--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Prolog/prolog.ML Mon Nov 20 21:23:12 2006 +0100
@@ -0,0 +1,130 @@
+(* Title: HOL/Prolog/prolog.ML
+ ID: $Id$
+ Author: David von Oheimb (based on a lecture on Lambda Prolog by Nadathur)
+*)
+
+set Proof.show_main_goal;
+
+structure Prolog =
+struct
+
+exception not_HOHH;
+
+fun isD t = case t of
+ Const("Trueprop",_)$t => isD t
+ | Const("op &" ,_)$l$r => isD l andalso isD r
+ | Const("op -->",_)$l$r => isG l andalso isD r
+ | Const( "==>",_)$l$r => isG l andalso isD r
+ | Const("All",_)$Abs(s,_,t) => isD t
+ | Const("all",_)$Abs(s,_,t) => isD t
+ | Const("op |",_)$_$_ => false
+ | Const("Ex" ,_)$_ => false
+ | Const("not",_)$_ => false
+ | Const("True",_) => false
+ | Const("False",_) => false
+ | l $ r => isD l
+ | Const _ (* rigid atom *) => true
+ | Bound _ (* rigid atom *) => true
+ | Free _ (* rigid atom *) => true
+ | _ (* flexible atom,
+ anything else *) => false
+and
+ isG t = case t of
+ Const("Trueprop",_)$t => isG t
+ | Const("op &" ,_)$l$r => isG l andalso isG r
+ | Const("op |" ,_)$l$r => isG l andalso isG r
+ | Const("op -->",_)$l$r => isD l andalso isG r
+ | Const( "==>",_)$l$r => isD l andalso isG r
+ | Const("All",_)$Abs(_,_,t) => isG t
+ | Const("all",_)$Abs(_,_,t) => isG t
+ | Const("Ex" ,_)$Abs(_,_,t) => isG t
+ | Const("True",_) => true
+ | Const("not",_)$_ => false
+ | Const("False",_) => false
+ | _ (* atom *) => true;
+
+val check_HOHH_tac1 = PRIMITIVE (fn thm =>
+ if isG (concl_of thm) then thm else raise not_HOHH);
+val check_HOHH_tac2 = PRIMITIVE (fn thm =>
+ if forall isG (prems_of thm) then thm else raise not_HOHH);
+fun check_HOHH thm = (if isD (concl_of thm) andalso forall isG (prems_of thm)
+ then thm else raise not_HOHH);
+
+fun atomizeD thm = let
+ fun at thm = case concl_of thm of
+ _$(Const("All" ,_)$Abs(s,_,_))=> at(thm RS (read_instantiate [("x",
+ "?"^(if s="P" then "PP" else s))] spec))
+ | _$(Const("op &",_)$_$_) => at(thm RS conjunct1)@at(thm RS conjunct2)
+ | _$(Const("op -->",_)$_$_) => at(thm RS mp)
+ | _ => [thm]
+in map zero_var_indexes (at thm) end;
+
+val atomize_ss =
+ Simplifier.theory_context (the_context ()) empty_ss
+ setmksimps (mksimps mksimps_pairs)
+ addsimps [
+ all_conj_distrib, (* "(! x. P x & Q x) = ((! x. P x) & (! x. Q x))" *)
+ imp_conjL RS sym, (* "(D :- G1 :- G2) = (D :- G1 & G2)" *)
+ imp_conjR, (* "(D1 & D2 :- G) = ((D1 :- G) & (D2 :- G))" *)
+ imp_all]; (* "((!x. D) :- G) = (!x. D :- G)" *)
+
+(*val hyp_resolve_tac = METAHYPS (fn prems =>
+ resolve_tac (List.concat (map atomizeD prems)) 1);
+ -- is nice, but cannot instantiate unknowns in the assumptions *)
+fun hyp_resolve_tac i st = let
+ fun ap (Const("All",_)$Abs(_,_,t))=(case ap t of (k,a,t) => (k+1,a ,t))
+ | ap (Const("op -->",_)$_$t) =(case ap t of (k,_,t) => (k,true ,t))
+ | ap t = (0,false,t);
+(*
+ fun rep_goal (Const ("all",_)$Abs (_,_,t)) = rep_goal t
+ | rep_goal (Const ("==>",_)$s$t) =
+ (case rep_goal t of (l,t) => (s::l,t))
+ | rep_goal t = ([] ,t);
+ val (prems, Const("Trueprop", _)$concl) = rep_goal
+ (#3(dest_state (st,i)));
+*)
+ val subgoal = #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' [dtac 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 (etac 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 etac mp i THEN drot_tac (~n) i else atac 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) st end;
+
+fun ptac prog = let
+ val proga = List.concat (map atomizeD prog) (* atomize the prog *)
+ in (REPEAT_DETERM1 o FIRST' [
+ rtac TrueI, (* "True" *)
+ rtac conjI, (* "[| P; Q |] ==> P & Q" *)
+ rtac allI, (* "(!!x. P x) ==> ! x. P x" *)
+ rtac exI, (* "P x ==> ? x. P x" *)
+ rtac impI THEN' (* "(P ==> Q) ==> P --> Q" *)
+ asm_full_simp_tac atomize_ss THEN' (* atomize the asms *)
+ (REPEAT_DETERM o (etac conjE)) (* split the asms *)
+ ])
+ ORELSE' resolve_tac [disjI1,disjI2] (* "P ==> P | Q","Q ==> P | Q"*)
+ ORELSE' ((resolve_tac proga APPEND' hyp_resolve_tac)
+ THEN' (fn _ => check_HOHH_tac2))
+end;
+
+fun prolog_tac prog = check_HOHH_tac1 THEN
+ DEPTH_SOLVE (ptac (map check_HOHH prog) 1);
+
+val prog_HOHH = [];
+
+end;