--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/TFL/post.ML Wed Jan 03 21:20:40 2001 +0100
@@ -0,0 +1,229 @@
+(* Title: TFL/post.ML
+ ID: $Id$
+ Author: Konrad Slind, Cambridge University Computer Laboratory
+ Copyright 1997 University of Cambridge
+
+Second part of main module (postprocessing of TFL definitions).
+*)
+
+signature TFL =
+sig
+ val trace: bool ref
+ val quiet_mode: bool ref
+ val message: string -> unit
+ val tgoalw: theory -> thm list -> thm list -> thm list
+ val tgoal: theory -> thm list -> thm list
+ val std_postprocessor: claset -> simpset -> thm list -> theory ->
+ {induction: thm, rules: thm, TCs: term list list} ->
+ {induction: thm, rules: thm, nested_tcs: thm list}
+ val define_i: theory -> claset -> simpset -> thm list -> thm list -> xstring ->
+ term -> term list -> theory * {rules: (thm * int) list, induct: thm, tcs: term list}
+ val define: theory -> claset -> simpset -> thm list -> thm list -> xstring ->
+ string -> string list -> theory * {rules: (thm * int) list, induct: thm, tcs: term list}
+ val defer_i: theory -> thm list -> xstring -> term list -> theory * thm
+ val defer: theory -> thm list -> xstring -> string list -> theory * thm
+end;
+
+structure Tfl: TFL =
+struct
+
+structure S = USyntax
+
+
+(* messages *)
+
+val trace = Prim.trace
+
+val quiet_mode = ref false;
+fun message s = if ! quiet_mode then () else writeln s;
+
+
+(* misc *)
+
+fun read_term thy = Sign.simple_read_term (Theory.sign_of thy) HOLogic.termT;
+
+
+(*---------------------------------------------------------------------------
+ * Extract termination goals so that they can be put it into a goalstack, or
+ * have a tactic directly applied to them.
+ *--------------------------------------------------------------------------*)
+fun termination_goals rules =
+ map (#1 o Type.freeze_thaw o HOLogic.dest_Trueprop)
+ (foldr (fn (th,A) => union_term (prems_of th, A)) (rules, []));
+
+(*---------------------------------------------------------------------------
+ * Finds the termination conditions in (highly massaged) definition and
+ * puts them into a goalstack.
+ *--------------------------------------------------------------------------*)
+fun tgoalw thy defs rules =
+ case termination_goals rules of
+ [] => error "tgoalw: no termination conditions to prove"
+ | L => goalw_cterm defs
+ (Thm.cterm_of (Theory.sign_of thy)
+ (HOLogic.mk_Trueprop(USyntax.list_mk_conj L)));
+
+fun tgoal thy = tgoalw thy [];
+
+(*---------------------------------------------------------------------------
+ * Three postprocessors are applied to the definition. It
+ * attempts to prove wellfoundedness of the given relation, simplifies the
+ * non-proved termination conditions, and finally attempts to prove the
+ * simplified termination conditions.
+ *--------------------------------------------------------------------------*)
+fun std_postprocessor cs ss wfs =
+ Prim.postprocess
+ {wf_tac = REPEAT (ares_tac wfs 1),
+ terminator = asm_simp_tac ss 1
+ THEN TRY (fast_tac (cs addSDs [not0_implies_Suc] addss ss) 1),
+ simplifier = Rules.simpl_conv ss []};
+
+
+
+val concl = #2 o Rules.dest_thm;
+
+(*---------------------------------------------------------------------------
+ * Postprocess a definition made by "define". This is a separate stage of
+ * processing from the definition stage.
+ *---------------------------------------------------------------------------*)
+local
+structure R = Rules
+structure U = Utils
+
+(* The rest of these local definitions are for the tricky nested case *)
+val solved = not o can S.dest_eq o #2 o S.strip_forall o concl
+
+fun id_thm th =
+ let val {lhs,rhs} = S.dest_eq (#2 (S.strip_forall (#2 (R.dest_thm th))));
+ in lhs aconv rhs end
+ handle U.ERR _ => false;
+
+
+fun prover s = prove_goal HOL.thy s (fn _ => [fast_tac HOL_cs 1]);
+val P_imp_P_iff_True = prover "P --> (P= True)" RS mp;
+val P_imp_P_eq_True = P_imp_P_iff_True RS eq_reflection;
+fun mk_meta_eq r = case concl_of r of
+ Const("==",_)$_$_ => r
+ | _ $(Const("op =",_)$_$_) => r RS eq_reflection
+ | _ => r RS P_imp_P_eq_True
+
+(*Is this the best way to invoke the simplifier??*)
+fun rewrite L = rewrite_rule (map mk_meta_eq (filter(not o id_thm) L))
+
+fun join_assums th =
+ let val {sign,...} = rep_thm th
+ val tych = cterm_of sign
+ val {lhs,rhs} = S.dest_eq(#2 (S.strip_forall (concl th)))
+ val cntxtl = (#1 o S.strip_imp) lhs (* cntxtl should = cntxtr *)
+ val cntxtr = (#1 o S.strip_imp) rhs (* but union is solider *)
+ val cntxt = gen_union (op aconv) (cntxtl, cntxtr)
+ in
+ R.GEN_ALL
+ (R.DISCH_ALL
+ (rewrite (map (R.ASSUME o tych) cntxt) (R.SPEC_ALL th)))
+ end
+ val gen_all = S.gen_all
+in
+fun proof_stage cs ss wfs theory {f, R, rules, full_pats_TCs, TCs} =
+ let
+ val _ = message "Proving induction theorem ..."
