(* 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: bool -> 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 string_of_mode : mode -> string
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 print_all_modes: 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 list -> theory -> theory
val code_pred_intros_attrib : attribute
(* used by Quickcheck_Generator *)
(*val funT_of : mode -> typ -> typ
val mk_if_pred : term -> term
val mk_Eval : term * term -> term*)
val mk_tupleT : typ list -> typ
(* val mk_predT : typ -> typ *)
(* temporary for testing of the compilation *)
datatype indprem = Prem of term list * term | Negprem of term list * term | Sidecond of term |
GeneratorPrem of term list * term | Generator of (string * typ);
val prepare_intrs: theory -> string list ->
(string * typ) list * int * string list * string list * (string * mode list) list *
(string * (term list * indprem list) list) list * (string * (int option list * int)) list
datatype compilation_funs = CompilationFuns of {
mk_predT : typ -> typ,
dest_predT : typ -> typ,
mk_bot : typ -> term,
mk_single : term -> term,
mk_bind : term * term -> term,
mk_sup : term * term -> term,
mk_if : term -> term,
mk_not : term -> term,
lift_pred : term -> term
};
datatype tmode = Mode of mode * int list * tmode option list;
type moded_clause = term list * (indprem * tmode) list
type 'a pred_mode_table = (string * (mode * 'a) list) list
val infer_modes : bool -> theory -> (string * (int list option list * int list) list) list
-> (string * (int option list * int)) list -> string list
-> (string * (term list * indprem list) list) list
-> (moded_clause list) pred_mode_table
val infer_modes_with_generator : theory -> (string * (int list option list * int list) list) list
-> (string * (int option list * int)) list -> string list
-> (string * (term list * indprem list) list) list
-> (moded_clause list) pred_mode_table
(*val compile_preds : theory -> compilation_funs -> string list -> string list
-> (string * typ) list -> (moded_clause list) pred_mode_table -> term pred_mode_table
val rpred_create_definitions :(string * typ) list -> string * mode list
-> theory -> theory
val split_smode : int list -> term list -> (term list * term list) *)
val print_moded_clauses :
theory -> (moded_clause list) pred_mode_table -> unit
val print_compiled_terms : theory -> term pred_mode_table -> unit
(*val rpred_prove_preds : theory -> term pred_mode_table -> thm pred_mode_table*)
val rpred_compfuns : compilation_funs
val dest_funT : typ -> typ * typ
(* val depending_preds_of : theory -> thm list -> string list *)
val add_quickcheck_equations : string list -> theory -> theory
val add_sizelim_equations : string list -> theory -> theory
val is_inductive_predicate : theory -> string -> bool
val terms_vs : term list -> string list
val subsets : int -> int -> int list list
val check_mode_clause : bool -> theory -> string list ->
(string * mode list) list -> (string * mode list) list -> mode -> (term list * indprem list)
-> (term list * (indprem * tmode) list) option
val string_of_moded_prem : theory -> (indprem * tmode) -> string
val all_modes_of : theory -> (string * mode list) list
val all_generator_modes_of : theory -> (string * mode list) list
val compile_clause : compilation_funs -> term option -> (term list -> term) ->
theory -> string list -> string list -> mode -> term -> moded_clause -> term
val preprocess_intro : theory -> thm -> thm
val is_constrt : theory -> term -> bool
val is_predT : typ -> bool
val guess_nparams : typ -> int
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 = Seq.single; (* (if ! Toplevel.debug then Tactical.print_tac s else Seq.single); *)
fun debug_tac msg = Seq.single; (* (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_scomp (t, u) =
let
val T = fastype_of t
val U = fastype_of u
val [A] = binder_types T
val D = body_type U
in
Const (@{const_name "scomp"}, T --> U --> A --> D) $ t $ u
end;
fun dest_funT (Type ("fun",[S, T])) = (S, T)
| dest_funT T = raise TYPE ("dest_funT", [T], [])
fun mk_fun_comp (t, u) =
let
val (_, B) = dest_funT (fastype_of t)
val (C, A) = dest_funT (fastype_of u)
in
Const(@{const_name "Fun.comp"}, (A --> B) --> (C --> A) --> C --> B) $ t $ u
end;
fun dest_randomT (Type ("fun", [@{typ Random.seed},
Type ("*", [Type ("*", [T, @{typ "unit => Code_Eval.term"}]) ,@{typ Random.seed}])])) = T
| dest_randomT T = raise TYPE ("dest_randomT", [T], [])
(* 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 smode = int list;
type mode = smode option list * smode;
datatype tmode = Mode of mode * int list * tmode option list;
fun split_smode is ts =
let
fun split_smode' _ _ [] = ([], [])
| split_smode' is i (t::ts) = (if i mem is then apfst else apsnd) (cons t)
(split_smode' is (i+1) ts)
in split_smode' is 1 ts end
fun split_mode (iss, is) ts =
let
val (t1, t2) = chop (length iss) ts
in (t1, split_smode is t2) end
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 string_of_tmode (Mode (predmode, termmode, param_modes)) =
"predmode: " ^ (string_of_mode predmode) ^
(if null param_modes then "" else
"; " ^ "params: " ^ commas (map (the_default "NONE" o Option.map string_of_tmode) param_modes))
datatype indprem = Prem of term list * term | Negprem of term list * term | Sidecond of term |
GeneratorPrem of term list * term | Generator of (string * typ);
type moded_clause = term list * (indprem * tmode) list
type 'a pred_mode_table = (string * (mode * 'a) list) list
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 function_data = FunctionData of {
name : string,
equation : thm option (* is not used at all? *)
};
fun rep_function_data (FunctionData data) = data;
fun mk_function_data (name, equation) =
FunctionData {name = name, equation = equation}
datatype pred_data = PredData of {
intros : thm list,
elim : thm option,
nparams : int,
functions : (mode * predfun_data) list,
generators : (mode * function_data) list,
sizelim_functions : (mode * function_data) list
};
fun rep_pred_data (PredData data) = data;
fun mk_pred_data ((intros, elim, nparams), (functions, generators, sizelim_functions)) =
PredData {intros = intros, elim = elim, nparams = nparams,
functions = functions, generators = generators, sizelim_functions = sizelim_functions}
fun map_pred_data f (PredData {intros, elim, nparams, functions, generators, sizelim_functions}) =
mk_pred_data (f ((intros, elim, nparams), (functions, generators, sizelim_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 function defined for mode " ^ string_of_mode mode ^ " of predicate " ^ name)
| 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 lookup_generator_data thy name mode =
Option.map rep_function_data (AList.lookup (op =)
