(* Title: HOL/Statespace/state_space.ML
Author: Norbert Schirmer, TU Muenchen
*)
signature STATE_SPACE =
sig
val distinct_compsN : string
val getN : string
val putN : string
val injectN : string
val namespaceN : string
val projectN : string
val valuetypesN : string
val namespace_definition :
bstring ->
typ ->
(xstring, string) Expression.expr * (binding * string option * mixfix) list ->
string list -> string list -> theory -> theory
val define_statespace :
string list ->
string ->
((string * bool) * (string list * bstring * (string * string) list)) list ->
(string * string) list -> theory -> theory
val define_statespace_i :
string option ->
string list ->
string ->
((string * bool) * (typ list * bstring * (string * string) list)) list ->
(string * typ) list -> theory -> theory
val statespace_decl :
((string list * bstring) *
(((string * bool) * (string list * xstring * (bstring * bstring) list)) list *
(bstring * string) list)) parser
val neq_x_y : Proof.context -> term -> term -> thm option
val distinctNameSolver : Simplifier.solver
val distinctTree_tac : Proof.context -> int -> tactic
val distinct_simproc : Simplifier.simproc
val get_comp : Context.generic -> string -> (typ * string) option
val get_silent : Context.generic -> bool
val set_silent : bool -> Context.generic -> Context.generic
val gen_lookup_tr : Proof.context -> term -> string -> term
val lookup_swap_tr : Proof.context -> term list -> term
val lookup_tr : Proof.context -> term list -> term
val lookup_tr' : Proof.context -> term list -> term
val gen_update_tr :
bool -> Proof.context -> string -> term -> term -> term
val update_tr : Proof.context -> term list -> term
val update_tr' : Proof.context -> term list -> term
end;
structure StateSpace : STATE_SPACE =
struct
(* Names *)
val distinct_compsN = "distinct_names"
val namespaceN = "_namespace"
val valuetypesN = "_valuetypes"
val projectN = "project"
val injectN = "inject"
val getN = "get"
val putN = "put"
val project_injectL = "StateSpaceLocale.project_inject";
(* Library *)
fun fold1 f xs = fold f (tl xs) (hd xs)
fun fold1' f [] x = x
| fold1' f xs _ = fold1 f xs
fun sorted_subset eq [] ys = true
| sorted_subset eq (x::xs) [] = false
| sorted_subset eq (x::xs) (y::ys) = if eq (x,y) then sorted_subset eq xs ys
else sorted_subset eq (x::xs) ys;
type namespace_info =
{declinfo: (typ*string) Termtab.table, (* type, name of statespace *)
distinctthm: thm Symtab.table,
silent: bool
};
structure NameSpaceData = Generic_Data
(
type T = namespace_info;
val empty = {declinfo = Termtab.empty, distinctthm = Symtab.empty, silent = false};
val extend = I;
fun merge
({declinfo=declinfo1, distinctthm=distinctthm1, silent=silent1},
{declinfo=declinfo2, distinctthm=distinctthm2, silent=silent2}) : T =
{declinfo = Termtab.merge (K true) (declinfo1, declinfo2),
distinctthm = Symtab.merge (K true) (distinctthm1, distinctthm2),
silent = silent1 andalso silent2 (* FIXME odd merge *)}
);
fun make_namespace_data declinfo distinctthm silent =
{declinfo=declinfo,distinctthm=distinctthm,silent=silent};
fun update_declinfo (n,v) ctxt =
let val {declinfo,distinctthm,silent} = NameSpaceData.get ctxt;
in NameSpaceData.put
(make_namespace_data (Termtab.update (n,v) declinfo) distinctthm silent) ctxt
end;
fun set_silent silent ctxt =
let val {declinfo,distinctthm,...} = NameSpaceData.get ctxt;
in NameSpaceData.put
(make_namespace_data declinfo distinctthm silent) ctxt
end;
