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(* Title: HOL/Prolog/prolog.ML
Author: David von Oheimb (based on a lecture on Lambda Prolog by Nadathur)
*)
Options.default_put_bool \<^system_option>\<open>show_main_goal\<close> true;
structure Prolog =
struct
exception not_HOHH;
fun isD t = case t of
Const(\<^const_name>\<open>Trueprop\<close>,_)$t => isD t
| Const(\<^const_name>\<open>HOL.conj\<close> ,_)$l$r => isD l andalso isD r
| Const(\<^const_name>\<open>HOL.implies\<close>,_)$l$r => isG l andalso isD r
| Const(\<^const_name>\<open>Pure.imp\<close>,_)$l$r => isG l andalso isD r
| Const(\<^const_name>\<open>All\<close>,_)$Abs(s,_,t) => isD t
| Const(\<^const_name>\<open>Pure.all\<close>,_)$Abs(s,_,t) => isD t
| Const(\<^const_name>\<open>HOL.disj\<close>,_)$_$_ => false
| Const(\<^const_name>\<open>Ex\<close> ,_)$_ => false
| Const(\<^const_name>\<open>Not\<close>,_)$_ => false
| Const(\<^const_name>\<open>True\<close>,_) => false
| Const(\<^const_name>\<open>False\<close>,_) => false
| l $ r => isD l
| Const _ (* rigid atom *) => true
| Bound _ (* rigid atom *) => true
| Free _ (* rigid atom *) => true
| _ (* flexible atom,
anything else *)
and
isG t = case t of
Const(\<^const_name>\<open>Trueprop\<close>,_)$t => isG t
| Const(\<^const_name>\<open>HOL.conj\<close> ,_)$l$r => isG l andalso isG r
| Const(\<^const_name>\<open>HOL.disj\<close> ,_)$l$r => isG l andalso isG r
| Const(\<^const_name>\<open>HOL.implies\<close>,_)$l$r => isD l andalso isG r
| Const(\<^const_name>\<open>Pure.imp\<close>,_)$l$r => isD l andalso isG r
| Const(\<^const_name>\<open>All\<close>,_)$Abs(_,_,t) => isG t
| Const(\<^const_name>\<open>Pure.all\<close>,_)$Abs(_,_,t) => isG t
| Const(\<^const_name>\<open>Ex\<close> ,_)$Abs(_,_,t) => isG t
| Const(\<^const_name>\<open>True\<close>,_) => true
| Const(\<^const_name>\<open>Not\<close>,_)$_ => false
| Const(\<^const_name>\<open>False\<close>,_) => false
| _ (* atom *) => true;
val check_HOHH_tac1 = PRIMITIVE (fn thm =>
if isG (Thm.concl_of thm) then thm else raise not_HOHH);
val check_HOHH_tac2 = PRIMITIVE (fn thm =>
if forall isG (Thm.prems_of thm) then thm else raise not_HOHH);
fun check_HOHH thm = (if isD (Thm.concl_of thm) andalso forall isG (Thm.prems_of thm)
then thm else raise not_HOHH);
fun atomizeD ctxt thm =
let
fun at thm = case Thm.concl_of thm of
_$(Const(\<^const_name>\<open>All\<close> ,_)$Abs(s,_,_))=>
let val s' = if s="P" then "PP" else s in
at(thm RS (Rule_Insts.read_instantiate ctxt [((("x", 0), Position.none), s')] [s'] spec))
end
| _$(Const(\<^const_name>\<open>HOL.conj\<close>,_)$_$_) => at(thm RS conjunct1)@at(thm RS conjunct2)
| _$(Const(\<^const_name>\<open>HOL.implies\<close>,_)$_$_) => at(thm RS mp)
| _ => [thm]
in map zero_var_indexes (at thm) end;
val atomize_ss =
(empty_simpset \<^context> |> Simplifier.set_mksimps (mksimps mksimps_pairs))
