(* Title: HOL/Tools/Predicate_Compile/predicate_compile_core.ML
Author: Lukas Bulwahn, TU Muenchen
A compiler from predicates specified by intro/elim rules to equations.
*)
signature PREDICATE_COMPILE_CORE =
sig
val setup : theory -> theory
val code_pred : Predicate_Compile_Aux.options -> string -> Proof.context -> Proof.state
val code_pred_cmd : Predicate_Compile_Aux.options -> string -> Proof.context -> Proof.state
val values_cmd : string list -> Predicate_Compile_Aux.mode' option list option
-> int option * (bool * bool) -> int -> string -> Toplevel.state -> unit
val register_predicate : (string * thm list * thm * int) -> theory -> theory
val register_intros : string * thm list -> theory -> theory
val is_registered : theory -> string -> bool
val predfun_intro_of: theory -> string -> Predicate_Compile_Aux.mode -> thm
val predfun_elim_of: theory -> string -> Predicate_Compile_Aux.mode -> thm
val predfun_name_of: theory -> string -> Predicate_Compile_Aux.mode -> string
val all_preds_of : theory -> string list
val modes_of: theory -> string -> Predicate_Compile_Aux.mode list
val depth_limited_modes_of: theory -> string -> Predicate_Compile_Aux.mode list
val depth_limited_function_name_of : theory -> string -> Predicate_Compile_Aux.mode -> string
val random_modes_of: theory -> string -> Predicate_Compile_Aux.mode list
val random_function_name_of : theory -> string -> Predicate_Compile_Aux.mode -> string
val all_modes_of : theory -> (string * Predicate_Compile_Aux.mode list) list
val all_random_modes_of : theory -> (string * Predicate_Compile_Aux.mode list) list
val intros_of : theory -> string -> thm list
val nparams_of : theory -> string -> int
val add_intro : thm -> theory -> theory
val set_elim : thm -> theory -> theory
val set_nparams : string -> int -> theory -> theory
val print_stored_rules : theory -> unit
val print_all_modes : theory -> unit
val mk_casesrule : Proof.context -> term -> int -> thm list -> term
val eval_ref : (unit -> term Predicate.pred) option Unsynchronized.ref
val random_eval_ref : (unit -> int * int -> term Predicate.pred * (int * int))
option Unsynchronized.ref
val code_pred_intro_attrib : attribute
(* used by Quickcheck_Generator *)
(* temporary for testing of the compilation *)
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,
mk_map : typ -> typ -> term -> term -> term
};
val pred_compfuns : compilation_funs
val randompred_compfuns : compilation_funs
val add_equations : Predicate_Compile_Aux.options -> string list -> theory -> theory
val add_quickcheck_equations : Predicate_Compile_Aux.options -> string list -> theory -> theory
val add_depth_limited_equations : Predicate_Compile_Aux.options
-> string list -> theory -> theory
val mk_tracing : string -> term -> term
end;
structure Predicate_Compile_Core : PREDICATE_COMPILE_CORE =
struct
open Predicate_Compile_Aux;
(** auxiliary **)
(* debug stuff *)
fun print_tac s = Seq.single;
fun print_tac' options s =
if show_proof_trace options then Tactical.print_tac s else Seq.single;
fun debug_tac msg = Seq.single; (* (fn st => (Output.tracing msg; Seq.single st)); *)
datatype assertion = Max_number_of_subgoals of int
fun assert_tac (Max_number_of_subgoals i) st =
if (nprems_of st <= i) then Seq.single st
else error ("assert_tac: Numbers of subgoals mismatch at goal state :"
^ "\n" ^ Pretty.string_of (Pretty.chunks
(Goal_Display.pretty_goals_without_context (! Goal_Display.goals_limit) st)));
(* reference to preprocessing of InductiveSet package *)
