author  blanchet 
Mon, 28 Jun 2010 18:02:36 +0200  
changeset 37618  fa57a87f92a0 
parent 37616  c8d2d84d6011 
child 37620  537beae999d7 
permissions  rwrr 
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(* Title: HOL/Tools/Sledgehammer/metis_clauses.ML 
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Author: Jia Meng, Cambridge University Computer Laboratory 
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Author: Jasmin Blanchette, TU Muenchen 
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Storing/printing FOL clauses and arity clauses. Typed equality is 
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treated differently. 

15347  7 
*) 
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signature METIS_CLAUSES = 
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sig 
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type cnf_thm = Clausifier.cnf_thm 
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type name = string * string 
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type name_pool = string Symtab.table * string Symtab.table 
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datatype kind = Axiom  Conjecture 
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datatype type_literal = 
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TyLitVar of string * name  
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TyLitFree of string * name 
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datatype arLit = 
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TConsLit of class * string * string list 
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 TVarLit of class * string 
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datatype arity_clause = ArityClause of 
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{axiom_name: string, conclLit: arLit, premLits: arLit list} 
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datatype classrel_clause = ClassrelClause of 
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{axiom_name: string, subclass: class, superclass: class} 
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datatype combtyp = 
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TyVar of name  
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TyFree of name  
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TyConstr of name * combtyp list 
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datatype combterm = 
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CombConst of name * combtyp * combtyp list (* Const and Free *)  
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CombVar of name * combtyp  
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CombApp of combterm * combterm 
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datatype literal = Literal of bool * combterm 
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datatype hol_clause = 
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HOLClause of {clause_id: int, axiom_name: string, th: thm, kind: kind, 
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literals: literal list, ctypes_sorts: typ list} 
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exception TRIVIAL of unit 
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val trace : bool Unsynchronized.ref 
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val type_wrapper_name : string 
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val schematic_var_prefix: string 
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val fixed_var_prefix: string 

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val tvar_prefix: string 

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val tfree_prefix: string 

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val const_prefix: string 

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val tconst_prefix: string 

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val class_prefix: string 

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val union_all: ''a list list > ''a list 

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val invert_const: string > string 
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val ascii_of: string > string 
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val undo_ascii_of: string > string 

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val strip_prefix: string > string > string option 
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val make_schematic_var : string * int > string 
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val make_fixed_var : string > string 
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val make_schematic_type_var : string * int > string 

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val make_fixed_type_var : string > string 
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val make_fixed_const : string > string 
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val make_fixed_type_const : string > string 
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val make_type_class : string > string 
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val skolem_theory_name: string 
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val skolem_prefix: string 
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val skolem_infix: string 
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val is_skolem_const_name: string > bool 
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val num_type_args: theory > string > int 
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val empty_name_pool : bool > name_pool option 
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val pool_map : ('a > 'b > 'c * 'b) > 'a list > 'b > 'c list * 'b 
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val nice_name : name > name_pool option > string * name_pool option 
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val type_literals_for_types : typ list > type_literal list 
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val make_classrel_clauses: theory > class list > class list > classrel_clause list 
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val make_arity_clauses: theory > string list > class list > class list * arity_clause list 

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val type_of_combterm : combterm > combtyp 
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val strip_combterm_comb : combterm > combterm * combterm list 
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val literals_of_term : theory > term > literal list * typ list 
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val conceal_skolem_somes : 
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int > (string * term) list > term > (string * term) list * term 
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val is_quasi_fol_theorem : theory > thm > bool 
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val tfree_classes_of_terms : term list > string list 
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val tvar_classes_of_terms : term list > string list 
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val type_consts_of_terms : theory > term list > string list 
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val prepare_clauses : 
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bool > thm list > cnf_thm list > cnf_thm list > theory 
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> string vector 
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* (hol_clause list * hol_clause list * hol_clause list * hol_clause list 
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* classrel_clause list * arity_clause list) 
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end 
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structure Metis_Clauses : METIS_CLAUSES = 
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struct 
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open Clausifier 
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val trace = Unsynchronized.ref false 
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fun trace_msg msg = if !trace then tracing (msg ()) else () 
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val type_wrapper_name = "ti" 
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val schematic_var_prefix = "V_"; 
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val fixed_var_prefix = "v_"; 

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val tvar_prefix = "T_"; 
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val tfree_prefix = "t_"; 
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val classrel_clause_prefix = "clsrel_"; 
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val const_prefix = "c_"; 
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val tconst_prefix = "tc_"; 
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val class_prefix = "class_"; 

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fun union_all xss = fold (union (op =)) xss [] 
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(* Readable names for the more common symbolic functions. Do not mess with the 
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last nine entries of the table unless you know what you are doing. *) 
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val const_trans_table = 
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Symtab.make [(@{const_name "op ="}, "equal"), 
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(@{const_name "op &"}, "and"), 

