(* 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 prove_equation: string -> mode option -> theory -> theory
val intro_rule: theory -> string -> mode -> thm
val elim_rule: theory -> string -> mode -> thm
val strip_intro_concl: term -> int -> term * (term list * term list)
val modename_of: theory -> string -> mode -> string
val modes_of: theory -> string -> mode list
val pred_intros: theory -> string -> thm list
val get_nparams: theory -> string -> int
val setup: theory -> theory
val code_pred: string -> Proof.context -> Proof.state
val code_pred_cmd: string -> Proof.context -> Proof.state
val print_alternative_rules: theory -> theory (*FIXME diagnostic command?*)
val do_proofs: bool ref
val analyze_compr: theory -> term -> term
val eval_ref: (unit -> term Predicate.pred) option ref
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 debug_tac msg = (fn st => (tracing msg; Seq.single st));
val do_proofs = ref true;
(** 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 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 ("Predicate.pred", [T])
fun dest_pred_enumT (Type ("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
(* data structures *)
type mode = int list option list * int list;
val mode_ord = prod_ord (list_ord (option_ord (list_ord int_ord))) (list_ord int_ord);
structure PredModetab = TableFun(
type key = string * mode
val ord = prod_ord fast_string_ord mode_ord
);
(*FIXME scrap boilerplate*)
structure IndCodegenData = TheoryDataFun
(
type T = {names : string PredModetab.table,
modes : mode list Symtab.table,
function_defs : Thm.thm Symtab.table,
function_intros : Thm.thm Symtab.table,
function_elims : Thm.thm Symtab.table,
intro_rules : Thm.thm list Symtab.table,
elim_rules : Thm.thm Symtab.table,
nparams : int Symtab.table
}; (*FIXME: better group tables according to key*)
(* names: map from inductive predicate and mode to function name (string).
modes: map from inductive predicates to modes
function_defs: map from function name to definition
function_intros: map from function name to intro rule
function_elims: map from function name to elim rule
intro_rules: map from inductive predicate to alternative intro rules
elim_rules: map from inductive predicate to alternative elimination rule
nparams: map from const name to number of parameters (* assuming there exist intro and elimination rules *)
*)
val empty = {names = PredModetab.empty,
modes = Symtab.empty,
function_defs = Symtab.empty,
function_intros = Symtab.empty,
function_elims = Symtab.empty,
intro_rules = Symtab.empty,
elim_rules = Symtab.empty,
nparams = Symtab.empty};
val copy = I;
val extend = I;
fun merge _ r = {names = PredModetab.merge (op =) (pairself #names r),
modes = Symtab.merge (op =) (pairself #modes r),
function_defs = Symtab.merge Thm.eq_thm (pairself #function_defs r),
function_intros = Symtab.merge Thm.eq_thm (pairself #function_intros r),
function_elims = Symtab.merge Thm.eq_thm (pairself #function_elims r),
intro_rules = Symtab.merge ((forall Thm.eq_thm) o (op ~~)) (pairself #intro_rules r),
elim_rules = Symtab.merge Thm.eq_thm (pairself #elim_rules r),
nparams = Symtab.merge (op =) (pairself #nparams r)};
);
fun map_names f thy = IndCodegenData.map
(fn x => {names = f (#names x), modes = #modes x, function_defs = #function_defs x,
function_intros = #function_intros x, function_elims = #function_elims x,
intro_rules = #intro_rules x, elim_rules = #elim_rules x,
nparams = #nparams x}) thy
fun map_modes f thy = IndCodegenData.map
(fn x => {names = #names x, modes = f (#modes x), function_defs = #function_defs x,
function_intros = #function_intros x, function_elims = #function_elims x,
intro_rules = #intro_rules x, elim_rules = #elim_rules x,
nparams = #nparams x}) thy
fun map_function_defs f thy = IndCodegenData.map
(fn x => {names = #names x, modes = #modes x, function_defs = f (#function_defs x),
function_intros = #function_intros x, function_elims = #function_elims x,
intro_rules = #intro_rules x, elim_rules = #elim_rules x,
nparams = #nparams x}) thy
fun map_function_elims f thy = IndCodegenData.map
(fn x => {names = #names x, modes = #modes x, function_defs = #function_defs x,
function_intros = #function_intros x, function_elims = f (#function_elims x),
