)
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| Fmla_type of tptp_formula (*only THF*)
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| Subtype of symbol * symbol (*only THF*)
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type general_list = general_term list
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type parent_details = general_list
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type useful_info = general_term list
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type info = useful_info
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(*type annotation = (source * info option)*)
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type annotation = general_term * general_term list
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exception DEQUOTE of string
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(*
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datatype defined_functor =
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ITE_T | UMINUS | SUM | DIFFERENCE | PRODUCT | QUOTIENT | QUOTIENT_E |
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QUOTIENT_T | QUOTIENT_F | REMAINDER_E | REMAINDER_T | REMAINDER_F |
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FLOOR | CEILING | TRUNCATE | ROUND | TO_INT | TO_RAT | TO_REAL
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*)
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type position = string * int * int
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datatype tptp_line =
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Annotated_Formula of position * language * string * role * tptp_formula * annotation option
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| Include of string * string list
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type tptp_problem = tptp_line list
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fun debug f x = if !Runtime.debug then (f x; ()) else ()
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fun nameof_tff_atom_type (Atom_type str) = str
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| nameof_tff_atom_type _ = raise TPTP_SYNTAX "nameof_tff_atom_type called on non-atom type"
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(*Used for debugging. Returns all files contained within a directory or its
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subdirectories. Follows symbolic links, filters away directories.*)
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fun get_file_list path =
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let
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fun check_file_entry f rest =
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let
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(*NOTE needed since no File.is_link and File.read_link*)
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val f_str = Path.implode f
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in
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if File.is_dir f then
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rest @ get_file_list f
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else if OS.FileSys.isLink f_str then
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(*follow links -- NOTE this breaks if links are relative paths*)
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check_file_entry (Path.explode (OS.FileSys.readLink f_str)) rest
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else f :: rest
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end
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in
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File.read_dir path
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|> map
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(Path.explode
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#> Path.append path)
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|> (fn l => fold check_file_entry l [])
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end
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fun role_to_string role =
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case role of
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Role_Axiom => "axiom"
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| Role_Hypothesis => "hypothesis"
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| Role_Definition => "definition"
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| Role_Assumption => "assumption"
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| Role_Lemma => "lemma"
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| Role_Theorem => "theorem"
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| Role_Conjecture => "conjecture"
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| Role_Negated_Conjecture => "negated_conjecture"
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| Role_Plain => "plain"
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| Role_Fi_Domain => "fi_domain"
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| Role_Fi_Functors => "fi_functors"
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| Role_Fi_Predicates => "fi_predicates"
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| Role_Type => "type"
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| Role_Unknown => "unknown"
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(*accepts a string "'abc'" and returns "abc"*)
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fun dequote str : single_quoted =
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if str = "" then
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raise (DEQUOTE "empty string")
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else
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(unprefix "'" str
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|> unsuffix "'"
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handle (Fail str) =>
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if str = "unprefix" then
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raise DEQUOTE ("string doesn't open with quote:" ^ str)
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else if str = "unsuffix" then
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raise DEQUOTE ("string doesn't close with quote:" ^ str)
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else raise Fail str)
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(* Printing parsed TPTP formulas *)