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(@{const_name "op "}, "or"), 

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(@{const_name "op >"}, "implies"), 

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(@{const_name "op :"}, "in"), 
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(@{const_name fequal}, "fequal"), 
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(@{const_name COMBI}, "COMBI"), 
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(@{const_name COMBK}, "COMBK"), 
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(@{const_name COMBB}, "COMBB"), 
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(@{const_name COMBC}, "COMBC"), 
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(@{const_name COMBS}, "COMBS"), 
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(@{const_name True}, "True"), 
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(@{const_name False}, "False"), 
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(@{const_name If}, "If"), 
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(@{type_name "*"}, "prod"), 
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(@{type_name "+"}, "sum")] 
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(* Invert the table of translations between Isabelle and ATPs. *) 
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val const_trans_table_inv = 
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Symtab.update ("fequal", @{const_name "op ="}) 
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(Symtab.make (map swap (Symtab.dest const_trans_table))) 
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val invert_const = perhaps (Symtab.lookup const_trans_table_inv) 
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(*Escaping of special characters. 
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Alphanumeric characters are left unchanged. 

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The character _ goes to __ 

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Characters in the range ASCII space to / go to _A to _P, respectively. 

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Other printing characters go to _nnn where nnn is the decimal ASCII code.*) 
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val A_minus_space = Char.ord #"A"  Char.ord #" "; 

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fun stringN_of_int 0 _ = "" 
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 stringN_of_int k n = stringN_of_int (k1) (n div 10) ^ Int.toString (n mod 10); 

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fun ascii_of_c c = 
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if Char.isAlphaNum c then String.str c 
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else if c = #"_" then "__" 

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else if #" " <= c andalso c <= #"/" 
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then "_" ^ String.str (Char.chr (Char.ord c + A_minus_space)) 
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else if Char.isPrint c 
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then ("_" ^ stringN_of_int 3 (Char.ord c)) (*fixed width, in case more digits follow*) 
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else "" 
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val ascii_of = String.translate ascii_of_c; 
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(** Remove ASCII armouring from names in proof files **) 
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(*We don't raise error exceptions because this code can run inside the watcher. 

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Also, the errors are "impossible" (hah!)*) 

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fun undo_ascii_aux rcs [] = String.implode(rev rcs) 

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 undo_ascii_aux rcs [#"_"] = undo_ascii_aux (#"_"::rcs) [] (*ERROR*) 

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(*Three types of _ escapes: __, _A to _P, _nnn*) 

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 undo_ascii_aux rcs (#"_" :: #"_" :: cs) = undo_ascii_aux (#"_"::rcs) cs 

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 undo_ascii_aux rcs (#"_" :: c :: cs) = 
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if #"A" <= c andalso c<= #"P" (*translation of #" " to #"/"*) 
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then undo_ascii_aux (Char.chr(Char.ord c  A_minus_space) :: rcs) cs 

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else 
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let val digits = List.take (c::cs, 3) handle Subscript => [] 
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in 
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case Int.fromString (String.implode digits) of 
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NONE => undo_ascii_aux (c:: #"_"::rcs) cs (*ERROR*) 

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 SOME n => undo_ascii_aux (Char.chr n :: rcs) (List.drop (cs, 2)) 

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end 

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 undo_ascii_aux rcs (c::cs) = undo_ascii_aux (c::rcs) cs; 

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val undo_ascii_of = undo_ascii_aux [] o String.explode; 