val get_silent = #silent o NameSpaceData.get;
fun expression_no_pos (expr, fixes) : Expression.expression =
(map (fn (name, inst) => ((name, Position.none), inst)) expr, fixes);
fun prove_interpretation_in ctxt_tac (name, expr) thy =
thy
|> Expression.sublocale_global_cmd (name, Position.none) (expression_no_pos expr) []
|> Proof.global_terminal_proof
((Method.Basic (fn ctxt => SIMPLE_METHOD (ctxt_tac ctxt)), Position.no_range), NONE)
|> Proof_Context.theory_of
fun add_locale name expr elems thy =
thy
|> Expression.add_locale (Binding.name name) (Binding.name name) expr elems
|> snd
|> Local_Theory.exit;
fun add_locale_cmd name expr elems thy =
thy
|> Expression.add_locale_cmd (Binding.name name) Binding.empty (expression_no_pos expr) elems
|> snd
|> Local_Theory.exit;
type statespace_info =
{args: (string * sort) list, (* type arguments *)
parents: (typ list * string * string option list) list,
(* type instantiation, state-space name, component renamings *)
components: (string * typ) list,
types: typ list (* range types of state space *)
};
structure StateSpaceData = Generic_Data
(
type T = statespace_info Symtab.table;
val empty = Symtab.empty;
val extend = I;
fun merge data : T = Symtab.merge (K true) data;
);
fun add_statespace name args parents components types ctxt =
StateSpaceData.put
(Symtab.update_new (name, {args=args,parents=parents,
components=components,types=types}) (StateSpaceData.get ctxt))
ctxt;
fun get_statespace ctxt name =
Symtab.lookup (StateSpaceData.get ctxt) name;
fun mk_free ctxt name =
if Variable.is_fixed ctxt name orelse Variable.is_declared ctxt name
then
let val n' = Variable.intern_fixed ctxt name
in SOME (Free (n', Proof_Context.infer_type ctxt (n', dummyT))) end
else NONE
fun get_dist_thm ctxt name = Symtab.lookup (#distinctthm (NameSpaceData.get ctxt)) name;
fun get_comp ctxt name =
Option.mapPartial
(Termtab.lookup (#declinfo (NameSpaceData.get ctxt)))
(mk_free (Context.proof_of ctxt) name);
(*** Tactics ***)
fun neq_x_y ctxt x y =
(let
val dist_thm = the (get_dist_thm (Context.Proof ctxt) (#1 (dest_Free x)));
val ctree = cprop_of dist_thm |> Thm.dest_comb |> #2 |> Thm.dest_comb |> #2;
val tree = term_of ctree;
val x_path = the (DistinctTreeProver.find_tree x tree);
val y_path = the (DistinctTreeProver.find_tree y tree);
val thm = DistinctTreeProver.distinctTreeProver dist_thm x_path y_path;
in SOME thm
end handle Option.Option => NONE)
fun distinctTree_tac ctxt = SUBGOAL (fn (goal, i) =>
(case goal of
Const (@{const_name Trueprop}, _) $
(Const (@{const_name Not}, _) $
(Const (@{const_name HOL.eq}, _) $ (x as Free _) $ (y as Free _))) =>
(case neq_x_y ctxt x y of
SOME neq => rtac neq i
| NONE => no_tac)
| _ => no_tac));
val distinctNameSolver = mk_solver "distinctNameSolver" distinctTree_tac;
val distinct_simproc =
Simplifier.simproc_global @{theory HOL} "StateSpace.distinct_simproc" ["x = y"]
(fn ctxt => (fn (Const (@{const_name HOL.eq},_)$(x as Free _)$(y as Free _)) =>
Option.map (fn neq => DistinctTreeProver.neq_to_eq_False OF [neq]) (neq_x_y ctxt x y)
| _ => NONE));
fun interprete_parent name dist_thm_name parent_expr thy =
let
fun solve_tac ctxt = CSUBGOAL (fn (goal, i) =>
let
val distinct_thm = Proof_Context.get_thm ctxt dist_thm_name;
val rule = DistinctTreeProver.distinct_implProver distinct_thm goal;
in rtac rule i end);
fun tac ctxt =
Locale.intro_locales_tac true ctxt [] THEN ALLGOALS (solve_tac ctxt);
in
thy |> prove_interpretation_in tac (name, parent_expr)
