author  bulwahn 
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permissions  rwrr 
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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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type code_options = {ensure_groundness : bool} 
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val options : code_options ref 
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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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 Ground of string * typ; 
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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 : code_options > 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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(* code generation options *) 
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type code_options = {ensure_groundness : bool} 
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val options = Unsynchronized.ref {ensure_groundness = false}; 
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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 maybe_AppF (c, []) = Cons c 
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 maybe_AppF (c, xs) = AppF (c, xs) 
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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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 Ground of string * typ; 
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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' andalso not (is_Var 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 mk_groundness_prems t = map Ground (Term.add_frees t []) 
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fun translate_prem options ctxt constant_table t = 
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case try HOLogic.dest_not t of 
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SOME t => 
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if #ensure_groundness options then 
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Conj (mk_groundness_prems t @ [NegRel_of (translate_literal ctxt constant_table t)]) 
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else 
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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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167 

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fun Trueprop_conv cv ct = 
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case Thm.term_of ct of 
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Const (@{const_name 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 options ctxt gr const constant_table = 
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let 
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val intros = map (preprocess_intro (ProofContext.theory_of ctxt)) (Graph.get_node gr const) 
38073  182 
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 
38073  184 
fun translate_intro intro = 
185 
let 

186 
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 options ctxt' constant_table') prems) 
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val clause = (dest_Rel (translate_literal ctxt' constant_table' head), prems') 
38073  190 
in clause end 
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in (map translate_intro intros', constant_table') end 
38073  192 

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fun generate options ctxt const = 
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let 
195 
fun strong_conn_of gr keys = 

196 
Graph.strong_conn (Graph.subgraph (member (op =) (Graph.all_succs gr keys)) gr) 

197 
val gr = Predicate_Compile_Core.intros_graph_of ctxt 

198 
val scc = strong_conn_of gr const 

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val constant_table = mk_constant_table (flat scc) 
38073  200 
in 
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apfst flat (fold_map (translate_intros options ctxt gr) (flat scc) constant_table) 
38073  202 
end 
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(* add implementation for ground predicates *) 
38073  205 

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fun add_ground_typ (Conj prems) = fold add_ground_typ prems 
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 add_ground_typ (Ground (_, T)) = insert (op =) T 
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 add_ground_typ _ = I 
38073  209 

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fun mk_relname (Type (Tcon, Targs)) = 
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first_lower (Long_Name.base_name Tcon) ^ space_implode "_" (map mk_relname Targs) 
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 mk_relname _ = raise Fail "unexpected type" 
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213 

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(* This is copied from "pat_completeness.ML" *) 
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fun inst_constrs_of thy (T as Type (name, _)) = 
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map (fn (Cn,CT) => 
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Envir.subst_term_types (Sign.typ_match thy (body_type CT, T) Vartab.empty) (Const (Cn, CT))) 
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(the (Datatype.get_constrs thy name)) 
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 inst_constrs_of thy T = raise TYPE ("inst_constrs_of", [T], []) 
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220 

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fun mk_ground_impl ctxt (T as Type (Tcon, Targs)) (seen, constant_table) = 
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if member (op =) seen T then ([], (seen, constant_table)) 
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else 
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let 
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val rel_name = mk_relname T 
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fun mk_impl (Const (constr_name, T)) (seen, constant_table) = 
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let 
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val constant_table' = declare_consts [constr_name] constant_table 
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val (rec_clauses, (seen', constant_table'')) = 
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fold_map (mk_ground_impl ctxt) (binder_types T) (seen, constant_table') 
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val vars = map (fn i => Var ("x" ^ string_of_int i)) (1 upto (length (binder_types T))) 
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fun mk_prem v T = Rel (mk_relname T, [v]) 
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val clause = 
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((rel_name, [maybe_AppF (translate_const constant_table'' constr_name, vars)]), 
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Conj (map2 mk_prem vars (binder_types T))) 
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in 
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(clause :: flat rec_clauses, (seen', constant_table'')) 
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end 
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val constrs = inst_constrs_of (ProofContext.theory_of ctxt) T 
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in apfst flat (fold_map mk_impl constrs (T :: seen, constant_table)) end 
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 mk_ground_impl ctxt T (seen, constant_table) = 
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raise Fail ("unexpected type :" ^ Syntax.string_of_typ ctxt T) 
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243 