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(* If string s has the prefix s1, return the result of deleting it, 
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unASCII'd. *) 
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fun strip_prefix s1 s = 
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if String.isPrefix s1 s then 
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SOME (undo_ascii_of (String.extract (s, size s1, NONE))) 
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else 
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NONE 
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(*Remove the initial ' character from a type variable, if it is present*) 
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fun trim_type_var s = 
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if s <> "" andalso String.sub(s,0) = #"'" then String.extract(s,1,NONE) 
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else error ("trim_type: Malformed type variable encountered: " ^ s); 
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fun ascii_of_indexname (v,0) = ascii_of v 
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 ascii_of_indexname (v,i) = ascii_of v ^ "_" ^ Int.toString i; 
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fun make_schematic_var v = schematic_var_prefix ^ (ascii_of_indexname v); 
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fun make_fixed_var x = fixed_var_prefix ^ (ascii_of x); 
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fun make_schematic_type_var (x,i) = 
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tvar_prefix ^ (ascii_of_indexname (trim_type_var x,i)); 
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fun make_fixed_type_var x = tfree_prefix ^ (ascii_of (trim_type_var x)); 
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fun lookup_const c = 
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case Symtab.lookup const_trans_table c of 
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SOME c' => c' 
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 NONE => ascii_of c 
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(* "op =" MUST BE "equal" because it's built into ATPs. *) 
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fun make_fixed_const @{const_name "op ="} = "equal" 
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 make_fixed_const c = const_prefix ^ lookup_const c 
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fun make_fixed_type_const c = tconst_prefix ^ lookup_const c 
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17261  215 
fun make_type_class clas = class_prefix ^ ascii_of clas; 
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val skolem_theory_name = "Sledgehammer" ^ Long_Name.separator ^ "Sko" 
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val skolem_prefix = "sko_" 
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val skolem_infix = "$" 
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(*Keep the full complexity of the original name*) 
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fun flatten_name s = space_implode "_X" (Long_Name.explode s); 
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(* Hack: Could return false positives (e.g., a user happens to declare a 
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constant called "SomeTheory.sko_means_shoe_in_$wedish". *) 
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val is_skolem_const_name = 
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Long_Name.base_name 
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#> String.isPrefix skolem_prefix andf String.isSubstring skolem_infix 
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(* The number of type arguments of a constant, zero if it's monomorphic. For 
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(instances of) Skolem pseudoconstants, this information is encoded in the 
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constant name. *) 
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fun num_type_args thy s = 
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if String.isPrefix skolem_theory_name s then 
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s > unprefix skolem_theory_name 
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> space_explode skolem_infix > hd 
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> space_explode "_" > List.last > Int.fromString > the 
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else 
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(s, Sign.the_const_type thy s) > Sign.const_typargs thy > length 
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(**** name pool ****) 
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type name = string * string 
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type name_pool = string Symtab.table * string Symtab.table 
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fun empty_name_pool readable_names = 
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if readable_names then SOME (`I Symtab.empty) else NONE 
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fun pool_fold f xs z = pair z #> fold_rev (fn x => uncurry (f x)) xs 
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fun pool_map f xs = 
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pool_fold (fn x => fn ys => fn pool => f x pool >> (fn y => y :: ys)) xs [] 
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252 

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fun add_nice_name full_name nice_prefix j the_pool = 
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let 
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val nice_name = nice_prefix ^ (if j = 0 then "" else "_" ^ Int.toString j) 
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in 
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case Symtab.lookup (snd the_pool) nice_name of 
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SOME full_name' => 
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if full_name = full_name' then (nice_name, the_pool) 
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else add_nice_name full_name nice_prefix (j + 1) the_pool 
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 NONE => 
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(nice_name, (Symtab.update_new (full_name, nice_name) (fst the_pool), 
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Symtab.update_new (nice_name, full_name) (snd the_pool))) 
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end 
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fun translate_first_char f s = 
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String.str (f (String.sub (s, 0))) ^ String.extract (s, 1, NONE) 
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fun readable_name full_name s = 
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let 
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val s = s > Long_Name.base_name > Name.desymbolize false 
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val s' = s > explode > rev > dropwhile (curry (op =) "'") 
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val s' = 
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(s' > rev 
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> implode 
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> String.translate 
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(fn c => if Char.isAlphaNum c orelse c = #"_" then String.str c 
278 
else "")) 

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^ replicate_string (String.size s  length s') "_" 
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val s' = 
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if s' = "" orelse not (Char.isAlpha (String.sub (s', 0))) then "X" ^ s' 
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else s' 
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(* Avoid "equal", since it's built into ATPs; and "op" is very ambiguous 
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("op &", "op ", etc.). *) 
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val s' = if s' = "equal" orelse s' = "op" then full_name else s' 
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in 
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case (Char.isLower (String.sub (full_name, 0)), 
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Char.isLower (String.sub (s', 0))) of 
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(true, false) => translate_first_char Char.toLower s' 
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 (false, true) => translate_first_char Char.toUpper s' 
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 _ => s' 
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end 
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293 

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fun nice_name (full_name, _) NONE = (full_name, NONE) 
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 nice_name (full_name, desired_name) (SOME the_pool) = 
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case Symtab.lookup (fst the_pool) full_name of 
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SOME nice_name => (nice_name, SOME the_pool) 
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 NONE => add_nice_name full_name (readable_name full_name desired_name) 0 
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the_pool 
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> apsnd SOME 
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(**** Definitions and functions for FOL clauses for TPTP format output ****) 
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datatype kind = Axiom  Conjecture 
23385  305 

15347  306 
(**** Isabelle FOL clauses ****) 
307 

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(* The first component is the type class; the second is a TVar or TFree. *) 
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datatype type_literal = 
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TyLitVar of string * name  
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TyLitFree of string * name 
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exception CLAUSE of string * term; 
15347  314 

24310  315 
(*Make literals for sorted type variables*) 
24940  316 
fun sorts_on_typs_aux (_, []) = [] 
317 
 sorts_on_typs_aux ((x,i), s::ss) = 

318 
let val sorts = sorts_on_typs_aux ((x,i), ss) 