(#generators (the_pred_data thy name)) mode)
fun the_generator_data thy name mode = case lookup_generator_data thy name mode
of NONE => error ("No generator defined for mode " ^ string_of_mode mode ^ " of predicate " ^ name)
| SOME data => data
val generator_name_of = #name ooo the_generator_data
val generator_modes_of = (map fst) o #generators oo the_pred_data
fun all_generator_modes_of thy =
map (fn name => (name, generator_modes_of thy name)) (all_preds_of thy)
fun lookup_sizelim_function_data thy name mode =
Option.map rep_function_data (AList.lookup (op =)
(#sizelim_functions (the_pred_data thy name)) mode)
fun the_sizelim_function_data thy name mode = case lookup_sizelim_function_data thy name mode
of NONE => error ("No size-limited function defined for mode " ^ string_of_mode mode
^ " of predicate " ^ name)
| SOME data => data
val sizelim_function_name_of = #name ooo the_sizelim_function_data
(*val generator_modes_of = (map fst) o #generators oo the_pred_data*)
(* diagnostic display functions *)
fun print_modes modes = Output.tracing ("Inferred modes:\n" ^
cat_lines (map (fn (s, ms) => s ^ ": " ^ commas (map
string_of_mode ms)) modes));
fun print_pred_mode_table string_of_entry thy pred_mode_table =
let
fun print_mode pred (mode, entry) = "mode : " ^ (string_of_mode mode)
^ (string_of_entry pred mode entry)
fun print_pred (pred, modes) =
"predicate " ^ pred ^ ": " ^ cat_lines (map (print_mode pred) modes)
val _ = Output.tracing (cat_lines (map print_pred pred_mode_table))
in () end;
fun string_of_moded_prem thy (Prem (ts, p), tmode) =
(Syntax.string_of_term_global thy (list_comb (p, ts))) ^
"(" ^ (string_of_tmode tmode) ^ ")"
| string_of_moded_prem thy (GeneratorPrem (ts, p), Mode (predmode, is, _)) =
(Syntax.string_of_term_global thy (list_comb (p, ts))) ^
"(generator_mode: " ^ (string_of_mode predmode) ^ ")"
| string_of_moded_prem thy (Generator (v, T), _) =
"Generator for " ^ v ^ " of Type " ^ (Syntax.string_of_typ_global thy T)
| string_of_moded_prem thy (Negprem (ts, p), Mode (_, is, _)) =
(Syntax.string_of_term_global thy (list_comb (p, ts))) ^
"(negative mode: " ^ (space_implode ", " (map string_of_int is)) ^ ")"
| string_of_moded_prem thy (Sidecond t, Mode (_, is, _)) =
(Syntax.string_of_term_global thy t) ^
"(sidecond mode: " ^ (space_implode ", " (map string_of_int is)) ^ ")"
| string_of_moded_prem _ _ = error "string_of_moded_prem: unimplemented"
fun print_moded_clauses thy =
let
fun string_of_clause pred mode clauses =
cat_lines (map (fn (ts, prems) => (space_implode " --> "
(map (string_of_moded_prem thy) prems)) ^ " --> " ^ pred ^ " "
^ (space_implode " " (map (Syntax.string_of_term_global thy) ts))) clauses)
in print_pred_mode_table string_of_clause thy end;
fun print_compiled_terms thy =
print_pred_mode_table (fn _ => fn _ => Syntax.string_of_term_global thy) thy
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_global thy thm))
(rev (intros_of thy pred)) ()
in
if (has_elim thy pred) then
writeln ("elimrule: " ^ Display.string_of_thm_global thy (the_elim_of thy pred))
else
writeln ("no elimrule defined")
end
in
fold print preds ()
end;
fun print_all_modes thy =
let
val _ = writeln ("Inferred modes:")
fun print (pred, modes) u =
let
val _ = writeln ("predicate: " ^ pred)
val _ = writeln ("modes: " ^ (commas (map string_of_mode modes)))
in u end
in
fold print (all_modes_of thy) ()
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 nparams 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
val prems = Thm.prems_of elimrule
val nargs = length (snd (strip_comb (HOLogic.dest_Trueprop (hd prems)))) - nparams
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 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;
(* special case: predicate with no introduction rule *)
fun noclause thy predname elim = let
val T = (Logic.unvarifyT o Sign.the_const_type thy) predname
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 elim 1)
in
([intro], elim)
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 = ind_set_codegen_preproc thy ((map (preprocess_intro thy))
(filter is_intro_of (#intrs result)))
val pre_elim = nth (#elims result) (find_index (fn s => s = name) (#names (fst info)))
val nparams = length (Inductive.params_of (#raw_induct result))
val elim = singleton (ind_set_codegen_preproc thy) (preprocess_elim thy nparams pre_elim)
val (intros, elim) = if null intros then noclause thy name elim else (intros, elim)
in
mk_pred_data ((intros, SOME elim, nparams), ([], [], []))
end
| NONE => error ("No such predicate: " ^ quote name)
(* updaters *)
fun apfst3 f (x, y, z) = (f x, y, z)
fun apsnd3 f (x, y, z) = (x, f y, z)
fun aptrd3 f (x, y, z) = (x, y, f z)
fun add_predfun name mode data =
let
val add = (apsnd o apfst3 o 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 (key, value) =
let
val intros = (#intros o rep_pred_data) value
in
fold Term.add_const_names (map Thm.prop_of intros) []
|> filter (fn c => (not (c = key)) andalso (is_inductive_predicate thy c orelse is_registered thy c))
end;
(* 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;
*)
(* guessing number of parameters *)
fun find_indexes pred xs =
let
fun find is n [] = is
| find is n (x :: xs) = find (if pred x then (n :: is) else is) (n + 1) xs;
in rev (find [] 0 xs) end;
fun is_predT (T as Type("fun", [_, _])) = (snd (strip_type T) = HOLogic.boolT)
| is_predT _ = false
fun guess_nparams T =
let
val argTs = binder_types T
val nparams = fold (curry Int.max)
(map (fn x => x + 1) (find_indexes is_predT argTs)) 0
in nparams end;
fun add_intro thm thy = let
val (name, T) = 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 (guess_nparams T) (try (#nparams o rep_pred_data 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 (pre_intros, pre_elim, nparams) thy = let
val (name, _) = dest_Const (fst (strip_intro_concl nparams (prop_of (hd pre_intros))))
(* preprocessing *)
val intros = ind_set_codegen_preproc thy (map (preprocess_intro thy) pre_intros)
val elim = singleton (ind_set_codegen_preproc thy) (preprocess_elim thy nparams pre_elim)
in
PredData.map
(Graph.new_node (name, mk_pred_data ((intros, SOME elim, nparams), ([], [], [])))) thy
end
fun set_generator_name pred mode name =
let
val set = (apsnd o apsnd3 o cons) (mode, mk_function_data (name, NONE))
in
PredData.map (Graph.map_node pred (map_pred_data set))
end
fun set_sizelim_function_name pred mode name =
let
val set = (apsnd o aptrd3 o cons) (mode, mk_function_data (name, NONE))
in
PredData.map (Graph.map_node pred (map_pred_data set))
end
(** data structures for generic compilation for different monads **)
(* maybe rename functions more generic:
mk_predT -> mk_monadT; dest_predT -> dest_monadT
mk_single -> mk_return (?)
