--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/BNF_Examples/IsaFoR_Datatypes.thy Mon Jul 21 18:04:08 2014 +0200
@@ -0,0 +1,380 @@
+(* Title: HOL/BNF_Examples/IsaFoR_Datatypes.thy
+ Author: René Thiemann
+ Copyright 2014
+
+Benchmark of datatypes defined in IsaFoR
+*)
+
+theory IsaFoR_Datatypes
+imports
+ Real
+begin
+
+datatype_new ('f, 'l) lab =
+ Lab "('f, 'l) lab" 'l
+| FunLab "('f, 'l) lab" "('f, 'l) lab list"
+| UnLab 'f
+| Sharp "('f, 'l) lab"
+
+datatype_new 'f projL = Projection "(('f \<times> nat) \<times> nat) list"
+
+datatype_new ('f, 'v) "term" = Var 'v | Fun 'f "('f, 'v) term list"
+datatype_new ('f, 'v) ctxt =
+ Hole ("\<box>")
+| More 'f "('f, 'v) term list" "('f, 'v) ctxt" "('f, 'v) term list"
+
+
+type_synonym ('f, 'v) rule = "('f, 'v) term \<times> ('f, 'v) term"
+type_synonym ('f, 'v) trs = "('f, 'v) rule set"
+
+type_synonym ('f, 'v) rules = "('f,'v) rule list"
+type_synonym ('f, 'l, 'v) ruleLL = "(('f, 'l) lab, 'v) rule"
+type_synonym ('f, 'l, 'v) trsLL = "(('f, 'l) lab, 'v) rules"
+type_synonym ('f, 'l, 'v) termsLL = "(('f, 'l) lab, 'v) term list"
+datatype_new pos = Empty ("\<epsilon>") | PCons "nat" "pos" (infixr "<#" 70)
+type_synonym ('f, 'v) prseq = "(pos \<times> ('f, 'v) rule \<times> bool \<times> ('f, 'v) term) list"
+type_synonym ('f, 'v) rseq = "(pos \<times> ('f, 'v) rule \<times> ('f, 'v) term) list"
+
+type_synonym ('f, 'l, 'v) rseqL = "((('f, 'l) lab, 'v) rule \<times> (('f, 'l) lab, 'v) rseq) list"
+type_synonym ('f, 'l, 'v) dppLL =
+ "bool \<times> bool \<times> ('f, 'l, 'v) trsLL \<times> ('f, 'l, 'v) trsLL \<times>
+ ('f, 'l, 'v) termsLL \<times>
+ ('f, 'l, 'v) trsLL \<times> ('f, 'l, 'v) trsLL"
+
+type_synonym ('f, 'l, 'v) qreltrsLL =
+ "bool \<times> ('f, 'l, 'v) termsLL \<times> ('f, 'l, 'v) trsLL \<times> ('f, 'l, 'v) trsLL"
+
+type_synonym ('f, 'l, 'v) qtrsLL =
+ "bool \<times> ('f, 'l, 'v) termsLL \<times> ('f, 'l, 'v) trsLL"
+
+datatype_new location = H | A | B | R
+
+type_synonym ('f,'v)forb_pattern = "('f,'v)ctxt \<times> ('f,'v)term \<times> location"
+type_synonym ('f,'v)forb_patterns = "('f,'v)forb_pattern set"
+
+type_synonym ('f, 'l, 'v) fptrsLL =
+ "(('f, 'l)lab, 'v) forb_pattern list \<times> ('f, 'l, 'v) trsLL"
+
+type_synonym ('f, 'l, 'v) prob = "('f, 'l, 'v) qreltrsLL + ('f, 'l, 'v) dppLL"
+
+type_synonym ('f, 'a) lpoly_inter = "'f \<times> nat \<Rightarrow> ('a \<times> 'a list)"
+type_synonym ('f, 'a) lpoly_interL = "(('f \<times> nat) \<times> ('a \<times> 'a list)) list"