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in 
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if s = "HOL.type" then sorts 
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321 
else if i = ~1 then TyLitFree (make_type_class s, `make_fixed_type_var x) :: sorts 
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322 
else TyLitVar (make_type_class s, (make_schematic_type_var (x,i), x)) :: sorts 
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323 
end; 
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324 

24940  325 
fun sorts_on_typs (TFree (a,s)) = sorts_on_typs_aux ((a,~1),s) 
326 
 sorts_on_typs (TVar (v,s)) = sorts_on_typs_aux (v,s); 

327 

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328 
(*Given a list of sorted type variables, return a list of type literals.*) 
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329 
fun type_literals_for_types Ts = 
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330 
fold (union (op =)) (map sorts_on_typs Ts) [] 
20015
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331 

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332 
(** make axiom and conjecture clauses. **) 
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333 

15347  334 
(**** Isabelle arities ****) 
335 

24310  336 
datatype arLit = TConsLit of class * string * string list 
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337 
 TVarLit of class * string; 
24310  338 

35865  339 
datatype arity_clause = 
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340 
ArityClause of {axiom_name: string, conclLit: arLit, premLits: arLit list} 
15347  341 

342 

18798  343 
fun gen_TVars 0 = [] 
344 
 gen_TVars n = ("T_" ^ Int.toString n) :: gen_TVars (n1); 

15347  345 

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346 
fun pack_sort(_,[]) = [] 
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347 
 pack_sort(tvar, "HOL.type"::srt) = pack_sort(tvar, srt) (*IGNORE sort "type"*) 
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348 
 pack_sort(tvar, cls::srt) = (cls, tvar) :: pack_sort(tvar, srt); 
24310  349 

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350 
(*Arity of type constructor tcon :: (arg1,...,argN)res*) 
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351 
fun make_axiom_arity_clause (tcons, axiom_name, (cls,args)) = 
21560  352 
let val tvars = gen_TVars (length args) 
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353 
val tvars_srts = ListPair.zip (tvars,args) 
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354 
in 
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355 
ArityClause {axiom_name = axiom_name, 
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356 
conclLit = TConsLit (cls, make_fixed_type_const tcons, tvars), 
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357 
premLits = map TVarLit (union_all(map pack_sort tvars_srts))} 
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358 
end; 
15347  359 

360 

361 
(**** Isabelle class relations ****) 

362 

35865  363 
datatype classrel_clause = 
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364 
ClassrelClause of {axiom_name: string, subclass: class, superclass: class} 
24310  365 

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366 
(*Generate all pairs (sub,super) such that sub is a proper subclass of super in theory thy.*) 
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367 
fun class_pairs _ [] _ = [] 
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368 
 class_pairs thy subs supers = 
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369 
let 
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370 
val class_less = Sorts.class_less (Sign.classes_of thy) 
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371 
fun add_super sub super = class_less (sub, super) ? cons (sub, super) 
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372 
fun add_supers sub = fold (add_super sub) supers 
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373 
in fold add_supers subs [] end 
15347  374 

35865  375 
fun make_classrel_clause (sub,super) = 
37509
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376 
ClassrelClause {axiom_name = classrel_clause_prefix ^ ascii_of sub ^ "_" ^ 
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377 
ascii_of super, 
24310  378 
subclass = make_type_class sub, 
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379 
superclass = make_type_class super}; 
15347  380 

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381 
fun make_classrel_clauses thy subs supers = 
35865  382 
map make_classrel_clause (class_pairs thy subs supers); 
18868  383 

384 

385 
(** Isabelle arities **) 

17845
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386 

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387 
fun arity_clause _ _ (_, []) = [] 
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388 
 arity_clause seen n (tcons, ("HOL.type",_)::ars) = (*ignore*) 
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389 
arity_clause seen n (tcons,ars) 
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390 
 arity_clause seen n (tcons, (ar as (class,_)) :: ars) = 
36692
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farewell to oldstyle mem infixes  type inference in situations with mem_int and mem_string should provide enough information to resolve the type of (op =)
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391 
if member (op =) seen class then (*multiple arities for the same tycon, class pair*) 
37572
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392 
make_axiom_arity_clause (tcons, lookup_const tcons ^ "_" ^ class ^ "_" ^ Int.toString n, ar) :: 
37498
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393 
arity_clause seen (n+1) (tcons,ars) 
21373
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394 
else 
37572
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395 
make_axiom_arity_clause (tcons, lookup_const tcons ^ "_" ^ class, ar) :: 
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396 
arity_clause (class::seen) n (tcons,ars) 
17845
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397 

37498
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398 
fun multi_arity_clause [] = [] 
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399 
 multi_arity_clause ((tcons, ars) :: tc_arlists) = 
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400 
arity_clause [] 1 (tcons, ars) @ multi_arity_clause tc_arlists 
17845
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401 