end;
fun namespace_definition name nameT parent_expr parent_comps new_comps thy =
let
val all_comps = parent_comps @ new_comps;
val vars = (map (fn n => (Binding.name n, NONE, NoSyn)) all_comps);
val dist_thm_name = distinct_compsN;
val dist_thm_full_name = dist_thm_name;
fun comps_of_thm thm = prop_of thm
|> (fn (_$(_$t)) => DistinctTreeProver.dest_tree t) |> map (fst o dest_Free);
fun type_attr phi = Thm.declaration_attribute (fn thm => fn context =>
(case context of
Context.Theory _ => context
| Context.Proof ctxt =>
let
val {declinfo,distinctthm=tt,silent} = NameSpaceData.get context;
val all_names = comps_of_thm thm;
fun upd name tt =
(case Symtab.lookup tt name of
SOME dthm => if sorted_subset (op =) (comps_of_thm dthm) all_names
then Symtab.update (name,thm) tt else tt
| NONE => Symtab.update (name,thm) tt)
val tt' = tt |> fold upd all_names;
val context' =
Context_Position.set_visible false ctxt
addsimprocs [distinct_simproc]
|> Context_Position.restore_visible ctxt
|> Context.Proof
|> NameSpaceData.put {declinfo=declinfo,distinctthm=tt',silent=silent};
in context' end));
val attr = Attrib.internal type_attr;
val assume =
((Binding.name dist_thm_name, [attr]),
[(HOLogic.Trueprop $
(Const (@{const_name all_distinct}, Type (@{type_name tree}, [nameT]) --> HOLogic.boolT) $
DistinctTreeProver.mk_tree (fn n => Free (n, nameT)) nameT
(sort fast_string_ord all_comps)), [])]);
in
thy
|> add_locale name ([], vars) [Element.Assumes [assume]]
|> Proof_Context.theory_of
|> interprete_parent name dist_thm_full_name parent_expr
end;
fun encode_dot x = if x = #"." then #"_" else x;
fun encode_type (TFree (s, _)) = s
| encode_type (TVar ((s,i),_)) = "?" ^ s ^ string_of_int i
| encode_type (Type (n,Ts)) =
let
val Ts' = fold1' (fn x => fn y => x ^ "_" ^ y) (map encode_type Ts) "";
val n' = String.map encode_dot n;
in if Ts'="" then n' else Ts' ^ "_" ^ n' end;
fun project_name T = projectN ^"_"^encode_type T;
fun inject_name T = injectN ^"_"^encode_type T;
fun add_declaration name decl thy =
thy
|> Named_Target.init name
|> (fn lthy => Local_Theory.declaration {syntax = false, pervasive = false} (decl lthy) lthy)
|> Local_Theory.exit_global;
fun parent_components thy (Ts, pname, renaming) =
let
val ctxt = Context.Theory thy;
fun rename [] xs = xs
| rename (NONE::rs) (x::xs) = x::rename rs xs
| rename (SOME r::rs) ((x,T)::xs) = (r,T)::rename rs xs;
val {args, parents, components, ...} = the (Symtab.lookup (StateSpaceData.get ctxt) pname);
val inst = map fst args ~~ Ts;
val subst = Term.map_type_tfree (the o AList.lookup (op =) inst o fst);
val parent_comps =
maps (fn (Ts',n,rs) => parent_components thy (map subst Ts', n, rs)) parents;
val all_comps = rename renaming (parent_comps @ map (apsnd subst) components);
in all_comps end;
fun statespace_definition state_type args name parents parent_comps components thy =
let
val full_name = Sign.full_bname thy name;
val all_comps = parent_comps @ components;
val components' = map (fn (n,T) => (n,(T,full_name))) components;
fun parent_expr (prefix, (_, n, rs)) =
(suffix namespaceN n, (prefix, Expression.Positional rs));
val parents_expr = map parent_expr parents;
fun distinct_types Ts =
let val tab = fold (fn T => fn tab => Typtab.update (T,()) tab) Ts Typtab.empty;
in map fst (Typtab.dest tab) end;
val Ts = distinct_types (map snd all_comps);
val arg_names = map fst args;
val valueN = singleton (Name.variant_list arg_names) "'value";