intro_rules = #intro_rules x, elim_rules = #elim_rules x,
nparams = #nparams x}) thy
fun map_function_intros f thy = IndCodegenData.map
(fn x => {names = #names x, modes = #modes x, function_defs = #function_defs x,
function_intros = f (#function_intros x), function_elims = #function_elims x,
intro_rules = #intro_rules x, elim_rules = #elim_rules x,
nparams = #nparams x}) thy
fun map_intro_rules f thy = IndCodegenData.map
(fn x => {names = #names x, modes = #modes x, function_defs = #function_defs x,
function_intros = #function_intros x, function_elims = #function_elims x,
intro_rules = f (#intro_rules x), elim_rules = #elim_rules x,
nparams = #nparams x}) thy
fun map_elim_rules f thy = IndCodegenData.map
(fn x => {names = #names x, modes = #modes x, function_defs = #function_defs x,
function_intros = #function_intros x, function_elims = #function_elims x,
intro_rules = #intro_rules x, elim_rules = f (#elim_rules x),
nparams = #nparams x}) thy
fun map_nparams f thy = IndCodegenData.map
(fn x => {names = #names x, modes = #modes x, function_defs = #function_defs x,
function_intros = #function_intros x, function_elims = #function_elims x,
intro_rules = #intro_rules x, elim_rules = #elim_rules x,
nparams = f (#nparams x)}) thy
(* removes first subgoal *)
fun mycheat_tac thy i st =
(Tactic.rtac (SkipProof.make_thm thy (Var (("A", 0), propT))) i) st
(* Lightweight mode analysis **********************************************)
(**************************************************************************)
(* source code from old code generator ************************************)
(**** 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 (DatatypePackage.get_datatypes 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;
(**** mode inference ****)
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 = tracing ("Inferred modes:\n" ^
cat_lines (map (fn (s, ms) => s ^ ": " ^ commas (map
string_of_mode ms)) modes));
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 [[]];
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!?*)
fun 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)
| _ => 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);
(*****************************************************************************************)
(**** end of old source code *************************************************************)
(*****************************************************************************************)
(**** 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 => ((names, (s, [])::vs), Free (s, T))
| SOME xs =>
let
val s' = Name.variant names s;
val v = Free (s', T)
in
((s'::names, AList.update (op =) (s, v::xs) vs), v)
end);
fun distinct_v (nvs, Free (s, T)) = mk_v nvs s T
| distinct_v (nvs, t $ u) =
let
val (nvs', t') = distinct_v (nvs, t);
val (nvs'', u') = distinct_v (nvs', u);
in (nvs'', t' $ u') end
| distinct_v x = x;
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 (DatatypePackage.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;
fun modename_of thy name mode = let
val v = (PredModetab.lookup (#names (IndCodegenData.get thy)) (name, mode))
in if (is_some v) then the v (*FIXME use case here*)
else error ("fun modename_of - definition not found: name: " ^ name ^ " mode: " ^ (makestring mode))
end
fun modes_of thy =
these o Symtab.lookup ((#modes o IndCodegenData.get) thy);
(*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 thy modes (NONE, t) = t
| compile_param thy modes (m as SOME (Mode ((iss, is'), is, ms)), t) = let
val (f, args) = strip_comb 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 (modename_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)
val mode_id = modename_of thy name mode
in list_comb (Const (mode_id, ((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 ((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, out_ts) = get_args is ts;
val ((all_vs', eqs), in_ts') =
(*FIXME*) Library.foldl_map check_constrt ((all_vs, []), in_ts);
fun compile_prems out_ts' vs names [] =
let
val ((names', eqs'), out_ts'') =
(*FIXME*) Library.foldl_map check_constrt ((names, []), out_ts');
val (nvs, out_ts''') = (*FIXME*) Library.foldl_map distinct_v
((names', map (rpair []) vs), out_ts'');
in
