author  bulwahn 
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(* Title: HOL/Tools/Predicate_Compile/code_prolog.ML 
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Author: Lukas Bulwahn, TU Muenchen 

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Prototype of an code generator for logic programming languages (a.k.a. Prolog) 

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*) 

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signature CODE_PROLOG = 

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sig 

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datatype arith_op = Plus  Minus 
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datatype prol_term = Var of string  Cons of string  AppF of string * prol_term list 
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 Number of int  ArithOp of arith_op * prol_term list; 
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datatype prem = Conj of prem list 
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 Rel of string * prol_term list  NotRel of string * prol_term list 
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 Eq of prol_term * prol_term  NotEq of prol_term * prol_term 
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 ArithEq of prol_term * prol_term  NotArithEq of prol_term * prol_term; 
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type clause = ((string * prol_term list) * prem); 
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type logic_program = clause list; 
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type constant_table = (string * string) list 
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val generate : Proof.context > string list > (logic_program * constant_table) 
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val write_program : logic_program > string 
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val run : logic_program > string > string list > int option > prol_term list list 
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val trace : bool Unsynchronized.ref 
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end; 
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structure Code_Prolog : CODE_PROLOG = 

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struct 

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(* diagnostic tracing *) 
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val trace = Unsynchronized.ref false 
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fun tracing s = if !trace then Output.tracing s else () 
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(* general string functions *) 
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val first_upper = implode o nth_map 0 Symbol.to_ascii_upper o explode; 

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val first_lower = implode o nth_map 0 Symbol.to_ascii_lower o explode; 

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(* internal program representation *) 

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datatype arith_op = Plus  Minus 
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datatype prol_term = Var of string  Cons of string  AppF of string * prol_term list 
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 Number of int  ArithOp of arith_op * prol_term list; 
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fun is_Var (Var _) = true 
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 is_Var _ = false 
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fun is_arith_term (Var _) = true 
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 is_arith_term (Number _) = true 
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 is_arith_term (ArithOp (_, operands)) = forall is_arith_term operands 
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 is_arith_term _ = false 
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fun string_of_prol_term (Var s) = "Var " ^ s 
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 string_of_prol_term (Cons s) = "Cons " ^ s 
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 string_of_prol_term (AppF (f, args)) = f ^ "(" ^ commas (map string_of_prol_term args) ^ ")" 

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 string_of_prol_term (Number n) = "Number " ^ string_of_int n 
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datatype prem = Conj of prem list 
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 Rel of string * prol_term list  NotRel of string * prol_term list 
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 Eq of prol_term * prol_term  NotEq of prol_term * prol_term 
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 ArithEq of prol_term * prol_term  NotArithEq of prol_term * prol_term; 
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fun dest_Rel (Rel (c, ts)) = (c, ts) 
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type clause = ((string * prol_term list) * prem); 
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type logic_program = clause list; 

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(* translation from introduction rules to internal representation *) 