val nameN = singleton (Name.variant_list (valueN :: arg_names)) "'name";
val valueT = TFree (valueN, Sign.defaultS thy);
val nameT = TFree (nameN, Sign.defaultS thy);
val stateT = nameT --> valueT;
fun projectT T = valueT --> T;
fun injectT T = T --> valueT;
val locinsts = map (fn T => (project_injectL,
((encode_type T,false),Expression.Positional
[SOME (Free (project_name T,projectT T)),
SOME (Free ((inject_name T,injectT T)))]))) Ts;
val locs = maps (fn T => [(Binding.name (project_name T),NONE,NoSyn),
(Binding.name (inject_name T),NONE,NoSyn)]) Ts;
val constrains = maps (fn T => [(project_name T,projectT T),(inject_name T,injectT T)]) Ts;
fun interprete_parent_valuetypes (prefix, (Ts, pname, _)) thy =
let
val {args,types,...} =
the (Symtab.lookup (StateSpaceData.get (Context.Theory thy)) pname);
val inst = map fst args ~~ Ts;
val subst = Term.map_type_tfree (the o AList.lookup (op =) inst o fst);
val pars = maps ((fn T => [project_name T,inject_name T]) o subst) types;
val expr = ([(suffix valuetypesN name,
(prefix, Expression.Positional (map SOME pars)))],[]);
in
prove_interpretation_in (ALLGOALS o solve_tac o Assumption.all_prems_of)
(suffix valuetypesN name, expr) thy
end;
fun interprete_parent (prefix, (_, pname, rs)) =
let
val expr = ([(pname, (prefix, Expression.Positional rs))],[])
in prove_interpretation_in
(fn ctxt => Locale.intro_locales_tac false ctxt [])
(full_name, expr) end;
fun declare_declinfo updates lthy phi ctxt =
let
fun upd_prf ctxt =
let
fun upd (n,v) =
let
val nT = Proof_Context.infer_type (Local_Theory.target_of lthy) (n, dummyT)
in Context.proof_map
(update_declinfo (Morphism.term phi (Free (n,nT)),v))
end;
in ctxt |> fold upd updates end;
in Context.mapping I upd_prf ctxt end;
fun string_of_typ T =
Print_Mode.setmp []
(Syntax.string_of_typ (Config.put show_sorts true (Syntax.init_pretty_global thy))) T;
val fixestate = (case state_type of
NONE => []
| SOME s =>
let
val fx = Element.Fixes [(Binding.name s,SOME (string_of_typ stateT),NoSyn)];
val cs = Element.Constrains
(map (fn (n,T) => (n,string_of_typ T))
((map (fn (n,_) => (n,nameT)) all_comps) @
constrains))
in [fx,cs] end
)
in thy
|> namespace_definition
(suffix namespaceN name) nameT (parents_expr,[])
(map fst parent_comps) (map fst components)
|> Context.theory_map (add_statespace full_name args (map snd parents) components [])
|> add_locale (suffix valuetypesN name) (locinsts,locs) []
|> Proof_Context.theory_of
|> fold interprete_parent_valuetypes parents
|> add_locale_cmd name
([(suffix namespaceN full_name ,(("",false),Expression.Named [])),
(suffix valuetypesN full_name,(("",false),Expression.Named []))],[]) fixestate
|> Proof_Context.theory_of
|> fold interprete_parent parents
|> add_declaration full_name (declare_declinfo components')
end;
(* prepare arguments *)
fun read_typ ctxt raw_T env =
let
val ctxt' = fold (Variable.declare_typ o TFree) env ctxt;
val T = Syntax.read_typ ctxt' raw_T;
val env' = Term.add_tfreesT T env;
in (T, env') end;
fun cert_typ ctxt raw_T env =
let
val thy = Proof_Context.theory_of ctxt;
val T = Type.no_tvars (Sign.certify_typ thy raw_T)
handle TYPE (msg, _, _) => error msg;
val env' = Term.add_tfreesT T env;
in (T, env') end;
fun gen_define_statespace prep_typ state_space args name parents comps thy =
let (* - args distinct
- only args may occur in comps and parent-instantiations
- number of insts must match parent args
- no duplicate renamings
- renaming should occur in namespace