+
+type_synonym 'v monom = "('v \<times> nat)list"
+type_synonym ('v,'a)poly = "('v monom \<times> 'a)list"
+type_synonym ('f,'a)poly_inter_list = "(('f \<times> nat) \<times> (nat,'a)poly)list"
+type_synonym 'a vec = "'a list"
+type_synonym 'a mat = "'a vec list"
+
+
+datatype_new arctic = MinInfty | Num_arc int
+datatype_new 'a arctic_delta = MinInfty_delta | Num_arc_delta 'a
+datatype_new order_tag = Lex | Mul
+
+type_synonym 'f status_prec_repr = "(('f \<times> nat) \<times> (nat \<times> order_tag))list"
+datatype_new af_entry = Collapse nat | AFList "nat list"
+type_synonym 'f afs_list = "(('f \<times> nat) \<times> af_entry)list"
+type_synonym 'f prec_weight_repr = "(('f \<times> nat) \<times> (nat \<times> nat \<times> (nat list option)))list \<times> nat"
+
+
+datatype_new 'f redtriple_impl =
+ Int_carrier "('f, int) lpoly_interL"
+ | Int_nl_carrier "('f, int) poly_inter_list"
+ | Rat_carrier "('f, rat) lpoly_interL"
+ | Rat_nl_carrier rat "('f, rat) poly_inter_list"
+ | Real_carrier "('f, real) lpoly_interL"
+ | Real_nl_carrier real "('f, real) poly_inter_list"
+ | Arctic_carrier "('f, arctic) lpoly_interL"
+ | Arctic_rat_carrier "('f, rat arctic_delta) lpoly_interL"
+ | Int_mat_carrier nat nat "('f, int mat) lpoly_interL"
+ | Rat_mat_carrier nat nat "('f, rat mat) lpoly_interL"
+ | Real_mat_carrier nat nat "('f, real mat) lpoly_interL"
+ | Arctic_mat_carrier nat "('f, arctic mat) lpoly_interL"
+ | Arctic_rat_mat_carrier nat "('f, rat arctic_delta mat) lpoly_interL"
+ | RPO "'f status_prec_repr" "'f afs_list"
+ | KBO "'f prec_weight_repr" "'f afs_list"
+
+datatype_new list_order_type = MS_Ext | Max_Ext | Min_Ext | Dms_Ext
+type_synonym 'f scnp_af = "(('f \<times> nat) \<times> (nat \<times> nat) list) list"
+
+datatype_new 'f root_redtriple_impl = SCNP list_order_type "'f scnp_af" "'f redtriple_impl"
+
+type_synonym 'f sig_map_list = "(('f \<times> nat) \<times> 'f list) list"
+type_synonym ('f,'v) uncurry_info = "'f \<times> 'f sig_map_list \<times> ('f,'v)rules \<times> ('f,'v)rules"
+
+datatype_new arithFun =
+ Arg nat
+| Const nat
+| Sum "arithFun list"
+| Max "arithFun list"
+| Min "arithFun list"
+| Prod "arithFun list"
+| IfEqual arithFun arithFun arithFun arithFun
+
+datatype_new 'f sl_inter = SL_Inter nat "(('f \<times> nat) \<times> arithFun) list"
+datatype_new ('f,'v)sl_variant = Rootlab "('f \<times> nat) option" | Finitelab "'f sl_inter" | QuasiFinitelab "'f sl_inter" 'v