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(** constant table **) 
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type constant_table = (string * string) list 
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(* assuming no clashing *) 
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fun mk_constant_table consts = 
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AList.make (first_lower o Long_Name.base_name) consts 
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fun declare_consts consts constant_table = 
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fold (fn c => AList.update (op =) (c, first_lower (Long_Name.base_name c))) consts constant_table 
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fun translate_const constant_table c = 
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case AList.lookup (op =) constant_table c of 
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SOME c' => c' 
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 NONE => error ("No such constant: " ^ c) 
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fun inv_lookup _ [] _ = NONE 
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 inv_lookup eq ((key, value)::xs) value' = 
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if eq (value', value) then SOME key 
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else inv_lookup eq xs value'; 
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fun restore_const constant_table c = 
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case inv_lookup (op =) constant_table c of 
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SOME c' => c' 
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 NONE => error ("No constant corresponding to " ^ c) 
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(** translation of terms, literals, premises, and clauses **) 
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fun translate_arith_const @{const_name "Groups.plus_class.plus"} = SOME Plus 
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 translate_arith_const @{const_name "Groups.minus_class.minus"} = SOME Minus 
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 translate_arith_const _ = NONE 
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fun translate_term ctxt constant_table t = 
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case try HOLogic.dest_number t of 
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SOME (@{typ "int"}, n) => Number n 
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 NONE => 
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(case strip_comb t of 
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(Free (v, T), []) => Var v 
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 (Const (c, _), []) => Cons (translate_const constant_table c) 
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 (Const (c, _), args) => 
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(case translate_arith_const c of 
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SOME aop => ArithOp (aop, map (translate_term ctxt constant_table) args) 
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 NONE => 
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AppF (translate_const constant_table c, map (translate_term ctxt constant_table) args)) 
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 _ => error ("illegal term for translation: " ^ Syntax.string_of_term ctxt t)) 
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fun translate_literal ctxt constant_table t = 
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case strip_comb t of 
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(Const (@{const_name "op ="}, _), [l, r]) => 
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let 
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val l' = translate_term ctxt constant_table l 
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val r' = translate_term ctxt constant_table r 
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in 
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(if is_Var l' andalso is_arith_term r' then ArithEq else Eq) (l', r') 
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end 
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 (Const (c, _), args) => 
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Rel (translate_const constant_table c, map (translate_term ctxt constant_table) args) 
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 _ => error ("illegal literal for translation: " ^ Syntax.string_of_term ctxt t) 
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fun NegRel_of (Rel lit) = NotRel lit 

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 NegRel_of (Eq eq) = NotEq eq 

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 NegRel_of (ArithEq eq) = NotArithEq eq 
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fun translate_prem ctxt constant_table t = 
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case try HOLogic.dest_not t of 
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SOME t => NegRel_of (translate_literal ctxt constant_table t) 
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 NONE => translate_literal ctxt constant_table t 
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fun imp_prems_conv cv ct = 
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case Thm.term_of ct of 
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Const ("==>", _) $ _ $ _ => Conv.combination_conv (Conv.arg_conv cv) (imp_prems_conv cv) ct 
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 _ => Conv.all_conv ct 
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fun Trueprop_conv cv ct = 
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case Thm.term_of ct of 
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Const ("Trueprop", _) $ _ => Conv.arg_conv cv ct 
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 _ => raise Fail "Trueprop_conv" 
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fun preprocess_intro thy rule = 
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Conv.fconv_rule 
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(imp_prems_conv 
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(Trueprop_conv (Conv.try_conv (Conv.rewr_conv @{thm Predicate.eq_is_eq})))) 
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(Thm.transfer thy rule) 
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fun translate_intros ctxt gr const constant_table = 
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val intros = map (preprocess_intro (ProofContext.theory_of ctxt)) (Graph.get_node gr const) 
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val (intros', ctxt') = Variable.import_terms true (map prop_of intros) ctxt 
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val constant_table' = declare_consts (fold Term.add_const_names intros' []) constant_table 
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fun translate_intro intro = 
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let 

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val head = HOLogic.dest_Trueprop (Logic.strip_imp_concl intro) 

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val prems = map HOLogic.dest_Trueprop (Logic.strip_imp_prems intro) 

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val prems' = Conj (map (translate_prem ctxt' constant_table') prems) 
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val clause = (dest_Rel (translate_literal ctxt' constant_table' head), prems') 
38073  170 
in clause end 
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in (map translate_intro intros', constant_table') end 
38073  172 

173 
fun generate ctxt const = 

174 
let 

175 
fun strong_conn_of gr keys = 

176 
Graph.strong_conn (Graph.subgraph (member (op =) (Graph.all_succs gr keys)) gr) 

177 
val gr = Predicate_Compile_Core.intros_graph_of ctxt 

178 
val scc = strong_conn_of gr const 

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val constant_table = mk_constant_table (flat scc) 
38073  180 
in 
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apfst flat (fold_map (translate_intros ctxt gr) (flat scc) constant_table) 
38073  182 
end 
183 

184 
(* transform logic program *) 

185 

186 
(** ensure groundness of terms before negation **) 

