(* Author: Lukas Bulwahn, TU Muenchen
(Prototype of) A compiler from predicates specified by intro/elim rules
to equations.
*)
signature PREDICATE_COMPILE =
sig
type mode = int list option list * int list
val add_equations_of: string list -> theory -> theory
val register_predicate : (thm list * thm * int) -> theory -> theory
val is_registered : theory -> string -> bool
val fetch_pred_data : theory -> string -> (thm list * thm * int)
val predfun_intro_of: theory -> string -> mode -> thm
val predfun_elim_of: theory -> string -> mode -> thm
val strip_intro_concl: int -> term -> term * (term list * term list)
val predfun_name_of: theory -> string -> mode -> string
val all_preds_of : theory -> string list
val modes_of: theory -> string -> mode list
val intros_of: theory -> string -> thm list
val nparams_of: theory -> string -> int
val add_intro: thm -> theory -> theory
val set_elim: thm -> theory -> theory
val setup: theory -> theory
val code_pred: string -> Proof.context -> Proof.state
val code_pred_cmd: string -> Proof.context -> Proof.state
val print_stored_rules: theory -> unit
val do_proofs: bool ref
val mk_casesrule : Proof.context -> int -> thm list -> term
val analyze_compr: theory -> term -> term
val eval_ref: (unit -> term Predicate.pred) option ref
val add_equations : string -> theory -> theory
val code_pred_intros_attrib : attribute
end;
structure Predicate_Compile : PREDICATE_COMPILE =
struct
(** auxiliary **)
(* debug stuff *)
fun tracing s = (if ! Toplevel.debug then Output.tracing s else ());
fun print_tac s = (if ! Toplevel.debug then Tactical.print_tac s else Seq.single);
fun new_print_tac s = Tactical.print_tac s
fun debug_tac msg = (fn st => (Output.tracing msg; Seq.single st));
val do_proofs = ref true;
fun mycheat_tac thy i st =
(Tactic.rtac (SkipProof.make_thm thy (Var (("A", 0), propT))) i) st
fun remove_last_goal thy st =
(Tactic.rtac (SkipProof.make_thm thy (Var (("A", 0), propT))) (nprems_of st)) st
(* reference to preprocessing of InductiveSet package *)
val ind_set_codegen_preproc = Inductive_Set.codegen_preproc;
(** fundamentals **)
(* syntactic operations *)
fun mk_eq (x, xs) =
let fun mk_eqs _ [] = []
| mk_eqs a (b::cs) =
HOLogic.mk_eq (Free (a, fastype_of b), b) :: mk_eqs a cs
in mk_eqs x xs end;
fun mk_tupleT [] = HOLogic.unitT
| mk_tupleT Ts = foldr1 HOLogic.mk_prodT Ts;
fun dest_tupleT (Type (@{type_name Product_Type.unit}, [])) = []
| dest_tupleT (Type (@{type_name "*"}, [T1, T2])) = T1 :: (dest_tupleT T2)
| dest_tupleT t = [t]
fun mk_tuple [] = HOLogic.unit
| mk_tuple ts = foldr1 HOLogic.mk_prod ts;
fun dest_tuple (Const (@{const_name Product_Type.Unity}, _)) = []
| dest_tuple (Const (@{const_name Pair}, _) $ t1 $ t2) = t1 :: (dest_tuple t2)
| dest_tuple t = [t]
fun mk_pred_enumT T = Type (@{type_name "Predicate.pred"}, [T])
fun dest_pred_enumT (Type (@{type_name "Predicate.pred"}, [T])) = T
| dest_pred_enumT T = raise TYPE ("dest_pred_enumT", [T], []);
fun mk_Enum f =
let val T as Type ("fun", [T', _]) = fastype_of f
in
Const (@{const_name Predicate.Pred}, T --> mk_pred_enumT T') $ f
end;
fun mk_Eval (f, x) =
let val T = fastype_of x
in
Const (@{const_name Predicate.eval}, mk_pred_enumT T --> T --> HOLogic.boolT) $ f $ x
end;
fun mk_empty T = Const (@{const_name Orderings.bot}, mk_pred_enumT T);
fun mk_single t =
let val T = fastype_of t
in Const(@{const_name Predicate.single}, T --> mk_pred_enumT T) $ t end;
fun mk_bind (x, f) =
let val T as Type ("fun", [_, U]) = fastype_of f
in
Const (@{const_name Predicate.bind}, fastype_of x --> T --> U) $ x $ f
end;
val mk_sup = HOLogic.mk_binop @{const_name sup};
fun mk_if_predenum cond = Const (@{const_name Predicate.if_pred},
HOLogic.boolT --> mk_pred_enumT HOLogic.unitT) $ cond;
fun mk_not_pred t = let val T = mk_pred_enumT HOLogic.unitT
in Const (@{const_name Predicate.not_pred}, T --> T) $ t end
(* destruction of intro rules *)
(* FIXME: look for other place where this functionality was used before *)
fun strip_intro_concl nparams intro = let
val _ $ u = Logic.strip_imp_concl intro
val (pred, all_args) = strip_comb u
val (params, args) = chop nparams all_args
in (pred, (params, args)) end
(* data structures *)
type mode = int list option list * int list; (*pmode FIMXE*)
fun string_of_mode (iss, is) = space_implode " -> " (map
(fn NONE => "X"
| SOME js => enclose "[" "]" (commas (map string_of_int js)))
(iss @ [SOME is]));
fun print_modes modes = Output.tracing ("Inferred modes:\n" ^
cat_lines (map (fn (s, ms) => s ^ ": " ^ commas (map
string_of_mode ms)) modes));
datatype predfun_data = PredfunData of {
name : string,
definition : thm,
intro : thm,
elim : thm
};
fun rep_predfun_data (PredfunData data) = data;
fun mk_predfun_data (name, definition, intro, elim) =
PredfunData {name = name, definition = definition, intro = intro, elim = elim}
datatype pred_data = PredData of {
intros : thm list,
elim : thm option,
nparams : int,
functions : (mode * predfun_data) list
};
fun rep_pred_data (PredData data) = data;
fun mk_pred_data ((intros, elim, nparams), functions) =
PredData {intros = intros, elim = elim, nparams = nparams, functions = functions}
fun map_pred_data f (PredData {intros, elim, nparams, functions}) =
mk_pred_data (f ((intros, elim, nparams), functions))
fun eq_option eq (NONE, NONE) = true
| eq_option eq (SOME x, SOME y) = eq (x, y)
| eq_option eq _ = false
fun eq_pred_data (PredData d1, PredData d2) =
eq_list (Thm.eq_thm) (#intros d1, #intros d2) andalso
eq_option (Thm.eq_thm) (#elim d1, #elim d2) andalso
#nparams d1 = #nparams d2
structure PredData = TheoryDataFun
(
type T = pred_data Graph.T;
val empty = Graph.empty;
val copy = I;
val extend = I;
fun merge _ = Graph.merge eq_pred_data;
);
(* queries *)
fun lookup_pred_data thy name =
Option.map rep_pred_data (try (Graph.get_node (PredData.get thy)) name)
fun the_pred_data thy name = case lookup_pred_data thy name
of NONE => error ("No such predicate " ^ quote name)
| SOME data => data;
val is_registered = is_some oo lookup_pred_data
val all_preds_of = Graph.keys o PredData.get
val intros_of = #intros oo the_pred_data
fun the_elim_of thy name = case #elim (the_pred_data thy name)
of NONE => error ("No elimination rule for predicate " ^ quote name)
| SOME thm => thm
val has_elim = is_some o #elim oo the_pred_data;
val nparams_of = #nparams oo the_pred_data
val modes_of = (map fst) o #functions oo the_pred_data
fun all_modes_of thy = map (fn name => (name, modes_of thy name)) (all_preds_of thy)
val is_compiled = not o null o #functions oo the_pred_data
fun lookup_predfun_data thy name mode =
Option.map rep_predfun_data (AList.lookup (op =)
(#functions (the_pred_data thy name)) mode)
fun the_predfun_data thy name mode = case lookup_predfun_data thy name mode
of NONE => error ("No such mode" ^ string_of_mode mode)
| SOME data => data;
val predfun_name_of = #name ooo the_predfun_data
val predfun_definition_of = #definition ooo the_predfun_data