+
+type_synonym ('f,'v)crit_pair_joins = "(('f,'v)term \<times> ('f,'v)rseq \<times> ('f,'v)term \<times> ('f,'v)rseq)list"
+datatype_new 'f join_info = Guided "('f,string)crit_pair_joins" | Join_NF | Join_BFS nat
+
+type_synonym unknown_info = string
+
+type_synonym dummy_prf = unit
+
+
+datatype_new ('f,'v)complex_constant_removal_prf = Complex_Constant_Removal_Proof
+ "('f,'v)term"
+ "(('f,'v)rule \<times> ('f,'v)rule) list"
+
+datatype_new ('f,'v)cond_constraint
+ = CC_cond bool "('f,'v)rule"
+ | CC_rewr "('f,'v)term" "('f,'v)term"
+ | CC_impl "('f,'v)cond_constraint list" "('f,'v)cond_constraint"
+ | CC_all 'v "('f,'v)cond_constraint"
+
+type_synonym ('f, 'v, 'w) gsubstL = "('v \<times> ('f, 'w) term) list"
+type_synonym ('f, 'v) substL = "('f, 'v, 'v) gsubstL"
+
+datatype_new ('f,'v)cond_constraint_prf =
+ Final
+| Delete_Condition "('f,'v)cond_constraint" "('f,'v)cond_constraint_prf"
+| Different_Constructor "('f,'v)cond_constraint"
+| Same_Constructor "('f,'v)cond_constraint" "('f,'v)cond_constraint" "('f,'v)cond_constraint_prf"
+| Variable_Equation 'v "('f,'v)term" "('f,'v)cond_constraint" "('f,'v)cond_constraint_prf"
+| Funarg_Into_Var "('f,'v)cond_constraint" nat 'v "('f,'v)cond_constraint" "('f,'v)cond_constraint_prf"
+| Simplify_Condition "('f,'v)cond_constraint" "('f,'v)substL" "('f,'v)cond_constraint" "('f,'v)cond_constraint_prf"
+| Induction "('f,'v)cond_constraint" "('f,'v)cond_constraint list" "(('f,'v)rule \<times> (('f,'v)term \<times> 'v list) list \<times> ('f,'v)cond_constraint \<times> ('f,'v)cond_constraint_prf) list"
+
+
+datatype_new ('f,'v)cond_red_pair_prf = Cond_Red_Pair_Prf
+ 'f
+ "(('f,'v)cond_constraint \<times> ('f,'v)rules \<times> ('f,'v)cond_constraint_prf) list"
+ nat
+ nat
+
+datatype_new ('q,'f)ta_rule = TA_rule 'f "'q list" 'q ("_ _ \<rightarrow> _")
+datatype_new ('q,'f)tree_automaton = Tree_Automaton "'q list" "('q,'f)ta_rule list" "('q \<times> 'q)list"
+datatype_new 'q ta_relation = Decision_Proc | Id_Relation | Some_Relation "('q \<times> 'q) list"
+
+datatype_new boundstype = Roof | Match
+datatype_new ('f,'q)bounds_info = Bounds_Info boundstype nat "'q list" "('q, 'f \<times> nat) tree_automaton" "'q ta_relation"
+
+datatype_new ('f, 'v) pat_eqv_prf =
+ Pat_Dom_Renaming "('f, 'v) substL"
+| Pat_Irrelevant "('f, 'v) substL" "('f, 'v) substL"
+| Pat_Simplify "('f, 'v) substL" "('f, 'v) substL"
+
+datatype_new pat_rule_pos = Pat_Base | Pat_Pump | Pat_Close
