author  blanchet 
Tue, 22 Jun 2010 14:28:22 +0200  
changeset 37498  b426cbdb5a23 
parent 37479  f6b1ee5b420b 
child 37500  7587b6e63454 
permissions  rwrr 
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(* Title: HOL/Tools/Sledgehammer/sledgehammer_fol_clause.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. 

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FIXME: combine with sledgehammer_hol_clause! 
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*) 
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signature SLEDGEHAMMER_FOL_CLAUSE = 
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sig 
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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 clause_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 const_trans_table: string Symtab.table 

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val type_const_trans_table: string Symtab.table 

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val ascii_of: string > string 

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val undo_ascii_of: string > string 

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val paren_pack : string list > string 

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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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type name = string * string 
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type name_pool = string Symtab.table * string Symtab.table 
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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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datatype kind = Axiom  Conjecture 
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type axiom_name = string 

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datatype fol_type = 

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TyVar of name  
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TyFree of name  
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TyConstr of name * fol_type list 
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val string_of_fol_type : 
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fol_type > name_pool option > string * name_pool option 
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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 
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val type_literals_for_types : typ list > type_literal list 
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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: axiom_name, conclLit: arLit, premLits: arLit list} 
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datatype classrel_clause = ClassrelClause of 
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{axiom_name: axiom_name, subclass: class, superclass: class} 
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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 tptp_sign: bool > string > string 
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val tptp_of_type_literal : 
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bool > type_literal > name_pool option > string * name_pool option 
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val gen_tptp_cls : int * string * kind * string list * string list > string 
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val tptp_tfree_clause : string > string 
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val tptp_arity_clause : arity_clause > string 
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val tptp_classrel_clause : classrel_clause > string 

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end 
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structure Sledgehammer_FOL_Clause : SLEDGEHAMMER_FOL_CLAUSE = 
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struct 
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open Sledgehammer_Util 
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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 clause_prefix = "cls_"; 
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val arclause_prefix = "clsarity_" 

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val clrelclause_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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val type_const_trans_table = 
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Symtab.make [(@{type_name "*"}, "prod"), 
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(@{type_name "+"}, "sum")] 
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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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(* convert a list of strings into one single string; surrounded by brackets *) 
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fun paren_pack [] = "" (*empty argument list*) 
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 paren_pack strings = "(" ^ commas strings ^ ")"; 
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fun tptp_clause strings = "(" ^ space_implode "  " strings ^ ")" 
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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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fun lookup_type_const c = 
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case Symtab.lookup type_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_type_const c 
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fun make_type_class clas = class_prefix ^ ascii_of clas; 
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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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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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220 

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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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223 

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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 
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> fold remove_all ["\<^sub>", "\<^bsub>", "\<^esub>", "\<^isub>"] 
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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 
234 
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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249 

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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  261 

15347  262 
type axiom_name = string; 
263 

264 
(**** Isabelle FOL clauses ****) 

265 

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datatype fol_type = 
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TyVar of name  
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TyFree of name  
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TyConstr of name * fol_type list 
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270 

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fun string_of_fol_type (TyVar sp) pool = nice_name sp pool 
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 string_of_fol_type (TyFree sp) pool = nice_name sp pool 
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 string_of_fol_type (TyConstr (sp, tys)) pool = 
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let 
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val (s, pool) = nice_name sp pool 
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val (ss, pool) = pool_map string_of_fol_type tys pool 
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in (s ^ paren_pack ss, pool) end 
24310  278 

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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  285 

24310  286 
(*Make literals for sorted type variables*) 
24940  287 
fun sorts_on_typs_aux (_, []) = [] 
288 
 sorts_on_typs_aux ((x,i), s::ss) = 

289 
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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else if i = ~1 then TyLitFree (make_type_class s, `make_fixed_type_var x) :: sorts 
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else TyLitVar (make_type_class s, (make_schematic_type_var (x,i), x)) :: sorts 
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end; 
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24940  296 
fun sorts_on_typs (TFree (a,s)) = sorts_on_typs_aux ((a,~1),s) 
297 
 sorts_on_typs (TVar (v,s)) = sorts_on_typs_aux (v,s); 