val ind_set_codegen_preproc = (fn thy => I) (*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_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_Evaluation.term"}]) ,@{typ Random.seed}])])) = T
| dest_randomT T = raise TYPE ("dest_randomT", [T], [])
fun mk_tracing s t =
Const(@{const_name Code_Evaluation.tracing},
@{typ String.literal} --> (fastype_of t) --> (fastype_of t)) $ (HOLogic.mk_literal s) $ 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 **)
fun gen_split_smode (mk_tuple, strip_tuple) smode ts =
let
fun split_tuple' _ _ [] = ([], [])
| split_tuple' is i (t::ts) =
(if member (op =) is i then apfst else apsnd) (cons t)
(split_tuple' is (i+1) ts)
fun split_tuple is t = split_tuple' is 1 (strip_tuple t)
fun split_smode' _ _ [] = ([], [])
| split_smode' smode i (t::ts) =
(if member (op =) (map fst smode) i then
case (the (AList.lookup (op =) smode i)) of
NONE => apfst (cons t)
| SOME is =>
let
val (ts1, ts2) = split_tuple is t
fun cons_tuple ts = if null ts then I else cons (mk_tuple ts)
in (apfst (cons_tuple ts1)) o (apsnd (cons_tuple ts2)) end
else apsnd (cons t))
(split_smode' smode (i+1) ts)
in split_smode' smode 1 ts end
fun split_smode smode ts = gen_split_smode (HOLogic.mk_tuple, HOLogic.strip_tuple) smode ts
fun split_smodeT smode ts = gen_split_smode (HOLogic.mk_tupleT, HOLogic.strip_tupleT) smode ts
fun gen_split_mode split_smode (iss, is) ts =
let
val (t1, t2) = chop (length iss) ts
in (t1, split_smode is t2) end
fun split_mode (iss, is) ts = gen_split_mode split_smode (iss, is) ts
fun split_modeT (iss, is) ts = gen_split_mode split_smodeT (iss, is) ts
datatype indprem = Prem of term list * term | Negprem of term list * term | Sidecond of 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 : bool * (mode * predfun_data) list,
random_functions : bool * (mode * function_data) list,
depth_limited_functions : bool * (mode * function_data) list,
annotated_functions : bool * (mode * function_data) list
};
fun rep_pred_data (PredData data) = data;
fun mk_pred_data ((intros, elim, nparams),
(functions, random_functions, depth_limited_functions, annotated_functions)) =
PredData {intros = intros, elim = elim, nparams = nparams,
functions = functions, random_functions = random_functions,
depth_limited_functions = depth_limited_functions, annotated_functions = annotated_functions}
fun map_pred_data f (PredData {intros, elim, nparams,
functions, random_functions, depth_limited_functions, annotated_functions}) =
mk_pred_data (f ((intros, elim, nparams), (functions, random_functions,
depth_limited_functions, annotated_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 = Theory_Data
(
type T = pred_data Graph.T;
val empty = Graph.empty;
val extend = I;
val 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
fun intros_of thy = map (Thm.transfer thy) o #intros o the_pred_data thy
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.transfer thy 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 snd o #functions oo the_pred_data
fun all_modes_of thy = map (fn name => (name, modes_of thy name)) (all_preds_of thy)
val defined_functions = fst o #functions oo the_pred_data
fun lookup_predfun_data thy name mode =
Option.map rep_predfun_data
(AList.lookup (op =) (snd (#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 thy name 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_random_function_data thy name mode =
Option.map rep_function_data