*)
datatype compilation_funs = CompilationFuns of {
mk_predT : typ -> typ,
dest_predT : typ -> typ,
mk_bot : typ -> term,
mk_single : term -> term,
mk_bind : term * term -> term,
mk_sup : term * term -> term,
mk_if : term -> term,
mk_not : term -> term,
(* funT_of : mode -> typ -> typ, *)
(* mk_fun_of : theory -> (string * typ) -> mode -> term, *)
lift_pred : term -> term
};
fun mk_predT (CompilationFuns funs) = #mk_predT funs
fun dest_predT (CompilationFuns funs) = #dest_predT funs
fun mk_bot (CompilationFuns funs) = #mk_bot funs
fun mk_single (CompilationFuns funs) = #mk_single funs
fun mk_bind (CompilationFuns funs) = #mk_bind funs
fun mk_sup (CompilationFuns funs) = #mk_sup funs
fun mk_if (CompilationFuns funs) = #mk_if funs
fun mk_not (CompilationFuns funs) = #mk_not funs
(*fun funT_of (CompilationFuns funs) = #funT_of funs*)
(*fun mk_fun_of (CompilationFuns funs) = #mk_fun_of funs*)
fun lift_pred (CompilationFuns funs) = #lift_pred funs
fun funT_of compfuns (iss, is) T =
let
val Ts = binder_types T
val (paramTs, (inargTs, outargTs)) = split_mode (iss, is) Ts
val paramTs' = map2 (fn NONE => I | SOME is => funT_of compfuns ([], is)) iss paramTs
in
(paramTs' @ inargTs) ---> (mk_predT compfuns (mk_tupleT outargTs))
end;
fun sizelim_funT_of compfuns (iss, is) T =
let
val Ts = binder_types T
val (paramTs, (inargTs, outargTs)) = split_mode (iss, is) Ts
val paramTs' = map2 (fn SOME is => sizelim_funT_of compfuns ([], is) | NONE => I) iss paramTs
in
(paramTs' @ inargTs @ [@{typ "code_numeral"}]) ---> (mk_predT compfuns (mk_tupleT outargTs))
end;
fun mk_fun_of compfuns thy (name, T) mode =
Const (predfun_name_of thy name mode, funT_of compfuns mode T)
fun mk_sizelim_fun_of compfuns thy (name, T) mode =
Const (sizelim_function_name_of thy name mode, sizelim_funT_of compfuns mode T)
fun mk_generator_of compfuns thy (name, T) mode =
Const (generator_name_of thy name mode, sizelim_funT_of compfuns mode T)
structure PredicateCompFuns =
struct
fun mk_predT T = Type (@{type_name "Predicate.pred"}, [T])
fun dest_predT (Type (@{type_name "Predicate.pred"}, [T])) = T
| dest_predT T = raise TYPE ("dest_predT", [T], []);
fun mk_bot T = Const (@{const_name Orderings.bot}, mk_predT T);
fun mk_single t =
let val T = fastype_of t
in Const(@{const_name Predicate.single}, T --> mk_predT 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 cond = Const (@{const_name Predicate.if_pred},
HOLogic.boolT --> mk_predT HOLogic.unitT) $ cond;
fun mk_not t = let val T = mk_predT HOLogic.unitT
in Const (@{const_name Predicate.not_pred}, T --> T) $ t end
fun mk_Enum f =
let val T as Type ("fun", [T', _]) = fastype_of f
in
Const (@{const_name Predicate.Pred}, T --> mk_predT T') $ f
end;
fun mk_Eval (f, x) =
let
val T = fastype_of x
in
Const (@{const_name Predicate.eval}, mk_predT T --> T --> HOLogic.boolT) $ f $ x
end;
val lift_pred = I
val compfuns = CompilationFuns {mk_predT = mk_predT, dest_predT = dest_predT, mk_bot = mk_bot,
mk_single = mk_single, mk_bind = mk_bind, mk_sup = mk_sup, mk_if = mk_if, mk_not = mk_not,
lift_pred = lift_pred}
end;
(* termify_code:
val termT = Type ("Code_Eval.term", []);
fun termifyT T = HOLogic.mk_prodT (T, HOLogic.unitT --> termT)
*)
(*
fun lift_random random =
let
val T = dest_randomT (fastype_of random)
in
mk_scomp (random,
mk_fun_comp (HOLogic.pair_const (PredicateCompFuns.mk_predT T) @{typ Random.seed},
mk_fun_comp (Const (@{const_name Predicate.single}, T --> (PredicateCompFuns.mk_predT T)),
Const (@{const_name "fst"}, HOLogic.mk_prodT (T, @{typ "unit => term"}) --> T))))
end;
*)
structure RPredCompFuns =
struct
fun mk_rpredT T =
@{typ "Random.seed"} --> HOLogic.mk_prodT (PredicateCompFuns.mk_predT T, @{typ "Random.seed"})
fun dest_rpredT (Type ("fun", [_,
Type (@{type_name "*"}, [Type (@{type_name "Predicate.pred"}, [T]), _])])) = T
| dest_rpredT T = raise TYPE ("dest_rpredT", [T], []);
fun mk_bot T = Const(@{const_name RPred.bot}, mk_rpredT T)
fun mk_single t =
let
val T = fastype_of t
in
Const (@{const_name RPred.return}, T --> mk_rpredT T) $ t
end;
fun mk_bind (x, f) =
let
val T as (Type ("fun", [_, U])) = fastype_of f
in
Const (@{const_name RPred.bind}, fastype_of x --> T --> U) $ x $ f
end
val mk_sup = HOLogic.mk_binop @{const_name RPred.supp}
fun mk_if cond = Const (@{const_name RPred.if_rpred},
HOLogic.boolT --> mk_rpredT HOLogic.unitT) $ cond;
fun mk_not t = error "Negation is not defined for RPred"
fun lift_pred t =
let
val T = PredicateCompFuns.dest_predT (fastype_of t)
val lift_predT = PredicateCompFuns.mk_predT T --> mk_rpredT T
in
Const (@{const_name "RPred.lift_pred"}, lift_predT) $ t
end;
val compfuns = CompilationFuns {mk_predT = mk_rpredT, dest_predT = dest_rpredT, mk_bot = mk_bot,
mk_single = mk_single, mk_bind = mk_bind, mk_sup = mk_sup, mk_if = mk_if, mk_not = mk_not,
lift_pred = lift_pred}
end;
(* for external use with interactive mode *)
val rpred_compfuns = RPredCompFuns.compfuns;
fun lift_random random =
let
val T = dest_randomT (fastype_of random)
in
Const (@{const_name lift_random}, (@{typ Random.seed} -->
HOLogic.mk_prodT (HOLogic.mk_prodT (T, @{typ "unit => term"}), @{typ Random.seed})) -->
RPredCompFuns.mk_rpredT T) $ random
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 [];
(*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;
(*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
*)
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 (Envir.eta_contract 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 _, []) => error "Abs at param position" (* modes_of_param default modes t *)