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fun replace_ground (Conj prems) = Conj (map replace_ground prems) 
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 replace_ground (Ground (x, T)) = 
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Rel (mk_relname T, [Var x]) 
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 replace_ground p = p 
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fun add_ground_predicates ctxt (p, constant_table) = 
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let 
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val ground_typs = fold (add_ground_typ o snd) p [] 
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val (grs, (_, constant_table')) = fold_map (mk_ground_impl ctxt) ground_typs ([], constant_table) 
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val p' = map (apsnd replace_ground) p 
38073  254 
in 
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((flat grs) @ p', constant_table') 
38073  256 
end 
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38073  258 
(* code printer *) 
259 

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fun write_arith_op Plus = "+" 
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 write_arith_op Minus = "" 
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262 

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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  268 

269 
fun write_rel (pred, args) = 

270 
pred ^ "(" ^ space_implode ", " (map write_term args) ^ ")" 

271 

272 
fun write_prem (Conj prems) = space_implode ", " (map write_prem prems) 

273 
 write_prem (Rel p) = write_rel p 

274 
 write_prem (NotRel p) = "not(" ^ write_rel p ^ ")" 

275 
 write_prem (Eq (l, r)) = write_term l ^ " = " ^ write_term r 

276 
 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  279 

280 
fun write_clause (head, prem) = 

281 
write_rel head ^ (if prem = Conj [] then "." else " : " ^ write_prem prem ^ ".") 

282 

283 
fun write_program p = 

284 
cat_lines (map write_clause p) 

285 

38078  286 
(** query templates **) 
287 

38073  288 
fun query_first rel vnames = 
289 
"eval : once(" ^ rel ^ "(" ^ space_implode ", " vnames ^ ")),\n" ^ 

38082  290 
"writef('" ^ space_implode ";" (map (fn v => v ^ " = %w") vnames) ^ 
291 
"\\n', [" ^ space_implode ", " vnames ^ "]).\n" 

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292 

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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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38073  301 
val prelude = 
302 
"#!/usr/bin/swipl q t main f\n\n" ^ 

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": use_module(library('dialect/ciao/aggregates')).\n" ^ 
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": style_check(singleton).\n" ^ 
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": style_check(discontiguous).\n" ^ 
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": style_check(atom).\n\n" ^ 
38073  307 
"main : catch(eval, E, (print_message(error, E), fail)), halt.\n" ^ 
308 
"main : halt(1).\n" 

38075  309 

310 
(* parsing prolog solution *) 

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val scan_number = 
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Scan.many1 Symbol.is_ascii_digit 
38075  313 

314 
val scan_atom = 

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Scan.many1 (fn s => Symbol.is_ascii_lower s orelse Symbol.is_ascii_digit s orelse Symbol.is_ascii_quasi s) 
38075  316 

317 
val scan_var = 

38078  318 
Scan.many1 
319 
(fn s => Symbol.is_ascii_upper s orelse Symbol.is_ascii_digit s orelse Symbol.is_ascii_quasi s) 

38075  320 

38076  321 
val scan_ident = 
322 
Scan.repeat (Scan.one 

323 
(fn s => Symbol.is_ascii_letter s orelse Symbol.is_ascii_digit s orelse Symbol.is_ascii_quasi s)) 

324 

38075  325 
fun dest_Char (Symbol.Char s) = s 
326 

327 
val string_of = concat o map (dest_Char o Symbol.decode) 

328 

38076  329 
val is_atom_ident = forall Symbol.is_ascii_lower 
330 

331 
val is_var_ident = 

332 
forall (fn s => Symbol.is_ascii_upper s orelse Symbol.is_ascii_digit s orelse Symbol.is_ascii_quasi s) 

38078  333 

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fun int_of_symbol_list xs = fold (fn x => fn s => s * 10 + (ord x  ord "0")) xs 0 
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335 