(AList.lookup (op =) (snd (#random_functions (the_pred_data thy name))) mode)
fun the_random_function_data thy name mode = case lookup_random_function_data thy name mode of
NONE => error ("No random function defined for mode " ^ string_of_mode thy name mode ^
" of predicate " ^ name)
| SOME data => data
val random_function_name_of = #name ooo the_random_function_data
val random_modes_of = (map fst) o snd o #random_functions oo the_pred_data
val defined_random_functions = fst o #random_functions oo the_pred_data
fun all_random_modes_of thy =
map (fn name => (name, random_modes_of thy name)) (all_preds_of thy)
fun lookup_depth_limited_function_data thy name mode =
Option.map rep_function_data
(AList.lookup (op =) (snd (#depth_limited_functions (the_pred_data thy name))) mode)
fun the_depth_limited_function_data thy name mode =
case lookup_depth_limited_function_data thy name mode of
NONE => error ("No depth-limited function defined for mode " ^ string_of_mode thy name mode
^ " of predicate " ^ name)
| SOME data => data
val depth_limited_function_name_of = #name ooo the_depth_limited_function_data
val depth_limited_modes_of = (map fst) o snd o #depth_limited_functions oo the_pred_data
val defined_depth_limited_functions = fst o #depth_limited_functions oo the_pred_data
fun lookup_annotated_function_data thy name mode =
Option.map rep_function_data
(AList.lookup (op =) (snd (#annotated_functions (the_pred_data thy name))) mode)
fun the_annotated_function_data thy name mode = case lookup_annotated_function_data thy name mode
of NONE => error ("No annotated function defined for mode " ^ string_of_mode thy name mode
^ " of predicate " ^ name)
| SOME data => data
val annotated_function_name_of = #name ooo the_annotated_function_data
val annotated_modes_of = (map fst) o snd o #annotated_functions oo the_pred_data
val defined_annotated_functions = fst o #annotated_functions oo the_pred_data
(* diagnostic display functions *)
fun print_modes options thy modes =
if show_modes options then
tracing ("Inferred modes:\n" ^
cat_lines (map (fn (s, ms) => s ^ ": " ^ commas (map
(string_of_mode thy s) ms)) modes))
else ()
fun print_pred_mode_table string_of_entry thy pred_mode_table =
let
fun print_mode pred (mode, entry) = "mode : " ^ string_of_mode thy pred mode
^ string_of_entry pred mode entry
fun print_pred (pred, modes) =
"predicate " ^ pred ^ ": " ^ cat_lines (map (print_mode pred) modes)
val _ = tracing (cat_lines (map print_pred pred_mode_table))
in () end;
fun string_of_prem thy (Prem (ts, p)) =
(Syntax.string_of_term_global thy (list_comb (p, ts))) ^ "(premise)"
| string_of_prem thy (Negprem (ts, p)) =
(Syntax.string_of_term_global thy (HOLogic.mk_not (list_comb (p, ts)))) ^ "(negative premise)"
| string_of_prem thy (Sidecond t) =
(Syntax.string_of_term_global thy t) ^ "(sidecondition)"
| string_of_prem thy _ = error "string_of_prem: unexpected input"
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 (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: " ^ string_of_smode is ^ ")"
| string_of_moded_prem thy (Sidecond t, Mode (_, is, _)) =
(Syntax.string_of_term_global thy t) ^
"(sidecond mode: " ^ string_of_smode 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 string_of_clause thy pred (ts, prems) =
(space_implode " --> "
(map (string_of_prem thy) prems)) ^ " --> " ^ pred ^ " "
^ (space_implode " " (map (Syntax.string_of_term_global thy) ts))
fun print_compiled_terms options thy =
if show_compilation options then
