(* Title: HOL/Tools/Lifting/lifting_util.ML
Author: Ondrej Kuncar
General-purpose functions used by the Lifting package.
*)
signature LIFTING_UTIL =
sig
val MRSL: thm list * thm -> thm
val option_fold: 'b -> ('a -> 'b) -> 'a option -> 'b
val map_snd: ('b -> 'c) -> ('a * 'b) list -> ('a * 'c) list
val dest_Quotient: term -> term * term * term * term
val quot_thm_rel: thm -> term
val quot_thm_abs: thm -> term
val quot_thm_rep: thm -> term
val quot_thm_crel: thm -> term
val quot_thm_rty_qty: thm -> typ * typ
val undisch: thm -> thm
val undisch_all: thm -> thm
val is_fun_type: typ -> bool
val get_args: int -> term -> term list
val strip_args: int -> term -> term
val all_args_conv: conv -> conv
val is_Type: typ -> bool
val is_fun_rel: term -> bool
val relation_types: typ -> typ * typ
val mk_HOL_eq: thm -> thm
val safe_HOL_meta_eq: thm -> thm
end
structure Lifting_Util: LIFTING_UTIL =
struct
infix 0 MRSL
fun ants MRSL thm = fold (fn rl => fn thm => rl RS thm) ants thm
fun option_fold a _ NONE = a
| option_fold _ f (SOME x) = f x
fun map_snd f xs = map (fn (a, b) => (a, f b)) xs
fun dest_Quotient (Const (@{const_name Quotient}, _) $ rel $ abs $ rep $ cr)
= (rel, abs, rep, cr)
| dest_Quotient t = raise TERM ("dest_Quotient", [t])
(*
quot_thm_rel, quot_thm_abs, quot_thm_rep and quot_thm_rty_qty - simple functions
for destructing quotient theorems (Quotient R Abs Rep T).
*)
fun quot_thm_rel quot_thm =
case (dest_Quotient o HOLogic.dest_Trueprop o prop_of) quot_thm of
(rel, _, _, _) => rel
fun quot_thm_abs quot_thm =
case (dest_Quotient o HOLogic.dest_Trueprop o prop_of) quot_thm of
(_, abs, _, _) => abs
fun quot_thm_rep quot_thm =
case (dest_Quotient o HOLogic.dest_Trueprop o prop_of) quot_thm of
(_, _, rep, _) => rep
fun quot_thm_crel quot_thm =
case (dest_Quotient o HOLogic.dest_Trueprop o prop_of) quot_thm of
(_, _, _, crel) => crel
fun quot_thm_rty_qty quot_thm =
let
val abs = quot_thm_abs quot_thm
val abs_type = fastype_of abs
in
(domain_type abs_type, range_type abs_type)
end
fun undisch thm =
let
val assm = Thm.cprem_of thm 1
in
Thm.implies_elim thm (Thm.assume assm)
end
fun undisch_all thm = funpow (nprems_of thm) undisch thm
fun is_fun_type (Type (@{type_name fun}, _)) = true
| is_fun_type _ = false
fun get_args n = rev o fst o funpow_yield n (swap o dest_comb)
fun strip_args n = funpow n (fst o dest_comb)
fun all_args_conv conv ctm =
(Conv.combination_conv (Conv.try_conv (all_args_conv conv)) conv) ctm
fun is_Type (Type _) = true
| is_Type _ = false
fun is_fun_rel (Const (@{const_name "fun_rel"}, _) $ _ $ _) = true
| is_fun_rel _ = false
fun relation_types typ =
case strip_type typ of
([typ1, typ2], @{typ bool}) => (typ1, typ2)
| _ => error "relation_types: not a relation"
fun mk_HOL_eq r = r RS @{thm meta_eq_to_obj_eq}
fun safe_HOL_meta_eq r = mk_HOL_eq r handle Thm.THM _ => r
end