val predfun_intro_of = #intro ooo the_predfun_data
val predfun_elim_of = #elim ooo the_predfun_data
fun print_stored_rules thy =
let
val preds = (Graph.keys o PredData.get) thy
fun print pred () = let
val _ = writeln ("predicate: " ^ pred)
val _ = writeln ("number of parameters: " ^ string_of_int (nparams_of thy pred))
val _ = writeln ("introrules: ")
val _ = fold (fn thm => fn u => writeln (Display.string_of_thm thm))
(rev (intros_of thy pred)) ()
in
if (has_elim thy pred) then
writeln ("elimrule: " ^ Display.string_of_thm (the_elim_of thy pred))
else
writeln ("no elimrule defined")
end
in
fold print preds ()
end;
(** preprocessing rules **)
fun imp_prems_conv cv ct =
case Thm.term_of ct of
Const ("==>", _) $ _ $ _ => Conv.combination_conv (Conv.arg_conv cv) (imp_prems_conv cv) ct
| _ => Conv.all_conv ct
fun Trueprop_conv cv ct =
case Thm.term_of ct of
Const ("Trueprop", _) $ _ => Conv.arg_conv cv ct
| _ => error "Trueprop_conv"
fun preprocess_intro thy rule =
Conv.fconv_rule
(imp_prems_conv
(Trueprop_conv (Conv.try_conv (Conv.rewr_conv (Thm.symmetric @{thm Predicate.eq_is_eq})))))
(Thm.transfer thy rule)
fun preprocess_elim thy nargs elimrule = let
fun replace_eqs (Const ("Trueprop", _) $ (Const ("op =", T) $ lhs $ rhs)) =
HOLogic.mk_Trueprop (Const (@{const_name Predicate.eq}, T) $ lhs $ rhs)
| replace_eqs t = t
fun preprocess_case t = let
val params = Logic.strip_params t
val (assums1, assums2) = chop nargs (Logic.strip_assums_hyp t)
val assums_hyp' = assums1 @ (map replace_eqs assums2)
in list_all (params, Logic.list_implies (assums_hyp', Logic.strip_assums_concl t)) end
val prems = Thm.prems_of elimrule
val cases' = map preprocess_case (tl prems)
val elimrule' = Logic.list_implies ((hd prems) :: cases', Thm.concl_of elimrule)
in
Thm.equal_elim
(Thm.symmetric (Conv.implies_concl_conv (MetaSimplifier.rewrite true [@{thm eq_is_eq}])
(cterm_of thy elimrule')))
elimrule
end;
fun fetch_pred_data thy name =
case try (Inductive.the_inductive (ProofContext.init thy)) name of
SOME (info as (_, result)) =>
let
fun is_intro_of intro =
let
val (const, _) = strip_comb (HOLogic.dest_Trueprop (concl_of intro))
in (fst (dest_Const const) = name) end;
val intros = map (preprocess_intro thy) (filter is_intro_of (#intrs result))
val elim = nth (#elims result) (find_index (fn s => s = name) (#names (fst info)))
val nparams = length (Inductive.params_of (#raw_induct result))
in (intros, elim, nparams) end
| NONE => error ("No such predicate: " ^ quote name)
(* updaters *)
fun add_predfun name mode data = let
val add = apsnd (cons (mode, mk_predfun_data data))
in PredData.map (Graph.map_node name (map_pred_data add)) end
fun is_inductive_predicate thy name =
is_some (try (Inductive.the_inductive (ProofContext.init thy)) name)
fun depending_preds_of thy intros = fold Term.add_consts (map Thm.prop_of intros) [] |> map fst
|> filter (fn c => is_inductive_predicate thy c orelse is_registered thy c)
(* code dependency graph *)
fun dependencies_of thy name =
let
val (intros, elim, nparams) = fetch_pred_data thy name
val data = mk_pred_data ((intros, SOME elim, nparams), [])
val keys = depending_preds_of thy intros
in
(data, keys)
end;
(* TODO: add_edges - by analysing dependencies *)
fun add_intro thm thy = let
val (name, _) = dest_Const (fst (strip_intro_concl 0 (prop_of thm)))
fun cons_intro gr =
case try (Graph.get_node gr) name of
SOME pred_data => Graph.map_node name (map_pred_data
(apfst (fn (intro, elim, nparams) => (thm::intro, elim, nparams)))) gr
| NONE =>
let
val nparams = the_default 0 (try (#3 o fetch_pred_data thy) name)
in Graph.new_node (name, mk_pred_data (([thm], NONE, nparams), [])) gr end;
in PredData.map cons_intro thy end
fun set_elim thm = let
val (name, _) = dest_Const (fst
(strip_comb (HOLogic.dest_Trueprop (hd (prems_of thm)))))
fun set (intros, _, nparams) = (intros, SOME thm, nparams)
in PredData.map (Graph.map_node name (map_pred_data (apfst set))) end
fun set_nparams name nparams = let
fun set (intros, elim, _ ) = (intros, elim, nparams)
in PredData.map (Graph.map_node name (map_pred_data (apfst set))) end
fun register_predicate (intros, elim, nparams) thy = let
val (name, _) = dest_Const (fst (strip_intro_concl nparams (prop_of (hd intros))))
fun set _ = (intros, SOME elim, nparams)
in
PredData.map (Graph.new_node (name, mk_pred_data ((intros, SOME elim, nparams), []))
#> fold Graph.add_edge (map (pair name) (depending_preds_of thy intros))) thy
end
(* Mode analysis *)
(*** check if a term contains only constructor functions ***)
fun is_constrt thy =
let
val cnstrs = flat (maps
(map (fn (_, (Tname, _, cs)) => map (apsnd (rpair Tname o length)) cs) o #descr o snd)
(Symtab.dest (Datatype.get_all thy)));
fun check t = (case strip_comb t of
(Free _, []) => true
| (Const (s, T), ts) => (case (AList.lookup (op =) cnstrs s, body_type T) of
(SOME (i, Tname), Type (Tname', _)) => length ts = i andalso Tname = Tname' andalso forall check ts
| _ => false)
| _ => false)
in check end;
(*** check if a type is an equality type (i.e. doesn't contain fun)
FIXME this is only an approximation ***)
fun is_eqT (Type (s, Ts)) = s <> "fun" andalso forall is_eqT Ts
| is_eqT _ = true;
fun term_vs tm = fold_aterms (fn Free (x, T) => cons x | _ => I) tm [];
val terms_vs = distinct (op =) o maps term_vs;
(** collect all Frees in a term (with duplicates!) **)
fun term_vTs tm =
fold_aterms (fn Free xT => cons xT | _ => I) tm [];
fun get_args is ts = let
fun get_args' _ _ [] = ([], [])
| get_args' is i (t::ts) = (if i mem is then apfst else apsnd) (cons t)
(get_args' is (i+1) ts)
in get_args' is 1 ts end
(*FIXME this function should not be named merge... make it local instead*)
fun merge xs [] = xs
| merge [] ys = ys
| merge (x::xs) (y::ys) = if length x >= length y then x::merge xs (y::ys)
else y::merge (x::xs) ys;
fun subsets i j = if i <= j then
let val is = subsets (i+1) j
in merge (map (fn ks => i::ks) is) is end
else [[]];
(* FIXME: should be in library - map_prod *)
fun cprod ([], ys) = []
| cprod (x :: xs, ys) = map (pair x) ys @ cprod (xs, ys);
fun cprods xss = foldr (map op :: o cprod) [[]] xss;
datatype hmode = Mode of mode * int list * hmode option list; (*FIXME don't understand
why there is another mode type tmode !?*)
(*TODO: cleanup function and put together with modes_of_term *)
fun modes_of_param default modes t = let
val (vs, t') = strip_abs t
val b = length vs
fun mk_modes name args = Option.map (maps (fn (m as (iss, is)) =>
let
val (args1, args2) =
if length args < length iss then
error ("Too few arguments for inductive predicate " ^ name)
else chop (length iss) args;
val k = length args2;
val perm = map (fn i => (find_index_eq (Bound (b - i)) args2) + 1)
(1 upto b)
val partial_mode = (1 upto k) \\ perm
in
if not (partial_mode subset is) then [] else
let
val is' =
(fold_index (fn (i, j) => if j mem is then cons (i + 1) else I) perm [])
|> fold (fn i => if i > k then cons (i - k + b) else I) is
val res = map (fn x => Mode (m, is', x)) (cprods (map