compile_match thy (snd nvs) (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 ((names', eqs), out_ts') =
(*FIXME*) Library.foldl_map check_constrt ((names, []), out_ts)
val (nvs, out_ts'') = (*FIXME*) Library.foldl_map distinct_v
((names', map (rpair []) vs), out_ts')
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' (fst nvs) 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' (fst nvs) ps'
in
(mk_not_pred u, rest)
end
| Sidecond t =>
let
val rest = compile_prems [] vs' (fst nvs) ps';
in
(mk_if_predenum t, rest)
end
in
compile_match thy (snd nvs) 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 = modename_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;
(* end of term construction ******************************************************)
(* special setup for simpset *)
val HOL_basic_ss' = HOL_basic_ss setSolver
(mk_solver "all_tac_solver" (fn _ => fn _ => all_tac))
(* misc: constructing and proving tupleE rules ***********************************)
(* Creating definitions of functional programs
and proving intro and elim rules **********************************************)
fun is_ind_pred thy c =
(can (InductivePackage.the_inductive (ProofContext.init thy)) c) orelse
(c mem_string (Symtab.keys (#intro_rules (IndCodegenData.get thy))))
fun get_name_of_ind_calls_of_clauses thy preds intrs =
fold Term.add_consts intrs [] |> map fst
|> filter_out (member (op =) preds) |> filter (is_ind_pred thy)
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_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 (params', names) = fold_map mk_Eval_of ((params ~~ Ts1) ~~ (fst mode)) []
val predprop = HOLogic.mk_Trueprop (list_comb (pred, params' @ io_args))
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.mk_implies (predprop, funpropI)
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 @ ["y"]) [] introtrm (fn {...} => unfolddef_tac)
val P = HOLogic.mk_Trueprop (Free ("P", HOLogic.boolT));
val elimtrm = Logic.list_implies ([funpropE, Logic.mk_implies (predprop, P)], P)
val elimthm = Goal.prove (ProofContext.init thy) (argnames @ ["y", "P"]) [] elimtrm (fn {...} => unfolddef_tac)
in
map_function_intros (Symtab.update_new (mode_id, introthm)) thy
|> map_function_elims (Symtab.update_new (mode_id, elimthm))
|> PureThy.store_thm (Binding.name (Long_Name.base_name mode_id ^ "I"), introthm) |> snd
|> PureThy.store_thm (Binding.name (Long_Name.base_name mode_id ^ "E"), elimthm) |> snd
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 ([defthm], 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), [])]
in thy' |> map_names (PredModetab.update_new ((name, mode), mode_id))
|> map_function_defs (Symtab.update_new (mode_id, defthm))
|> create_intro_rule nparams mode defthm mode_id funT (Const (name, T))
end;
in
fold create_definition modes thy
end;
(**************************************************************************************)
(* Proving equivalence of term *)
fun intro_rule thy pred mode = modename_of thy pred mode
|> Symtab.lookup (#function_intros (IndCodegenData.get thy)) |> the
fun elim_rule thy pred mode = modename_of thy pred mode
|> Symtab.lookup (#function_elims (IndCodegenData.get thy)) |> the
fun pred_intros thy predname = let
fun is_intro_of pred intro = let
val const = fst (strip_comb (HOLogic.dest_Trueprop (concl_of intro)))
in (fst (dest_Const const) = pred) end;
val d = IndCodegenData.get thy
in
if (Symtab.defined (#intro_rules d) predname) then
rev (Symtab.lookup_list (#intro_rules d) predname)
else
InductivePackage.the_inductive (ProofContext.init thy) predname
|> snd |> #intrs |> filter (is_intro_of predname)
end
fun function_definition thy pred mode =
modename_of thy pred mode |> Symtab.lookup (#function_defs (IndCodegenData.get thy)) |> the
fun is_Type (Type _) = true
| is_Type _ = false
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;
(* 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 DatatypePackage.get_datatype 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) = 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}::function_definition thy name mode::[]) 1
| Free _ => all_tac
in
print_tac "before simplification in prove_args:"
THEN debug_tac ("mode" ^ (makestring mode))
THEN f_tac
THEN print_tac "after simplification in prove_args"