addsimps [
@{thm all_conj_distrib}, (* "(! x. P x & Q x) = ((! x. P x) & (! x. Q x))" *)
@{thm imp_conjL} RS sym, (* "(D :- G1 :- G2) = (D :- G1 & G2)" *)
@{thm imp_conjR}, (* "(D1 & D2 :- G) = ((D1 :- G) & (D2 :- G))" *)
@{thm imp_all}] (* "((!x. D) :- G) = (!x. D :- G)" *)
|> simpset_of;
(*val hyp_resolve_tac = Subgoal.FOCUS_PREMS (fn {prems, ...} =>
resolve_tac (maps atomizeD prems) 1);
-- is nice, but cannot instantiate unknowns in the assumptions *)
fun hyp_resolve_tac ctxt = SUBGOAL (fn (subgoal, i) =>
let
fun ap (Const(\<^const_name>\<open>All\<close>,_)$Abs(_,_,t))=(case ap t of (k,a,t) => (k+1,a ,t))
| ap (Const(\<^const_name>\<open>HOL.implies\<close>,_)$_$t) =(case ap t of (k,_,t) => (k,true ,t))
| ap t = (0,false,t);
(*
fun rep_goal (Const (@{const_name Pure.all},_)$Abs (_,_,t)) = rep_goal t
| rep_goal (Const (@{const_name Pure.imp},_)$s$t) =
(case rep_goal t of (l,t) => (s::l,t))
| rep_goal t = ([] ,t);
val (prems, Const(@{const_name Trueprop}, _)$concl) = rep_goal
(#3(dest_state (st,i)));
*)
val prems = Logic.strip_assums_hyp subgoal;
val concl = HOLogic.dest_Trueprop (Logic.strip_assums_concl subgoal);
fun drot_tac k i = DETERM (rotate_tac k i);
fun spec_tac 0 i = all_tac
| spec_tac k i = EVERY' [dresolve_tac ctxt [spec], drot_tac ~1, spec_tac (k-1)] i;
fun dup_spec_tac k i = if k = 0 then all_tac else EVERY'
[DETERM o (eresolve_tac ctxt [all_dupE]), drot_tac ~2, spec_tac (k-1)] i;
fun same_head _ (Const (x,_)) (Const (y,_)) = x = y
| same_head k (s$_) (t$_) = same_head k s t
| same_head k (Bound i) (Bound j) = i = j + k
| same_head _ _ _ = true;
fun mapn f n [] = []
| mapn f n (x::xs) = f n x::mapn f (n+1) xs;
fun pres_tac (k,arrow,t) n i = drot_tac n i THEN (
if same_head k t concl
then dup_spec_tac k i THEN
(if arrow then eresolve_tac ctxt [mp] i THEN drot_tac (~n) i else assume_tac ctxt i)
else no_tac);
val ptacs = mapn (fn n => fn t =>
pres_tac (ap (HOLogic.dest_Trueprop t)) n i) 0 prems;
in Library.foldl (op APPEND) (no_tac, ptacs) end);
fun ptac ctxt prog = let
val proga = maps (atomizeD ctxt) prog (* atomize the prog *)
in (REPEAT_DETERM1 o FIRST' [
resolve_tac ctxt [TrueI], (* "True" *)
resolve_tac ctxt [conjI], (* "[| P; Q |] ==> P & Q" *)
resolve_tac ctxt [allI], (* "(!!x. P x) ==> ! x. P x" *)
resolve_tac ctxt [exI], (* "P x ==> ? x. P x" *)
resolve_tac ctxt [impI] THEN' (* "(P ==> Q) ==> P --> Q" *)
asm_full_simp_tac (put_simpset atomize_ss ctxt) THEN' (* atomize the asms *)
(REPEAT_DETERM o (eresolve_tac ctxt [conjE])) (* split the asms *)
])
ORELSE' resolve_tac ctxt [disjI1,disjI2] (* "P ==> P | Q","Q ==> P | Q"*)
ORELSE' ((resolve_tac ctxt proga APPEND' hyp_resolve_tac ctxt)
THEN' (fn _ => check_HOHH_tac2))
end;
fun prolog_tac ctxt prog =
check_HOHH_tac1 THEN
DEPTH_SOLVE (ptac ctxt (map check_HOHH prog) 1);
val prog_HOHH = [];
end;
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