(fn (NONE, _) => [NONE]
| (SOME js, arg) => map SOME (filter
(fn Mode (_, js', _) => js=js') (modes_of_term modes arg)))
(iss ~~ args1)))
in res end
end)) (AList.lookup op = modes name)
in case strip_comb t' of
(Const (name, _), args) => the_default default (mk_modes name args)
| (Var ((name, _), _), args) => the (mk_modes name args)
| (Free (name, _), args) => the (mk_modes name args)
| _ => default end
and modes_of_term modes t =
let
val ks = 1 upto length (binder_types (fastype_of t));
val default = [Mode (([], ks), ks, [])];
fun mk_modes name args = Option.map (maps (fn (m as (iss, is)) =>
let
val (args1, args2) =
if length args < length iss then
error ("Too few arguments for inductive predicate " ^ name)
else chop (length iss) args;
val k = length args2;
val prfx = 1 upto k
in
if not (is_prefix op = prfx is) then [] else
let val is' = map (fn i => i - k) (List.drop (is, k))
in map (fn x => Mode (m, is', x)) (cprods (map
(fn (NONE, _) => [NONE]
| (SOME js, arg) => map SOME (filter
(fn Mode (_, js', _) => js=js') (modes_of_term modes arg)))
(iss ~~ args1)))
end
end)) (AList.lookup op = modes name)
in (case strip_comb t of
(Const (name, _), args) => the_default default (mk_modes name args)
| (Var ((name, _), _), args) => the (mk_modes name args)
| (Free (name, _), args) => the (mk_modes name args)
| (Abs _, []) => modes_of_param default modes t
| _ => default)
end
datatype indprem = Prem of term list * term | Negprem of term list * term | Sidecond of term;
fun select_mode_prem thy modes vs ps =
find_first (is_some o snd) (ps ~~ map
(fn Prem (us, t) => find_first (fn Mode (_, is, _) =>
let
val (in_ts, out_ts) = get_args is us;
val (out_ts', in_ts') = List.partition (is_constrt thy) out_ts;
val vTs = maps term_vTs out_ts';
val dupTs = map snd (duplicates (op =) vTs) @
List.mapPartial (AList.lookup (op =) vTs) vs;
in
terms_vs (in_ts @ in_ts') subset vs andalso
forall (is_eqT o fastype_of) in_ts' andalso
term_vs t subset vs andalso
forall is_eqT dupTs
end)
(modes_of_term modes t handle Option =>
error ("Bad predicate: " ^ Syntax.string_of_term_global thy t))
| Negprem (us, t) => find_first (fn Mode (_, is, _) =>
length us = length is andalso
terms_vs us subset vs andalso
term_vs t subset vs)
(modes_of_term modes t handle Option =>
error ("Bad predicate: " ^ Syntax.string_of_term_global thy t))
| Sidecond t => if term_vs t subset vs then SOME (Mode (([], []), [], []))
else NONE
) ps);
fun check_mode_clause thy param_vs modes (iss, is) (ts, ps) =
let
val modes' = modes @ List.mapPartial
(fn (_, NONE) => NONE | (v, SOME js) => SOME (v, [([], js)]))
(param_vs ~~ iss);
fun check_mode_prems vs [] = SOME vs
| check_mode_prems vs ps = (case select_mode_prem thy modes' vs ps of
NONE => NONE
| SOME (x, _) => check_mode_prems
(case x of Prem (us, _) => vs union terms_vs us | _ => vs)
(filter_out (equal x) ps))
val (in_ts, in_ts') = List.partition (is_constrt thy) (fst (get_args is ts));
val in_vs = terms_vs in_ts;
val concl_vs = terms_vs ts
in
forall is_eqT (map snd (duplicates (op =) (maps term_vTs in_ts))) andalso
forall (is_eqT o fastype_of) in_ts' andalso
(case check_mode_prems (param_vs union in_vs) ps of
NONE => false
| SOME vs => concl_vs subset vs)
end;
fun check_modes_pred thy param_vs preds modes (p, ms) =
let val SOME rs = AList.lookup (op =) preds p
in (p, List.filter (fn m => case find_index
(not o check_mode_clause thy param_vs modes m) rs of
~1 => true
| i => (tracing ("Clause " ^ string_of_int (i+1) ^ " of " ^
p ^ " violates mode " ^ string_of_mode m); false)) ms)
end;
fun fixp f (x : (string * mode list) list) =
let val y = f x
in if x = y then x else fixp f y end;
fun infer_modes thy extra_modes arities param_vs preds = fixp (fn modes =>
map (check_modes_pred thy param_vs preds (modes @ extra_modes)) modes)
(map (fn (s, (ks, k)) => (s, cprod (cprods (map
(fn NONE => [NONE]
| SOME k' => map SOME (subsets 1 k')) ks),
subsets 1 k))) arities);
(* term construction *)
(* for simple modes (e.g. parameters) only: better call it param_funT *)
(* or even better: remove it and only use funT'_of - some modifications to funT'_of necessary *)
fun funT_of T NONE = T
| funT_of T (SOME mode) = let
val Ts = binder_types T;
val (Us1, Us2) = get_args mode Ts
in Us1 ---> (mk_pred_enumT (mk_tupleT Us2)) end;
fun funT'_of (iss, is) T = let
val Ts = binder_types T
val (paramTs, argTs) = chop (length iss) Ts
val paramTs' = map2 (fn SOME is => funT'_of ([], is) | NONE => I) iss paramTs
val (inargTs, outargTs) = get_args is argTs
in
(paramTs' @ inargTs) ---> (mk_pred_enumT (mk_tupleT outargTs))
end;
fun mk_v (names, vs) s T = (case AList.lookup (op =) vs s of
NONE => (Free (s, T), (names, (s, [])::vs))
| SOME xs =>
let
val s' = Name.variant names s;
val v = Free (s', T)
in
(v, (s'::names, AList.update (op =) (s, v::xs) vs))
end);
fun distinct_v (Free (s, T)) nvs = mk_v nvs s T
| distinct_v (t $ u) nvs =
let
val (t', nvs') = distinct_v t nvs;
val (u', nvs'') = distinct_v u nvs';
in (t' $ u', nvs'') end
| distinct_v x nvs = (x, nvs);
fun compile_match thy eqs eqs' out_ts success_t =
let
val eqs'' = maps mk_eq eqs @ eqs'
val names = fold Term.add_free_names (success_t :: eqs'' @ out_ts) [];
val name = Name.variant names "x";
val name' = Name.variant (name :: names) "y";
val T = mk_tupleT (map fastype_of out_ts);
val U = fastype_of success_t;
val U' = dest_pred_enumT U;
val v = Free (name, T);
val v' = Free (name', T);
in
lambda v (fst (Datatype.make_case
(ProofContext.init thy) false [] v
[(mk_tuple out_ts,
if null eqs'' then success_t
else Const (@{const_name HOL.If}, HOLogic.boolT --> U --> U --> U) $
foldr1 HOLogic.mk_conj eqs'' $ success_t $
mk_empty U'),
(v', mk_empty U')]))
end;
(*FIXME function can be removed*)
fun mk_funcomp f t =
let
val names = Term.add_free_names t [];
val Ts = binder_types (fastype_of t);
val vs = map Free
(Name.variant_list names (replicate (length Ts) "x") ~~ Ts)
in
fold_rev lambda vs (f (list_comb (t, vs)))
end;
fun compile_param_ext thy modes (NONE, t) = t
| compile_param_ext thy modes (m as SOME (Mode ((iss, is'), is, ms)), t) =
let
val (vs, u) = strip_abs t
val (ivs, ovs) = get_args is vs
val (f, args) = strip_comb u
val (params, args') = chop (length ms) args
val (inargs, outargs) = get_args is' args'
val b = length vs
val perm = map (fn i => (find_index_eq (Bound (b - i)) args') + 1) (1 upto b)
val outp_perm =
snd (get_args is perm)
|> map (fn i => i - length (filter (fn x => x < i) is'))
val names = [] (* TODO *)
val out_names = Name.variant_list names (replicate (length outargs) "x")
val f' = case f of
Const (name, T) =>
if AList.defined op = modes name then
Const (predfun_name_of thy name (iss, is'), funT'_of (iss, is') T)
else error "compile param: Not an inductive predicate with correct mode"
| Free (name, T) => Free (name, funT_of T (SOME is'))
val outTs = dest_tupleT (dest_pred_enumT (body_type (fastype_of f')))
val out_vs = map Free (out_names ~~ outTs)