187 

188 
fun add_vars (Var x) vs = insert (op =) x vs 

189 
 add_vars (Cons c) vs = vs 

190 
 add_vars (AppF (f, args)) vs = fold add_vars args vs 

191 

192 
fun string_of_typ (Type (s, Ts)) = Long_Name.base_name s 

193 

194 
fun mk_groundness_prems ts = 

195 
let 

196 
val vars = fold add_vars ts [] 

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fun mk_ground v = 
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Rel ("ground", [Var v]) 
38073  199 
in 
200 
map mk_ground vars 

201 
end 

202 

203 
fun ensure_groundness_prem (NotRel (c, ts)) = Conj (mk_groundness_prems ts @ [NotRel (c, ts)]) 

204 
 ensure_groundness_prem (NotEq (l, r)) = Conj (mk_groundness_prems [l, r] @ [NotEq (l, r)]) 

205 
 ensure_groundness_prem (Conj ps) = Conj (map ensure_groundness_prem ps) 

206 
 ensure_groundness_prem p = p 

207 

208 
fun ensure_groundness_before_negation p = 

209 
map (apsnd ensure_groundness_prem) p 

210 

211 
(* code printer *) 

212 

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fun write_arith_op Plus = "+" 
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 write_arith_op Minus = "" 
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215 

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fun write_term (Var v) = first_upper v 
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 write_term (Cons c) = c 
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 write_term (AppF (f, args)) = f ^ "(" ^ space_implode ", " (map write_term args) ^ ")" 
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 write_term (ArithOp (oper, [a1, a2])) = write_term a1 ^ " " ^ write_arith_op oper ^ " " ^ write_term a2 
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 write_term (Number n) = string_of_int n 
38073  221 

222 
fun write_rel (pred, args) = 

223 
pred ^ "(" ^ space_implode ", " (map write_term args) ^ ")" 

224 

225 
fun write_prem (Conj prems) = space_implode ", " (map write_prem prems) 

226 
 write_prem (Rel p) = write_rel p 

227 
 write_prem (NotRel p) = "not(" ^ write_rel p ^ ")" 

228 
 write_prem (Eq (l, r)) = write_term l ^ " = " ^ write_term r 

229 
 write_prem (NotEq (l, r)) = write_term l ^ " \\= " ^ write_term r 

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 write_prem (ArithEq (l, r)) = write_term l ^ " is " ^ write_term r 
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 write_prem (NotArithEq (l, r)) = write_term l ^ " =\\= " ^ write_term r 
38073  232 

233 
fun write_clause (head, prem) = 

234 
write_rel head ^ (if prem = Conj [] then "." else " : " ^ write_prem prem ^ ".") 

235 

236 
fun write_program p = 

237 
cat_lines (map write_clause p) 

238 

38078  239 
(** query templates **) 
240 

38073  241 
fun query_first rel vnames = 
242 
"eval : once(" ^ rel ^ "(" ^ space_implode ", " vnames ^ ")),\n" ^ 

38082  243 
"writef('" ^ space_implode ";" (map (fn v => v ^ " = %w") vnames) ^ 
244 
"\\n', [" ^ space_implode ", " vnames ^ "]).\n" 

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245 

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fun query_firstn n rel vnames = 
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"eval : findnsols(" ^ string_of_int n ^ ", (" ^ space_implode ", " vnames ^ "), " ^ 
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rel ^ "(" ^ space_implode ", " vnames ^ "), Sols), writelist(Sols).\n" ^ 
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"writelist([]).\n" ^ 
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"writelist([(" ^ space_implode ", " vnames ^ ")T]) : " ^ 
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"writef('" ^ space_implode ";" (map (fn v => v ^ " = %w") vnames) ^ 
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"\\n', [" ^ space_implode ", " vnames ^ "]), writelist(T).\n" 
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253 

38073  254 
val prelude = 
255 
"#!/usr/bin/swipl q t main f\n\n" ^ 

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": use_module(library('dialect/ciao/aggregates')).\n" ^ 
38073  257 
": style_check(singleton).\n\n" ^ 
258 
"main : catch(eval, E, (print_message(error, E), fail)), halt.\n" ^ 

