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(* Title: Pure/HOL/inductive_codegen.ML
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ID: $Id$
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Author: Stefan Berghofer
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Copyright 2000 TU Muenchen
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Code generator for inductive predicates
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*)
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signature INDUCTIVE_CODEGEN =
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sig
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val setup : (theory -> theory) list
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end;
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structure InductiveCodegen : INDUCTIVE_CODEGEN =
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struct
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open Codegen;
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exception Modes of (string * int list list) list * (string * int list list) list;
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datatype indprem = Prem of string * term list * term list
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| Sidecond of term;
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fun prod_factors p (Const ("Pair", _) $ t $ u) =
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p :: prod_factors (1::p) t @ prod_factors (2::p) u
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| prod_factors p _ = [];
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fun split_prod p ps t = if p mem ps then (case t of
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Const ("Pair", _) $ t $ u =>
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split_prod (1::p) ps t @ split_prod (2::p) ps u
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| _ => error "Inconsistent use of products") else [t];
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fun string_of_factors p ps = if p mem ps then
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"(" ^ string_of_factors (1::p) ps ^ ", " ^ string_of_factors (2::p) ps ^ ")"
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else "_";
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(**** check if a term contains only constructor functions ****)
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fun is_constrt thy =
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let
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val cnstrs = flat (flat (map
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(map (fn (_, (_, _, cs)) => map (apsnd length) cs) o #descr o snd)
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(Symtab.dest (DatatypePackage.get_datatypes thy))));
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fun check t = (case strip_comb t of
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(Var _, []) => true
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| (Const (s, _), ts) => (case assoc (cnstrs, s) of
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None => false
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| Some i => length ts = i andalso forall check ts)
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| _ => false)
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in check end;
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(**** check if a type is an equality type (i.e. doesn't contain fun) ****)
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fun is_eqT (Type (s, Ts)) = s <> "fun" andalso forall is_eqT Ts
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| is_eqT _ = true;
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(**** mode inference ****)
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val term_vs = map (fst o fst o dest_Var) o term_vars;
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val terms_vs = distinct o flat o (map term_vs);
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(** collect all Vars in a term (with duplicates!) **)
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fun term_vTs t = map (apfst fst o dest_Var)
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(filter is_Var (foldl_aterms (op :: o Library.swap) ([], t)));
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fun known_args _ _ [] = []
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| known_args vs i (t::ts) = if term_vs t subset vs then i::known_args vs (i+1) ts
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else known_args vs (i+1) ts;
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fun get_args _ _ [] = ([], [])
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| get_args is i (x::xs) = (if i mem is then apfst else apsnd) (cons x)
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(get_args is (i+1) xs);
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fun merge xs [] = xs
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| merge [] ys = ys
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| merge (x::xs) (y::ys) = if length x >= length y then x::merge xs (y::ys)
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else y::merge (x::xs) ys;
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fun subsets i j = if i <= j then
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let val is = subsets (i+1) j
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in merge (map (fn ks => i::ks) is) is end
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else [[]];
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fun select_mode_prem thy modes vs ps =
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find_first (is_some o snd) (ps ~~ map
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(fn Prem (s, us, args) => find_first (fn is =>
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let
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val (_, out_ts) = get_args is 1 us;
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val vTs = flat (map term_vTs out_ts);
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val dupTs = map snd (duplicates vTs) @
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mapfilter (curry assoc vTs) vs;
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in
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is subset known_args vs 1 us andalso
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forall (is_constrt thy) (snd (get_args is 1 us)) andalso
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terms_vs args subset vs andalso
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forall is_eqT dupTs
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end)
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(the (assoc (modes, s)))
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| Sidecond t => if term_vs t subset vs then Some [] else None) ps);
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fun check_mode_clause thy arg_vs modes mode (ts, ps) =
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let
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fun check_mode_prems vs [] = Some vs
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| check_mode_prems vs ps = (case select_mode_prem thy modes vs ps of
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None => None
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| Some (x, _) => check_mode_prems
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(case x of Prem (_, us, _) => vs union terms_vs us | _ => vs)
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(filter_out (equal x) ps));