val params' = map (compile_param thy modes) (ms ~~ params)
val f_app = list_comb (f', params' @ inargs)
val single_t = (mk_single (mk_tuple (map (fn i => nth out_vs (i - 1)) outp_perm)))
val match_t = compile_match thy [] [] out_vs single_t
in list_abs (ivs,
mk_bind (f_app, match_t))
end
| compile_param_ext _ _ _ = error "compile params"
and compile_param thy modes (NONE, t) = t
| compile_param thy modes (m as SOME (Mode ((iss, is'), is, ms)), t) =
(* (case t of
Abs _ => error "compile_param: Invalid term" *) (* compile_param_ext thy modes (m, t) *)
(* | _ => let *)
let
val (f, args) = strip_comb (Envir.eta_contract t)
val (params, args') = chop (length ms) args
val params' = map (compile_param thy modes) (ms ~~ params)
val f' = case f of
Const (name, T) =>
if AList.defined op = modes name then
Const (predfun_name_of thy name (iss, is'), funT'_of (iss, is') T)
else error "compile param: Not an inductive predicate with correct mode"
| Free (name, T) => Free (name, funT_of T (SOME is'))
in list_comb (f', params' @ args') end
| compile_param _ _ _ = error "compile params"
fun compile_expr thy modes (SOME (Mode (mode, is, ms)), t) =
(case strip_comb t of
(Const (name, T), params) =>
if AList.defined op = modes name then
let
val (Ts, Us) = get_args is
(curry Library.drop (length ms) (fst (strip_type T)))
val params' = map (compile_param thy modes) (ms ~~ params)
in list_comb (Const (predfun_name_of thy name mode, ((map fastype_of params') @ Ts) --->
mk_pred_enumT (mk_tupleT Us)), params')
end
else error "not a valid inductive expression"
| (Free (name, T), args) =>
(*if name mem param_vs then *)
(* Higher order mode call *)
let val r = Free (name, funT_of T (SOME is))
in list_comb (r, args) end)
| compile_expr _ _ _ = error "not a valid inductive expression"
fun compile_clause thy all_vs param_vs modes (iss, is) (ts, ps) inp =
let
val modes' = modes @ List.mapPartial
(fn (_, NONE) => NONE | (v, SOME js) => SOME (v, [([], js)]))
(param_vs ~~ iss);
fun check_constrt t (names, eqs) =
if is_constrt thy t then (t, (names, eqs)) else
let
val s = Name.variant names "x";
val v = Free (s, fastype_of t)
in (v, (s::names, HOLogic.mk_eq (v, t)::eqs)) end;
val (in_ts, out_ts) = get_args is ts;
val (in_ts', (all_vs', eqs)) =
fold_map check_constrt in_ts (all_vs, []);
fun compile_prems out_ts' vs names [] =
let
val (out_ts'', (names', eqs')) =
fold_map check_constrt out_ts' (names, []);
val (out_ts''', (names'', constr_vs)) = fold_map distinct_v
out_ts'' (names', map (rpair []) vs);
in
compile_match thy constr_vs (eqs @ eqs') out_ts'''
(mk_single (mk_tuple out_ts))
end
| compile_prems out_ts vs names ps =
let
val vs' = distinct (op =) (flat (vs :: map term_vs out_ts));
val SOME (p, mode as SOME (Mode (_, js, _))) =
select_mode_prem thy modes' vs' ps
val ps' = filter_out (equal p) ps
val (out_ts', (names', eqs)) =
fold_map check_constrt out_ts (names, [])
val (out_ts'', (names'', constr_vs')) = fold_map distinct_v
out_ts' ((names', map (rpair []) vs))
val (compiled_clause, rest) = case p of
Prem (us, t) =>
let
val (in_ts, out_ts''') = get_args js us;
val u = list_comb (compile_expr thy modes (mode, t), in_ts)
val rest = compile_prems out_ts''' vs' names'' ps'
in
(u, rest)
end
| Negprem (us, t) =>
let
val (in_ts, out_ts''') = get_args js us
val u = list_comb (compile_expr thy modes (mode, t), in_ts)
val rest = compile_prems out_ts''' vs' names'' ps'
in
(mk_not_pred u, rest)
end
| Sidecond t =>
let
val rest = compile_prems [] vs' names'' ps';
in
(mk_if_predenum t, rest)
end
in
compile_match thy constr_vs' eqs out_ts''
(mk_bind (compiled_clause, rest))
end
val prem_t = compile_prems in_ts' param_vs all_vs' ps;
in
mk_bind (mk_single inp, prem_t)
end
fun compile_pred thy all_vs param_vs modes s T cls mode =
let
val Ts = binder_types T;
val (Ts1, Ts2) = chop (length param_vs) Ts;
val Ts1' = map2 funT_of Ts1 (fst mode)
val (Us1, Us2) = get_args (snd mode) Ts2;
val xnames = Name.variant_list param_vs
(map (fn i => "x" ^ string_of_int i) (snd mode));
val xs = map2 (fn s => fn T => Free (s, T)) xnames Us1;
val cl_ts =
map (fn cl => compile_clause thy
all_vs param_vs modes mode cl (mk_tuple xs)) cls;
val mode_id = predfun_name_of thy s mode
in
HOLogic.mk_Trueprop (HOLogic.mk_eq
(list_comb (Const (mode_id, (Ts1' @ Us1) --->
mk_pred_enumT (mk_tupleT Us2)),
map2 (fn s => fn T => Free (s, T)) param_vs Ts1' @ xs),
foldr1 mk_sup cl_ts))
end;
fun compile_preds thy all_vs param_vs modes preds =
map (fn (s, (T, cls)) =>
map (compile_pred thy all_vs param_vs modes s T cls)
((the o AList.lookup (op =) modes) s)) preds;
(* special setup for simpset *)
val HOL_basic_ss' = HOL_basic_ss setSolver
(mk_solver "all_tac_solver" (fn _ => fn _ => all_tac))
(* Definition of executable functions and their intro and elim rules *)
fun print_arities arities = tracing ("Arities:\n" ^
cat_lines (map (fn (s, (ks, k)) => s ^ ": " ^
space_implode " -> " (map
(fn NONE => "X" | SOME k' => string_of_int k')
(ks @ [SOME k]))) arities));
fun mk_Eval_of ((x, T), NONE) names = (x, names)
| mk_Eval_of ((x, T), SOME mode) names = let
val Ts = binder_types T
val argnames = Name.variant_list names
(map (fn i => "x" ^ string_of_int i) (1 upto (length Ts)));
val args = map Free (argnames ~~ Ts)
val (inargs, outargs) = get_args mode args
val r = mk_Eval (list_comb (x, inargs), mk_tuple outargs)
val t = fold_rev lambda args r
in
(t, argnames @ names)
end;
fun create_intro_elim_rule nparams mode defthm mode_id funT pred thy =
let
val Ts = binder_types (fastype_of pred)
val funtrm = Const (mode_id, funT)
val argnames = Name.variant_list []
(map (fn i => "x" ^ string_of_int i) (1 upto (length Ts)));
val (Ts1, Ts2) = chop nparams Ts;
val Ts1' = map2 funT_of Ts1 (fst mode)
val args = map Free (argnames ~~ (Ts1' @ Ts2))
val (params, io_args) = chop nparams args
val (inargs, outargs) = get_args (snd mode) io_args
val param_names = Name.variant_list argnames
(map (fn i => "p" ^ string_of_int i) (1 upto nparams))
val param_vs = map Free (param_names ~~ Ts1)
val (params', names) = fold_map mk_Eval_of ((params ~~ Ts1) ~~ (fst mode)) []
val predpropI = HOLogic.mk_Trueprop (list_comb (pred, param_vs @ io_args))
val predpropE = HOLogic.mk_Trueprop (list_comb (pred, params' @ io_args))
val param_eqs = map (HOLogic.mk_Trueprop o HOLogic.mk_eq) (param_vs ~~ params')
val funargs = params @ inargs
val funpropE = HOLogic.mk_Trueprop (mk_Eval (list_comb (funtrm, funargs),
if null outargs then Free("y", HOLogic.unitT) else mk_tuple outargs))
val funpropI = HOLogic.mk_Trueprop (mk_Eval (list_comb (funtrm, funargs),
mk_tuple outargs))
val introtrm = Logic.list_implies (predpropI :: param_eqs, funpropI)
val _ = Output.tracing (Syntax.string_of_term_global thy introtrm)
val simprules = [defthm, @{thm eval_pred},
@{thm "split_beta"}, @{thm "fst_conv"}, @{thm "snd_conv"}]
val unfolddef_tac = (Simplifier.asm_full_simp_tac (HOL_basic_ss addsimps simprules) 1)