+
+datatype_new ('f, 'v) pat_rule_prf =
+ Pat_OrigRule "('f, 'v) rule" bool
+| Pat_InitPump "('f, 'v) pat_rule_prf" "('f, 'v) substL" "('f, 'v) substL"
+| Pat_InitPumpCtxt "('f, 'v) pat_rule_prf" "('f, 'v) substL" pos 'v
+| Pat_Equiv "('f, 'v) pat_rule_prf" bool "('f, 'v) pat_eqv_prf"
+| Pat_Narrow "('f, 'v) pat_rule_prf" "('f, 'v) pat_rule_prf" pos
+| Pat_Inst "('f, 'v) pat_rule_prf" "('f, 'v) substL" pat_rule_pos
+| Pat_Rewr "('f, 'v) pat_rule_prf" "('f, 'v) term \<times> ('f, 'v) rseq" pat_rule_pos 'v
+| Pat_Exp_Sigma "('f, 'v) pat_rule_prf" nat
+
+datatype_new ('f, 'v) non_loop_prf =
+ Non_Loop_Prf "('f, 'v) pat_rule_prf" "('f, 'v) substL" "('f, 'v) substL" nat nat pos
+
+
+datatype_new ('f, 'l, 'v) problem =
+ SN_TRS "('f,'l,'v)qreltrsLL"
+| SN_FP_TRS "('f,'l,'v)fptrsLL"
+| Finite_DPP "('f,'l,'v) dppLL"
+| Unknown_Problem unknown_info
+| Not_SN_TRS "('f,'l,'v)qtrsLL"
+| Not_RelSN_TRS "('f,'l,'v)qreltrsLL"
+| Infinite_DPP "('f,'l,'v) dppLL"
+| Not_SN_FP_TRS "('f,'l,'v)fptrsLL"
+declare [[bnf_timing]]
+datatype_new ('f, 'l, 'v, 'a, 'b, 'c, 'd, 'e) generic_assm_proof =
+ SN_assm_proof "('f,'l,'v)qreltrsLL" 'a
+| Finite_assm_proof "('f,'l,'v)dppLL" 'b
+| SN_FP_assm_proof "('f,'l,'v)fptrsLL" 'c
+| Not_SN_assm_proof "('f,'l,'v)qtrsLL" 'a
+| Infinite_assm_proof "('f,'l,'v)dppLL" 'b
+| Not_RelSN_assm_proof "('f,'l,'v)qreltrsLL" 'c
+| Not_SN_FP_assm_proof "('f,'l,'v)fptrsLL" 'd
+| Unknown_assm_proof unknown_info 'e
+
+type_synonym ('f,'l,'v,'a,'b,'c,'d)assm_proof = "('f,'l,'v,'a,'b,'c,dummy_prf,'d)generic_assm_proof"
+
+datatype_new ('f, 'l, 'v) assm =
+ SN_assm "('f,'l,'v)problem list" "('f,'l,'v)qreltrsLL"
+| SN_FP_assm "('f,'l,'v)problem list" "('f,'l,'v)fptrsLL"
+| Finite_assm "('f,'l,'v)problem list" "('f,'l,'v)dppLL"
+| Unknown_assm "('f,'l,'v)problem list" unknown_info
+| Not_SN_assm "('f,'l,'v)problem list" "('f,'l,'v)qtrsLL"
+| Not_RelSN_assm "('f,'l,'v)problem list" "('f,'l,'v)qreltrsLL"
+| Not_SN_FP_assm "('f,'l,'v)problem list" "('f,'l,'v)fptrsLL"
+| Infinite_assm "('f,'l,'v)problem list" "('f,'l,'v)dppLL"
+
+fun satisfied :: "('f,'l,'v)problem \<Rightarrow> bool" where
+ "satisfied (SN_TRS t) = (t = t)"
+| "satisfied (SN_FP_TRS t) = (t \<noteq> t)"
+| "satisfied (Finite_DPP d) = (d \<noteq> d)"
+| "satisfied (Unknown_Problem s) = (s = ''foo'')"
+| "satisfied (Not_SN_TRS (nfs,q,r)) = (length q = length r)"
+| "satisfied (Not_RelSN_TRS (nfs,q,r,rw)) = (r = rw)"
+| "satisfied (Infinite_DPP d) = (d = d)"