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val (in_ts', _) = get_args mode 1 ts;
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val in_ts = filter (is_constrt thy) in_ts';
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val in_vs = terms_vs in_ts;
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val concl_vs = terms_vs ts
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in
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forall is_eqT (map snd (duplicates (flat (map term_vTs in_ts')))) andalso
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(case check_mode_prems (arg_vs union in_vs) ps of
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None => false
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| Some vs => concl_vs subset vs)
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end;
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fun check_modes_pred thy arg_vs preds modes (p, ms) =
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let val Some rs = assoc (preds, p)
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in (p, filter (fn m => forall (check_mode_clause thy arg_vs modes m) rs) ms) end
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fun fixp f x =
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let val y = f x
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in if x = y then x else fixp f y end;
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fun infer_modes thy extra_modes arg_vs preds = fixp (fn modes =>
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map (check_modes_pred thy arg_vs preds (modes @ extra_modes)) modes)
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(map (fn (s, (ts, _)::_) => (s, subsets 1 (length ts))) preds);
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(**** code generation ****)
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fun mk_eq (x::xs) =
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let fun mk_eqs _ [] = []
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| mk_eqs a (b::cs) = Pretty.str (a ^ " = " ^ b) :: mk_eqs b cs
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in mk_eqs x xs end;
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fun mk_tuple xs = Pretty.block (Pretty.str "(" ::
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flat (separate [Pretty.str ",", Pretty.brk 1] (map single xs)) @
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[Pretty.str ")"]);
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fun mk_v ((names, vs), s) = (case assoc (vs, s) of
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None => ((names, (s, [s])::vs), s)
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| Some xs => let val s' = variant names s in
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((s'::names, overwrite (vs, (s, s'::xs))), s') end);
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fun distinct_v (nvs, Var ((s, 0), T)) =
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apsnd (Var o rpair T o rpair 0) (mk_v (nvs, s))
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| distinct_v (nvs, t $ u) =
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let
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val (nvs', t') = distinct_v (nvs, t);
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val (nvs'', u') = distinct_v (nvs', u);
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in (nvs'', t' $ u') end
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| distinct_v x = x;
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fun compile_match nvs eq_ps out_ps success_p fail_p =
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let val eqs = flat (separate [Pretty.str " andalso", Pretty.brk 1]
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(map single (flat (map (mk_eq o snd) nvs) @ eq_ps)));
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in
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Pretty.block
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([Pretty.str "(fn ", mk_tuple out_ps, Pretty.str " =>", Pretty.brk 1] @
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(Pretty.block ((if eqs=[] then [] else Pretty.str "if " ::
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[Pretty.block eqs, Pretty.brk 1, Pretty.str "then "]) @
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(success_p ::
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(if eqs=[] then [] else [Pretty.brk 1, Pretty.str "else ", fail_p]))) ::
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[Pretty.brk 1, Pretty.str "| _ => ", fail_p, Pretty.str ")"]))
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end;
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fun modename thy s mode = space_implode "_"
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(mk_const_id (sign_of thy) s :: map string_of_int mode);
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fun compile_clause thy gr dep all_vs arg_vs modes mode (ts, ps) =
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let
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fun check_constrt ((names, eqs), t) =
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if is_constrt thy t then ((names, eqs), t) else
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let val s = variant names "x";
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in ((s::names, (s, t)::eqs), Var ((s, 0), fastype_of t)) end;
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val (in_ts, out_ts) = get_args mode 1 ts;
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val ((all_vs', eqs), in_ts') =
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foldl_map check_constrt ((all_vs, []), in_ts);
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fun compile_prems out_ts' vs names gr [] =
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let
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val (gr2, out_ps) = foldl_map (fn (gr, t) =>
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invoke_codegen thy gr dep false t) (gr, out_ts);
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val (gr3, eq_ps) = foldl_map (fn (gr, (s, t)) =>
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apsnd (Pretty.block o cons (Pretty.str (s ^ " = ")) o single)
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(invoke_codegen thy gr dep false t)) (gr2, eqs);
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val (nvs, out_ts'') = foldl_map distinct_v
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((names, map (fn x => (x, [x])) vs), out_ts');
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val (gr4, out_ps') = foldl_map (fn (gr, t) =>
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invoke_codegen thy gr dep false t) (gr3, out_ts'');
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in
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(gr4, compile_match (snd nvs) eq_ps out_ps'
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(Pretty.block [Pretty.str "Seq.single", Pretty.brk 1, mk_tuple out_ps])
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(Pretty.str "Seq.empty"))
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end
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| compile_prems out_ts vs names gr ps =
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let
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val vs' = distinct (flat (vs :: map term_vs out_ts));
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val Some (p, Some mode') =
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select_mode_prem thy modes (arg_vs union vs') ps;
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val ps' = filter_out (equal p) ps;