val introthm = Goal.prove (ProofContext.init thy) (argnames @ param_names @ ["y"]) [] introtrm (fn {...} => unfolddef_tac)
val P = HOLogic.mk_Trueprop (Free ("P", HOLogic.boolT));
val elimtrm = Logic.list_implies ([funpropE, Logic.mk_implies (predpropE, P)], P)
val elimthm = Goal.prove (ProofContext.init thy) (argnames @ param_names @ ["y", "P"]) [] elimtrm (fn {...} => unfolddef_tac)
in
(introthm, elimthm)
end;
fun create_definitions preds nparams (name, modes) thy =
let
val _ = tracing "create definitions"
val T = AList.lookup (op =) preds name |> the
fun create_definition mode thy = let
fun string_of_mode mode = if null mode then "0"
else space_implode "_" (map string_of_int mode)
val HOmode = let
fun string_of_HOmode m s = case m of NONE => s | SOME mode => s ^ "__" ^ (string_of_mode mode)
in (fold string_of_HOmode (fst mode) "") end;
val mode_id = name ^ (if HOmode = "" then "_" else HOmode ^ "___")
^ (string_of_mode (snd mode))
val Ts = binder_types T;
val (Ts1, Ts2) = chop nparams Ts;
val Ts1' = map2 funT_of Ts1 (fst mode)
val (Us1, Us2) = get_args (snd mode) Ts2;
val names = Name.variant_list []
(map (fn i => "x" ^ string_of_int i) (1 upto (length Ts)));
val xs = map Free (names ~~ (Ts1' @ Ts2));
val (xparams, xargs) = chop nparams xs;
val (xparams', names') = fold_map mk_Eval_of ((xparams ~~ Ts1) ~~ (fst mode)) names
val (xins, xouts) = get_args (snd mode) xargs;
fun mk_split_lambda [] t = lambda (Free (Name.variant names' "x", HOLogic.unitT)) t
| mk_split_lambda [x] t = lambda x t
| mk_split_lambda xs t = let
fun mk_split_lambda' (x::y::[]) t = HOLogic.mk_split (lambda x (lambda y t))
| mk_split_lambda' (x::xs) t = HOLogic.mk_split (lambda x (mk_split_lambda' xs t))
in mk_split_lambda' xs t end;
val predterm = mk_Enum (mk_split_lambda xouts (list_comb (Const (name, T), xparams' @ xargs)))
val funT = (Ts1' @ Us1) ---> (mk_pred_enumT (mk_tupleT Us2))
val mode_id = Sign.full_bname thy (Long_Name.base_name mode_id)
val lhs = list_comb (Const (mode_id, funT), xparams @ xins)
val def = Logic.mk_equals (lhs, predterm)
val ([definition], thy') = thy |>
Sign.add_consts_i [(Binding.name (Long_Name.base_name mode_id), funT, NoSyn)] |>
PureThy.add_defs false [((Binding.name (Long_Name.base_name mode_id ^ "_def"), def), [])]
val (intro, elim) = create_intro_elim_rule nparams mode definition mode_id funT (Const (name, T)) thy'
in thy' |> add_predfun name mode (mode_id, definition, intro, elim)
|> PureThy.store_thm (Binding.name (Long_Name.base_name mode_id ^ "I"), intro) |> snd
|> PureThy.store_thm (Binding.name (Long_Name.base_name mode_id ^ "E"), elim) |> snd
|> Theory.checkpoint
end;
in
fold create_definition modes thy
end;
(**************************************************************************************)
(* Proving equivalence of term *)
fun is_Type (Type _) = true
| is_Type _ = false
(* returns true if t is an application of an datatype constructor *)
(* which then consequently would be splitted *)
(* else false *)
fun is_constructor thy t =
if (is_Type (fastype_of t)) then
(case Datatype.get_info thy ((fst o dest_Type o fastype_of) t) of
NONE => false
| SOME info => (let
val constr_consts = maps (fn (_, (_, _, constrs)) => map fst constrs) (#descr info)
val (c, _) = strip_comb t
in (case c of
Const (name, _) => name mem_string constr_consts
| _ => false) end))
else false
(* MAJOR FIXME: prove_params should be simple
- different form of introrule for parameters ? *)
fun prove_param thy modes (NONE, t) =
all_tac
| prove_param thy modes (m as SOME (Mode (mode, is, ms)), t) =
REPEAT_DETERM (etac @{thm thin_rl} 1)
THEN REPEAT_DETERM (rtac @{thm ext} 1)
THEN (rtac @{thm iffI} 1)
THEN new_print_tac "prove_param"
(* proof in one direction *)
THEN (atac 1)
(* proof in the other direction *)
THEN (atac 1)
THEN new_print_tac "after prove_param"
(* let
val (f, args) = strip_comb t
val (params, _) = chop (length ms) args
val f_tac = case f of
Const (name, T) => simp_tac (HOL_basic_ss addsimps
(@{thm eval_pred}::(predfun_definition_of thy name mode)::
@{thm "Product_Type.split_conv"}::[])) 1
| Free _ => all_tac
| Abs _ => error "TODO: implement here"
in
print_tac "before simplification in prove_args:"
THEN f_tac
THEN print_tac "after simplification in prove_args"
THEN (EVERY (map (prove_param thy modes) (ms ~~ params)))
THEN (REPEAT_DETERM (atac 1))
end
*)
fun prove_expr thy modes (SOME (Mode (mode, is, ms)), t, us) (premposition : int) =
(case strip_comb t of
(Const (name, T), args) =>
if AList.defined op = modes name then (let
val introrule = predfun_intro_of thy name mode
(*val (in_args, out_args) = get_args is us
val (pred, rargs) = strip_comb (HOLogic.dest_Trueprop
(hd (Logic.strip_imp_prems (prop_of introrule))))
val nparams = length ms (* get_nparams thy (fst (dest_Const pred)) *)
val (_, args) = chop nparams rargs
val subst = map (pairself (cterm_of thy)) (args ~~ us)
val inst_introrule = Drule.cterm_instantiate subst introrule*)
(* the next line is old and probably wrong *)
val (args1, args2) = chop (length ms) args
in
rtac @{thm bindI} 1
THEN print_tac "before intro rule:"
(* for the right assumption in first position *)
THEN rotate_tac premposition 1
THEN rtac introrule 1
THEN new_print_tac "after intro rule"
(* work with parameter arguments *)
THEN (atac 1)
THEN (new_print_tac "parameter goal")
THEN (EVERY (map (prove_param thy modes) (ms ~~ args1)))
THEN (REPEAT_DETERM (atac 1)) end)
else error "Prove expr if case not implemented"
| _ => rtac @{thm bindI} 1
THEN atac 1)
| prove_expr _ _ _ _ = error "Prove expr not implemented"
fun SOLVED tac st = FILTER (fn st' => nprems_of st' = nprems_of st - 1) tac st;
fun SOLVEDALL tac st = FILTER (fn st' => nprems_of st' = 0) tac st
fun prove_match thy (out_ts : term list) = let
fun get_case_rewrite t =
if (is_constructor thy t) then let
val case_rewrites = (#case_rewrites (Datatype.the_info thy
((fst o dest_Type o fastype_of) t)))
in case_rewrites @ (flat (map get_case_rewrite (snd (strip_comb t)))) end
else []
val simprules = @{thm "unit.cases"} :: @{thm "prod.cases"} :: (flat (map get_case_rewrite out_ts))
(* replace TRY by determining if it necessary - are there equations when calling compile match? *)
in
(* make this simpset better! *)
asm_simp_tac (HOL_basic_ss' addsimps simprules) 1
THEN print_tac "after prove_match:"
THEN (DETERM (TRY (EqSubst.eqsubst_tac (ProofContext.init thy) [0] [@{thm "HOL.if_P"}] 1
THEN (REPEAT_DETERM (rtac @{thm conjI} 1 THEN (SOLVED (asm_simp_tac HOL_basic_ss 1))))
THEN (SOLVED (asm_simp_tac HOL_basic_ss 1)))))
THEN print_tac "after if simplification"
end;
(* corresponds to compile_fun -- maybe call that also compile_sidecond? *)
fun prove_sidecond thy modes t =
let
fun preds_of t nameTs = case strip_comb t of
(f as Const (name, T), args) =>
if AList.defined (op =) modes name then (name, T) :: nameTs
else fold preds_of args nameTs
| _ => nameTs
val preds = preds_of t []
val defs = map
(fn (pred, T) => predfun_definition_of thy pred ([], (1 upto (length (binder_types T)))))