+| "satisfied (Not_SN_FP_TRS t) = (t = t)"
+
+fun collect_assms :: "('tp \<Rightarrow> ('f,'l,'v) assm list)
+ \<Rightarrow> ('dpp \<Rightarrow> ('f,'l,'v) assm list)
+ \<Rightarrow> ('fptp \<Rightarrow> ('f,'l,'v) assm list)
+ \<Rightarrow> ('unk \<Rightarrow> ('f,'l,'v) assm list)
+ \<Rightarrow> ('f,'l,'v,'tp,'dpp,'fptp,'unk) assm_proof \<Rightarrow> ('f,'l,'v) assm list" where
+ "collect_assms tp dpp fptp unk (SN_assm_proof t prf) = tp prf"
+| "collect_assms tp dpp fptp unk (SN_FP_assm_proof t prf) = fptp prf"
+| "collect_assms tp dpp fptp unk (Finite_assm_proof d prf) = dpp prf"
+| "collect_assms tp dpp fptp unk (Unknown_assm_proof p prf) = unk prf"
+| "collect_assms _ _ _ _ _ = []"
+
+fun collect_neg_assms :: "('tp \<Rightarrow> ('f,'l,'v) assm list)
+ \<Rightarrow> ('dpp \<Rightarrow> ('f,'l,'v) assm list)
+ \<Rightarrow> ('rtp \<Rightarrow> ('f,'l,'v) assm list)
+ \<Rightarrow> ('fptp \<Rightarrow> ('f,'l,'v) assm list)
+ \<Rightarrow> ('unk \<Rightarrow> ('f,'l,'v) assm list)
+ \<Rightarrow> ('f,'l,'v,'tp,'dpp,'rtp,'fptp,'unk) generic_assm_proof \<Rightarrow> ('f,'l,'v) assm list" where
+ "collect_neg_assms tp dpp rtp fptp unk (Not_SN_assm_proof t prf) = tp prf"
+| "collect_neg_assms tp dpp rtp fptp unk (Infinite_assm_proof d prf) = dpp prf"
+| "collect_neg_assms tp dpp rtp fptp unk (Not_RelSN_assm_proof t prf) = rtp prf"
+| "collect_neg_assms tp dpp rtp fptp unk (Not_SN_FP_assm_proof t prf) = fptp prf"
+| "collect_neg_assms tp dpp rtp fptp unk (Unknown_assm_proof p prf) = unk prf"
+| "collect_neg_assms tp dpp rtp fptp unk _ = []"
+
+
+
+datatype_new ('f, 'l, 'v) dp_nontermination_proof =
+ DP_Loop "(('f,'l)lab, 'v) term" "(('f,'l)lab, 'v) prseq" "(('f,'l)lab, 'v) substL" "(('f,'l)lab, 'v) ctxt"
+| DP_Nonloop "(('f,'l)lab, 'v)non_loop_prf"
+| DP_Rule_Removal "('f,'l,'v)trsLL option" "('f,'l,'v)trsLL option" "('f,'l,'v) dp_nontermination_proof"
+| DP_Q_Increase "('f,'l,'v)termsLL" "('f,'l,'v) dp_nontermination_proof"
+| DP_Q_Reduction "('f,'l,'v)termsLL" "('f,'l,'v) dp_nontermination_proof"
+| DP_Termination_Switch "('f,'l)lab join_info" "('f,'l,'v) dp_nontermination_proof"
+| DP_Instantiation "('f,'l,'v)trsLL" "('f,'l,'v) dp_nontermination_proof"
+| DP_Rewriting "('f,'l,'v)trsLL option" "('f,'l,'v)ruleLL" "('f,'l,'v)ruleLL" "('f,'l,'v)ruleLL" "(('f,'l)lab,'v)rule" pos "('f,'l,'v) dp_nontermination_proof"
+| DP_Narrowing "('f,'l,'v)ruleLL" pos "('f,'l,'v)trsLL" "('f,'l,'v) dp_nontermination_proof"