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in
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(case p of
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Prem (s, us, args) =>
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let
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val (in_ts, out_ts') = get_args mode' 1 us;
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val (gr1, in_ps) = foldl_map (fn (gr, t) =>
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invoke_codegen thy gr dep false t) (gr, in_ts);
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val (gr2, arg_ps) = foldl_map (fn (gr, t) =>
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invoke_codegen thy gr dep true t) (gr1, args);
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val (nvs, out_ts'') = foldl_map distinct_v
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((names, map (fn x => (x, [x])) vs), out_ts);
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val (gr3, out_ps) = foldl_map (fn (gr, t) =>
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invoke_codegen thy gr dep false t) (gr2, out_ts'')
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val (gr4, rest) = compile_prems out_ts' vs' (fst nvs) gr3 ps';
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in
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(gr4, compile_match (snd nvs) [] out_ps
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(Pretty.block (separate (Pretty.brk 1)
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(Pretty.str (modename thy s mode') :: arg_ps) @
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[Pretty.brk 1, mk_tuple in_ps,
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Pretty.str " :->", Pretty.brk 1, rest]))
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(Pretty.str "Seq.empty"))
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end
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| Sidecond t =>
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let
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val (gr1, side_p) = invoke_codegen thy gr dep true t;
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val (nvs, out_ts') = foldl_map distinct_v
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((names, map (fn x => (x, [x])) vs), out_ts);
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val (gr2, out_ps) = foldl_map (fn (gr, t) =>
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invoke_codegen thy gr dep false t) (gr1, out_ts')
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val (gr3, rest) = compile_prems [] vs' (fst nvs) gr2 ps';
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in
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(gr3, compile_match (snd nvs) [] out_ps
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(Pretty.block [Pretty.str "?? ", side_p,
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Pretty.str " :->", Pretty.brk 1, rest])
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(Pretty.str "Seq.empty"))
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end)
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end;
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val (gr', prem_p) = compile_prems in_ts' [] all_vs' gr ps;
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in
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(gr', Pretty.block [Pretty.str "Seq.single inp :->", Pretty.brk 1, prem_p])
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end;
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fun compile_pred thy gr dep prfx all_vs arg_vs modes s cls mode =
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let val (gr', cl_ps) = foldl_map (fn (gr, cl) =>
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compile_clause thy gr dep all_vs arg_vs modes mode cl) (gr, cls)
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in
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((gr', "and "), Pretty.block
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([Pretty.block (separate (Pretty.brk 1)
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(Pretty.str (prfx ^ modename thy s mode) :: map Pretty.str arg_vs) @
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[Pretty.str " inp ="]),
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Pretty.brk 1] @
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flat (separate [Pretty.str " ++", Pretty.brk 1] (map single cl_ps))))
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end;
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fun compile_preds thy gr dep all_vs arg_vs modes preds =
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let val ((gr', _), prs) = foldl_map (fn ((gr, prfx), (s, cls)) =>
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foldl_map (fn ((gr', prfx'), mode) =>
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compile_pred thy gr' dep prfx' all_vs arg_vs modes s cls mode)
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((gr, prfx), the (assoc (modes, s)))) ((gr, "fun "), preds)
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in
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(gr', space_implode "\n\n" (map Pretty.string_of (flat prs)) ^ ";\n\n")
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end;
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(**** processing of introduction rules ****)
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val string_of_mode = enclose "[" "]" o commas o map string_of_int;
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fun print_modes modes = message ("Inferred modes:\n" ^
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space_implode "\n" (map (fn (s, ms) => s ^ ": " ^ commas (map
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string_of_mode ms)) modes));
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fun print_factors factors = message ("Factors:\n" ^
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space_implode "\n" (map (fn (s, fs) => s ^ ": " ^ string_of_factors [] fs) factors));
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fun get_modes (Some (Modes x), _) = x
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| get_modes _ = ([], []);
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fun mk_ind_def thy gr dep names intrs =
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let val ids = map (mk_const_id (sign_of thy)) names
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in Graph.add_edge (hd ids, dep) gr handle Graph.UNDEF _ =>
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let
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fun process_prem factors (gr, t' as _ $ (Const ("op :", _) $ t $ u)) =
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(case strip_comb u of
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(Const (name, _), args) =>
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(case InductivePackage.get_inductive thy name of
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None => (gr, Sidecond t')
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| Some ({names=names', ...}, {intrs=intrs', ...}) =>
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(if names = names' then gr
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else mk_ind_def thy gr (hd ids) names' intrs',
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Prem (name, split_prod []
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(the (assoc (factors, name))) t, args)))
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| _ => (gr, Sidecond t'))