preds
in
(* remove not_False_eq_True when simpset in prove_match is better *)
simp_tac (HOL_basic_ss addsimps @{thm not_False_eq_True} :: @{thm eval_pred} :: defs) 1
(* need better control here! *)
end
fun prove_clause thy nargs all_vs param_vs modes (iss, is) (ts, ps) = let
val modes' = modes @ List.mapPartial
(fn (_, NONE) => NONE | (v, SOME js) => SOME (v, [([], js)]))
(param_vs ~~ iss);
fun check_constrt ((names, eqs), t) =
if is_constrt thy t then ((names, eqs), t) else
let
val s = Name.variant names "x";
val v = Free (s, fastype_of t)
in ((s::names, HOLogic.mk_eq (v, t)::eqs), v) end;
val (in_ts, clause_out_ts) = get_args is ts;
val ((all_vs', eqs), in_ts') =
(*FIXME*) Library.foldl_map check_constrt ((all_vs, []), in_ts);
fun prove_prems out_ts vs [] =
(prove_match thy out_ts)
THEN asm_simp_tac HOL_basic_ss' 1
THEN print_tac "before the last rule of singleI:"
THEN (rtac (if null clause_out_ts then @{thm singleI_unit} else @{thm singleI}) 1)
| prove_prems out_ts vs rps =
let
val vs' = distinct (op =) (flat (vs :: map term_vs out_ts));
val SOME (p, mode as SOME (Mode ((iss, js), _, param_modes))) =
select_mode_prem thy modes' vs' rps;
val premposition = (find_index (equal p) ps) + nargs
val rps' = filter_out (equal p) rps;
val rest_tac = (case p of Prem (us, t) =>
let
val (in_ts, out_ts''') = get_args js us
val rec_tac = prove_prems out_ts''' vs' rps'
in
print_tac "before clause:"
THEN asm_simp_tac HOL_basic_ss 1
THEN print_tac "before prove_expr:"
THEN prove_expr thy modes (mode, t, us) premposition
THEN print_tac "after prove_expr:"
THEN rec_tac
end
| Negprem (us, t) =>
let
val (in_ts, out_ts''') = get_args js us
val rec_tac = prove_prems out_ts''' vs' rps'
val name = (case strip_comb t of (Const (c, _), _) => SOME c | _ => NONE)
val (_, params) = strip_comb t
in
rtac @{thm bindI} 1
THEN (if (is_some name) then
simp_tac (HOL_basic_ss addsimps [predfun_definition_of thy (the name) (iss, js)]) 1
THEN rtac @{thm not_predI} 1
(* FIXME: work with parameter arguments *)
THEN (EVERY (map (prove_param thy modes) (param_modes ~~ params)))
else
rtac @{thm not_predI'} 1)
THEN (REPEAT_DETERM (atac 1))
THEN rec_tac
end
| Sidecond t =>
rtac @{thm bindI} 1
THEN rtac @{thm if_predI} 1
THEN print_tac "before sidecond:"
THEN prove_sidecond thy modes t
THEN print_tac "after sidecond:"
THEN prove_prems [] vs' rps')
in (prove_match thy out_ts)
THEN rest_tac
end;
val prems_tac = prove_prems in_ts' param_vs ps
in
rtac @{thm bindI} 1
THEN rtac @{thm singleI} 1
THEN prems_tac
end;
fun select_sup 1 1 = []
| select_sup _ 1 = [rtac @{thm supI1}]
| select_sup n i = (rtac @{thm supI2})::(select_sup (n - 1) (i - 1));
fun prove_one_direction thy all_vs param_vs modes clauses ((pred, T), mode) = let
(* val ind_result = Inductive.the_inductive (ProofContext.init thy) pred
val index = find_index (fn s => s = pred) (#names (fst ind_result))
val (_, T) = dest_Const (nth (#preds (snd ind_result)) index) *)
val nargs = length (binder_types T) - nparams_of thy pred
val pred_case_rule = singleton (ind_set_codegen_preproc thy)
(preprocess_elim thy nargs (the_elim_of thy pred))
(* FIXME preprocessor |> Simplifier.full_simplify (HOL_basic_ss addsimps [@{thm Predicate.memb_code}])*)
in
REPEAT_DETERM (CHANGED (rewtac @{thm "split_paired_all"}))
THEN etac (predfun_elim_of thy pred mode) 1
THEN etac pred_case_rule 1
THEN (EVERY (map
(fn i => EVERY' (select_sup (length clauses) i) i)
(1 upto (length clauses))))
THEN (EVERY (map (prove_clause thy nargs all_vs param_vs modes mode) clauses))
THEN new_print_tac "proved one direction"
end;
(*******************************************************************************************************)
(* Proof in the other direction ************************************************************************)
(*******************************************************************************************************)
fun prove_match2 thy out_ts = let
fun split_term_tac (Free _) = all_tac
| split_term_tac t =
if (is_constructor thy t) then let
val info = Datatype.the_info thy ((fst o dest_Type o fastype_of) t)
val num_of_constrs = length (#case_rewrites info)
(* special treatment of pairs -- because of fishing *)
val split_rules = case (fst o dest_Type o fastype_of) t of
"*" => [@{thm prod.split_asm}]
| _ => PureThy.get_thms thy (((fst o dest_Type o fastype_of) t) ^ ".split_asm")
val (_, ts) = strip_comb t
in
(Splitter.split_asm_tac split_rules 1)
(* THEN (Simplifier.asm_full_simp_tac HOL_basic_ss 1)
THEN (DETERM (TRY (etac @{thm Pair_inject} 1))) *)
THEN (REPEAT_DETERM_N (num_of_constrs - 1) (etac @{thm botE} 1 ORELSE etac @{thm botE} 2))
THEN (EVERY (map split_term_tac ts))
end
else all_tac
in
split_term_tac (mk_tuple out_ts)
THEN (DETERM (TRY ((Splitter.split_asm_tac [@{thm "split_if_asm"}] 1) THEN (etac @{thm botE} 2))))
end
(* VERY LARGE SIMILIRATIY to function prove_param
-- join both functions
*)
fun prove_param2 thy modes (NONE, t) = all_tac
| prove_param2 thy modes (m as SOME (Mode (mode, is, ms)), t) = let
val (f, args) = strip_comb t
val (params, _) = chop (length ms) args
val f_tac = case f of
Const (name, T) => full_simp_tac (HOL_basic_ss addsimps
(@{thm eval_pred}::(predfun_definition_of thy name mode)
:: @{thm "Product_Type.split_conv"}::[])) 1
| Free _ => all_tac
in
print_tac "before simplification in prove_args:"
THEN f_tac
THEN print_tac "after simplification in prove_args"
THEN (EVERY (map (prove_param2 thy modes) (ms ~~ params)))
end
fun prove_expr2 thy modes (SOME (Mode (mode, is, ms)), t) =
(case strip_comb t of
(Const (name, T), args) =>
if AList.defined op = modes name then
etac @{thm bindE} 1
THEN (REPEAT_DETERM (CHANGED (rewtac @{thm "split_paired_all"})))
THEN new_print_tac "prove_expr2-before"
THEN (debug_tac (Syntax.string_of_term_global thy
(prop_of (predfun_elim_of thy name mode))))
THEN (etac (predfun_elim_of thy name mode) 1)
THEN new_print_tac "prove_expr2"
(* TODO -- FIXME: replace remove_last_goal*)
(* THEN (EVERY (replicate (length args) (remove_last_goal thy))) *)
THEN (EVERY (map (prove_param thy modes) (ms ~~ args)))
THEN new_print_tac "finished prove_expr2"
else error "Prove expr2 if case not implemented"
| _ => etac @{thm bindE} 1)
| prove_expr2 _ _ _ = error "Prove expr2 not implemented"
fun prove_sidecond2 thy modes t = let
fun preds_of t nameTs = case strip_comb t of
(f as Const (name, T), args) =>
if AList.defined (op =) modes name then (name, T) :: nameTs
else fold preds_of args nameTs
| _ => nameTs
val preds = preds_of t []
val defs = map
(fn (pred, T) => predfun_definition_of thy pred ([], (1 upto (length (binder_types T)))))
preds
in
(* only simplify the one assumption *)
full_simp_tac (HOL_basic_ss' addsimps @{thm eval_pred} :: defs) 1
(* need better control here! *)
THEN print_tac "after sidecond2 simplification"
end
fun prove_clause2 thy all_vs param_vs modes (iss, is) (ts, ps) pred i = let
val modes' = modes @ List.mapPartial
(fn (_, NONE) => NONE | (v, SOME js) => SOME (v, [([], js)]))