+| DP_Assume_Infinite "('f, 'l, 'v) dppLL"
+ "('f,'l,'v,('f, 'l, 'v) trs_nontermination_proof,
+ ('f, 'l, 'v) dp_nontermination_proof,
+ ('f, 'l, 'v) reltrs_nontermination_proof,
+ ('f, 'l, 'v) fp_nontermination_proof,
+ ('f, 'l, 'v) neg_unknown_proof) generic_assm_proof list"
+ and
+('f,'l,'v) "trs_nontermination_proof" =
+ TRS_Loop "(('f,'l)lab, 'v) term" "(('f,'l)lab, 'v) rseq" "(('f,'l)lab, 'v) substL" "(('f,'l)lab, 'v) ctxt"
+| TRS_Not_Well_Formed
+| TRS_Rule_Removal "('f,'l,'v)trsLL" "('f,'l,'v) trs_nontermination_proof"
+| TRS_String_Reversal "('f,'l,'v) trs_nontermination_proof"
+| TRS_DP_Trans "('f,'l,'v)trsLL" "('f,'l,'v) dp_nontermination_proof"
+| TRS_Nonloop "(('f,'l)lab,'v) non_loop_prf"
+| TRS_Q_Increase "('f,'l,'v)termsLL" "('f,'l,'v) trs_nontermination_proof"
+| TRS_Assume_Not_SN "('f, 'l, 'v)qtrsLL"
+ "('f,'l,'v,('f, 'l, 'v) trs_nontermination_proof,
+ ('f, 'l, 'v) dp_nontermination_proof,
+ ('f, 'l, 'v) reltrs_nontermination_proof,
+ ('f, 'l, 'v) fp_nontermination_proof,
+ ('f, 'l, 'v) neg_unknown_proof) generic_assm_proof list"
+ and
+('f,'l,'v)"reltrs_nontermination_proof" =
+ Rel_Loop "(('f,'l)lab,'v) term" "(('f,'l)lab, 'v) prseq" "(('f,'l)lab, 'v) substL" "(('f,'l)lab, 'v) ctxt"
+| Rel_Not_Well_Formed
+| Rel_Rule_Removal "('f,'l,'v)trsLL option" "('f,'l,'v)trsLL option" "('f,'l,'v) reltrs_nontermination_proof"
+| Rel_R_Not_SN "('f,'l,'v) trs_nontermination_proof"
+| Rel_TRS_Assume_Not_SN "('f, 'l, 'v)qreltrsLL"
+ "('f,'l,'v,('f, 'l, 'v) trs_nontermination_proof,
+ ('f, 'l, 'v) dp_nontermination_proof,
+ ('f, 'l, 'v) reltrs_nontermination_proof,
+ ('f, 'l, 'v) fp_nontermination_proof,
+ ('f, 'l, 'v) neg_unknown_proof) generic_assm_proof list"
+ and
+ ('f, 'l, 'v) "fp_nontermination_proof" =
+ FPTRS_Loop "(('f,'l)lab, 'v) term" "(('f,'l)lab, 'v) rseq" "(('f,'l)lab, 'v) substL" "(('f,'l)lab, 'v) ctxt"
+| FPTRS_Rule_Removal "('f,'l,'v)trsLL" "('f,'l,'v) fp_nontermination_proof"
+| FPTRS_Assume_Not_SN "('f, 'l, 'v)fptrsLL"
+ "('f,'l,'v,('f, 'l, 'v) trs_nontermination_proof,
+ ('f, 'l, 'v) dp_nontermination_proof,
+ ('f, 'l, 'v) reltrs_nontermination_proof,
+ ('f, 'l, 'v) fp_nontermination_proof,
+ ('f, 'l, 'v) neg_unknown_proof) generic_assm_proof list"
+ and
+ ('f, 'l, 'v) neg_unknown_proof =
+ Assume_NT_Unknown unknown_info
+ "('f,'l,'v,('f, 'l, 'v) trs_nontermination_proof,
+ ('f, 'l, 'v) dp_nontermination_proof,
+ ('f, 'l, 'v) reltrs_nontermination_proof,
+ ('f, 'l, 'v) fp_nontermination_proof,
