File ‹Tools/BNF/bnf_lfp_util.ML›
signature BNF_LFP_UTIL =
sig
val mk_bij_betw: term -> term -> term -> term
val mk_cardSuc: term -> term
val mk_not_empty: term -> term
val mk_not_eq: term -> term -> term
val mk_rapp: term -> typ -> term
val mk_relChain: term -> term -> term
val mk_underS: term -> term
val mk_worec: term -> term -> term
end;
structure BNF_LFP_Util : BNF_LFP_UTIL =
struct
open BNF_Util
fun mk_rapp arg T = Term.absdummy (fastype_of arg --> T) (Bound 0 $ arg);
fun mk_underS r =
let val T = fst (dest_relT (fastype_of r));
in Const (\<^const_name>‹underS›, mk_relT (T, T) --> T --> HOLogic.mk_setT T) $ r end;
fun mk_worec r f =
let val (A, AB) = apfst domain_type (dest_funT (fastype_of f));
in Const (\<^const_name>‹wo_rel.worec›, mk_relT (A, A) --> (AB --> AB) --> AB) $ r $ f end;
fun mk_relChain r f =
let val (A, AB) = `domain_type (fastype_of f);
in Const (\<^const_name>‹relChain›, mk_relT (A, A) --> AB --> HOLogic.boolT) $ r $ f end;
fun mk_cardSuc r =
let val T = fst (dest_relT (fastype_of r));
in Const (\<^const_name>‹cardSuc›, mk_relT (T, T) --> mk_relT (`I (HOLogic.mk_setT T))) $ r end;
fun mk_bij_betw f A B =
Const (\<^const_name>‹bij_betw›,
fastype_of f --> fastype_of A --> fastype_of B --> HOLogic.boolT) $ f $ A $ B;
fun mk_not_eq x y = HOLogic.mk_not (HOLogic.mk_eq (x, y));
fun mk_not_empty B = mk_not_eq B (HOLogic.mk_set (HOLogic.dest_setT (fastype_of B)) []);
end;