22643
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Improved and simplified the treatment of classrel/arity clauses
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402 
(*Generate all pairs (tycon,class,sorts) such that tycon belongs to class in theory thy 
bc3bb8e9594a
Improved and simplified the treatment of classrel/arity clauses
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changeset

403 
provided its arguments have the corresponding sorts.*) 
21373
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404 
fun type_class_pairs thy tycons classes = 
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405 
let val alg = Sign.classes_of thy 
36218
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406 
fun domain_sorts tycon = Sorts.mg_domain alg tycon o single 
0e4a01f3e7d3
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407 
fun add_class tycon class = 
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changeset

408 
cons (class, domain_sorts tycon class) 
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changeset

409 
handle Sorts.CLASS_ERROR _ => I 
0e4a01f3e7d3
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changeset

410 
fun try_classes tycon = (tycon, fold (add_class tycon) classes []) 
21373
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paulson
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411 
in map try_classes tycons end; 
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paulson
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changeset

412 

22643
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Improved and simplified the treatment of classrel/arity clauses
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413 
(*Proving one (tycon, class) membership may require proving others, so iterate.*) 
37498
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414 
fun iter_type_class_pairs _ _ [] = ([], []) 
22643
bc3bb8e9594a
Improved and simplified the treatment of classrel/arity clauses
paulson
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22383
diff
changeset

415 
 iter_type_class_pairs thy tycons classes = 
bc3bb8e9594a
Improved and simplified the treatment of classrel/arity clauses
paulson
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diff
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416 
let val cpairs = type_class_pairs thy tycons classes 
33040  417 
val newclasses = union_all (union_all (union_all (map (map #2 o #2) cpairs))) 
418 
> subtract (op =) classes > subtract (op =) HOLogic.typeS 

24310  419 
val (classes', cpairs') = iter_type_class_pairs thy tycons newclasses 
33042  420 
in (union (op =) classes' classes, union (op =) cpairs' cpairs) end; 
24310  421 

37498
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422 
fun make_arity_clauses thy tycons classes = 
24310  423 
let val (classes', cpairs) = iter_type_class_pairs thy tycons classes 
37498
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changeset

424 
in (classes', multi_arity_clause cpairs) end; 
18863  425 

37577
5379f41a1322
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426 
datatype combtyp = 
5379f41a1322
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427 
TyVar of name  
5379f41a1322
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428 
TyFree of name  
5379f41a1322
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changeset

429 
TyConstr of name * combtyp list 
5379f41a1322
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changeset

430 

5379f41a1322
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431 
datatype combterm = 
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432 
CombConst of name * combtyp * combtyp list (* Const and Free *)  
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433 
CombVar of name * combtyp  
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434 
CombApp of combterm * combterm 
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changeset

435 

5379f41a1322
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changeset

436 
datatype literal = Literal of bool * combterm 
5379f41a1322
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437 

5379f41a1322
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changeset

438 
datatype hol_clause = 
5379f41a1322
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diff
changeset

439 
HOLClause of {clause_id: int, axiom_name: string, th: thm, kind: kind, 
5379f41a1322
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440 
literals: literal list, ctypes_sorts: typ list} 
5379f41a1322
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441 

5379f41a1322
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442 
(*********************************************************************) 
5379f41a1322
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443 
(* convert a clause with type Term.term to a clause with type clause *) 
5379f41a1322
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444 
(*********************************************************************) 
5379f41a1322
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changeset

445 

5379f41a1322
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446 
(*Result of a function type; no need to check that the argument type matches.*) 
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447 
fun result_type (TyConstr (_, [_, tp2])) = tp2 
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448 
 result_type _ = raise Fail "nonfunction type" 
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449 

5379f41a1322
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450 
fun type_of_combterm (CombConst (_, tp, _)) = tp 
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451 
 type_of_combterm (CombVar (_, tp)) = tp 
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452 
 type_of_combterm (CombApp (t1, _)) = result_type (type_of_combterm t1) 
5379f41a1322
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changeset

453 

5379f41a1322
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changeset

454 
(*gets the head of a combinator application, along with the list of arguments*) 
5379f41a1322
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changeset

455 
fun strip_combterm_comb u = 
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456 
let fun stripc (CombApp(t,u), ts) = stripc (t, u::ts) 
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457 
 stripc x = x 
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458 
in stripc(u,[]) end 
5379f41a1322
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changeset

459 

5379f41a1322
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460 
fun isFalse (Literal (pol, CombConst ((c, _), _, _))) = 
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461 
(pol andalso c = "c_False") orelse (not pol andalso c = "c_True") 
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462 
 isFalse _ = false; 
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changeset

463 

5379f41a1322
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464 
fun isTrue (Literal (pol, CombConst ((c, _), _, _))) = 
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465 
(pol andalso c = "c_True") orelse 
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466 
(not pol andalso c = "c_False") 
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467 
 isTrue _ = false; 
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changeset

