(* Title: HOL/Tools/Function/relation.ML
Author: Alexander Krauss, TU Muenchen
A package for general recursive function definitions.
Method "relation" to commence a termination proof using a user-specified relation.
*)
signature FUNCTION_RELATION =
sig
val relation_tac: Proof.context -> term -> int -> tactic
val setup: theory -> theory
end
structure Function_Relation : FUNCTION_RELATION =
struct
fun gen_inst_state_tac prep ctxt rel st =
case Term.add_vars (prop_of st) [] of
[v as (_, T)] =>
let
val cert = Thm.cterm_of (ProofContext.theory_of ctxt)
val rel' = prep T (singleton (Variable.polymorphic ctxt) rel)
|> cert
val st' = Thm.incr_indexes (#maxidx (Thm.rep_cterm rel') + 1) st (*FIXME??*)
in
PRIMITIVE (Drule.cterm_instantiate [(cert (Var v), rel')]) st'
end
| _ => Seq.empty;
fun gen_relation_tac prep ctxt rel i =
TRY (Function_Common.apply_termination_rule ctxt i)
THEN gen_inst_state_tac prep ctxt rel
val relation_tac = gen_relation_tac (K I)
fun relation_meth rel ctxt = SIMPLE_METHOD'
(gen_relation_tac (fn T => map_types Type_Infer.paramify_vars
#> Type.constraint T #> Syntax.check_term ctxt)
ctxt rel)
val setup =
Method.setup @{binding relation} (Args.term >> relation_meth)
"proves termination using a user-specified wellfounded relation"
end