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(* Title: HOL/Tools/Predicate_Compile/predicate_compile_fun.ML
Author: Lukas Bulwahn, TU Muenchen
Preprocessing functions to predicates.
*)
signature PREDICATE_COMPILE_FUN =
sig
val define_predicates : (string * thm list) list -> theory -> (string * thm list) list * theory
val rewrite_intro : theory -> thm -> thm list
val pred_of_function : theory -> string -> string option
val add_function_predicate_translation : (term * term) -> theory -> theory
end;
structure Predicate_Compile_Fun : PREDICATE_COMPILE_FUN =
struct
open Predicate_Compile_Aux;
(* Table from function to inductive predicate *)
structure Fun_Pred = Theory_Data
(
type T = (term * term) Item_Net.T;
val empty : T = Item_Net.init (op aconv o apply2 fst) (single o fst);
val extend = I;
val merge = Item_Net.merge;
)
fun lookup thy net t =
let
val poss_preds = map_filter (fn (f, p) =>
SOME (Envir.subst_term (Pattern.match thy (f, t) (Vartab.empty, Vartab.empty)) p)
handle Pattern.MATCH => NONE) (Item_Net.retrieve net t)
in
(case poss_preds of
[p] => SOME p
| _ => NONE)
end
fun pred_of_function thy name =
(case Item_Net.retrieve (Fun_Pred.get thy) (Const (name, dummyT)) of
[] => NONE
| [(_, p)] => SOME (fst (dest_Const p))
| _ => error ("Multiple matches possible for lookup of constant " ^ name))
fun defined_const thy name = is_some (pred_of_function thy name)
fun add_function_predicate_translation (f, p) =
Fun_Pred.map (Item_Net.update (f, p))
fun transform_ho_typ (T as Type ("fun", _)) =
let
val (Ts, T') = strip_type T
in if T' = HOLogic.boolT then T else (Ts @ [T']) ---> HOLogic.boolT end
| transform_ho_typ t = t
fun transform_ho_arg arg =
(case (fastype_of arg) of
(T as Type ("fun", _)) =>
(case arg of
Free (name, _) => Free (name, transform_ho_typ T)
| _ => raise Fail "A non-variable term at a higher-order position")
| _ => arg)
fun pred_type T =
let
val (Ts, T') = strip_type T
val Ts' = map transform_ho_typ Ts
in
(Ts' @ [T']) ---> HOLogic.boolT
end;
(* creates the list of premises for every intro rule *)
(* theory -> term -> (string list, term list list) *)
fun dest_code_eqn eqn = let
val (lhs, rhs) = Logic.dest_equals (Logic.unvarify_global (Thm.prop_of eqn))
val (func, args) = strip_comb lhs
in ((func, args), rhs) end;
fun folds_map f xs y =
let
fun folds_map' acc [] y = [(rev acc, y)]
| folds_map' acc (x :: xs) y =
maps (fn (x, y) => folds_map' (x :: acc) xs y) (f x y)
in
folds_map' [] xs y
end;
fun keep_functions thy t =
(case try dest_Const (fst (strip_comb t)) of
SOME (c, _) => Predicate_Compile_Data.keep_function thy c
| _ => false)
fun flatten thy lookup_pred t (names, prems) =
let
val ctxt = Proof_Context.init_global thy;
fun lift t (names, prems) =
(case lookup_pred (Envir.eta_contract t) of
SOME pred => [(pred, (names, prems))]
| NONE =>
let
val (vars, body) = strip_abs t
val _ = \<^assert> (fastype_of body = body_type (fastype_of body))
val absnames = Name.variant_list names (map fst vars)
val frees = map2 (curry Free) absnames (map snd vars)
val body' = subst_bounds (rev frees, body)
val resname = singleton (Name.variant_list (absnames @ names)) "res"
val resvar = Free (resname, fastype_of body)
val t = flatten' body' ([], [])
|> map (fn (res, (inner_names, inner_prems)) =>
let
fun mk_exists (x, T) t = HOLogic.mk_exists (x, T, t)
val vTs =
fold Term.add_frees inner_prems []
|> filter (fn (x, _) => member (op =) inner_names x)
val t =
fold mk_exists vTs
(foldr1 HOLogic.mk_conj (HOLogic.mk_eq (res, resvar) ::
map HOLogic.dest_Trueprop inner_prems))
in
t
end)
|> foldr1 HOLogic.mk_disj
|> fold lambda (resvar :: rev frees)
in
[(t, (names, prems))]
end)
and flatten_or_lift (t, T) (names, prems) =
if fastype_of t = T then
flatten' t (names, prems)
else
(* note pred_type might be to general! *)
if (pred_type (fastype_of t) = T) then
lift t (names, prems)
else