468 

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469 
fun isTaut (HOLClause {literals,...}) = exists isTrue literals; 
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470 

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471 
fun type_of (Type (a, Ts)) = 
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472 
let val (folTypes,ts) = types_of Ts in 
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473 
(TyConstr (`make_fixed_type_const a, folTypes), ts) 
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474 
end 
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475 
 type_of (tp as TFree (a, _)) = (TyFree (`make_fixed_type_var a), [tp]) 
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476 
 type_of (tp as TVar (x, _)) = 
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477 
(TyVar (make_schematic_type_var x, string_of_indexname x), [tp]) 
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478 
and types_of Ts = 
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479 
let val (folTyps, ts) = ListPair.unzip (map type_of Ts) in 
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480 
(folTyps, union_all ts) 
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481 
end 
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changeset

482 

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483 
(* same as above, but no gathering of sort information *) 
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484 
fun simp_type_of (Type (a, Ts)) = 
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485 
TyConstr (`make_fixed_type_const a, map simp_type_of Ts) 
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486 
 simp_type_of (TFree (a, _)) = TyFree (`make_fixed_type_var a) 
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487 
 simp_type_of (TVar (x, _)) = 
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488 
TyVar (make_schematic_type_var x, string_of_indexname x) 
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489 

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490 
(* convert a Term.term (with combinators) into a combterm, also accummulate sort info *) 
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491 
fun combterm_of thy (Const (c, T)) = 
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492 
let 
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493 
val (tp, ts) = type_of T 
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494 
val tvar_list = 
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495 
(if String.isPrefix skolem_theory_name c then 
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496 
[] > Term.add_tvarsT T > map TVar 
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497 
else 
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498 
(c, T) > Sign.const_typargs thy) 
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499 
> map simp_type_of 
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500 
val c' = CombConst (`make_fixed_const c, tp, tvar_list) 
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501 
in (c',ts) end 
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502 
 combterm_of _ (Free(v, T)) = 
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503 
let val (tp,ts) = type_of T 
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504 
val v' = CombConst (`make_fixed_var v, tp, []) 
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505 
in (v',ts) end 
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506 
 combterm_of _ (Var(v, T)) = 
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507 
let val (tp,ts) = type_of T 
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508 
val v' = CombVar ((make_schematic_var v, string_of_indexname v), tp) 
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509 
in (v',ts) end 
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510 
 combterm_of thy (P $ Q) = 
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511 
let val (P', tsP) = combterm_of thy P 
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512 
val (Q', tsQ) = combterm_of thy Q 
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513 
in (CombApp (P', Q'), union (op =) tsP tsQ) end 
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514 
 combterm_of _ (t as Abs _) = raise Fail "HOL clause: Abs" 
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515 

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516 
fun predicate_of thy ((@{const Not} $ P), pos) = predicate_of thy (P, not pos) 
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517 
 predicate_of thy (t, pos) = (combterm_of thy (Envir.eta_contract t), pos) 
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518 

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519 
fun literals_of_term1 args thy (@{const Trueprop} $ P) = 
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520 
literals_of_term1 args thy P 
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521 
 literals_of_term1 args thy (@{const "op "} $ P $ Q) = 
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522 
literals_of_term1 (literals_of_term1 args thy P) thy Q 
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523 
 literals_of_term1 (lits, ts) thy P = 
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524 
let val ((pred, ts'), pol) = predicate_of thy (P, true) in 
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525 
(Literal (pol, pred) :: lits, union (op =) ts ts') 
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526 
end 
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527 
val literals_of_term = literals_of_term1 ([], []) 
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528 

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529 
fun skolem_name i j num_T_args = 
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530 
skolem_prefix ^ (space_implode "_" (map Int.toString [i, j, num_T_args])) ^ 
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531 
skolem_infix ^ "g" 
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532 

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533 
fun conceal_skolem_somes i skolem_somes t = 
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534 
if exists_Const (curry (op =) @{const_name skolem_id} o fst) t then 
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535 
let 
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536 
fun aux skolem_somes 
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537 
(t as (Const (@{const_name skolem_id}, Type (_, [_, T])) $ _)) = 
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538 
let 
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539 
val (skolem_somes, s) = 
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540 
if i = ~1 then 
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541 
(skolem_somes, @{const_name undefined}) 
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542 
else case AList.find (op aconv) skolem_somes t of 
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543 
s :: _ => (skolem_somes, s) 
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544 
 [] => 
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545 
let 
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546 
val s = skolem_theory_name ^ "." ^ 
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547 
skolem_name i (length skolem_somes) 
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548 
(length (Term.add_tvarsT T [])) 
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549 
in ((s, t) :: skolem_somes, s) end 
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550 
in (skolem_somes, Const (s, T)) end 
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551 
 aux skolem_somes (t1 $ t2) = 
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552 
let 
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553 
val (skolem_somes, t1) = aux skolem_somes t1 
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554 
val (skolem_somes, t2) = aux skolem_somes t2 
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555 
in (skolem_somes, t1 $ t2) end 
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556 
 aux skolem_somes (Abs (s, T, t')) = 
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557 
let val (skolem_somes, t') = aux skolem_somes t' in 
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558 
(skolem_somes, Abs (s, T, t')) 
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559 
end 
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560 
 aux skolem_somes t = (skolem_somes, t) 
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561 
in aux skolem_somes t end 
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562 
else 
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563 
(skolem_somes, t) 
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564 