print_pred_mode_table (fn _ => fn _ => Syntax.string_of_term_global thy) thy
else K ()
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 thy pred) modes)))
in u end
in
fold print (all_modes_of thy) ()
end
(* validity checks *)
fun check_expected_modes preds (options : Predicate_Compile_Aux.options) modes =
case expected_modes options of
SOME (s, ms) => (case AList.lookup (op =) modes s of
SOME modes =>
let
val modes' = map (translate_mode (the (AList.lookup (op =) preds s))) modes
in
if not (eq_set eq_mode' (ms, modes')) then
error ("expected modes were not inferred:\n"
^ " inferred modes for " ^ s ^ ": " ^ commas (map string_of_mode' modes') ^ "\n"
^ " expected modes for " ^ s ^ ": " ^ commas (map string_of_mode' ms))
else ()
end
| NONE => ())
| NONE => ()
(* importing introduction rules *)
fun unify_consts thy cs intr_ts =
(let
val add_term_consts_2 = fold_aterms (fn Const c => insert (op =) c | _ => I);
fun varify (t, (i, ts)) =
let val t' = map_types (Logic.incr_tvar (i + 1)) (#2 (Type.varify [] t))
in (maxidx_of_term t', t'::ts) end;
val (i, cs') = List.foldr varify (~1, []) cs;
val (i', intr_ts') = List.foldr varify (i, []) intr_ts;
val rec_consts = fold add_term_consts_2 cs' [];
val intr_consts = fold add_term_consts_2 intr_ts' [];
fun unify (cname, cT) =
let val consts = map snd (filter (fn c => fst c = cname) intr_consts)
in fold (Sign.typ_unify thy) ((replicate (length consts) cT) ~~ consts) end;
val (env, _) = fold unify rec_consts (Vartab.empty, i');
val subst = map_types (Envir.norm_type env)
in (map subst cs', map subst intr_ts')
end) handle Type.TUNIFY =>
(warning "Occurrences of recursive constant have non-unifiable types"; (cs, intr_ts));
fun import_intros inp_pred nparams [] ctxt =
let
val ([outp_pred], ctxt') = Variable.import_terms false [inp_pred] ctxt
val (paramTs, _) = chop nparams (binder_types (fastype_of outp_pred))
val (param_names, ctxt'') = Variable.variant_fixes (map (fn i => "p" ^ (string_of_int i))
(1 upto nparams)) ctxt'
val params = map2 (curry Free) param_names paramTs
in (((outp_pred, params), []), ctxt') end
| import_intros inp_pred nparams (th :: ths) ctxt =
let
val ((_, [th']), ctxt') = Variable.import false [th] ctxt
val thy = ProofContext.theory_of ctxt'
val (pred, (params, args)) = strip_intro_concl nparams (prop_of th')
val ho_args = filter (is_predT o fastype_of) args
fun subst_of (pred', pred) =
let
val subst = Sign.typ_match thy (fastype_of pred', fastype_of pred) Vartab.empty
in map (fn (indexname, (s, T)) => ((indexname, s), T)) (Vartab.dest subst) end
fun instantiate_typ th =
let
val (pred', _) = strip_intro_concl 0 (prop_of th)
val _ = if not (fst (dest_Const pred) = fst (dest_Const pred')) then
error "Trying to instantiate another predicate" else ()
in Thm.certify_instantiate (subst_of (pred', pred), []) th end;
fun instantiate_ho_args th =
let
val (_, (params', args')) = strip_intro_concl nparams (prop_of th)
val ho_args' = map dest_Var (filter (is_predT o fastype_of) args')
in Thm.certify_instantiate ([], map dest_Var params' ~~ params) th end
val outp_pred =
Term_Subst.instantiate (subst_of (inp_pred, pred), []) inp_pred
val ((_, ths'), ctxt1) =
Variable.import false (map (instantiate_typ #> instantiate_ho_args) ths) ctxt'
in
(((outp_pred, params), th' :: ths'), ctxt1)
end
(* generation of case rules from user-given introduction rules *)
fun mk_casesrule ctxt pred nparams introrules =
let
val (((pred, params), intros_th), ctxt1) = import_intros pred nparams introrules ctxt