(* work with parameter arguments *)
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 = intro_rule 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 _ = tracing ("args: " ^ (makestring args))
val subst = map (pairself (cterm_of thy)) (args ~~ us)
val _ = tracing ("subst: " ^ (makestring subst))
val inst_introrule = Drule.cterm_instantiate subst introrule*)
(* the next line is old and probably wrong *)
val (args1, args2) = chop (length ms) args
val _ = tracing ("premposition: " ^ (makestring premposition))
in
rtac @{thm bindI} 1
THEN print_tac "before intro rule:"
THEN debug_tac ("mode" ^ (makestring mode))
THEN debug_tac (makestring introrule)
THEN debug_tac ("premposition: " ^ (makestring premposition))
(* for the right assumption in first position *)
THEN rotate_tac premposition 1
THEN rtac introrule 1
THEN print_tac "after intro rule"
(* work with parameter arguments *)
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 (DatatypePackage.the_datatype 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
print_tac ("before prove_match rewriting: simprules = " ^ (makestring simprules))
(* make this simpset better! *)
THEN 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
val _ = tracing ("prove_sidecond:" ^ (makestring t))
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 _ = tracing ("preds: " ^ (makestring preds))
val defs = map
(fn (pred, T) => function_definition thy pred ([], (1 upto (length (binder_types T)))))
preds
val _ = tracing ("defs: " ^ (makestring defs))
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! *)
THEN print_tac "after sidecond simplification"
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
print_tac "before negated clause:"
THEN rtac @{thm bindI} 1
THEN (if (is_some name) then
simp_tac (HOL_basic_ss addsimps [function_definition thy (the name) (iss, js)]) 1
THEN rtac @{thm not_predI} 1
THEN print_tac "after neg. intro rule"
THEN print_tac ("t = " ^ (makestring t))
(* 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));
(* FIXME: This function relies on the derivation of an induction rule *)
fun get_nparams thy s = let
val _ = tracing ("get_nparams: " ^ s)
in
if Symtab.defined (#nparams (IndCodegenData.get thy)) s then
the (Symtab.lookup (#nparams (IndCodegenData.get thy)) s)
else
case try (InductivePackage.the_inductive (ProofContext.init thy)) s of
SOME info => info |> snd |> #raw_induct |> Thm.unvarify
|> InductivePackage.params_of |> length
| NONE => 0 (* default value *)
end
val ind_set_codegen_preproc = InductiveSetPackage.codegen_preproc;
fun pred_elim thy predname =
if (Symtab.defined (#elim_rules (IndCodegenData.get thy)) predname) then
the (Symtab.lookup (#elim_rules (IndCodegenData.get thy)) predname)
else
(let
val ind_result = InductivePackage.the_inductive (ProofContext.init thy) predname
val index = find_index (fn s => s = predname) (#names (fst ind_result))
in nth (#elims (snd ind_result)) index end)
fun prove_one_direction thy all_vs param_vs modes clauses ((pred, T), mode) = let
val elim_rule = the (Symtab.lookup (#function_elims (IndCodegenData.get thy)) (modename_of thy pred mode))
(* val ind_result = InductivePackage.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) - get_nparams thy pred
val pred_case_rule = singleton (ind_set_codegen_preproc thy)
(preprocess_elim thy nargs (pred_elim thy pred))
(* FIXME preprocessor |> Simplifier.full_simplify (HOL_basic_ss addsimps [@ {thm Predicate.memb_code}])*)
val _ = tracing ("pred_case_rule " ^ (makestring pred_case_rule))
in
REPEAT_DETERM (CHANGED (rewtac @{thm "split_paired_all"}))
THEN etac elim_rule 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))
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 = DatatypePackage.the_datatype 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
print_tac ("splitting with t = " ^ (makestring t))
THEN (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}::function_definition thy name mode::[]) 1
| Free _ => all_tac
in
print_tac "before simplification in prove_args:"
THEN debug_tac ("function : " ^ (makestring f) ^ " - mode" ^ (makestring mode))
THEN f_tac
THEN print_tac "after simplification in prove_args"
(* work with parameter arguments *)