| _ => default
end
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) = split_smode 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 fold_prem f (Prem (args, _)) = fold f args
| fold_prem f (Negprem (args, _)) = fold f args
| fold_prem f (Sidecond t) = f t
fun all_subsets [] = [[]]
| all_subsets (x::xs) = let val xss' = all_subsets xs in xss' @ (map (cons x) xss') end
fun generator vTs v =
let
val T = the (AList.lookup (op =) vTs v)
in
(Generator (v, T), Mode (([], []), [], []))
end;
fun gen_prem (Prem (us, t)) = GeneratorPrem (us, t)
| gen_prem _ = error "gen_prem : invalid input for gen_prem"
fun param_gen_prem param_vs (p as Prem (us, t as Free (v, _))) =
if member (op =) param_vs v then
GeneratorPrem (us, t)
else p
| param_gen_prem param_vs p = p
fun check_mode_clause with_generator thy param_vs modes gen_modes (iss, is) (ts, ps) =
let
val modes' = modes @ List.mapPartial
(fn (_, NONE) => NONE | (v, SOME js) => SOME (v, [([], js)]))
(param_vs ~~ iss);
val gen_modes' = gen_modes @ List.mapPartial
(fn (_, NONE) => NONE | (v, SOME js) => SOME (v, [([], js)]))
(param_vs ~~ iss);
val vTs = distinct (op =) ((fold o fold_prem) Term.add_frees ps (fold Term.add_frees ts []))
val prem_vs = distinct (op =) ((fold o fold_prem) Term.add_free_names ps [])
fun check_mode_prems acc_ps vs [] = SOME (acc_ps, vs)
| check_mode_prems acc_ps vs ps = (case select_mode_prem thy modes' vs ps of
NONE =>
(if with_generator then
(case select_mode_prem thy gen_modes' vs ps of
SOME (p, SOME mode) => check_mode_prems ((gen_prem p, mode) :: acc_ps)
(case p of Prem (us, _) => vs union terms_vs us | _ => vs)
(filter_out (equal p) ps)
| NONE =>
let
val all_generator_vs = all_subsets (prem_vs \\ vs) |> sort (int_ord o (pairself length))
in
case (find_first (fn generator_vs => is_some
(select_mode_prem thy modes' (vs union generator_vs) ps)) all_generator_vs) of
SOME generator_vs => check_mode_prems ((map (generator vTs) generator_vs) @ acc_ps)
(vs union generator_vs) ps
| NONE => NONE
end)
else
NONE)
| SOME (p, SOME mode) => check_mode_prems ((if with_generator then param_gen_prem param_vs p else p, mode) :: acc_ps)
(case p of Prem (us, _) => vs union terms_vs us | _ => vs)
(filter_out (equal p) ps))
val (in_ts, in_ts') = List.partition (is_constrt thy) (fst (split_smode is ts));
val in_vs = terms_vs in_ts;
val concl_vs = terms_vs ts
in
if forall is_eqT (map snd (duplicates (op =) (maps term_vTs in_ts))) andalso
forall (is_eqT o fastype_of) in_ts' then
case check_mode_prems [] (param_vs union in_vs) ps of
NONE => NONE
| SOME (acc_ps, vs) =>
if with_generator then
SOME (ts, (rev acc_ps) @ (map (generator vTs) (concl_vs \\ vs)))
else
if concl_vs subset vs then SOME (ts, rev acc_ps) else NONE
else NONE
end;
fun check_modes_pred with_generator thy param_vs preds modes gen_modes (p, ms) =
let val SOME rs = AList.lookup (op =) preds p
in (p, List.filter (fn m => case find_index
(is_none o check_mode_clause with_generator thy param_vs modes gen_modes m) rs of
~1 => true
| i => (Output.tracing ("Clause " ^ string_of_int (i + 1) ^ " of " ^
p ^ " violates mode " ^ string_of_mode m); false)) ms)
end;
fun get_modes_pred with_generator thy param_vs preds modes gen_modes (p, ms) =
let
val SOME rs = AList.lookup (op =) preds p
in
(p, map (fn m =>
(m, map (the o check_mode_clause with_generator thy param_vs modes gen_modes m) rs)) 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 modes_of_arities arities =
(map (fn (s, (ks, k)) => (s, cprod (cprods (map
(fn NONE => [NONE]
| SOME k' => map SOME (subsets 1 k')) ks),
subsets 1 k))) arities)
fun infer_modes with_generator thy extra_modes arities param_vs preds =
let
val modes =
fixp (fn modes =>
map (check_modes_pred with_generator thy param_vs preds (modes @ extra_modes) []) modes)
(modes_of_arities arities)
in
map (get_modes_pred with_generator thy param_vs preds (modes @ extra_modes) []) modes
end;
fun remove_from rem [] = []
| remove_from rem ((k, vs) :: xs) =
(case AList.lookup (op =) rem k of
NONE => (k, vs)
| SOME vs' => (k, vs \\ vs'))
:: remove_from rem xs
fun infer_modes_with_generator thy extra_modes arities param_vs preds =
let
val prednames = map fst preds
val extra_modes = all_modes_of thy
val gen_modes = all_generator_modes_of thy
|> filter_out (fn (name, _) => member (op =) prednames name)
val starting_modes = remove_from extra_modes (modes_of_arities arities)
val modes =
fixp (fn modes =>
map (check_modes_pred true thy param_vs preds extra_modes (gen_modes @ modes)) modes)
starting_modes
in
map (get_modes_pred true thy param_vs preds extra_modes (gen_modes @ modes)) modes
end;
(* term construction *)
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 compfuns 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_predT compfuns 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_bot compfuns U'),
(v', mk_bot compfuns 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 compfuns modes (NONE, t) = t
| compile_param_ext thy compfuns modes (m as SOME (Mode ((iss, is'), is, ms)), t) =
let
val (vs, u) = strip_abs t
val (ivs, ovs) = split_mode is vs
val (f, args) = strip_comb u
val (params, args') = chop (length ms) args
val (inargs, outargs) = split_mode 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 (split_mode 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
mk_predfun_of thy compfuns (name, T) (iss, is')
else error "compile param: Not an inductive predicate with correct mode"
