(* 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",_)$_ => false | Const("False",_) => false | _ (* atom *) => true; val check_HOHH_tac1 = PRIMITIVE (fn thm => if isG (concl_of thm) then thm else raise not_HOHH); val check_HOHH_tac2 = PRIMITIVE (fn thm => if forall isG (prems_of thm) then thm else raise not_HOHH); fun check_HOHH thm = (if isD (concl_of thm) andalso forall isG (prems_of thm) then thm else raise not_HOHH); fun atomizeD ctxt thm = let fun at thm = case concl_of thm of _$(Const("All" ,_)$Abs(s,_,_))=> at(thm RS (read_instantiate ctxt [(("x", 0), "?" ^ (if s="P" then "PP" else s))] spec)) | _$(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 ctxt prog = let val proga = List.concat (map (atomizeD ctxt) 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 ctxt prog = check_HOHH_tac1 THEN DEPTH_SOLVE (ptac ctxt (map check_HOHH prog) 1); val prog_HOHH = []; end;