*)
val _ = writeln ("Defining statespace " ^ quote name ^ " ...");
val ctxt = Proof_Context.init_global thy;
fun add_parent (prefix, (Ts, pname, rs)) env =
let
val prefix' =
(case prefix of
("", mandatory) => (pname, mandatory)
| _ => prefix);
val full_pname = Sign.full_bname thy pname;
val {args,components,...} =
(case get_statespace (Context.Theory thy) full_pname of
SOME r => r
| NONE => error ("Undefined statespace " ^ quote pname));
val (Ts',env') = fold_map (prep_typ ctxt) Ts env
handle ERROR msg => cat_error msg
("The error(s) above occurred in parent statespace specification "
^ quote pname);
val err_insts = if length args <> length Ts' then
["number of type instantiation(s) does not match arguments of parent statespace "
^ quote pname]
else [];
val rnames = map fst rs
val err_dup_renamings = (case duplicates (op =) rnames of
[] => []
| dups => ["Duplicate renaming(s) for " ^ commas dups])
val cnames = map fst components;
val err_rename_unknowns = (case subtract (op =) cnames rnames of
[] => []
| rs => ["Unknown components " ^ commas rs]);
val rs' = map (AList.lookup (op =) rs o fst) components;
val errs =err_insts @ err_dup_renamings @ err_rename_unknowns
in
if null errs then ((prefix', (Ts', full_pname, rs')), env')
else error (cat_lines (errs @ ["in parent statespace " ^ quote pname]))
end;
val (parents',env) = fold_map add_parent parents [];
val err_dup_args =
(case duplicates (op =) args of
[] => []
| dups => ["Duplicate type argument(s) " ^ commas dups]);
val err_dup_components =
(case duplicates (op =) (map fst comps) of
[] => []
| dups => ["Duplicate state-space components " ^ commas dups]);
fun prep_comp (n,T) env =
let val (T', env') = prep_typ ctxt T env handle ERROR msg =>
cat_error msg ("The error(s) above occurred in component " ^ quote n)
in ((n,T'), env') end;
val (comps',env') = fold_map prep_comp comps env;
val err_extra_frees =
(case subtract (op =) args (map fst env') of
[] => []
| extras => ["Extra free type variable(s) " ^ commas extras]);
val defaultS = Sign.defaultS thy;
val args' = map (fn x => (x, AList.lookup (op =) env x |> the_default defaultS)) args;
fun fst_eq ((x:string,_),(y,_)) = x = y;
fun snd_eq ((_,t:typ),(_,u)) = t = u;
val raw_parent_comps = maps (parent_components thy o snd) parents';
fun check_type (n,T) =
(case distinct (snd_eq) (filter (curry fst_eq (n,T)) raw_parent_comps) of
[] => []
| [_] => []
| rs => ["Different types for component " ^ quote n ^ ": " ^
commas (map (Syntax.string_of_typ ctxt o snd) rs)])
val err_dup_types = maps check_type (duplicates fst_eq raw_parent_comps)
val parent_comps = distinct (fst_eq) raw_parent_comps;
val all_comps = parent_comps @ comps';
val err_comp_in_parent = (case duplicates (op =) (map fst all_comps) of
[] => []
| xs => ["Components already defined in parents: " ^ commas_quote xs]);
val errs = err_dup_args @ err_dup_components @ err_extra_frees @
err_dup_types @ err_comp_in_parent;
in if null errs
then thy |> statespace_definition state_space args' name parents' parent_comps comps'
else error (cat_lines errs)
end
handle ERROR msg => cat_error msg ("Failed to define statespace " ^ quote name);
val define_statespace = gen_define_statespace read_typ NONE;
val define_statespace_i = gen_define_statespace cert_typ;
(*** parse/print - translations ***)
local
fun map_get_comp f ctxt (Free (name,_)) =
(case (get_comp ctxt name) of
SOME (T,_) => f T T dummyT