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(*FIXME this is not pretty-printing, just printing*)
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fun status_to_string status_value =
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case status_value of
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Suc => "suc" | Unp => "unp"
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| Sap => "sap" | Esa => "esa"
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| Sat => "sat" | Fsa => "fsa"
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| Thm => "thm" | Wuc => "wuc"
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| Eqv => "eqv" | Tac => "tac"
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| Wec => "wec" | Eth => "eth"
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| Tau => "tau" | Wtc => "wtc"
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| Wth => "wth" | Cax => "cax"
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| Sca => "sca" | Tca => "tca"
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| Wca => "wca" | Cup => "cup"
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| Csp => "csp" | Ecs => "ecs"
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| Csa => "csa" | Cth => "cth"
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| Ceq => "ceq" | Unc => "unc"
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| Wcc => "wcc" | Ect => "ect"
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| Fun => "fun" | Uns => "uns"
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| Wct => "wct" | Scc => "scc"
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| Uca => "uca" | Noc => "noc"
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fun string_of_tptp_term x =
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case x of
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Term_Func (symbol, tptp_term_list) =>
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"(" ^ string_of_symbol symbol ^ " " ^
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375 |
String.concatWith " " (map string_of_tptp_term tptp_term_list) ^ ")"
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|
376 |
| Term_Var str => str
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|
377 |
| Term_Conditional (tptp_formula, tptp_term1, tptp_term2) => "" (*FIXME*)
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|
378 |
| Term_Num (_, str) => str
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|
379 |
| Term_Distinct_Object str => str
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|
380 |
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|
381 |
and string_of_symbol (Uninterpreted str) = str
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382 |
| string_of_symbol (Interpreted_ExtraLogic interpreted_symbol) = string_of_interpreted_symbol interpreted_symbol
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|
383 |
| string_of_symbol (Interpreted_Logic logic_symbol) = string_of_logic_symbol logic_symbol
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|
384 |
| string_of_symbol (TypeSymbol tptp_base_type) = string_of_tptp_base_type tptp_base_type
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|
385 |
| string_of_symbol (System str) = str
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|
386 |
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|
387 |
and string_of_tptp_base_type Type_Ind = "$i"
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|
388 |
| string_of_tptp_base_type Type_Bool = "$o"
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|
389 |
| string_of_tptp_base_type Type_Type = "$tType"
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|
390 |
| string_of_tptp_base_type Type_Int = "$int"
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|
391 |
| string_of_tptp_base_type Type_Rat = "$rat"
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|
392 |
| string_of_tptp_base_type Type_Real = "$real"
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|
393 |
|
|
394 |
and string_of_interpreted_symbol x =
|
|
395 |
case x of
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|
396 |
UMinus => "$uminus"
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|
397 |
| Sum => "$sum"
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|
398 |
| Difference => "$difference"
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|
399 |
| Product => "$product"
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|
400 |
| Quotient => "$quotient"
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|
401 |
| Quotient_E => "$quotient_e"
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|
402 |
| Quotient_T => "$quotient_t"
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|
403 |
| Quotient_F => "$quotient_f"
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|
404 |
| Remainder_E => "$remainder_e"
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|
405 |
| Remainder_T => "$remainder_t"
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|
406 |
| Remainder_F => "$remainder_f"
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|
407 |
| Floor => "$floor"
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|
408 |
| Ceiling => "$ceiling"
|
|
409 |
| Truncate => "$truncate"
|
|
410 |
| Round => "$round"
|
|
411 |
| To_Int => "$to_int"
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|
412 |
| To_Rat => "$to_rat"
|
|
413 |
| To_Real => "$to_real"
|
|
414 |
| Less => "$less"
|
|
415 |
| LessEq => "$lesseq"
|
|
416 |
| Greater => "$greater"
|
|
417 |
| GreaterEq => "$greatereq"
|
|
418 |
| EvalEq => "$evaleq"
|
|
419 |
| Is_Int => "$is_int"
|
|
420 |
| Is_Rat => "$is_rat"
|
|
421 |
| Apply => "@"
|
|
422 |
|
|
423 |
and string_of_logic_symbol Equals = "="
|
|
424 |
| string_of_logic_symbol NEquals = "!="
|
|
425 |
| string_of_logic_symbol Or = "|"
|
|
426 |
| string_of_logic_symbol And = "&"
|
|
427 |
| string_of_logic_symbol Iff = "<=>"
|
|
428 |
| string_of_logic_symbol If = "=>"
|
|
429 |
| string_of_logic_symbol Fi = "<="
|
|
430 |
| string_of_logic_symbol Xor = "<~>"
|
|
431 |
| string_of_logic_symbol Nor = "~|"
|
|
432 |
| string_of_logic_symbol Nand = "~&"
|
|
433 |
| string_of_logic_symbol Not = "~"
|
|
434 |
| string_of_logic_symbol Op_Forall = "!!"
|
|
435 |
| string_of_logic_symbol Op_Exists = "??"
|
|
436 |
| string_of_logic_symbol True = "$true"
|
|
437 |
| string_of_logic_symbol False = "$false"
|
|
438 |
|
|
439 |
and string_of_quantifier Forall = "!"