259 
"main : halt(1).\n" 

38075  260 

261 
(* parsing prolog solution *) 

262 

263 
val scan_atom = 

38078  264 
Scan.many1 (fn s => Symbol.is_ascii_lower s orelse Symbol.is_ascii_quasi s) 
38075  265 

266 
val scan_var = 

38078  267 
Scan.many1 
268 
(fn s => Symbol.is_ascii_upper s orelse Symbol.is_ascii_digit s orelse Symbol.is_ascii_quasi s) 

38075  269 

38076  270 
val scan_ident = 
271 
Scan.repeat (Scan.one 

272 
(fn s => Symbol.is_ascii_letter s orelse Symbol.is_ascii_digit s orelse Symbol.is_ascii_quasi s)) 

273 

38075  274 
fun dest_Char (Symbol.Char s) = s 
275 

276 
val string_of = concat o map (dest_Char o Symbol.decode) 

277 

38076  278 
val is_atom_ident = forall Symbol.is_ascii_lower 
279 

280 
val is_var_ident = 

281 
forall (fn s => Symbol.is_ascii_upper s orelse Symbol.is_ascii_digit s orelse Symbol.is_ascii_quasi s) 

38078  282 

283 
fun scan_terms xs = (((scan_term  $$ ",") ::: scan_terms) 

284 
 (scan_term >> single)) xs 

285 
and scan_term xs = 

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((scan_var >> (Var o string_of)) 
38078  287 
 ((scan_atom  ($$ "("  scan_terms  $$ ")")) 
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>> (fn (f, ts) => AppF (string_of f, ts))) 
38078  289 
 (scan_atom >> (Cons o string_of))) xs 
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290 

38075  291 
val parse_term = fst o Scan.finite Symbol.stopper 
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(Scan.error (!! (fn _ => raise Fail "parsing prolog output failed")) scan_term) 
38075  293 
o explode 
294 

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fun parse_solutions sol = 
38075  296 
let 
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fun dest_eq s = case space_explode "=" s of 
38075  298 
(l :: r :: []) => parse_term (unprefix " " r) 
38078  299 
 _ => raise Fail "unexpected equation in prolog output" 
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fun parse_solution s = map dest_eq (space_explode ";" s) 
38075  301 
in 
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map parse_solution (fst (split_last (space_explode "\n" sol))) 
38075  303 
end 
38073  304 

305 
(* calling external interpreter and getting results *) 

306 

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307 
fun run p query_rel vnames nsols = 
38073  308 
let 
309 
val cmd = Path.named_root 

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val query = case nsols of NONE => query_first  SOME n => query_firstn n 
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val prog = prelude ^ query query_rel vnames ^ write_program p 
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val _ = tracing ("Generated prolog program:\n" ^ prog) 
38073  313 
val prolog_file = File.tmp_path (Path.basic "prolog_file") 
314 
val _ = File.write prolog_file prog 

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val (solution, _) = bash_output ("/usr/local/bin/swipl f " ^ File.shell_path prolog_file) 
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val _ = tracing ("Prolog returned solution(s):\n" ^ solution) 
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317 
val tss = parse_solutions solution 
38073  318 
in 
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319 
tss 
38073  320 
end 
321 

38075  322 
(* values command *) 
323 

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324 
fun restore_term ctxt constant_table (Var s, T) = Free (s, T) 
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 restore_term ctxt constant_table (Cons s, T) = Const (restore_const constant_table s, T) 
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326 
 restore_term ctxt constant_table (AppF (f, args), T) = 
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327 
let 
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328 
val thy = ProofContext.theory_of ctxt 
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329 
val c = restore_const constant_table f 
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val cT = Sign.the_const_type thy c 
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331 
val (argsT, resT) = strip_type cT 
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332 
val subst = Sign.typ_match thy (resT, T) Vartab.empty 
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333 
val argsT' = map (Envir.subst_type subst) argsT 
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334 
in 
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335 
list_comb (Const (c, Envir.subst_type subst cT), 
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336 
map (restore_term ctxt constant_table) (args ~~ argsT')) 
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337 
end 
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338 