38078  336 
fun scan_terms xs = (((scan_term  $$ ",") ::: scan_terms) 
337 
 (scan_term >> single)) xs 

338 
and scan_term xs = 

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((scan_number >> (Number o int_of_symbol_list)) 
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 (scan_var >> (Var o string_of)) 
38078  341 
 ((scan_atom  ($$ "("  scan_terms  $$ ")")) 
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>> (fn (f, ts) => AppF (string_of f, ts))) 
38078  343 
 (scan_atom >> (Cons o string_of))) xs 
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344 

38075  345 
val parse_term = fst o Scan.finite Symbol.stopper 
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346 
(Scan.error (!! (fn _ => raise Fail "parsing prolog output failed")) scan_term) 
38075  347 
o explode 
348 

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349 
fun parse_solutions sol = 
38075  350 
let 
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351 
fun dest_eq s = case space_explode "=" s of 
38075  352 
(l :: r :: []) => parse_term (unprefix " " r) 
38078  353 
 _ => raise Fail "unexpected equation in prolog output" 
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354 
fun parse_solution s = map dest_eq (space_explode ";" s) 
38075  355 
in 
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356 
map parse_solution (fst (split_last (space_explode "\n" sol))) 
38075  357 
end 
38073  358 

359 
(* calling external interpreter and getting results *) 

360 

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361 
fun run p query_rel vnames nsols = 
38073  362 
let 
363 
val cmd = Path.named_root 

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364 
val query = case nsols of NONE => query_first  SOME n => query_firstn n 
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365 
val prog = prelude ^ query query_rel vnames ^ write_program p 
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366 
val _ = tracing ("Generated prolog program:\n" ^ prog) 
38073  367 
val prolog_file = File.tmp_path (Path.basic "prolog_file") 
368 
val _ = File.write prolog_file prog 

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369 
val (solution, _) = bash_output ("/usr/local/bin/swipl f " ^ File.shell_path prolog_file) 
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370 
val _ = tracing ("Prolog returned solution(s):\n" ^ solution) 
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371 
val tss = parse_solutions solution 
38073  372 
in 
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373 
tss 
38073  374 
end 
375 

38075  376 
(* values command *) 
377 

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378 
fun restore_term ctxt constant_table (Var s, T) = Free (s, T) 
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379 
 restore_term ctxt constant_table (Number n, @{typ "int"}) = HOLogic.mk_number @{typ "int"} n 
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 restore_term ctxt constant_table (Number n, _) = raise (Fail "unexpected type for number") 
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381 
 restore_term ctxt constant_table (Cons s, T) = Const (restore_const constant_table s, T) 
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382 
 restore_term ctxt constant_table (AppF (f, args), T) = 
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383 
let 
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384 
val thy = ProofContext.theory_of ctxt 
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385 
val c = restore_const constant_table f 
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386 
val cT = Sign.the_const_type thy c 
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387 
val (argsT, resT) = strip_type cT 
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388 
val subst = Sign.typ_match thy (resT, T) Vartab.empty 
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389 
val argsT' = map (Envir.subst_type subst) argsT 
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390 
in 
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391 
list_comb (Const (c, Envir.subst_type subst cT), 
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392 
map (restore_term ctxt constant_table) (args ~~ argsT')) 
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393 
end 
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394 

38075  395 
fun values ctxt soln t_compr = 
396 
let 

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397 
val options = !options 
38075  398 
val split = case t_compr of (Const (@{const_name Collect}, _) $ t) => t 
399 
 _ => error ("Not a set comprehension: " ^ Syntax.string_of_term ctxt t_compr); 

400 
val (body, Ts, fp) = HOLogic.strip_psplits split; 

401 
val output_names = Name.variant_list (Term.add_free_names body []) 

402 
(map (fn i => "x" ^ string_of_int i) (1 upto length Ts)) 

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403 
val output_frees = rev (map2 (curry Free) output_names Ts) 
38075  404 
val body = subst_bounds (output_frees, body) 
405 
val (pred as Const (name, T), all_args) = 