| Free (name, T) => Free (name, param_funT_of compfuns T (SOME is'))
val outTs = dest_tupleT (dest_predT compfuns (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 compfuns (mk_tuple (map (fn i => nth out_vs (i - 1)) outp_perm)))
val match_t = compile_match thy compfuns [] [] out_vs single_t
in list_abs (ivs,
mk_bind compfuns (f_app, match_t))
end
| compile_param_ext _ _ _ _ = error "compile params"
*)
fun compile_param size thy compfuns (NONE, t) = t
| compile_param size thy compfuns (m as SOME (Mode ((iss, is'), is, ms)), t) =
let
val (f, args) = strip_comb (Envir.eta_contract t)
val (params, args') = chop (length ms) args
val params' = map (compile_param size thy compfuns) (ms ~~ params)
val mk_fun_of = case size of NONE => mk_fun_of | SOME _ => mk_sizelim_fun_of
val funT_of = case size of NONE => funT_of | SOME _ => sizelim_funT_of
val f' =
case f of
Const (name, T) =>
mk_fun_of compfuns thy (name, T) (iss, is')
| Free (name, T) => Free (name, funT_of compfuns (iss, is') T)
| _ => error ("PredicateCompiler: illegal parameter term")
in list_comb (f', params' @ args') end
fun compile_expr size thy ((Mode (mode, is, ms)), t) =
case strip_comb t of
(Const (name, T), params) =>
let
val params' = map (compile_param size thy PredicateCompFuns.compfuns) (ms ~~ params)
val mk_fun_of = case size of NONE => mk_fun_of | SOME _ => mk_sizelim_fun_of
in
list_comb (mk_fun_of PredicateCompFuns.compfuns thy (name, T) mode, params')
end
| (Free (name, T), args) =>
let
val funT_of = case size of NONE => funT_of | SOME _ => sizelim_funT_of
in
list_comb (Free (name, funT_of PredicateCompFuns.compfuns ([], is) T), args)
end;
fun compile_gen_expr size thy compfuns ((Mode (mode, is, ms)), t) =
case strip_comb t of
(Const (name, T), params) =>
let
val params' = map (compile_param size thy compfuns) (ms ~~ params)
in
list_comb (mk_generator_of compfuns thy (name, T) mode, params')
end
| (Free (name, T), args) =>
list_comb (Free (name, sizelim_funT_of RPredCompFuns.compfuns ([], is) T), args)
(** specific rpred functions -- move them to the correct place in this file *)
(* uncommented termify code; causes more trouble than expected at first *)
(*
fun mk_valtermify_term (t as Const (c, T)) = HOLogic.mk_prod (t, Abs ("u", HOLogic.unitT, HOLogic.reflect_term t))
| mk_valtermify_term (Free (x, T)) = Free (x, termifyT T)
| mk_valtermify_term (t1 $ t2) =
let
val T = fastype_of t1
val (T1, T2) = dest_funT T
val t1' = mk_valtermify_term t1
val t2' = mk_valtermify_term t2
in
Const ("Code_Eval.valapp", termifyT T --> termifyT T1 --> termifyT T2) $ t1' $ t2'
end
| mk_valtermify_term _ = error "Not a valid term for mk_valtermify_term"
*)
fun compile_clause compfuns size final_term thy all_vs param_vs (iss, is) inp (ts, moded_ps) =
let
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) = split_smode 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
(* termify code:
compile_match thy compfuns constr_vs (eqs @ eqs') out_ts'''
(mk_single compfuns (mk_tuple (map mk_valtermify_term out_ts)))
*)
compile_match thy compfuns constr_vs (eqs @ eqs') out_ts'''
(final_term out_ts)
end
| compile_prems out_ts vs names ((p, mode as Mode ((_, is), _, _)) :: ps) =
let
val vs' = distinct (op =) (flat (vs :: map term_vs out_ts));
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''') = split_smode is us;
val args = case size of
NONE => in_ts
| SOME size_t => in_ts @ [size_t]
val u = lift_pred compfuns
(list_comb (compile_expr size thy (mode, t), args))
val rest = compile_prems out_ts''' vs' names'' ps
in
(u, rest)
end
| Negprem (us, t) =>
let
val (in_ts, out_ts''') = split_smode is us
val u = lift_pred compfuns
(mk_not PredicateCompFuns.compfuns (list_comb (compile_expr NONE thy (mode, t), in_ts)))
val rest = compile_prems out_ts''' vs' names'' ps
in
(u, rest)
end
| Sidecond t =>
let
val rest = compile_prems [] vs' names'' ps;
in
(mk_if compfuns t, rest)
end
| GeneratorPrem (us, t) =>
let
val (in_ts, out_ts''') = split_smode is us;
val args = case size of
NONE => in_ts
| SOME size_t => in_ts @ [size_t]
val u = list_comb (compile_gen_expr size thy compfuns (mode, t), args)
val rest = compile_prems out_ts''' vs' names'' ps
in
(u, rest)
end
| Generator (v, T) =>
let
val u = lift_random (HOLogic.mk_random T @{term "1::code_numeral"})
val rest = compile_prems [Free (v, T)] vs' names'' ps;
in
(u, rest)
end
in
compile_match thy compfuns constr_vs' eqs out_ts''
(mk_bind compfuns (compiled_clause, rest))
end
val prem_t = compile_prems in_ts' param_vs all_vs' moded_ps;
in
mk_bind compfuns (mk_single compfuns inp, prem_t)
end
fun compile_pred compfuns mk_fun_of use_size thy all_vs param_vs s T mode moded_cls =
let
val (Ts1, (Us1, Us2)) = split_mode mode (binder_types T)
val funT_of = if use_size then sizelim_funT_of else funT_of
val Ts1' = map2 (fn NONE => I | SOME is => funT_of compfuns ([], is)) (fst mode) Ts1
val xnames = Name.variant_list (all_vs @ param_vs)
(map (fn i => "x" ^ string_of_int i) (snd mode));
val size_name = Name.variant (all_vs @ param_vs @ xnames) "size"
(* termify code: val xs = map2 (fn s => fn T => Free (s, termifyT T)) xnames Us1; *)
val xs = map2 (fn s => fn T => Free (s, T)) xnames Us1;
val params = map2 (fn s => fn T => Free (s, T)) param_vs Ts1'
val size = Free (size_name, @{typ "code_numeral"})
val decr_size =
if use_size then
SOME (Const ("HOL.minus_class.minus", @{typ "code_numeral => code_numeral => code_numeral"})
$ size $ Const ("HOL.one_class.one", @{typ "Code_Numeral.code_numeral"}))
else
NONE
val cl_ts =