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 (etac (elim_rule thy name mode) 1)
THEN (EVERY (map (prove_param2 thy modes) (ms ~~ args)))
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
val _ = tracing ("prove_sidecond:" ^ (makestring t))
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 _ = tracing ("preds: " ^ (makestring preds))
val defs = map
(fn (pred, T) => function_definition 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 (pred_intros 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 [function_definition thy (the name) (iss, js)]) 1
THEN etac @{thm not_predE} 1
THEN (EVERY (map (prove_param2 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
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 (intro_rule thy pred mode) 1)
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
(* look for other place where this functionality was used before *)
fun strip_intro_concl intro nparams = 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
(* setup for alternative introduction and elimination rules *)
fun add_intro_thm thm thy = let
val (pred, _) = dest_Const (fst (strip_intro_concl (prop_of thm) 0))
in map_intro_rules (Symtab.insert_list Thm.eq_thm (pred, thm)) thy end
fun add_elim_thm thm thy = let
val (pred, _) = dest_Const (fst
(strip_comb (HOLogic.dest_Trueprop (hd (prems_of thm)))))
in map_elim_rules (Symtab.update (pred, thm)) thy end
(* 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_thm = Goal.prove (ProofContext.init thy) names [] intro_t
(fn {...} => etac @{thm FalseE} 1)
val elim_thm = Goal.prove (ProofContext.init thy) ("P" :: names) [] elim_t
(fn {...} => etac (pred_elim thy predname) 1)
in
add_intro_thm intro_thm thy
|> add_elim_thm elim_thm
end
(*************************************************************************************)
(* main function *********************************************************************)
(*************************************************************************************)
fun prove_equation ind_name mode thy =
let
val _ = tracing ("starting prove_equation' with " ^ ind_name)
val (prednames, preds) =
case (try (InductivePackage.the_inductive (ProofContext.init thy)) ind_name) of
SOME info => let val preds = info |> snd |> #preds
in (map (fst o dest_Const) preds, map ((apsnd Logic.unvarifyT) o dest_Const) preds) end
| NONE => let
val pred = Symtab.lookup (#intro_rules (IndCodegenData.get thy)) ind_name
|> the |> hd |> prop_of
|> Logic.strip_imp_concl |> HOLogic.dest_Trueprop |> strip_comb
|> fst |> dest_Const |> apsnd Logic.unvarifyT
in ([ind_name], [pred]) end
val thy' = fold (fn pred as (predname, T) => fn thy =>
if null (pred_intros thy predname) then noclause pred thy else thy) preds thy
val intrs = map (preprocess_intro thy') (maps (pred_intros 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 _ = tracing ("preprocessed intro rules:" ^ (makestring (map (cterm_of thy') intrs)))
val name_of_calls = get_name_of_ind_calls_of_clauses thy' prednames intrs
val _ = tracing ("calling preds: " ^ makestring name_of_calls)
val _ = tracing "starting recursive compilations"
fun rec_call name thy =
(*FIXME use member instead of infix mem*)
if not (name mem (Symtab.keys (#modes (IndCodegenData.get thy)))) then
prove_equation name NONE thy else thy
val thy'' = fold rec_call name_of_calls thy'
val _ = tracing "returning from recursive calls"
val _ = tracing "starting mode inference"
val extra_modes = Symtab.dest (#modes (IndCodegenData.get thy''))
val nparams = get_nparams thy'' ind_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: " ^ (makestring (c $ t)))
| Sidecond t => Sidecond (c $ t))
| (c as Const (s, _), ts) =>
if is_ind_pred thy'' s then
let val (ts1, ts2) = chop (get_nparams 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 ([], []);
val modes = infer_modes thy'' extra_modes arities param_vs clauses
val _ = print_arities arities;
val _ = print_modes modes;
val modes = if (is_some mode) then AList.update (op =) (ind_name, [the mode]) modes else modes
val _ = print_modes modes
val thy''' = fold (create_definitions preds nparams) modes thy''
|> map_modes (fold Symtab.update_new modes)
val clauses' = map (fn (s, cls) => (s, (the (AList.lookup (op =) preds s), cls))) clauses
val _ = tracing "compiling predicates..."