298 

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(*Given a list of sorted type variables, return a list of type literals.*) 
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fun type_literals_for_types Ts = 
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fold (union (op =)) (map sorts_on_typs Ts) [] 
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302 

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(** make axiom and conjecture clauses. **) 
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15347  305 
(**** Isabelle arities ****) 
306 

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datatype arLit = TConsLit of class * string * string list 
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 TVarLit of class * string; 
24310  309 

35865  310 
datatype arity_clause = 
24310  311 
ArityClause of {axiom_name: axiom_name, 
312 
conclLit: arLit, 

313 
premLits: arLit list}; 

15347  314 

315 

18798  316 
fun gen_TVars 0 = [] 
317 
 gen_TVars n = ("T_" ^ Int.toString n) :: gen_TVars (n1); 

15347  318 

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fun pack_sort(_,[]) = [] 
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 pack_sort(tvar, "HOL.type"::srt) = pack_sort(tvar, srt) (*IGNORE sort "type"*) 
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 pack_sort(tvar, cls::srt) = (cls, tvar) :: pack_sort(tvar, srt); 
24310  322 

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(*Arity of type constructor tcon :: (arg1,...,argN)res*) 
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fun make_axiom_arity_clause (tcons, axiom_name, (cls,args)) = 
21560  325 
let val tvars = gen_TVars (length args) 
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val tvars_srts = ListPair.zip (tvars,args) 
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327 
in 
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328 
ArityClause {axiom_name = axiom_name, 
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conclLit = TConsLit (cls, make_fixed_type_const tcons, tvars), 
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premLits = map TVarLit (union_all(map pack_sort tvars_srts))} 
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331 
end; 
15347  332 

333 

334 
(**** Isabelle class relations ****) 

335 

35865  336 
datatype classrel_clause = 
24310  337 
ClassrelClause of {axiom_name: axiom_name, 
338 
subclass: class, 

339 
superclass: class}; 

340 

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(*Generate all pairs (sub,super) such that sub is a proper subclass of super in theory thy.*) 
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342 
fun class_pairs _ [] _ = [] 
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 class_pairs thy subs supers = 
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344 
let 
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345 
val class_less = Sorts.class_less (Sign.classes_of thy) 
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346 
fun add_super sub super = class_less (sub, super) ? cons (sub, super) 
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fun add_supers sub = fold (add_super sub) supers 
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in fold add_supers subs [] end 
15347  349 

35865  350 
fun make_classrel_clause (sub,super) = 
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ClassrelClause {axiom_name = clrelclause_prefix ^ ascii_of sub ^ "_" ^ ascii_of super, 
24310  352 
subclass = make_type_class sub, 
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superclass = make_type_class super}; 
15347  354 

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355 
fun make_classrel_clauses thy subs supers = 
35865  356 
map make_classrel_clause (class_pairs thy subs supers); 
18868  357 

358 

359 
(** Isabelle arities **) 

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360 

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361 
fun arity_clause _ _ (_, []) = [] 
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 arity_clause seen n (tcons, ("HOL.type",_)::ars) = (*ignore*) 
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363 
arity_clause seen n (tcons,ars) 
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364 
 arity_clause seen n (tcons, (ar as (class,_)) :: ars) = 
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365 
if member (op =) seen class then (*multiple arities for the same tycon, class pair*) 
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366 
make_axiom_arity_clause (tcons, lookup_type_const tcons ^ "_" ^ class ^ "_" ^ Int.toString n, ar) :: 
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367 
arity_clause seen (n+1) (tcons,ars) 
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368 
else 
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369 
make_axiom_arity_clause (tcons, lookup_type_const tcons ^ "_" ^ class, ar) :: 
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370 
arity_clause (class::seen) n (tcons,ars) 
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371 

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372 
fun multi_arity_clause [] = [] 
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373 
 multi_arity_clause ((tcons, ars) :: tc_arlists) = 
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374 
arity_clause [] 1 (tcons, ars) @ multi_arity_clause tc_arlists 
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375 

