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(* 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 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 Quotient_conv: conv -> conv -> conv -> conv -> conv
val Quotient_R_conv: conv -> conv
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 same_type_constrs: typ * typ -> bool
val Targs: typ -> typ list
val Tname: typ -> string
val is_rel_fun: term -> bool
val relation_types: typ -> typ * typ
val map_interrupt: ('a -> 'b option) -> 'a list -> 'b list option
val conceal_naming_result: (local_theory -> 'a * local_theory) -> local_theory -> 'a * local_theory
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 dest_Quotient (Const (\<^const_name>\<open>Quotient\<close>, _) $ 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 Thm.prop_of) quot_thm of
(rel, _, _, _) => rel
fun quot_thm_abs quot_thm =
case (dest_Quotient o HOLogic.dest_Trueprop o Thm.prop_of) quot_thm of
(_, abs, _, _) => abs
fun quot_thm_rep quot_thm =
case (dest_Quotient o HOLogic.dest_Trueprop o Thm.prop_of) quot_thm of
(_, _, rep, _) => rep
fun quot_thm_crel quot_thm =
case (dest_Quotient o HOLogic.dest_Trueprop o Thm.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 Quotient_conv R_conv Abs_conv Rep_conv T_conv = Conv.combination_conv (Conv.combination_conv
(Conv.combination_conv (Conv.arg_conv R_conv) Abs_conv) Rep_conv) T_conv;
fun Quotient_R_conv R_conv = Quotient_conv R_conv Conv.all_conv Conv.all_conv Conv.all_conv;
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 (Thm.nprems_of thm) undisch thm
fun is_fun_type (Type (\<^type_name>\<open>fun\<close>, _)) = 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.try_conv (Conv.combination_conv (all_args_conv conv) conv) ctm
fun same_type_constrs (Type (r, _), Type (q, _)) = (r = q)
| same_type_constrs _ = false
fun Targs (Type (_, args)) = args
| Targs _ = []
fun Tname (Type (name, _)) = name
| Tname _ = ""
fun is_rel_fun (Const (\<^const_name>\<open>rel_fun\<close>, _) $ _ $ _) = true
| is_rel_fun _ = false
fun relation_types typ =
case strip_type typ of
([typ1, typ2], \<^typ>\<open>bool\<close>) => (typ1, typ2)
| _ => error "relation_types: not a relation"
fun map_interrupt f l =
let
fun map_interrupt' _ [] l = SOME (rev l)
| map_interrupt' f (x::xs) l = (case f x of
NONE => NONE
| SOME v => map_interrupt' f xs (v::l))
in
map_interrupt' f l []
end
fun conceal_naming_result f lthy =
lthy |> Proof_Context.concealed |> f ||> Proof_Context.restore_naming lthy;
end
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