val intros = map prop_of intros_th
val ([propname], ctxt2) = Variable.variant_fixes ["thesis"] ctxt1
val prop = HOLogic.mk_Trueprop (Free (propname, HOLogic.boolT))
val (_, argsT) = chop nparams (binder_types (fastype_of pred))
val (argnames, ctxt3) = Variable.variant_fixes
(map (fn i => "a" ^ string_of_int i) (1 upto length argsT)) ctxt2
val argvs = map2 (curry Free) argnames argsT
fun mk_case intro =
let
val (_, (_, args)) = strip_intro_concl nparams intro
val prems = Logic.strip_imp_prems intro
val eqprems = map2 (HOLogic.mk_Trueprop oo (curry 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;
(** 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 ctxt = ProofContext.init thy
val ((_, [elimrule]), ctxt') = Variable.import false [elimrule] ctxt
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)
val bigeq = (Thm.symmetric (Conv.implies_concl_conv
(MetaSimplifier.rewrite true [@{thm Predicate.eq_is_eq}])
(cterm_of thy elimrule')))
val tac = (fn _ => Skip_Proof.cheat_tac thy)
val eq = Goal.prove ctxt' [] [] (Logic.mk_equals ((Thm.prop_of elimrule), elimrule')) tac
in
Thm.equal_elim eq elimrule |> singleton (Variable.export ctxt' ctxt)
end;
fun expand_tuples_elim th = th
(* updaters *)
fun apfst4 f (x1, x2, x3, x4) = (f x1, x2, x3, x4)
fun apsnd4 f (x1, x2, x3, x4) = (x1, f x2, x3, x4)
fun aptrd4 f (x1, x2, x3, x4) = (x1, x2, f x3, x4)
fun apfourth4 f (x1, x2, x3, x4) = (x1, x2, x3, f x4)
fun appair f g (x, y) = (f x, g x)
val no_compilation = ((false, []), (false, []), (false, []), (false, []))
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 (expand_tuples thy #> preprocess_intro thy) (filter is_intro_of (#intrs result)))
val index = find_index (fn s => s = name) (#names (fst info))
val pre_elim = nth (#elims result) index
val pred = nth (#preds result) index
val nparams = length (Inductive.params_of (#raw_induct result))
(*val elim = singleton (ind_set_codegen_preproc thy) (preprocess_elim thy nparams
(expand_tuples_elim pre_elim))*)
val elim =
(Drule.standard o Skip_Proof.make_thm thy)
(mk_casesrule (ProofContext.init thy) pred nparams intros)
in
mk_pred_data ((intros, SOME elim, nparams), no_compilation)
end
| NONE => error ("No such predicate: " ^ quote name)
fun add_predfun name mode data =
let
val add = (apsnd o apfst4) (fn (x, y) => (true, cons (mode, mk_predfun_data data) y))
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;
*)
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 (intros, elim, nparams) => (intros @ [thm], 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), no_compilation)) 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 (constname, pre_intros, pre_elim, nparams) thy =
let
(* 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
if not (member (op =) (Graph.keys (PredData.get thy)) constname) then
PredData.map
(Graph.new_node (constname,
mk_pred_data ((intros, SOME elim, nparams), no_compilation))) thy
else thy
end
fun register_intros (constname, pre_intros) thy =
let
val T = Sign.the_const_type thy constname
fun constname_of_intro intr = fst (dest_Const (fst (strip_intro_concl 0 (prop_of intr))))
val _ = if not (forall (fn intr => constname_of_intro intr = constname) pre_intros) then
error ("register_intros: Introduction rules of different constants are used\n" ^
"expected rules for " ^ constname ^ ", but received rules for " ^
commas (map constname_of_intro pre_intros))
else ()
val pred = Const (constname, T)
val nparams = guess_nparams T
val pre_elim =