val ts = compile_preds thy''' all_vs param_vs (extra_modes @ modes) clauses'
val _ = tracing "returned term from compile_preds"
val pred_mode = maps (fn (s, (T, _)) => map (pair (s, T)) ((the o AList.lookup (op =) modes) s)) clauses'
val _ = tracing "starting proof"
val result_thms = prove_preds thy''' all_vs param_vs (extra_modes @ modes) clauses (pred_mode ~~ (flat ts))
val (_, thy'''') = yield_singleton PureThy.add_thmss
((Binding.qualify true (Long_Name.base_name ind_name) (Binding.name "equation"), result_thms),
[Attrib.attribute_i thy''' Code.add_default_eqn_attrib]) thy'''
in
thy''''
end
fun set_nparams (pred, nparams) thy = map_nparams (Symtab.update (pred, nparams)) thy
fun print_alternative_rules thy = let
val d = IndCodegenData.get thy
val preds = (Symtab.keys (#intro_rules d)) union (Symtab.keys (#elim_rules d))
val _ = tracing ("preds: " ^ (makestring preds))
fun print pred = let
val _ = tracing ("predicate: " ^ pred)
val _ = tracing ("introrules: ")
val _ = fold (fn thm => fn u => tracing (makestring thm))
(rev (Symtab.lookup_list (#intro_rules d) pred)) ()
val _ = tracing ("casesrule: ")
val _ = tracing (makestring (Symtab.lookup (#elim_rules d) pred))
in () end
val _ = map print preds
in thy end;
(* generation of case rules from user-given introduction rules *)
fun mk_casesrule introrules nparams ctxt =
let
val intros = map prop_of introrules
val (pred, (params, args)) = strip_intro_concl (hd intros) nparams
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 = map Free (argnames ~~ (map fastype_of args))
(*FIXME map2*)
fun mk_case intro = let
val (_, (_, args)) = strip_intro_concl intro nparams
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
val (_, ctxt3) = ProofContext.add_assms_i Assumption.assume_export
[((Binding.name AutoBind.assmsN, []), map (fn t => (t, [])) (assm :: cases))]
ctxt2
in (pred, prop, ctxt3) end;
(** user interface **)
local
fun attrib f = Thm.declaration_attribute (fn thm => Context.mapping (f thm) I);
val add_elim_attrib = attrib add_elim_thm;
fun generic_code_pred prep_const raw_const lthy =
let
val thy = ProofContext.theory_of lthy
val const = prep_const thy raw_const
val nparams = get_nparams thy const
val intro_rules = pred_intros thy const
val (((tfrees, frees), fact), lthy') =
Variable.import_thms true intro_rules lthy;
val (pred, prop, lthy'') = mk_casesrule fact nparams lthy'
val (predname, _) = dest_Const pred
fun after_qed [[th]] lthy'' =
lthy''
|> LocalTheory.note Thm.generatedK
((Binding.empty, [Attrib.internal (K add_elim_attrib)]), [th])
|> snd
|> LocalTheory.theory (prove_equation predname NONE)
in
Proof.theorem_i NONE after_qed [[(prop, [])]] 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 =
Attrib.setup @{binding code_ind_intros} (Scan.succeed (attrib add_intro_thm))
"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 atribute 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 (get_nparams 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 all_modes = Symtab.dest (#modes (IndCodegenData.get thy));
val modes = filter (fn Mode (_, is, _) => is = user_mode)
(modes_of_term all_modes (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 (SOME m, list_comb (pred, params)),
inargs)
in t_eval end;
end;