map (compile_clause compfuns decr_size (fn out_ts => mk_single compfuns (mk_tuple out_ts))
thy all_vs param_vs mode (mk_tuple xs)) moded_cls;
val t = foldr1 (mk_sup compfuns) cl_ts
val T' = mk_predT compfuns (mk_tupleT Us2)
val size_t = Const (@{const_name "If"}, @{typ bool} --> T' --> T' --> T')
$ HOLogic.mk_eq (size, @{term "0 :: code_numeral"})
$ mk_bot compfuns (dest_predT compfuns T') $ t
val fun_const = mk_fun_of compfuns thy (s, T) mode
val eq = if use_size then
(list_comb (fun_const, params @ xs @ [size]), size_t)
else
(list_comb (fun_const, params @ xs), t)
in
HOLogic.mk_Trueprop (HOLogic.mk_eq eq)
end;
(* 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) = split_smode mode args
val r = PredicateCompFuns.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 (mode as (iss, is)) 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 (length iss) Ts;
val Ts1' = map2 (fn NONE => I | SOME is => funT_of (PredicateCompFuns.compfuns) ([], is)) iss Ts1
val args = map Free (argnames ~~ (Ts1' @ Ts2))
val (params, ioargs) = chop (length iss) args
val (inargs, outargs) = split_smode is ioargs
val param_names = Name.variant_list argnames
(map (fn i => "p" ^ string_of_int i) (1 upto (length iss)))
val param_vs = map Free (param_names ~~ Ts1)
val (params', names) = fold_map mk_Eval_of ((params ~~ Ts1) ~~ iss) []
val predpropI = HOLogic.mk_Trueprop (list_comb (pred, param_vs @ ioargs))
val predpropE = HOLogic.mk_Trueprop (list_comb (pred, params' @ ioargs))
val param_eqs = map (HOLogic.mk_Trueprop o HOLogic.mk_eq) (param_vs ~~ params')
val funargs = params @ inargs
val funpropE = HOLogic.mk_Trueprop (PredicateCompFuns.mk_Eval (list_comb (funtrm, funargs),
if null outargs then Free("y", HOLogic.unitT) else mk_tuple outargs))
val funpropI = HOLogic.mk_Trueprop (PredicateCompFuns.mk_Eval (list_comb (funtrm, funargs),
mk_tuple outargs))
val introtrm = Logic.list_implies (predpropI :: param_eqs, 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 @ 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_constname_of_mode thy prefix name mode =
let
fun string_of_mode mode = if null mode then "0"
else space_implode "_" (map string_of_int mode)
val HOmode = space_implode "_and_"
(fold (fn NONE => I | SOME mode => cons (string_of_mode mode)) (fst mode) [])
in
(Sign.full_bname thy (prefix ^ (Long_Name.base_name name))) ^
(if HOmode = "" then "_" else "_for_" ^ HOmode ^ "_yields_") ^ (string_of_mode (snd mode))
end;
fun create_definitions preds (name, modes) thy =
let
val compfuns = PredicateCompFuns.compfuns
val T = AList.lookup (op =) preds name |> the
fun create_definition (mode as (iss, is)) thy = let
val mode_cname = create_constname_of_mode thy "" name mode
val mode_cbasename = Long_Name.base_name mode_cname
val Ts = binder_types T
val (Ts1, Ts2) = chop (length iss) Ts
val (Us1, Us2) = split_smode is Ts2
val Ts1' = map2 (fn NONE => I | SOME is => funT_of compfuns ([], is)) iss Ts1
val funT = (Ts1' @ Us1) ---> (mk_predT compfuns (mk_tupleT Us2))
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 (length iss) xs;
val (xins, xouts) = split_smode is xargs
val (xparams', names') = fold_map mk_Eval_of ((xparams ~~ Ts1) ~~ iss) names
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 = PredicateCompFuns.mk_Enum (mk_split_lambda xouts
(list_comb (Const (name, T), xparams' @ xargs)))
val lhs = list_comb (Const (mode_cname, funT), xparams @ xins)
val def = Logic.mk_equals (lhs, predterm)
val ([definition], thy') = thy |>
Sign.add_consts_i [(Binding.name mode_cbasename, funT, NoSyn)] |>
PureThy.add_defs false [((Binding.name (mode_cbasename ^ "_def"), def), [])]
val (intro, elim) =
create_intro_elim_rule mode definition mode_cname funT (Const (name, T)) thy'
in thy' |> add_predfun name mode (mode_cname, definition, intro, elim)
|> PureThy.store_thm (Binding.name (mode_cbasename ^ "I"), intro) |> snd
|> PureThy.store_thm (Binding.name (mode_cbasename ^ "E"), elim) |> snd
|> Theory.checkpoint
end;
in
fold create_definition modes thy
end;
fun sizelim_create_definitions preds (name, modes) thy =
let
val T = AList.lookup (op =) preds name |> the
fun create_definition mode thy =
let
val mode_cname = create_constname_of_mode thy "sizelim_" name mode
val funT = sizelim_funT_of PredicateCompFuns.compfuns mode T
in
thy |> Sign.add_consts_i [(Binding.name (Long_Name.base_name mode_cname), funT, NoSyn)]
|> set_sizelim_function_name name mode mode_cname
end;
in
fold create_definition modes thy
end;
fun rpred_create_definitions preds (name, modes) thy =
let
val T = AList.lookup (op =) preds name |> the
fun create_definition mode thy =
let
val mode_cname = create_constname_of_mode thy "gen_" name mode
val funT = sizelim_funT_of RPredCompFuns.compfuns mode T
in
thy |> Sign.add_consts_i [(Binding.name (Long_Name.base_name mode_cname), funT, NoSyn)]
|> set_generator_name name mode mode_cname
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 (NONE, t) = TRY (rtac @{thm refl} 1)
| prove_param thy (m as SOME (Mode (mode, is, ms)), t) =
let
val (f, args) = strip_comb (Envir.eta_contract 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 _ => TRY (rtac @{thm refl} 1)
| Abs _ => error "prove_param: No valid parameter term"
in
REPEAT_DETERM (etac @{thm thin_rl} 1)
THEN REPEAT_DETERM (rtac @{thm ext} 1)
THEN print_tac "prove_param"
THEN f_tac
THEN print_tac "after simplification in prove_args"
THEN (EVERY (map (prove_param thy) (ms ~~ params)))
THEN (REPEAT_DETERM (atac 1))
end
fun prove_expr thy (Mode (mode, is, ms), t, us) (premposition : int) =