+ val ind = Prim.mk_induction theory {fconst=f, R=R, SV=[], pat_TCs_list=full_pats_TCs}
+ val _ = message "Postprocessing ...";
+ val {rules, induction, nested_tcs} =
+ std_postprocessor cs ss wfs theory {rules=rules, induction=ind, TCs=TCs}
+ in
+ case nested_tcs
+ of [] => {induction=induction, rules=rules,tcs=[]}
+ | L => let val dummy = message "Simplifying nested TCs ..."
+ val (solved,simplified,stubborn) =
+ U.itlist (fn th => fn (So,Si,St) =>
+ if (id_thm th) then (So, Si, th::St) else
+ if (solved th) then (th::So, Si, St)
+ else (So, th::Si, St)) nested_tcs ([],[],[])
+ val simplified' = map join_assums simplified
+ val rewr = full_simplify (ss addsimps (solved @ simplified'));
+ val induction' = rewr induction
+ and rules' = rewr rules
+ in
+ {induction = induction',
+ rules = rules',
+ tcs = map (gen_all o S.rhs o #2 o S.strip_forall o concl)
+ (simplified@stubborn)}
+ end
+ end;
+
+
+(*lcp: curry the predicate of the induction rule*)
+fun curry_rule rl = split_rule_var
+ (head_of (HOLogic.dest_Trueprop (concl_of rl)),
+ rl);
+
+(*lcp: put a theorem into Isabelle form, using meta-level connectives*)
+val meta_outer =
+ curry_rule o standard o
+ rule_by_tactic (REPEAT
+ (FIRSTGOAL (resolve_tac [allI, impI, conjI]
+ ORELSE' etac conjE)));
+
+(*Strip off the outer !P*)
+val spec'= read_instantiate [("x","P::?'b=>bool")] spec;
+
+fun simplify_defn thy cs ss congs wfs id pats def0 =
+ let val def = freezeT def0 RS meta_eq_to_obj_eq
+ val {theory,rules,rows,TCs,full_pats_TCs} = Prim.post_definition congs (thy, (def,pats))
+ val {lhs=f,rhs} = S.dest_eq (concl def)
+ val (_,[R,_]) = S.strip_comb rhs
+ val {induction, rules, tcs} =
+ proof_stage cs ss wfs theory
+ {f = f, R = R, rules = rules,
+ full_pats_TCs = full_pats_TCs,
+ TCs = TCs}
+ val rules' = map (standard o Rulify.rulify_no_asm) (R.CONJUNCTS rules)
+ in {induct = meta_outer (Rulify.rulify_no_asm (induction RS spec')),
+ rules = ListPair.zip(rules', rows),
+ tcs = (termination_goals rules') @ tcs}
+ end
+ handle U.ERR {mesg,func,module} =>
+ error (mesg ^
+ "\n (In TFL function " ^ module ^ "." ^ func ^ ")");
+
+(*---------------------------------------------------------------------------
+ * Defining a function with an associated termination relation.
+ *---------------------------------------------------------------------------*)
+fun define_i thy cs ss congs wfs fid R eqs =
+ let val {functional,pats} = Prim.mk_functional thy eqs
+ val (thy, def) = Prim.wfrec_definition0 thy (Sign.base_name fid) R functional
+ in (thy, simplify_defn thy cs ss congs wfs fid pats def) end;
+
+fun define thy cs ss congs wfs fid R seqs =
+ define_i thy cs ss congs wfs fid (read_term thy R) (map (read_term thy) seqs)
+ handle U.ERR {mesg,...} => error mesg;
+
+
+(*---------------------------------------------------------------------------
+ *
+ * Definitions with synthesized termination relation
+ *
+ *---------------------------------------------------------------------------*)
+
+fun func_of_cond_eqn tm =
+ #1 (S.strip_comb (#lhs (S.dest_eq (#2 (S.strip_forall (#2 (S.strip_imp tm)))))));
+
+fun defer_i thy congs fid eqs =
+ let val {rules,R,theory,full_pats_TCs,SV,...} =
+ Prim.lazyR_def thy (Sign.base_name fid) congs eqs
+ val f = func_of_cond_eqn (concl (R.CONJUNCT1 rules handle U.ERR _ => rules));
+ val dummy = message "Proving induction theorem ...";
+ val induction = Prim.mk_induction theory
+ {fconst=f, R=R, SV=SV, pat_TCs_list=full_pats_TCs}
+ in (theory,
+ (*return the conjoined induction rule and recursion equations,
+ with assumptions remaining to discharge*)
+ standard (induction RS (rules RS conjI)))
+ end
+
+fun defer thy congs fid seqs =
+ defer_i thy congs fid (map (read_term thy) seqs)
+ handle U.ERR {mesg,...} => error mesg;
+end;
+
+end;