|
|
440 |
| string_of_quantifier Exists = "?"
|
|
441 |
| string_of_quantifier Epsilon = "@+"
|
|
442 |
| string_of_quantifier Iota = "@-"
|
|
443 |
| string_of_quantifier Lambda = "^"
|
|
444 |
| string_of_quantifier Dep_Prod = "!>"
|
|
445 |
| string_of_quantifier Dep_Sum = "?*"
|
|
446 |
|
|
447 |
and string_of_tptp_atom (TFF_Typed_Atom (symbol, tptp_type_option)) =
|
|
448 |
(case tptp_type_option of
|
|
449 |
NONE => string_of_symbol symbol
|
|
450 |
| SOME tptp_type =>
|
|
451 |
string_of_symbol symbol ^ " : " ^ string_of_tptp_type tptp_type)
|
|
452 |
| string_of_tptp_atom (THF_Atom_term tptp_term) = string_of_tptp_term tptp_term
|
|
453 |
| string_of_tptp_atom (THF_Atom_conn_term symbol) = string_of_symbol symbol
|
|
454 |
|
|
455 |
and string_of_tptp_formula (Pred (symbol, tptp_term_list)) =
|
|
456 |
"(" ^ string_of_symbol symbol ^
|
|
457 |
String.concatWith " " (map string_of_tptp_term tptp_term_list) ^ ")"
|
|
458 |
| string_of_tptp_formula (Fmla (symbol, tptp_formula_list)) =
|
|
459 |
"(" ^
|
|
460 |
string_of_symbol symbol ^
|
|
461 |
String.concatWith " " (map string_of_tptp_formula tptp_formula_list) ^ ")"
|
|
462 |
| string_of_tptp_formula (Sequent (tptp_formula_list1, tptp_formula_list2)) = "" (*FIXME*)
|
|
463 |
| string_of_tptp_formula (Quant (quantifier, varlist, tptp_formula)) =
|
|
464 |
string_of_quantifier quantifier ^ "[" ^
|
|
465 |
String.concatWith ", " (map (fn (n, ty) =>
|
|
466 |
case ty of
|
|
467 |
NONE => n
|
|
468 |
| SOME ty => n ^ " : " ^ string_of_tptp_type ty) varlist) ^ "] : (" ^
|
|
469 |
string_of_tptp_formula tptp_formula ^ ")"
|
|
470 |
| string_of_tptp_formula (Conditional _) = "" (*FIXME*)
|
|
471 |
| string_of_tptp_formula (Let _) = "" (*FIXME*)
|
|
472 |
| string_of_tptp_formula (Atom tptp_atom) = string_of_tptp_atom tptp_atom
|
|
473 |
| string_of_tptp_formula (THF_type tptp_type) = string_of_tptp_type tptp_type
|
|
474 |
| string_of_tptp_formula (THF_typing (tptp_formula, tptp_type)) =
|
|
475 |
string_of_tptp_formula tptp_formula ^ " : " ^ string_of_tptp_type tptp_type
|
|
476 |
|
|
477 |
and string_of_tptp_type (Prod_type (tptp_type1, tptp_type2)) =
|
|
478 |
string_of_tptp_type tptp_type1 ^ " * " ^ string_of_tptp_type tptp_type2
|
|
479 |
| string_of_tptp_type (Fn_type (tptp_type1, tptp_type2)) =
|
|
480 |
string_of_tptp_type tptp_type1 ^ " > " ^ string_of_tptp_type tptp_type2
|
|
481 |
| string_of_tptp_type (Atom_type str) = str
|
|
482 |
| string_of_tptp_type (Defined_type tptp_base_type) =
|
|
483 |
string_of_tptp_base_type tptp_base_type
|
|
484 |
| string_of_tptp_type (Sum_type (tptp_type1, tptp_type2)) = ""
|
|
485 |
| string_of_tptp_type (Fmla_type tptp_formula) = string_of_tptp_formula tptp_formula
|
|
486 |
| string_of_tptp_type (Subtype (symbol1, symbol2)) =
|
|
487 |
string_of_symbol symbol1 ^ " << " ^ string_of_symbol symbol2
|
|
488 |
|
|
489 |
end
|