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565 
fun is_quasi_fol_theorem thy = 
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566 
Meson.is_fol_term thy o snd o conceal_skolem_somes ~1 [] o prop_of 
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567 

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568 
(* Trivial problem, which resolution cannot handle (empty clause) *) 
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569 
exception TRIVIAL of unit 
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changeset

570 

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571 
(* making axiom and conjecture clauses *) 
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572 
fun make_clause thy (clause_id, axiom_name, kind, th) skolem_somes = 
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573 
let 
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574 
val (skolem_somes, t) = 
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575 
th > prop_of > conceal_skolem_somes clause_id skolem_somes 
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576 
val (lits, ctypes_sorts) = literals_of_term thy t 
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577 
in 
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578 
if forall isFalse lits then 
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changeset

579 
raise TRIVIAL () 
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580 
else 
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changeset

581 
(skolem_somes, 
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582 
HOLClause {clause_id = clause_id, axiom_name = axiom_name, th = th, 
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changeset

583 
kind = kind, literals = lits, ctypes_sorts = ctypes_sorts}) 
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changeset

584 
end 
5379f41a1322
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changeset

585 

5379f41a1322
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586 
fun add_axiom_clause thy (th, ((name, id), _ : thm)) (skolem_somes, clss) = 
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587 
let 
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588 
val (skolem_somes, cls) = make_clause thy (id, name, Axiom, th) skolem_somes 
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589 
in (skolem_somes, clss > not (isTaut cls) ? cons (name, cls)) end 
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590 

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591 
fun make_axiom_clauses thy clauses = 
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592 
([], []) > fold_rev (add_axiom_clause thy) clauses > snd 
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593 

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594 
fun make_conjecture_clauses thy = 
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595 
let 
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596 
fun aux _ _ [] = [] 
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597 
 aux n skolem_somes (th :: ths) = 
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598 
let 
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599 
val (skolem_somes, cls) = 
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600 
make_clause thy (n, "conjecture", Conjecture, th) skolem_somes 
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601 
in cls :: aux (n + 1) skolem_somes ths end 
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602 
in aux 0 [] end 
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603 

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604 
(** Helper clauses **) 
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605 

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606 
fun count_combterm (CombConst ((c, _), _, _)) = 
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607 
Symtab.map_entry c (Integer.add 1) 
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608 
 count_combterm (CombVar _) = I 
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609 
 count_combterm (CombApp (t1, t2)) = count_combterm t1 #> count_combterm t2 
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610 
fun count_literal (Literal (_, t)) = count_combterm t 
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611 
fun count_clause (HOLClause {literals, ...}) = fold count_literal literals 
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changeset

612 

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613 
fun raw_cnf_rules_pairs ps = map (fn (name, thm) => (thm, ((name, 0), thm))) ps 
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614 
fun cnf_helper_thms thy raw = 
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615 
map (`Thm.get_name_hint) 
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616 
#> (if raw then raw_cnf_rules_pairs else cnf_rules_pairs thy) 
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617 

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618 
val optional_helpers = 
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619 
[(["c_COMBI", "c_COMBK"], (false, @{thms COMBI_def COMBK_def})), 
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620 
(["c_COMBB", "c_COMBC"], (false, @{thms COMBB_def COMBC_def})), 
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621 
(["c_COMBS"], (false, @{thms COMBS_def}))] 
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622 
val optional_typed_helpers = 
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623 
[(["c_True", "c_False"], (true, @{thms True_or_False})), 
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624 
(["c_If"], (true, @{thms if_True if_False True_or_False}))] 
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625 
val mandatory_helpers = @{thms fequal_imp_equal equal_imp_fequal} 
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changeset

626 

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627 
val init_counters = 
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628 
Symtab.make (maps (maps (map (rpair 0) o fst)) 
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629 
[optional_helpers, optional_typed_helpers]) 
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630 