406 
case strip_comb body of 

407 
(Const (name, T), all_args) => (Const (name, T), all_args) 

408 
 (head, _) => error ("Not a constant: " ^ Syntax.string_of_term ctxt head) 

409 
val vnames = 

410 
case try (map (fst o dest_Free)) all_args of 

411 
SOME vs => vs 

412 
 NONE => error ("Not only free variables in " ^ commas (map (Syntax.string_of_term ctxt) all_args)) 

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413 
val _ = tracing "Generating prolog program..." 
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414 
val (p, constant_table) = generate options ctxt [name] 
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415 
> (if #ensure_groundness options then add_ground_predicates ctxt else I) 
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416 
val _ = tracing "Running prolog program..." 
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417 
val tss = run p (translate_const constant_table name) (map first_upper vnames) soln 
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418 
val _ = tracing "Restoring terms..." 
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419 
val empty = Const("Orderings.bot_class.bot", fastype_of t_compr) 
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420 
fun mk_insert x S = 
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421 
Const (@{const_name "Set.insert"}, fastype_of x > fastype_of S > fastype_of S) $ x $ S 
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422 
fun mk_set_compr in_insert [] xs = 
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423 
rev ((Free ("...", fastype_of t_compr)) :: 
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424 
(if null in_insert then xs else (fold mk_insert in_insert empty) :: xs)) 
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425 
 mk_set_compr in_insert (t :: ts) xs = 
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426 
let 
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427 
val frees = Term.add_frees t [] 
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428 
in 
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429 
if null frees then 
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430 
mk_set_compr (t :: in_insert) ts xs 
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431 
else 
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432 
let 
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433 
val uu as (uuN, uuT) = singleton (Variable.variant_frees ctxt [t]) ("uu", fastype_of t) 
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434 
val set_compr = 
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435 
HOLogic.mk_Collect (uuN, uuT, fold (fn (s, T) => fn t => HOLogic.mk_exists (s, T, t)) 
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436 
frees (HOLogic.mk_conj (HOLogic.mk_eq (Free uu, t), @{term "True"}))) 
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437 
in 
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438 
mk_set_compr [] ts 
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439 
(set_compr :: (if null in_insert then xs else (fold mk_insert in_insert empty) :: xs)) 
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440 
end 
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441 
end 
38075  442 
in 
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443 
foldl1 (HOLogic.mk_binop @{const_name sup}) (mk_set_compr [] 
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444 
(map (fn ts => HOLogic.mk_tuple (map (restore_term ctxt constant_table) (ts ~~ Ts))) tss) []) 
38075  445 
end 
446 

447 
fun values_cmd print_modes soln raw_t state = 

448 
let 

449 
val ctxt = Toplevel.context_of state 

450 
val t = Syntax.read_term ctxt raw_t 

451 
val t' = values ctxt soln t 

452 
val ty' = Term.type_of t' 

453 
val ctxt' = Variable.auto_fixes t' ctxt 

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454 
val _ = tracing "Printing terms..." 
38075  455 
val p = Print_Mode.with_modes print_modes (fn () => 
456 
Pretty.block [Pretty.quote (Syntax.pretty_term ctxt' t'), Pretty.fbrk, 

457 
Pretty.str "::", Pretty.brk 1, Pretty.quote (Syntax.pretty_typ ctxt' ty')]) (); 

458 
in Pretty.writeln p end; 

459 

460 

461 
(* renewing the values command for Prolog queries *) 

462 

463 
val opt_print_modes = 

464 
Scan.optional (Parse.$$$ "("  Parse.!!! (Scan.repeat1 Parse.xname  Parse.$$$ ")")) []; 

465 

466 
val _ = Outer_Syntax.improper_command "values" "enumerate and print comprehensions" Keyword.diag 

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467 
(opt_print_modes  Scan.optional (Parse.nat >> SOME) NONE  Parse.term 
38075  468 
>> (fn ((print_modes, soln), t) => Toplevel.keep 
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469 
(values_cmd print_modes soln t))); (*FIXME does not preserve the previous functionality*) 
38075  470 

38073  471 
end; 