38075  339 
fun values ctxt soln t_compr = 
340 
let 

341 
val split = case t_compr of (Const (@{const_name Collect}, _) $ t) => t 

342 
 _ => error ("Not a set comprehension: " ^ Syntax.string_of_term ctxt t_compr); 

343 
val (body, Ts, fp) = HOLogic.strip_psplits split; 

344 
val output_names = Name.variant_list (Term.add_free_names body []) 

345 
(map (fn i => "x" ^ string_of_int i) (1 upto length Ts)) 

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346 
val output_frees = rev (map2 (curry Free) output_names Ts) 
38075  347 
val body = subst_bounds (output_frees, body) 
348 
val (pred as Const (name, T), all_args) = 

349 
case strip_comb body of 

350 
(Const (name, T), all_args) => (Const (name, T), all_args) 

351 
 (head, _) => error ("Not a constant: " ^ Syntax.string_of_term ctxt head) 

352 
val vnames = 

353 
case try (map (fst o dest_Free)) all_args of 

354 
SOME vs => vs 

355 
 NONE => error ("Not only free variables in " ^ commas (map (Syntax.string_of_term ctxt) all_args)) 

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356 
val _ = tracing "Generating prolog program..." 
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357 
val (p, constant_table) = generate ctxt [name] 
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358 
val _ = tracing "Running prolog program..." 
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359 
val tss = run p (translate_const constant_table name) (map first_upper vnames) soln 
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360 
val _ = tracing "Restoring terms..." 
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361 
fun mk_set_comprehension t = 
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362 
let 
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363 
val frees = Term.add_frees t [] 
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364 
val uu as (uuN, uuT) = singleton (Variable.variant_frees ctxt [t]) ("uu", fastype_of t) 
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365 
in HOLogic.mk_Collect (uuN, uuT, fold (fn (s, T) => fn t => HOLogic.mk_exists (s, T, t)) 
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366 
frees (HOLogic.mk_conj (HOLogic.mk_eq (Free uu, t), @{term "True"}))) end 
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367 
val set_comprs = map (fn ts => 
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mk_set_comprehension (HOLogic.mk_tuple (map (restore_term ctxt constant_table) (ts ~~ Ts)))) tss 
38075  369 
in 
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370 
foldl1 (HOLogic.mk_binop @{const_name sup}) (set_comprs @ [Free ("...", fastype_of t_compr)]) 
38075  371 
end 
372 

373 
fun values_cmd print_modes soln raw_t state = 

374 
let 

375 
val ctxt = Toplevel.context_of state 

376 
val t = Syntax.read_term ctxt raw_t 

377 
val t' = values ctxt soln t 

378 
val ty' = Term.type_of t' 

379 
val ctxt' = Variable.auto_fixes t' ctxt 

380 
val p = Print_Mode.with_modes print_modes (fn () => 

381 
Pretty.block [Pretty.quote (Syntax.pretty_term ctxt' t'), Pretty.fbrk, 

382 
Pretty.str "::", Pretty.brk 1, Pretty.quote (Syntax.pretty_typ ctxt' ty')]) (); 

383 
in Pretty.writeln p end; 

384 

385 

386 
(* renewing the values command for Prolog queries *) 

387 

388 
val opt_print_modes = 

389 
Scan.optional (Parse.$$$ "("  Parse.!!! (Scan.repeat1 Parse.xname  Parse.$$$ ")")) []; 

390 

391 
val _ = Outer_Syntax.improper_command "values" "enumerate and print comprehensions" Keyword.diag 

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392 
(opt_print_modes  Scan.optional (Parse.nat >> SOME) NONE  Parse.term 
38075  393 
>> (fn ((print_modes, soln), t) => Toplevel.keep 
394 
(values_cmd print_modes soln t))); 

395 

38073  396 
end; 