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| process_prem factors (gr, _ $ (Const ("op =", _) $ t $ u)) =
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(gr, Prem ("eq", [t, u], []))
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| process_prem factors (gr, _ $ t) = (gr, Sidecond t);
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fun add_clause factors ((clauses, gr), intr) =
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let
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val _ $ (_ $ t $ u) = Logic.strip_imp_concl intr;
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val (Const (name, _), args) = strip_comb u;
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val (gr', prems) = foldl_map (process_prem factors)
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(gr, Logic.strip_imp_prems intr);
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in
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(overwrite (clauses, (name, if_none (assoc (clauses, name)) [] @
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[(split_prod [] (the (assoc (factors, name))) t, prems)])), gr')
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end;
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fun add_prod_factors (fs, x as _ $ (Const ("op :", _) $ t $ u)) =
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(case strip_comb u of
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(Const (name, _), _) =>
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let val f = prod_factors [] t
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in overwrite (fs, (name, f inter if_none (assoc (fs, name)) f)) end
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| _ => fs)
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| add_prod_factors (fs, _) = fs;
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val intrs' = map (rename_term o #prop o rep_thm o standard) intrs;
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val factors = foldl add_prod_factors ([], flat (map (fn t =>
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Logic.strip_imp_concl t :: Logic.strip_imp_prems t) intrs'));
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val (clauses, gr') = foldl (add_clause factors) (([], Graph.add_edge (hd ids, dep)
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(Graph.new_node (hd ids, (None, "")) gr)), intrs');
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val _ $ (_ $ _ $ u) = Logic.strip_imp_concl (hd intrs');
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val (_, args) = strip_comb u;
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val arg_vs = flat (map term_vs args);
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val extra_modes = ("eq", [[1], [2], [1,2]]) :: (flat (map
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(fst o get_modes o Graph.get_node gr') (Graph.all_preds gr' [hd ids])));
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val modes = infer_modes thy extra_modes arg_vs clauses;
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val _ = print_modes modes;
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val _ = print_factors factors;
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val (gr'', s) = compile_preds thy gr' (hd ids) (terms_vs intrs') arg_vs
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(modes @ extra_modes) clauses;
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in
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(Graph.map_node (hd ids) (K (Some (Modes (modes, factors)), s)) gr'')
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end
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end;
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fun mk_ind_call thy gr dep t u is_query = (case strip_comb u of
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343 |
(Const (s, _), args) => (case InductivePackage.get_inductive thy s of
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344 |
None => None
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345 |
| Some ({names, ...}, {intrs, ...}) =>
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346 |
let
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347 |
fun mk_mode (((ts, mode), i), Var _) = ((ts, mode), i+1)
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348 |
| mk_mode (((ts, mode), i), Free _) = ((ts, mode), i+1)
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349 |
| mk_mode (((ts, mode), i), t) = ((ts @ [t], mode @ [i]), i+1);
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350 |
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351 |
val gr1 = mk_ind_def thy gr dep names intrs;
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352 |
val (modes, factors) = pairself flat (ListPair.unzip
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353 |
(map (get_modes o Graph.get_node gr1) (Graph.all_preds gr1 [dep])));
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354 |
val ts = split_prod [] (the (assoc (factors, s))) t;
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355 |
val (ts', mode) = if is_query then
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356 |
fst (foldl mk_mode ((([], []), 1), ts))
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357 |
else (ts, 1 upto length ts);
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358 |
val _ = if mode mem the (assoc (modes, s)) then () else
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359 |
error ("No such mode for " ^ s ^ ": " ^ string_of_mode mode);
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360 |
val (gr2, in_ps) = foldl_map (fn (gr, t) =>
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361 |
invoke_codegen thy gr dep false t) (gr1, ts');
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362 |
val (gr3, arg_ps) = foldl_map (fn (gr, t) =>
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363 |
invoke_codegen thy gr dep true t) (gr2, args);
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364 |
in
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365 |
Some (gr3, Pretty.block (separate (Pretty.brk 1)
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366 |
(Pretty.str (modename thy s mode) :: arg_ps @ [mk_tuple in_ps])))
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367 |
end)
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368 |
| _ => None);
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369 |
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370 |
fun inductive_codegen thy gr dep brack (Const ("op :", _) $ t $ u) =
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371 |
(case mk_ind_call thy gr dep t u false of
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372 |
None => None
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373 |
| Some (gr', call_p) => Some (gr', (if brack then parens else I)
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374 |
(Pretty.block [Pretty.str "nonempty (", call_p, Pretty.str ")"])))
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375 |
| inductive_codegen thy gr dep brack (Free ("query", _) $ (Const ("op :", _) $ t $ u)) =
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376 |
mk_ind_call thy gr dep t u true
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377 |
| inductive_codegen thy gr dep brack _ = None;
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378 |
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379 |
val setup = [add_codegen "inductive" inductive_codegen];
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|
380 |
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381 |
end;
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