(param_vs ~~ iss);
fun check_constrt ((names, eqs), t) =
if is_constrt thy t then ((names, eqs), t) else
let
val s = Name.variant names "x";
val v = Free (s, fastype_of t)
in ((s::names, HOLogic.mk_eq (v, t)::eqs), v) end;
val pred_intro_rule = nth (intros_of thy pred) (i - 1)
|> preprocess_intro thy
|> (fn thm => hd (ind_set_codegen_preproc thy [thm]))
(* FIXME preprocess |> Simplifier.full_simplify (HOL_basic_ss addsimps [@ {thm Predicate.memb_code}]) *)
val (in_ts, clause_out_ts) = get_args is ts;
val ((all_vs', eqs), in_ts') =
(*FIXME*) Library.foldl_map check_constrt ((all_vs, []), in_ts);
fun prove_prems2 out_ts vs [] =
print_tac "before prove_match2 - last call:"
THEN prove_match2 thy out_ts
THEN print_tac "after prove_match2 - last call:"
THEN (etac @{thm singleE} 1)
THEN (REPEAT_DETERM (etac @{thm Pair_inject} 1))
THEN (asm_full_simp_tac HOL_basic_ss' 1)
THEN (REPEAT_DETERM (etac @{thm Pair_inject} 1))
THEN (asm_full_simp_tac HOL_basic_ss' 1)
THEN SOLVED (print_tac "state before applying intro rule:"
THEN (rtac pred_intro_rule 1)
(* How to handle equality correctly? *)
THEN (print_tac "state before assumption matching")
THEN (REPEAT (atac 1 ORELSE
(CHANGED (asm_full_simp_tac HOL_basic_ss' 1)
THEN print_tac "state after simp_tac:"))))
| prove_prems2 out_ts vs ps = let
val vs' = distinct (op =) (flat (vs :: map term_vs out_ts));
val SOME (p, mode as SOME (Mode ((iss, js), _, param_modes))) =
select_mode_prem thy modes' vs' ps;
val ps' = filter_out (equal p) ps;
val rest_tac = (case p of Prem (us, t) =>
let
val (in_ts, out_ts''') = get_args js us
val rec_tac = prove_prems2 out_ts''' vs' ps'
in
(prove_expr2 thy modes (mode, t)) THEN rec_tac
end
| Negprem (us, t) =>
let
val (in_ts, out_ts''') = get_args js us
val rec_tac = prove_prems2 out_ts''' vs' ps'
val name = (case strip_comb t of (Const (c, _), _) => SOME c | _ => NONE)
val (_, params) = strip_comb t
in
print_tac "before neg prem 2"
THEN etac @{thm bindE} 1
THEN (if is_some name then
full_simp_tac (HOL_basic_ss addsimps [predfun_definition_of thy (the name) (iss, js)]) 1
THEN etac @{thm not_predE} 1
THEN (EVERY (map (prove_param thy modes) (param_modes ~~ params)))
else
etac @{thm not_predE'} 1)
THEN rec_tac
end
| Sidecond t =>
etac @{thm bindE} 1
THEN etac @{thm if_predE} 1
THEN prove_sidecond2 thy modes t
THEN prove_prems2 [] vs' ps')
in print_tac "before prove_match2:"
THEN prove_match2 thy out_ts
THEN print_tac "after prove_match2:"
THEN rest_tac
end;
val prems_tac = prove_prems2 in_ts' param_vs ps
in
new_print_tac "starting prove_clause2"
THEN etac @{thm bindE} 1
THEN (etac @{thm singleE'} 1)
THEN (TRY (etac @{thm Pair_inject} 1))
THEN print_tac "after singleE':"
THEN prems_tac
end;
fun prove_other_direction thy all_vs param_vs modes clauses (pred, mode) = let
fun prove_clause (clause, i) =
(if i < length clauses then etac @{thm supE} 1 else all_tac)
THEN (prove_clause2 thy all_vs param_vs modes mode clause pred i)
in
(DETERM (TRY (rtac @{thm unit.induct} 1)))
THEN (REPEAT_DETERM (CHANGED (rewtac @{thm split_paired_all})))
THEN (rtac (predfun_intro_of thy pred mode) 1)
THEN (REPEAT_DETERM (rtac @{thm refl} 2))
THEN (EVERY (map prove_clause (clauses ~~ (1 upto (length clauses)))))
end;
fun prove_pred thy all_vs param_vs modes clauses (((pred, T), mode), t) = let
val ctxt = ProofContext.init thy
val clauses' = the (AList.lookup (op =) clauses pred)
in
Goal.prove ctxt (Term.fold_aterms (fn Free (x, _) => insert (op =) x | _ => I) t []) [] t
(if !do_proofs then
(fn _ =>
rtac @{thm pred_iffI} 1
THEN prove_one_direction thy all_vs param_vs modes clauses' ((pred, T), mode)
THEN print_tac "proved one direction"
THEN prove_other_direction thy all_vs param_vs modes clauses' (pred, mode)
THEN print_tac "proved other direction")
else (fn _ => mycheat_tac thy 1))
end;
fun prove_preds thy all_vs param_vs modes clauses pmts =
map (prove_pred thy all_vs param_vs modes clauses) pmts
(* special case: inductive predicate with no clauses *)
fun noclause (predname, T) thy = let
val Ts = binder_types T
val names = Name.variant_list []
(map (fn i => "x" ^ (string_of_int i)) (1 upto (length Ts)))
val vs = map2 (curry Free) names Ts
val clausehd = HOLogic.mk_Trueprop (list_comb(Const (predname, T), vs))
val intro_t = Logic.mk_implies (@{prop False}, clausehd)
val P = HOLogic.mk_Trueprop (Free ("P", HOLogic.boolT))
val elim_t = Logic.list_implies ([clausehd, Logic.mk_implies (@{prop False}, P)], P)
val intro = Goal.prove (ProofContext.init thy) names [] intro_t
(fn {...} => etac @{thm FalseE} 1)
val elim = Goal.prove (ProofContext.init thy) ("P" :: names) [] elim_t
(fn {...} => etac (the_elim_of thy predname) 1)
in
add_intro intro thy
|> set_elim elim
end
fun prepare_intrs thy prednames =
let
(* FIXME: preprocessing moved to fetch_pred_data *)
val intrs = map (preprocess_intro thy) (maps (intros_of thy) prednames)
|> ind_set_codegen_preproc thy (*FIXME preprocessor
|> map (Simplifier.full_simplify (HOL_basic_ss addsimps [@ {thm Predicate.memb_code}]))*)
|> map (Logic.unvarify o prop_of)
val nparams = nparams_of thy (hd prednames)
val preds = distinct (op =) (map (dest_Const o fst o (strip_intro_concl nparams)) intrs)
val extra_modes = all_modes_of thy |> filter_out (fn (name, _) => member (op =) prednames name)
val _ $ u = Logic.strip_imp_concl (hd intrs);
val params = List.take (snd (strip_comb u), nparams);
val param_vs = maps term_vs params
val all_vs = terms_vs intrs
fun dest_prem t =
(case strip_comb t of
(v as Free _, ts) => if v mem params then Prem (ts, v) else Sidecond t
| (c as Const (@{const_name Not}, _), [t]) => (case dest_prem t of
Prem (ts, t) => Negprem (ts, t)
| Negprem _ => error ("Double negation not allowed in premise: " ^ (Syntax.string_of_term_global thy (c $ t)))
| Sidecond t => Sidecond (c $ t))
| (c as Const (s, _), ts) =>
if is_registered thy s then
let val (ts1, ts2) = chop (nparams_of thy s) ts
in Prem (ts2, list_comb (c, ts1)) end
else Sidecond t
| _ => Sidecond t)
fun add_clause intr (clauses, arities) =
let
val _ $ t = Logic.strip_imp_concl intr;
val (Const (name, T), ts) = strip_comb t;
val (ts1, ts2) = chop nparams ts;
val prems = map (dest_prem o HOLogic.dest_Trueprop) (Logic.strip_imp_prems intr);
val (Ts, Us) = chop nparams (binder_types T)
in
(AList.update op = (name, these (AList.lookup op = clauses name) @
[(ts2, prems)]) clauses,
AList.update op = (name, (map (fn U => (case strip_type U of
(Rs as _ :: _, Type ("bool", [])) => SOME (length Rs)
| _ => NONE)) Ts,
length Us)) arities)
end;
val (clauses, arities) = fold add_clause intrs ([], []);
in (preds, nparams, all_vs, param_vs, extra_modes, clauses, arities) end;
fun arrange kvs =
let
fun add (key, value) table =
AList.update op = (key, these (AList.lookup op = table key) @ [value]) table
in fold add kvs [] end;
(* main function *)
fun add_equations_of prednames thy =
let
val _ = tracing ("starting add_equations with " ^ commas prednames ^ "...")