error ("unexpected input for flatten or lift" ^ Syntax.string_of_term_global thy t ^
", " ^ Syntax.string_of_typ_global thy T)
and flatten' (t as Const _) (names, prems) = [(t, (names, prems))]
| flatten' (t as Free _) (names, prems) = [(t, (names, prems))]
| flatten' (t as Abs _) (names, prems) = [(t, (names, prems))]
| flatten' (t as _ $ _) (names, prems) =
if is_constrt ctxt t orelse keep_functions thy t then
[(t, (names, prems))]
else
case (fst (strip_comb t)) of
Const (\<^const_name>\<open>If\<close>, _) =>
(let
val (_, [B, x, y]) = strip_comb t
in
flatten' B (names, prems)
|> maps (fn (B', (names, prems)) =>
(flatten' x (names, prems)
|> map (fn (res, (names, prems)) => (res, (names, (HOLogic.mk_Trueprop B') :: prems))))
@ (flatten' y (names, prems)
|> map (fn (res, (names, prems)) =>
(* in general unsound! *)
(res, (names, (HOLogic.mk_Trueprop (HOLogic.mk_not B')) :: prems)))))
end)
| Const (\<^const_name>\<open>Let\<close>, _) =>
(let
val (_, [f, g]) = strip_comb t
in
flatten' f (names, prems)
|> maps (fn (res, (names, prems)) =>
flatten' (betapply (g, res)) (names, prems))
end)
| _ =>
case find_split_thm thy (fst (strip_comb t)) of
SOME raw_split_thm =>
let
val split_thm = prepare_split_thm (Proof_Context.init_global thy) raw_split_thm
val (assms, concl) = Logic.strip_horn (Thm.prop_of split_thm)
val (_, [split_t]) = strip_comb (HOLogic.dest_Trueprop concl)
val t' = case_betapply thy t
val subst = Pattern.match thy (split_t, t') (Vartab.empty, Vartab.empty)
fun flatten_of_assm assm =
let
val (vTs, assm') = strip_all (Envir.beta_norm (Envir.subst_term subst assm))
val var_names = Name.variant_list names (map fst vTs)
val vars = map Free (var_names ~~ (map snd vTs))
val (prems', pre_res) = Logic.strip_horn (subst_bounds (rev vars, assm'))
val (_, [inner_t]) = strip_comb (HOLogic.dest_Trueprop pre_res)
val (lhss : term list, rhss) =
split_list (map (HOLogic.dest_eq o HOLogic.dest_Trueprop) prems')
in
folds_map flatten' lhss (var_names @ names, prems)
|> map (fn (ress, (names, prems)) =>
let
val prems' = map (HOLogic.mk_Trueprop o HOLogic.mk_eq) (ress ~~ rhss)
in (names, prems' @ prems) end)
|> maps (flatten' inner_t)
end
in
maps flatten_of_assm assms
end
| NONE =>
let
val (f, args) = strip_comb t
val args = map (Envir.eta_long []) args
val _ = \<^assert> (fastype_of t = body_type (fastype_of t))
val f' = lookup_pred f
val Ts =
(case f' of
SOME pred => (fst (split_last (binder_types (fastype_of pred))))
| NONE => binder_types (fastype_of f))
in
folds_map flatten_or_lift (args ~~ Ts) (names, prems) |>
(case f' of
NONE =>
map (fn (argvs, (names', prems')) => (list_comb (f, argvs), (names', prems')))
| SOME pred =>
map (fn (argvs, (names', prems')) =>
let
fun lift_arg T t =
if (fastype_of t) = T then t
else
let
val _ = \<^assert> (T =
(binder_types (fastype_of t) @ [\<^typ>\<open>bool\<close>] ---> \<^typ>\<open>bool\<close>))
fun mk_if T (b, t, e) =
Const (\<^const_name>\<open>If\<close>, \<^typ>\<open>bool\<close> --> T --> T --> T) $ b $ t $ e
val Ts = binder_types (fastype_of t)
in
fold_rev Term.abs (map (pair "x") Ts @ [("b", \<^typ>\<open>bool\<close>)])
(mk_if \<^typ>\<open>bool\<close> (list_comb (t, map Bound (length Ts downto 1)),
HOLogic.mk_eq (\<^term>\<open>True\<close>, Bound 0),
HOLogic.mk_eq (\<^term>\<open>False\<close>, Bound 0)))
end
val argvs' = map2 lift_arg Ts argvs
val resname = singleton (Name.variant_list names') "res"
val resvar = Free (resname, body_type (fastype_of t))
val prem = HOLogic.mk_Trueprop (list_comb (pred, argvs' @ [resvar]))
in (resvar, (resname :: names', prem :: prems')) end))
end
in
map (apfst Envir.eta_contract) (flatten' (Envir.eta_long [] t) (names, prems))
end;
(* FIXME: create new predicate name -- does not avoid nameclashing *)
fun pred_of thy f =
let
val (name, T) = dest_Const f
val base_name' = (Long_Name.base_name name ^ "P")