| NONE => (Syntax.free "arbitrary"(*; error "context not ready"*)))
| map_get_comp _ _ _ = Syntax.free "arbitrary";
fun name_of (Free (n,_)) = n;
in
fun gen_lookup_tr ctxt s n =
(case get_comp (Context.Proof ctxt) n of
SOME (T, _) =>
Syntax.const @{const_name StateFun.lookup} $
Syntax.free (project_name T) $ Syntax.free n $ s
| NONE =>
if get_silent (Context.Proof ctxt)
then Syntax.const @{const_name StateFun.lookup} $
Syntax.const @{const_syntax undefined} $ Syntax.free n $ s
else raise TERM ("StateSpace.gen_lookup_tr: component " ^ quote n ^ " not defined", []));
fun lookup_tr ctxt [s, x] =
(case Term_Position.strip_positions x of
Free (n,_) => gen_lookup_tr ctxt s n
| _ => raise Match);
fun lookup_swap_tr ctxt [Free (n,_),s] = gen_lookup_tr ctxt s n;
fun lookup_tr' ctxt [_ $ Free (prj, _), n as (_ $ Free (name, _)), s] =
(case get_comp (Context.Proof ctxt) name of
SOME (T, _) =>
if prj = project_name T
then Syntax.const "_statespace_lookup" $ s $ n
else raise Match
| NONE => raise Match)
| lookup_tr' _ _ = raise Match;
fun gen_update_tr id ctxt n v s =
let
fun pname T = if id then @{const_name Fun.id} else project_name T;
fun iname T = if id then @{const_name Fun.id} else inject_name T;
in
(case get_comp (Context.Proof ctxt) n of
SOME (T, _) =>
Syntax.const @{const_name StateFun.update} $
Syntax.free (pname T) $ Syntax.free (iname T) $
Syntax.free n $ (Syntax.const @{const_name K_statefun} $ v) $ s
| NONE =>
if get_silent (Context.Proof ctxt) then
Syntax.const @{const_name StateFun.update} $
Syntax.const @{const_syntax undefined} $ Syntax.const @{const_syntax undefined} $
Syntax.free n $ (Syntax.const @{const_name K_statefun} $ v) $ s
else raise TERM ("StateSpace.gen_update_tr: component " ^ n ^ " not defined", []))
end;
fun update_tr ctxt [s, x, v] =
(case Term_Position.strip_positions x of
Free (n, _) => gen_update_tr false ctxt n v s
| _ => raise Match);
fun update_tr' ctxt
[_ $ Free (prj, _), _ $ Free (inj, _), n as (_ $ Free (name, _)), (Const (k, _) $ v), s] =
if Long_Name.base_name k = Long_Name.base_name @{const_name K_statefun} then
(case get_comp (Context.Proof ctxt) name of
SOME (T, _) =>
if inj = inject_name T andalso prj = project_name T then
Syntax.const "_statespace_update" $ s $ n $ v
else raise Match
| NONE => raise Match)
else raise Match
| update_tr' _ _ = raise Match;
end;
(*** outer syntax *)
local
val type_insts =
Parse.typ >> single ||
@{keyword "("} |-- Parse.!!! (Parse.list1 Parse.typ --| @{keyword ")"})
val comp = Parse.name -- (@{keyword "::"} |-- Parse.!!! Parse.typ);
fun plus1_unless test scan =
scan ::: Scan.repeat (@{keyword "+"} |-- Scan.unless test (Parse.!!! scan));
val mapsto = @{keyword "="};
val rename = Parse.name -- (mapsto |-- Parse.name);
val renames = Scan.optional (@{keyword "["} |-- Parse.!!! (Parse.list1 rename --| @{keyword "]"})) [];
val parent =
Parse_Spec.locale_prefix false --
((type_insts -- Parse.xname) || (Parse.xname >> pair [])) -- renames
>> (fn ((prefix, (insts, name)), renames) => (prefix, (insts, name, renames)));
in
val statespace_decl =
Parse.type_args -- Parse.name --
(@{keyword "="} |--
((Scan.repeat1 comp >> pair []) ||
(plus1_unless comp parent --
Scan.optional (@{keyword "+"} |-- Parse.!!! (Scan.repeat1 comp)) [])));
val _ =
Outer_Syntax.command @{command_spec "statespace"} "define state-space as locale context"
(statespace_decl >> (fn ((args, name), (parents, comps)) =>
Toplevel.theory (define_statespace args name parents comps)));
end;
end;