(* null clause handling *)
(*
val thy' = fold (fn pred as (predname, T) => fn thy =>
if null (intros_of thy predname) then noclause pred thy else thy) preds thy
*)
val (preds, nparams, all_vs, param_vs, extra_modes, clauses, arities) =
prepare_intrs thy prednames
val _ = tracing "Infering modes..."
val modes = infer_modes thy extra_modes arities param_vs clauses
val _ = print_modes modes
val _ = tracing "Defining executable functions..."
val thy' = fold (create_definitions preds nparams) modes thy |> Theory.checkpoint
val clauses' = map (fn (s, cls) => (s, (the (AList.lookup (op =) preds s), cls))) clauses
val _ = tracing "Compiling equations..."
val ts = compile_preds thy' all_vs param_vs (extra_modes @ modes) clauses'
val _ = map (Output.tracing o (Syntax.string_of_term_global thy')) (flat ts)
val pred_mode =
maps (fn (s, (T, _)) => map (pair (s, T)) ((the o AList.lookup (op =) modes) s)) clauses'
val _ = Output.tracing "Proving equations..."
val result_thms =
prove_preds thy' all_vs param_vs (extra_modes @ modes) clauses (pred_mode ~~ (flat ts))
val thy'' = fold (fn (name, result_thms) => fn thy => snd (PureThy.add_thmss
[((Binding.qualify true (Long_Name.base_name name) (Binding.name "equation"), result_thms),
[Attrib.attribute_i thy Code.add_default_eqn_attrib])] thy))
(arrange ((map (fn ((name, _), _) => name) pred_mode) ~~ result_thms)) thy'
|> Theory.checkpoint
in
thy''
end
(* generation of case rules from user-given introduction rules *)
fun mk_casesrule ctxt nparams introrules =
let
val intros = map (Logic.unvarify o prop_of) introrules
val (pred, (params, args)) = strip_intro_concl nparams (hd intros)
val ([propname], ctxt1) = Variable.variant_fixes ["thesis"] ctxt
val prop = HOLogic.mk_Trueprop (Free (propname, HOLogic.boolT))
val (argnames, ctxt2) = Variable.variant_fixes
(map (fn i => "a" ^ string_of_int i) (1 upto (length args))) ctxt1
val argvs = map2 (curry Free) argnames (map fastype_of args)
fun mk_case intro = let
val (_, (_, args)) = strip_intro_concl nparams intro
val prems = Logic.strip_imp_prems intro
val eqprems = map (HOLogic.mk_Trueprop o HOLogic.mk_eq) (argvs ~~ args)
val frees = (fold o fold_aterms)
(fn t as Free _ =>
if member (op aconv) params t then I else insert (op aconv) t
| _ => I) (args @ prems) []
in fold Logic.all frees (Logic.list_implies (eqprems @ prems, prop)) end
val assm = HOLogic.mk_Trueprop (list_comb (pred, params @ argvs))
val cases = map mk_case intros
in Logic.list_implies (assm :: cases, prop) end;
fun add_equations name thy =
let
val thy' = PredData.map (Graph.extend (dependencies_of thy) name) thy |> Theory.checkpoint;
(*val preds = Graph.all_preds (PredData.get thy') [name] |> filter_out (has_elim thy') *)
fun strong_conn_of gr keys =
Graph.strong_conn (Graph.subgraph (member (op =) (Graph.all_succs gr keys)) gr)
val scc = strong_conn_of (PredData.get thy') [name]
val thy'' = fold_rev
(fn preds => fn thy =>
if forall (null o modes_of thy) preds then add_equations_of preds thy else thy)
scc thy' |> Theory.checkpoint
in thy'' end
fun attrib f = Thm.declaration_attribute (fn thm => Context.mapping (f thm) I);
val code_pred_intros_attrib = attrib add_intro;
(** user interface **)
local
(* TODO: make TheoryDataFun to GenericDataFun & remove duplication of local theory and theory *)
(* TODO: must create state to prove multiple cases *)
fun generic_code_pred prep_const raw_const lthy =
let
val thy = ProofContext.theory_of lthy
val const = prep_const thy raw_const
val lthy' = LocalTheory.theory (PredData.map (Graph.extend (dependencies_of thy) const)) lthy
|> LocalTheory.checkpoint
val thy' = ProofContext.theory_of lthy'
val preds = Graph.all_preds (PredData.get thy') [const] |> filter_out (has_elim thy')
fun mk_cases const =
let
val nparams = nparams_of thy' const
val intros = intros_of thy' const
in mk_casesrule lthy' nparams intros end
val cases_rules = map mk_cases preds
val cases =
map (fn case_rule => RuleCases.Case {fixes = [],
assumes = [("", Logic.strip_imp_prems case_rule)],
binds = [], cases = []}) cases_rules
val case_env = map2 (fn p => fn c => (Long_Name.base_name p, SOME c)) preds cases
val _ = Output.tracing (commas (map fst case_env))
val lthy'' = ProofContext.add_cases true case_env lthy'
fun after_qed thms =
LocalTheory.theory (fold set_elim (map the_single thms) #> add_equations const)
in
Proof.theorem_i NONE after_qed (map (single o (rpair [])) cases_rules) lthy''
end;
structure P = OuterParse
in
val code_pred = generic_code_pred (K I);
val code_pred_cmd = generic_code_pred Code.read_const
val setup = PredData.put (Graph.empty) #>
Attrib.setup @{binding code_pred_intros} (Scan.succeed (attrib add_intro))
"adding alternative introduction rules for code generation of inductive predicates"
(* Attrib.setup @{binding code_ind_cases} (Scan.succeed add_elim_attrib)
"adding alternative elimination rules for code generation of inductive predicates";
*)
(*FIXME name discrepancy in attribs and ML code*)
(*FIXME intros should be better named intro*)
(*FIXME why distinguished attribute for cases?*)
val _ = OuterSyntax.local_theory_to_proof "code_pred"
"prove equations for predicate specified by intro/elim rules"
OuterKeyword.thy_goal (P.term_group >> code_pred_cmd)
end
(*FIXME
- Naming of auxiliary rules necessary?
- add default code equations P x y z = P_i_i_i x y z
*)
(* transformation for code generation *)
val eval_ref = ref (NONE : (unit -> term Predicate.pred) option);
fun analyze_compr thy t_compr =
let
val split = case t_compr of (Const (@{const_name Collect}, _) $ t) => t
| _ => error ("Not a set comprehension: " ^ Syntax.string_of_term_global thy t_compr);
val (body, Ts, fp) = HOLogic.strip_split split;
(*FIXME former order of tuple positions must be restored*)
val (pred as Const (name, T), all_args) = strip_comb body
val (params, args) = chop (nparams_of thy name) all_args
val user_mode = map_filter I (map_index
(fn (i, t) => case t of Bound j => if j < length Ts then NONE
else SOME (i+1) | _ => SOME (i+1)) args) (*FIXME dangling bounds should not occur*)
val (inargs, _) = get_args user_mode args;
val modes = filter (fn Mode (_, is, _) => is = user_mode)
(modes_of_term (all_modes_of thy) (list_comb (pred, params)));
val m = case modes
of [] => error ("No mode possible for comprehension "
^ Syntax.string_of_term_global thy t_compr)
| [m] => m
| m :: _ :: _ => (warning ("Multiple modes possible for comprehension "
^ Syntax.string_of_term_global thy t_compr); m);
val t_eval = list_comb (compile_expr thy (all_modes_of thy) (SOME m, list_comb (pred, params)),
inargs)
in t_eval end;
end;