(* 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 inst_state_tac ctxt rel st =
let
val cert = Thm.cterm_of (ProofContext.theory_of ctxt)
val rel' = cert (singleton (Variable.polymorphic ctxt) rel)
val st' = Thm.incr_indexes (#maxidx (Thm.rep_cterm rel') + 1) st
in case Term.add_vars (prop_of st') [] of
[v] =>
PRIMITIVE (Drule.cterm_instantiate [(cert (Var v), rel')]) st'
| _ => Seq.empty
end
fun relation_tac ctxt rel i =
TRY (Function_Common.apply_termination_rule ctxt i)
THEN inst_state_tac ctxt rel
val setup =
Method.setup @{binding relation}
(Args.term >> (fn rel => fn ctxt => SIMPLE_METHOD' (relation_tac ctxt rel)))
"proves termination using a user-specified wellfounded relation"
end