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376 
(*Generate all pairs (tycon,class,sorts) such that tycon belongs to class in theory thy 
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377 
provided its arguments have the corresponding sorts.*) 
21373
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378 
fun type_class_pairs thy tycons classes = 
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379 
let val alg = Sign.classes_of thy 
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380 
fun domain_sorts tycon = Sorts.mg_domain alg tycon o single 
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381 
fun add_class tycon class = 
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382 
cons (class, domain_sorts tycon class) 
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383 
handle Sorts.CLASS_ERROR _ => I 
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384 
fun try_classes tycon = (tycon, fold (add_class tycon) classes []) 
21373
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385 
in map try_classes tycons end; 
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386 

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387 
(*Proving one (tycon, class) membership may require proving others, so iterate.*) 
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388 
fun iter_type_class_pairs _ _ [] = ([], []) 
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389 
 iter_type_class_pairs thy tycons classes = 
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390 
let val cpairs = type_class_pairs thy tycons classes 
33040  391 
val newclasses = union_all (union_all (union_all (map (map #2 o #2) cpairs))) 
392 
> subtract (op =) classes > subtract (op =) HOLogic.typeS 

24310  393 
val (classes', cpairs') = iter_type_class_pairs thy tycons newclasses 
33042  394 
in (union (op =) classes' classes, union (op =) cpairs' cpairs) end; 
24310  395 

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396 
fun make_arity_clauses thy tycons classes = 
24310  397 
let val (classes', cpairs) = iter_type_class_pairs thy tycons classes 
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398 
in (classes', multi_arity_clause cpairs) end; 
18863  399 

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400 

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401 
(**** Produce TPTP files ****) 
18868  402 

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403 
fun string_of_clausename (cls_id, ax_name) = 
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404 
clause_prefix ^ ascii_of ax_name ^ "_" ^ Int.toString cls_id 
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405 

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406 
fun tptp_sign true s = s 
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407 
 tptp_sign false s = "~ " ^ s 
18868  408 

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409 
fun tptp_of_type_literal pos (TyLitVar (s, name)) = 
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410 
nice_name name #>> (fn s' => tptp_sign pos (s ^ "(" ^ s' ^ ")")) 
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411 
 tptp_of_type_literal pos (TyLitFree (s, name)) = 
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412 
nice_name name #>> (fn s' => tptp_sign pos (s ^ "(" ^ s' ^ ")")) 
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413 

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414 
fun tptp_cnf name kind formula = 
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415 
"cnf(" ^ name ^ ", " ^ kind ^ ",\n " ^ formula ^ ").\n" 
24310  416 

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417 
fun gen_tptp_cls (cls_id, ax_name, Axiom, lits, tylits) = 
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418 
tptp_cnf (string_of_clausename (cls_id, ax_name)) "axiom" 
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419 
(tptp_clause (tylits @ lits)) 
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420 
 gen_tptp_cls (cls_id, ax_name, Conjecture, lits, _) = 
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421 
tptp_cnf (string_of_clausename (cls_id, ax_name)) "negated_conjecture" 
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422 
(tptp_clause lits) 
15347  423 

18863  424 
fun tptp_tfree_clause tfree_lit = 
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425 
tptp_cnf "tfree_tcs" "negated_conjecture" (tptp_clause [tfree_lit]) 
24310  426 

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427 
fun tptp_of_arLit (TConsLit (c,t,args)) = 
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428 
tptp_sign true (make_type_class c ^ "(" ^ t ^ paren_pack args ^ ")") 
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429 
 tptp_of_arLit (TVarLit (c,str)) = 
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430 
tptp_sign false (make_type_class c ^ "(" ^ str ^ ")") 
24310  431 

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432 
fun tptp_arity_clause (ArityClause {axiom_name, conclLit, premLits, ...}) = 
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433 
tptp_cnf (arclause_prefix ^ ascii_of axiom_name) "axiom" 
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434 
(tptp_clause (map tptp_of_arLit (conclLit :: premLits))) 
15347  435 

24310  436 
fun tptp_classrelLits sub sup = 
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437 
let val tvar = "(T)" 
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438 
in tptp_clause [tptp_sign false (sub^tvar), tptp_sign true (sup^tvar)] end; 
15347  439 

35865  440 
fun tptp_classrel_clause (ClassrelClause {axiom_name,subclass,superclass,...}) = 
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441 
tptp_cnf axiom_name "axiom" (tptp_classrelLits subclass superclass) 
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442 

15347  443 
end; 