case strip_comb t of
(Const (name, T), args) =>
let
val introrule = predfun_intro_of thy name mode
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 debug_tac (Display.string_of_thm (ProofContext.init thy) introrule)
THEN rtac introrule 1
THEN print_tac "after intro rule"
(* work with parameter arguments *)
THEN (atac 1)
THEN (print_tac "parameter goal")
THEN (EVERY (map (prove_param thy) (ms ~~ args1)))
THEN (REPEAT_DETERM (atac 1))
end
| _ => rtac @{thm bindI} 1 THEN atac 1
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 modes (iss, is) (_, clauses) (ts, moded_ps) =
let
val (in_ts, clause_out_ts) = split_smode is ts;
fun prove_prems out_ts [] =
(prove_match thy out_ts)
THEN asm_simp_tac HOL_basic_ss' 1
THEN (rtac (if null clause_out_ts then @{thm singleI_unit} else @{thm singleI}) 1)
| prove_prems out_ts ((p, mode as Mode ((iss, is), _, param_modes)) :: ps) =
let
val premposition = (find_index (equal p) clauses) + nargs
val rest_tac = (case p of Prem (us, t) =>
let
val (_, out_ts''') = split_smode is us
val rec_tac = prove_prems out_ts''' ps
in
print_tac "before clause:"
THEN asm_simp_tac HOL_basic_ss 1
THEN print_tac "before prove_expr:"
THEN prove_expr thy (mode, t, us) premposition
THEN print_tac "after prove_expr:"
THEN rec_tac
end
| Negprem (us, t) =>
let
val (_, out_ts''') = split_smode is us
val rec_tac = prove_prems out_ts''' ps
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, is)]) 1
THEN rtac @{thm not_predI} 1
THEN simp_tac (HOL_basic_ss addsimps [@{thm not_False_eq_True}]) 1
THEN (REPEAT_DETERM (atac 1))
(* FIXME: work with parameter arguments *)
THEN (EVERY (map (prove_param thy) (param_modes ~~ params)))
else
rtac @{thm not_predI'} 1)
THEN simp_tac (HOL_basic_ss addsimps [@{thm not_False_eq_True}]) 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 [] ps)
in (prove_match thy out_ts)
THEN rest_tac
end;
val prems_tac = prove_prems in_ts moded_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 clauses preds modes pred mode moded_clauses =
let
val T = the (AList.lookup (op =) preds pred)
val nargs = length (binder_types T) - nparams_of thy pred
val pred_case_rule = the_elim_of thy pred
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 moded_clauses) i) i)
(1 upto (length moded_clauses))))
THEN (EVERY (map2 (prove_clause thy nargs modes mode) clauses moded_clauses))
THEN 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
*)
(* TODO: remove function *)
fun prove_param2 thy (NONE, t) = all_tac
| prove_param2 thy (m as SOME (Mode (mode, is, ms)), t) = let
val (f, args) = strip_comb (Envir.eta_contract 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
| _ => error "prove_param2: illegal parameter term"
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) (ms ~~ params)))
end
fun prove_expr2 thy (Mode (mode, is, ms), t) =
(case strip_comb t of
(Const (name, T), args) =>
etac @{thm bindE} 1
THEN (REPEAT_DETERM (CHANGED (rewtac @{thm "split_paired_all"})))
THEN 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 print_tac "prove_expr2"
THEN (EVERY (map (prove_param2 thy) (ms ~~ args)))
THEN print_tac "finished prove_expr2"
| _ => etac @{thm bindE} 1)
(* FIXME: what is this for? *)
(* replace defined by has_mode thy pred *)
(* TODO: rewrite function *)
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 modes pred (iss, is) (ts, ps) i =
let
val pred_intro_rule = nth (intros_of thy pred) (i - 1)
val (in_ts, clause_out_ts) = split_smode is ts;
fun prove_prems2 out_ts [] =
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 ((p, mode as Mode ((iss, is), _, param_modes)) :: ps) =
let
val rest_tac = (case p of
Prem (us, t) =>
let
val (_, out_ts''') = split_smode is us
val rec_tac = prove_prems2 out_ts''' ps
in
(prove_expr2 thy (mode, t)) THEN rec_tac
end
| Negprem (us, t) =>
let
val (_, out_ts''') = split_smode is us
val rec_tac = prove_prems2 out_ts''' 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, is)]) 1
THEN etac @{thm not_predE} 1
THEN simp_tac (HOL_basic_ss addsimps [@{thm not_False_eq_True}]) 1
THEN (EVERY (map (prove_param2 thy) (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 [] 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 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 modes pred mode moded_clauses =
let
fun prove_clause clause i =
(if i < length moded_clauses then etac @{thm supE} 1 else all_tac)
THEN (prove_clause2 thy modes pred mode clause 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 (map2 prove_clause moded_clauses (1 upto (length moded_clauses))))
end;
(** proof procedure **)
fun prove_pred thy clauses preds modes pred mode (moded_clauses, compiled_term) =
let
val ctxt = ProofContext.init thy
val clauses = the (AList.lookup (op =) clauses pred)
in
Goal.prove ctxt (Term.add_free_names compiled_term []) [] compiled_term
(if !do_proofs then
(fn _ =>
rtac @{thm pred_iffI} 1
THEN prove_one_direction thy clauses preds modes pred mode moded_clauses
THEN print_tac "proved one direction"
THEN prove_other_direction thy modes pred mode moded_clauses
THEN print_tac "proved other direction")
else (fn _ => mycheat_tac thy 1))
end;
(* composition of mode inference, definition, compilation and proof *)
(** auxillary combinators for table of preds and modes **)
fun map_preds_modes f preds_modes_table =
map (fn (pred, modes) =>
(pred, map (fn (mode, value) => (mode, f pred mode value)) modes)) preds_modes_table
fun join_preds_modes table1 table2 =
map_preds_modes (fn pred => fn mode => fn value =>