+ ('f, 'l, 'v) neg_unknown_proof) generic_assm_proof list"
+
+
+datatype_new ('f, 'l, 'v) dp_termination_proof =
+ P_is_Empty
+| Subterm_Criterion_Proc "('f, 'l) lab projL" "('f, 'l, 'v) rseqL"
+ "('f, 'l, 'v) trsLL" "('f, 'l, 'v) dp_termination_proof"
+| Redpair_Proc "('f,'l)lab root_redtriple_impl + ('f, 'l) lab redtriple_impl" "('f, 'l, 'v) trsLL" "('f, 'l, 'v) dp_termination_proof"
+| Redpair_UR_Proc "('f, 'l) lab root_redtriple_impl + ('f, 'l) lab redtriple_impl"
+ "('f, 'l, 'v) trsLL" "('f, 'l, 'v) trsLL" "('f, 'l, 'v) dp_termination_proof"
+| Usable_Rules_Proc "('f, 'l, 'v) trsLL" "('f, 'l, 'v) dp_termination_proof"
+| Dep_Graph_Proc "(('f, 'l, 'v) dp_termination_proof option \<times> ('f, 'l, 'v) trsLL) list"
+| Mono_Redpair_Proc "('f, 'l) lab redtriple_impl"
+ "('f, 'l, 'v) trsLL" "('f, 'l, 'v) trsLL" "('f, 'l, 'v) dp_termination_proof"
+| Mono_Redpair_UR_Proc "('f, 'l) lab redtriple_impl"
+ "('f, 'l, 'v) trsLL" "('f, 'l, 'v) trsLL" "('f, 'l, 'v) trsLL" "('f, 'l, 'v) dp_termination_proof"
+| Size_Change_Subterm_Proc "((('f, 'l) lab, 'v) rule \<times> ((nat \<times> nat) list \<times> (nat \<times> nat) list)) list"
+| Size_Change_Redpair_Proc "('f, 'l) lab redtriple_impl" "('f, 'l, 'v) trsLL option"
+ "((('f, 'l) lab, 'v) rule \<times> ((nat \<times> nat) list \<times> (nat \<times> nat) list)) list"
+| Uncurry_Proc "nat option" "(('f, 'l) lab, 'v) uncurry_info"
+ "('f, 'l, 'v) trsLL" "('f, 'l, 'v) trsLL" "('f, 'l, 'v) dp_termination_proof"
+| Fcc_Proc "('f, 'l) lab" "(('f, 'l) lab, 'v) ctxt list"
+ "('f, 'l, 'v) trsLL" "('f, 'l, 'v) trsLL" "('f, 'l, 'v) dp_termination_proof"
+| Split_Proc
+ "('f, 'l, 'v) trsLL" "('f, 'l, 'v) trsLL"
+ "('f, 'l, 'v) dp_termination_proof" "('f, 'l, 'v) dp_termination_proof"
+| Semlab_Proc
+ "(('f, 'l) lab, 'v) sl_variant" "('f, 'l, 'v) trsLL"
+ "(('f, 'l) lab, 'v) term list" "('f, 'l, 'v) trsLL"
+ "('f, 'l, 'v) dp_termination_proof"
+| Switch_Innermost_Proc "('f, 'l) lab join_info" "('f, 'l, 'v) dp_termination_proof"
+| Rewriting_Proc
+ "('f, 'l, 'v) trsLL option" "('f, 'l, 'v) ruleLL" "('f, 'l, 'v) ruleLL"
+ "('f, 'l, 'v) ruleLL" "('f, 'l, 'v) ruleLL" pos "('f, 'l, 'v) dp_termination_proof"
+| Instantiation_Proc "('f, 'l, 'v) ruleLL" "('f, 'l, 'v) trsLL" "('f, 'l, 'v) dp_termination_proof"
+| Forward_Instantiation_Proc
+ "('f, 'l, 'v) ruleLL" "('f, 'l, 'v) trsLL" "('f, 'l, 'v) trsLL option" "('f, 'l, 'v) dp_termination_proof"