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631 
fun get_helper_clauses thy is_FO full_types conjectures axcls = 
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632 
let 
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633 
val axclauses = map snd (make_axiom_clauses thy axcls) 
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634 
val ct = fold (fold count_clause) [conjectures, axclauses] init_counters 
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635 
fun is_needed c = the (Symtab.lookup ct c) > 0 
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636 
val cnfs = 
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637 
(optional_helpers 
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638 
> full_types ? append optional_typed_helpers 
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639 
> maps (fn (ss, (raw, ths)) => 
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640 
if exists is_needed ss then cnf_helper_thms thy raw ths 
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641 
else [])) 
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642 
@ (if is_FO then [] else cnf_helper_thms thy false mandatory_helpers) 
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643 
in map snd (make_axiom_clauses thy cnfs) end 
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644 

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645 
fun make_clause_table xs = 
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646 
fold (Termtab.update o `(prop_of o fst)) xs Termtab.empty 
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647 

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changeset

648 

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649 
(***************************************************************) 
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650 
(* Type Classes Present in the Axiom or Conjecture Clauses *) 
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651 
(***************************************************************) 
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652 

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653 
fun set_insert (x, s) = Symtab.update (x, ()) s 
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654 

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655 
fun add_classes (sorts, cset) = List.foldl set_insert cset (flat sorts) 
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656 

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657 
(*Remove this trivial type class*) 
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658 
fun delete_type cset = Symtab.delete_safe (the_single @{sort HOL.type}) cset; 
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659 

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660 
fun tfree_classes_of_terms ts = 
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661 
let val sorts_list = map (map #2 o OldTerm.term_tfrees) ts 
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662 
in Symtab.keys (delete_type (List.foldl add_classes Symtab.empty sorts_list)) end; 
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663 

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664 
fun tvar_classes_of_terms ts = 
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665 
let val sorts_list = map (map #2 o OldTerm.term_tvars) ts 
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666 
in Symtab.keys (delete_type (List.foldl add_classes Symtab.empty sorts_list)) end; 
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changeset

667 

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668 
(*fold type constructors*) 
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669 
fun fold_type_consts f (Type (a, Ts)) x = fold (fold_type_consts f) Ts (f (a,x)) 
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670 
 fold_type_consts _ _ x = x; 
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671 

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672 
(*Type constructors used to instantiate overloaded constants are the only ones needed.*) 
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673 
fun add_type_consts_in_term thy = 
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674 
let 
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675 
val const_typargs = Sign.const_typargs thy 
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676 
fun aux (Const x) = fold (fold_type_consts set_insert) (const_typargs x) 
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677 
 aux (Abs (_, _, u)) = aux u 
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678 
 aux (Const (@{const_name skolem_id}, _) $ _) = I 
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679 
 aux (t $ u) = aux t #> aux u 
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680 
 aux _ = I 
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681 
in aux end 
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changeset

682 

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683 
fun type_consts_of_terms thy ts = 
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684 
Symtab.keys (fold (add_type_consts_in_term thy) ts Symtab.empty); 
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changeset

685 

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686 
(* Remove existing axiom clauses from the conjecture clauses, as this can 
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687 
dramatically boost an ATP's performance (for some reason). *) 
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688 
fun subtract_cls ax_clauses = 
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689 
filter_out (Termtab.defined (make_clause_table ax_clauses) o prop_of) 
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changeset

690 

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691 
(* prepare for passing to writer, 
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692 
create additional clauses based on the information from extra_cls *) 
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693 
fun prepare_clauses full_types goal_cls axcls extra_cls thy = 
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694 
let 
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695 
val is_FO = forall (Meson.is_fol_term thy o prop_of) goal_cls 
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696 
val ccls = subtract_cls extra_cls goal_cls 
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697 
val _ = app (fn th => trace_msg (fn _ => Display.string_of_thm_global thy th)) ccls 
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698 
val ccltms = map prop_of ccls 
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699 
and axtms = map (prop_of o #1) extra_cls 
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700 
val subs = tfree_classes_of_terms ccltms 
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changeset

701 
and supers = tvar_classes_of_terms axtms 
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702 
and tycons = type_consts_of_terms thy (ccltms @ axtms) 
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703 
(*TFrees in conjecture clauses; TVars in axiom clauses*) 
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704 
val conjectures = make_conjecture_clauses thy ccls 
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705 
val (_, extra_clauses) = ListPair.unzip (make_axiom_clauses thy extra_cls) 
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706 
val (clnames, axiom_clauses) = ListPair.unzip (make_axiom_clauses thy axcls) 
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707 
val helper_clauses = 
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708 
get_helper_clauses thy is_FO full_types conjectures extra_cls 
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709 
val (supers', arity_clauses) = make_arity_clauses thy tycons supers 
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710 
val classrel_clauses = make_classrel_clauses thy subs supers' 
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711 
in 
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712 
(Vector.fromList clnames, 
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713 
(conjectures, axiom_clauses, extra_clauses, helper_clauses, classrel_clauses, arity_clauses)) 
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714 
end 
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715 

15347  716 
end; 