val name' = Sign.full_bname thy base_name'
val T' = if (body_type T = \<^typ>\bool\) then T else pred_type T
in
(name', Const (name', T'))
end
(* assumption: mutual recursive predicates all have the same parameters. *)
fun define_predicates specs thy =
if forall (fn (const, _) => defined_const thy const) specs then
([], thy)
else
let
val eqns = maps snd specs
(* create prednames *)
val ((funs, argss), rhss) = map_split dest_code_eqn eqns |>> split_list
val dst_funs = distinct (op =) funs
val argss' = map (map transform_ho_arg) argss
fun is_lifted (t1, t2) = (fastype_of t2 = pred_type (fastype_of t1))
(* FIXME: higher order arguments also occur in tuples! *)
val lifted_args = distinct (op =) (filter is_lifted (flat argss ~~ flat argss'))
val (prednames, preds) = split_list (map (pred_of thy) funs)
val dst_preds = distinct (op =) preds
val dst_prednames = distinct (op =) prednames
(* mapping from term (Free or Const) to term *)
val net = fold Item_Net.update
((dst_funs ~~ dst_preds) @ lifted_args)
(Fun_Pred.get thy)
fun lookup_pred t = lookup thy net t
(* create intro rules *)
fun mk_intros ((func, pred), (args, rhs)) =
if (body_type (fastype_of func) = \<^typ>\<open>bool\<close>) then
(* TODO: preprocess predicate definition of rhs *)
[Logic.list_implies
([HOLogic.mk_Trueprop rhs], HOLogic.mk_Trueprop (list_comb (pred, args)))]
else
let
val names = Term.add_free_names rhs []
in flatten thy lookup_pred rhs (names, [])
|> map (fn (resultt, (_, prems)) =>
Logic.list_implies (prems, HOLogic.mk_Trueprop (list_comb (pred, args @ [resultt]))))
end
val intr_tss = map mk_intros ((funs ~~ preds) ~~ (argss' ~~ rhss))
val (intrs, thy') = thy
|> Sign.add_consts
(map (fn Const (name, T) => (Binding.name (Long_Name.base_name name), T, NoSyn))
dst_preds)
|> fold_map Specification.axiom (* FIXME !?!?!?! *)
(map_index (fn (j, (predname, t)) =>
((Binding.name (Long_Name.base_name predname ^ "_intro_" ^ string_of_int (j + 1)), []), t))
(maps (uncurry (map o pair)) (prednames ~~ intr_tss)))
val specs = map (fn predname => (predname,
map Drule.export_without_context (filter (Predicate_Compile_Aux.is_intro predname) intrs)))
dst_prednames
val thy'' = Fun_Pred.map
(fold Item_Net.update (map (apply2 Logic.varify_global)
(dst_funs ~~ dst_preds))) thy'
fun functional_mode_of T =
list_fun_mode (replicate (length (binder_types T)) Input @ [Output])
val thy''' = fold
(fn (predname, Const (name, T)) => Core_Data.register_alternative_function
predname (functional_mode_of T) name)
(dst_prednames ~~ dst_funs) thy''
in
(specs, thy''')
end
fun rewrite_intro thy intro =
let
fun lookup_pred t = lookup thy (Fun_Pred.get thy) t
(*val _ = tracing ("Rewriting intro " ^ Thm.string_of_thm_global thy intro)*)
val intro_t = Logic.unvarify_global (Thm.prop_of intro)
val (prems, concl) = Logic.strip_horn intro_t
val frees = map fst (Term.add_frees intro_t [])
fun rewrite prem names =
let
(*val _ = tracing ("Rewriting premise " ^ Syntax.string_of_term_global thy prem ^ "...")*)
val t = HOLogic.dest_Trueprop prem
val (lit, mk_lit) =
(case try HOLogic.dest_not t of
SOME t => (t, HOLogic.mk_not)
| NONE => (t, I))
val (P, args) = strip_comb lit
in
folds_map (flatten thy lookup_pred) args (names, [])
|> map (fn (resargs, (names', prems')) =>
let
val prem' = HOLogic.mk_Trueprop (mk_lit (list_comb (P, resargs)))
in (prems' @ [prem'], names') end)
end
val intro_ts' = folds_map rewrite prems frees
|> maps (fn (prems', frees') =>
rewrite concl frees'
|> map (fn (conclprems, _) =>
let
val (conclprems', concl') = split_last conclprems
in
Logic.list_implies ((flat prems') @ conclprems', concl')
end))
(*val _ = tracing ("Rewritten intro to " ^
commas (map (Syntax.string_of_term_global thy) intro_ts'))*)
in
map (Drule.export_without_context o Skip_Proof.make_thm thy) intro_ts'
end
end
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