+| Narrowing_Proc "('f, 'l, 'v) ruleLL" pos "('f, 'l, 'v) trsLL" "('f, 'l, 'v) dp_termination_proof"
+| Assume_Finite
+ "('f, 'l, 'v) dppLL" "('f,'l,'v,('f, 'l, 'v) trs_termination_proof,('f, 'l, 'v) dp_termination_proof,('f, 'l, 'v) fptrs_termination_proof,('f, 'l, 'v) unknown_proof) assm_proof list"
+| Unlab_Proc "('f, 'l, 'v) trsLL" "('f, 'l, 'v) trsLL" "('f, 'l, 'v) dp_termination_proof"
+| Q_Reduction_Proc "('f, 'l, 'v) termsLL" "('f, 'l, 'v) dp_termination_proof"
+| Complex_Constant_Removal_Proc "(('f,'l)lab,'v)complex_constant_removal_prf" "('f, 'l, 'v) dp_termination_proof"
+| General_Redpair_Proc
+ "('f, 'l) lab redtriple_impl" "('f, 'l, 'v) trsLL" "('f, 'l, 'v) trsLL"
+ "(('f, 'l) lab, 'v) cond_red_pair_prf" "('f, 'l, 'v) dp_termination_proof list"
+| To_Trs_Proc "('f, 'l, 'v) trs_termination_proof"
+and ('f, 'l, 'v) trs_termination_proof =
+ DP_Trans bool bool "(('f, 'l) lab, 'v) rules" "('f, 'l, 'v) dp_termination_proof"
+| Rule_Removal "('f, 'l) lab redtriple_impl" "('f, 'l, 'v) trsLL" "('f, 'l, 'v)trs_termination_proof"
+| String_Reversal "('f, 'l, 'v) trs_termination_proof"
+| Bounds "(('f, 'l) lab, 'v) bounds_info"
+| Uncurry "(('f, 'l) lab, 'v) uncurry_info" "('f, 'l, 'v) trsLL" "('f, 'l, 'v) trs_termination_proof"
+| Semlab
+ "(('f, 'l) lab, 'v) sl_variant" "(('f, 'l) lab, 'v) term list"
+ "('f, 'l, 'v) trsLL" "('f, 'l, 'v) trs_termination_proof"
+| R_is_Empty
+| Fcc "(('f, 'l) lab, 'v) ctxt list" "('f, 'l, 'v) trsLL" "('f, 'l, 'v) trs_termination_proof"
+| Split "('f, 'l, 'v) trsLL" "('f, 'l, 'v) trs_termination_proof" "('f, 'l, 'v) trs_termination_proof"
+| Switch_Innermost "('f, 'l) lab join_info" "('f, 'l, 'v) trs_termination_proof"
+| Drop_Equality "('f, 'l, 'v) trs_termination_proof"
+| Remove_Nonapplicable_Rules "('f, 'l, 'v) trsLL" "('f, 'l, 'v) trs_termination_proof"
+| Assume_SN "('f, 'l, 'v) qreltrsLL" "('f,'l,'v,('f, 'l, 'v) trs_termination_proof,('f, 'l, 'v) dp_termination_proof,('f, 'l, 'v) fptrs_termination_proof,('f, 'l, 'v) unknown_proof) assm_proof list"
+and ('f, 'l, 'v) unknown_proof =
+ Assume_Unknown unknown_info "('f,'l,'v,('f, 'l, 'v) trs_termination_proof,('f, 'l, 'v) dp_termination_proof,('f, 'l, 'v) fptrs_termination_proof,('f, 'l, 'v) unknown_proof) assm_proof list"
+and ('f, 'l, 'v) fptrs_termination_proof =
+ Assume_FP_SN "('f,'l,'v)fptrsLL" "('f,'l,'v,('f, 'l, 'v) trs_termination_proof,('f, 'l, 'v) dp_termination_proof,('f, 'l, 'v) fptrs_termination_proof,('f, 'l, 'v) unknown_proof) assm_proof list"
+
+
+end