--- a/src/HOL/Tools/Function/decompose.ML Sat Jan 02 22:57:19 2010 +0100
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,100 +0,0 @@
-(* Title: HOL/Tools/Function/decompose.ML
- Author: Alexander Krauss, TU Muenchen
-
-Graph decomposition using "Shallow Dependency Pairs".
-*)
-
-signature DECOMPOSE =
-sig
-
- val derive_chains : Proof.context -> tactic
- -> (Termination.data -> int -> tactic)
- -> Termination.data -> int -> tactic
-
- val decompose_tac : Proof.context -> tactic
- -> Termination.ttac
-
-end
-
-structure Decompose : DECOMPOSE =
-struct
-
-structure TermGraph = Graph(type key = term val ord = TermOrd.fast_term_ord);
-
-
-fun derive_chains ctxt chain_tac cont D = Termination.CALLS (fn (cs, i) =>
- let
- val thy = ProofContext.theory_of ctxt
-
- fun prove_chain c1 c2 D =
- if is_some (Termination.get_chain D c1 c2) then D else
- let
- val goal = HOLogic.mk_eq (HOLogic.mk_binop @{const_name Relation.rel_comp} (c1, c2),
- Const (@{const_name Set.empty}, fastype_of c1))
- |> HOLogic.mk_Trueprop (* "C1 O C2 = {}" *)
-
- val chain = case Function_Lib.try_proof (cterm_of thy goal) chain_tac of
- Function_Lib.Solved thm => SOME thm
- | _ => NONE
- in
- Termination.note_chain c1 c2 chain D
- end
- in
- cont (fold_product prove_chain cs cs D) i
- end)
-
-
-fun mk_dgraph D cs =
- TermGraph.empty
- |> fold (fn c => TermGraph.new_node (c,())) cs
- |> fold_product (fn c1 => fn c2 =>
- if is_none (Termination.get_chain D c1 c2 |> the_default NONE)
- then TermGraph.add_edge (c1, c2) else I)
- cs cs
-
-
-fun ucomp_empty_tac T =
- REPEAT_ALL_NEW (rtac @{thm union_comp_emptyR}
- ORELSE' rtac @{thm union_comp_emptyL}
- ORELSE' SUBGOAL (fn (_ $ (_ $ (_ $ c1 $ c2) $ _), i) => rtac (T c1 c2) i))
-
-fun regroup_calls_tac cs = Termination.CALLS (fn (cs', i) =>
- let
- val is = map (fn c => find_index (curry op aconv c) cs') cs
- in
- CONVERSION (Conv.arg_conv (Conv.arg_conv (Function_Lib.regroup_union_conv is))) i
- end)
-
-
-fun solve_trivial_tac D = Termination.CALLS
-(fn ([c], i) =>
- (case Termination.get_chain D c c of
- SOME (SOME thm) => rtac @{thm wf_no_loop} i
- THEN rtac thm i
- | _ => no_tac)
- | _ => no_tac)
-
-fun decompose_tac' cont err_cont D = Termination.CALLS (fn (cs, i) =>
- let
- val G = mk_dgraph D cs
- val sccs = TermGraph.strong_conn G
-
- fun split [SCC] i = (solve_trivial_tac D i ORELSE cont D i)
- | split (SCC::rest) i =
- regroup_calls_tac SCC i
- THEN rtac @{thm wf_union_compatible} i
- THEN rtac @{thm less_by_empty} (i + 2)
- THEN ucomp_empty_tac (the o the oo Termination.get_chain D) (i + 2)
- THEN split rest (i + 1)
- THEN (solve_trivial_tac D i ORELSE cont D i)
- in
- if length sccs > 1 then split sccs i
- else solve_trivial_tac D i ORELSE err_cont D i
- end)
-
-fun decompose_tac ctxt chain_tac cont err_cont =
- derive_chains ctxt chain_tac
- (decompose_tac' cont err_cont)
-
-
-end