(value, the (AList.lookup (op =) (the (AList.lookup (op =) table2 pred)) mode))) table1
fun maps_modes preds_modes_table =
map (fn (pred, modes) =>
(pred, map (fn (mode, value) => value) modes)) preds_modes_table
fun compile_preds compfuns mk_fun_of use_size thy all_vs param_vs preds moded_clauses =
map_preds_modes (fn pred => compile_pred compfuns mk_fun_of use_size thy all_vs param_vs pred
(the (AList.lookup (op =) preds pred))) moded_clauses
fun prove thy clauses preds modes moded_clauses compiled_terms =
map_preds_modes (prove_pred thy clauses preds modes)
(join_preds_modes moded_clauses compiled_terms)
fun prove_by_skip thy _ _ _ _ compiled_terms =
map_preds_modes (fn pred => fn mode => fn t => Drule.standard (SkipProof.make_thm thy t))
compiled_terms
fun prepare_intrs thy prednames =
let
val intrs = maps (intros_of thy) prednames
|> map (Logic.unvarify o prop_of)
val nparams = nparams_of thy (hd prednames)
val extra_modes = all_modes_of thy |> filter_out (fn (name, _) => member (op =) prednames name)
val preds = distinct (op =) (map (dest_Const o fst o (strip_intro_concl nparams)) intrs)
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;
(** main function of predicate compiler **)
fun add_equations_of steps prednames thy =
let
val _ = Output.tracing ("Starting predicate compiler for predicates " ^ commas prednames ^ "...")
val (preds, nparams, all_vs, param_vs, extra_modes, clauses, arities) =
prepare_intrs thy prednames
val _ = Output.tracing "Infering modes..."
val moded_clauses = #infer_modes steps thy extra_modes arities param_vs clauses
val modes = map (fn (p, mps) => (p, map fst mps)) moded_clauses
val _ = print_modes modes
val _ = print_moded_clauses thy moded_clauses
val _ = Output.tracing "Defining executable functions..."
val thy' = fold (#create_definitions steps preds) modes thy
|> Theory.checkpoint
val _ = Output.tracing "Compiling equations..."
val compiled_terms =
(#compile_preds steps) thy' all_vs param_vs preds moded_clauses
val _ = print_compiled_terms thy' compiled_terms
val _ = Output.tracing "Proving equations..."
val result_thms = #prove steps thy' clauses preds (extra_modes @ modes)
moded_clauses compiled_terms
val qname = #qname steps
(* val attrib = gn thy => Attrib.attribute_i thy Code.add_eqn_attrib *)
val attrib = fn thy => Attrib.attribute_i thy (Attrib.internal (K (Thm.declaration_attribute
(fn thm => Context.mapping (Code.add_eqn thm) I))))
val thy'' = fold (fn (name, result_thms) => fn thy => snd (PureThy.add_thmss
[((Binding.qualify true (Long_Name.base_name name) (Binding.name qname), result_thms),
[attrib thy ])] thy))
(maps_modes result_thms) thy'
|> Theory.checkpoint
in
thy''
end
fun extend' value_of edges_of key (G, visited) =
let
val (G', v) = case try (Graph.get_node G) key of
SOME v => (G, v)
| NONE => (Graph.new_node (key, value_of key) G, value_of key)
val (G'', visited') = fold (extend' value_of edges_of) (edges_of (key, v) \\ visited)
(G', key :: visited)
in
(fold (Graph.add_edge o (pair key)) (edges_of (key, v)) G'', visited')
end;
fun extend value_of edges_of key G = fst (extend' value_of edges_of key (G, []))
fun gen_add_equations steps names thy =
let
val thy' = PredData.map (fold (extend (fetch_pred_data thy) (depending_preds_of thy)) names) thy
|> Theory.checkpoint;
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') names
val thy'' = fold_rev
(fn preds => fn thy =>
if #are_not_defined steps thy preds then add_equations_of steps preds thy else thy)
scc thy' |> Theory.checkpoint
in thy'' end
(* different instantiantions of the predicate compiler *)
val add_equations = gen_add_equations
{infer_modes = infer_modes false,
create_definitions = create_definitions,
compile_preds = compile_preds PredicateCompFuns.compfuns mk_fun_of false,
prove = prove,
are_not_defined = (fn thy => forall (null o modes_of thy)),
qname = "equation"}
val add_sizelim_equations = gen_add_equations
{infer_modes = infer_modes false,
create_definitions = sizelim_create_definitions,
compile_preds = compile_preds PredicateCompFuns.compfuns mk_sizelim_fun_of true,
prove = prove_by_skip,
are_not_defined = (fn thy => fn preds => true), (* TODO *)
qname = "sizelim_equation"
}
val add_quickcheck_equations = gen_add_equations
{infer_modes = infer_modes_with_generator,
create_definitions = rpred_create_definitions,
compile_preds = compile_preds RPredCompFuns.compfuns mk_generator_of true,
prove = prove_by_skip,
are_not_defined = (fn thy => fn preds => true), (* TODO *)
qname = "rpred_equation"}
(** user interface **)
(* 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;
(* code_pred_intro attribute *)
fun attrib f = Thm.declaration_attribute (fn thm => Context.mapping (f thm) I);
val code_pred_intros_attrib = attrib add_intro;
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
(extend (fetch_pred_data thy) (depending_preds_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 lthy'' = lthy'
|> fold Variable.auto_fixes cases_rules
|> ProofContext.add_cases true case_env
fun after_qed thms goal_ctxt =
let
val global_thms = ProofContext.export goal_ctxt
(ProofContext.init (ProofContext.theory_of goal_ctxt)) (map the_single thms)
in
goal_ctxt |> LocalTheory.theory (fold set_elim global_thms #> add_equations [const])
end
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_splits 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, _) = split_smode 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 NONE thy
(m, list_comb (pred, params)),
inargs)
in t_eval end;
end;