(* Title: HOL/Tools/function_package/fundef_lib.ML
Author: Alexander Krauss, TU Muenchen
A package for general recursive function definitions.
Some fairly general functions that should probably go somewhere else...
*)
structure FundefLib = struct
fun map_option f NONE = NONE
| map_option f (SOME x) = SOME (f x);
fun fold_option f NONE y = y
| fold_option f (SOME x) y = f x y;
fun fold_map_option f NONE y = (NONE, y)
| fold_map_option f (SOME x) y = apfst SOME (f x y);
(* Ex: "The variable" ^ plural " is" "s are" vs *)
fun plural sg pl [x] = sg
| plural sg pl _ = pl
(* lambda-abstracts over an arbitrarily nested tuple
==> hologic.ML? *)
fun tupled_lambda vars t =
case vars of
(Free v) => lambda (Free v) t
| (Var v) => lambda (Var v) t
| (Const ("Pair", Type ("fun", [Ta, Type ("fun", [Tb, _])]))) $ us $ vs =>
(HOLogic.split_const (Ta,Tb, fastype_of t)) $ (tupled_lambda us (tupled_lambda vs t))
| _ => raise Match
fun dest_all (Const ("all", _) $ Abs (a as (_,T,_))) =
let
val (n, body) = Term.dest_abs a
in
(Free (n, T), body)
end
| dest_all _ = raise Match
(* Removes all quantifiers from a term, replacing bound variables by frees. *)
fun dest_all_all (t as (Const ("all",_) $ _)) =
let
val (v,b) = dest_all t
val (vs, b') = dest_all_all b
in
(v :: vs, b')
end
| dest_all_all t = ([],t)
(* FIXME: similar to Variable.focus *)
fun dest_all_all_ctx ctx (Const ("all", _) $ Abs (a as (n,T,b))) =
let
val [(n', _)] = Variable.variant_frees ctx [] [(n,T)]
val (_, ctx') = ProofContext.add_fixes [(Binding.name n', SOME T, NoSyn)] ctx
val (n'', body) = Term.dest_abs (n', T, b)
val _ = (n' = n'') orelse error "dest_all_ctx"
(* Note: We assume that n' does not occur in the body. Otherwise it would be fixed. *)
val (ctx'', vs, bd) = dest_all_all_ctx ctx' body
in
(ctx'', (n', T) :: vs, bd)
end
| dest_all_all_ctx ctx t =
(ctx, [], t)
fun map3 _ [] [] [] = []
| map3 f (x :: xs) (y :: ys) (z :: zs) = f x y z :: map3 f xs ys zs
| map3 _ _ _ _ = raise Library.UnequalLengths;
fun map4 _ [] [] [] [] = []
| map4 f (x :: xs) (y :: ys) (z :: zs) (u :: us) = f x y z u :: map4 f xs ys zs us
| map4 _ _ _ _ _ = raise Library.UnequalLengths;
fun map6 _ [] [] [] [] [] [] = []
| map6 f (x :: xs) (y :: ys) (z :: zs) (u :: us) (v :: vs) (w :: ws) = f x y z u v w :: map6 f xs ys zs us vs ws
| map6 _ _ _ _ _ _ _ = raise Library.UnequalLengths;
fun map7 _ [] [] [] [] [] [] [] = []
| map7 f (x :: xs) (y :: ys) (z :: zs) (u :: us) (v :: vs) (w :: ws) (b :: bs) = f x y z u v w b :: map7 f xs ys zs us vs ws bs
| map7 _ _ _ _ _ _ _ _ = raise Library.UnequalLengths;
(* forms all "unordered pairs": [1, 2, 3] ==> [(1, 1), (1, 2), (1, 3), (2, 2), (2, 3), (3, 3)] *)
(* ==> library *)
fun unordered_pairs [] = []
| unordered_pairs (x::xs) = map (pair x) (x::xs) @ unordered_pairs xs
(* Replaces Frees by name. Works with loose Bounds. *)
fun replace_frees assoc =
map_aterms (fn c as Free (n, _) => the_default c (AList.lookup (op =) assoc n)
| t => t)
fun rename_bound n (Q $ Abs(_, T, b)) = (Q $ Abs(n, T, b))
| rename_bound n _ = raise Match
fun mk_forall_rename (n, v) =
rename_bound n o Logic.all v
fun forall_intr_rename (n, cv) thm =
let
val allthm = forall_intr cv thm
val (_ $ abs) = prop_of allthm
in
Thm.rename_boundvars abs (Abs (n, dummyT, Term.dummy_pattern dummyT)) allthm
end
(* Returns the frees in a term in canonical order, excluding the fixes from the context *)
fun frees_in_term ctxt t =
Term.add_frees t []
|> filter_out (Variable.is_fixed ctxt o fst)
|> rev
datatype proof_attempt = Solved of thm | Stuck of thm | Fail
fun try_proof cgoal tac =
case SINGLE tac (Goal.init cgoal) of
NONE => Fail
| SOME st => if Thm.no_prems st then Solved (Goal.finish st) else Stuck st
fun dest_binop_list cn (t as (Const (n, _) $ a $ b)) =
if cn = n then dest_binop_list cn a @ dest_binop_list cn b else [ t ]
| dest_binop_list _ t = [ t ]
(* separate two parts in a +-expression:
"a + b + c + d + e" --> "(a + b + d) + (c + e)"
Here, + can be any binary operation that is AC.
cn - The name of the binop-constructor (e.g. @{const_name Un})
ac - the AC rewrite rules for cn
is - the list of indices of the expressions that should become the first part
(e.g. [0,1,3] in the above example)
*)
fun regroup_conv neu cn ac is ct =
let
val mk = HOLogic.mk_binop cn
val t = term_of ct
val xs = dest_binop_list cn t
val js = 0 upto (length xs) - 1 \\ is
val ty = fastype_of t
val thy = theory_of_cterm ct
in
Goal.prove_internal []
(cterm_of thy
(Logic.mk_equals (t,
if is = []
then mk (Const (neu, ty), foldr1 mk (map (nth xs) js))
else if js = []
then mk (foldr1 mk (map (nth xs) is), Const (neu, ty))
else mk (foldr1 mk (map (nth xs) is), foldr1 mk (map (nth xs) js)))))
(K (rewrite_goals_tac ac
THEN rtac Drule.reflexive_thm 1))
end
(* instance for unions *)
fun regroup_union_conv t = regroup_conv @{const_name Set.empty} @{const_name Un}
(map (fn t => t RS eq_reflection) (@{thms "Un_ac"} @
@{thms "Un_empty_right"} @
@{thms "Un_empty_left"})) t
end