(Drule.standard o Skip_Proof.make_thm thy)
(mk_casesrule (ProofContext.init thy) pred nparams pre_intros)
in register_predicate (constname, pre_intros, pre_elim, nparams) thy end
fun set_random_function_name pred mode name =
let
val set = (apsnd o apsnd4) (fn (x, y) => (true, cons (mode, mk_function_data (name, NONE)) y))
in
PredData.map (Graph.map_node pred (map_pred_data set))
end
fun set_depth_limited_function_name pred mode name =
let
val set = (apsnd o aptrd4) (fn (x, y) => (true, cons (mode, mk_function_data (name, NONE)) y))
in
PredData.map (Graph.map_node pred (map_pred_data set))
end
fun set_annotated_function_name pred mode name =
let
val set = (apsnd o apfourth4)
(fn (x, y) => (true, cons (mode, mk_function_data (name, NONE)) y))
in
PredData.map (Graph.map_node pred (map_pred_data set))
end
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,
mk_map : typ -> typ -> term -> 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 mk_map (CompilationFuns funs) = #mk_map funs
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;
fun mk_map T1 T2 tf tp = Const (@{const_name Predicate.map},
(T1 --> T2) --> mk_predT T1 --> mk_predT T2) $ tf $ tp;
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,
mk_map = mk_map};
end;
structure RandomPredCompFuns =
struct
fun mk_randompredT T =
@{typ Random.seed} --> HOLogic.mk_prodT (PredicateCompFuns.mk_predT T, @{typ Random.seed})
fun dest_randompredT (Type ("fun", [@{typ Random.seed}, Type (@{type_name "*"},
[Type (@{type_name "Predicate.pred"}, [T]), @{typ Random.seed}])])) = T
| dest_randompredT T = raise TYPE ("dest_randompredT", [T], []);
fun mk_bot T = Const(@{const_name Quickcheck.empty}, mk_randompredT T)
fun mk_single t =
let
val T = fastype_of t
in
Const (@{const_name Quickcheck.single}, T --> mk_randompredT T) $ t
end;
fun mk_bind (x, f) =
let
val T as (Type ("fun", [_, U])) = fastype_of f
in
Const (@{const_name Quickcheck.bind}, fastype_of x --> T --> U) $ x $ f
end
val mk_sup = HOLogic.mk_binop @{const_name Quickcheck.union}
fun mk_if cond = Const (@{const_name Quickcheck.if_randompred},
HOLogic.boolT --> mk_randompredT HOLogic.unitT) $ cond;
fun mk_not t = let val T = mk_randompredT HOLogic.unitT
in Const (@{const_name Quickcheck.not_randompred}, T --> T) $ t end
fun mk_map T1 T2 tf tp = Const (@{const_name Quickcheck.map},
(T1 --> T2) --> mk_randompredT T1 --> mk_randompredT T2) $ tf $ tp
val compfuns = CompilationFuns {mk_predT = mk_randompredT, dest_predT = dest_randompredT,
mk_bot = mk_bot, mk_single = mk_single, mk_bind = mk_bind, mk_sup = mk_sup, mk_if = mk_if,
mk_not = mk_not, mk_map = mk_map};
end;
(* for external use with interactive mode *)
val pred_compfuns = PredicateCompFuns.compfuns
val randompred_compfuns = RandomPredCompFuns.compfuns;
fun lift_random random =
let
val T = dest_randomT (fastype_of random)
in
Const (@{const_name Quickcheck.Random}, (@{typ Random.seed} -->
HOLogic.mk_prodT (HOLogic.mk_prodT (T, @{typ "unit => term"}), @{typ Random.seed})) -->
RandomPredCompFuns.mk_randompredT T) $ random
end;
(* function types and names of different compilations *)
fun funT_of compfuns (iss, is) T =
let
val Ts = binder_types T
val (paramTs, (inargTs, outargTs)) = split_modeT (iss, is) Ts
val paramTs' = map2 (fn NONE => I | SOME is => funT_of compfuns ([], is)) iss paramTs
in
(paramTs' @ inargTs) ---> (mk_predT compfuns (HOLogic.mk_tupleT outargTs))
end;
fun depth_limited_funT_of compfuns (iss, is) T =
let
val Ts = binder_types T
val (paramTs, (inargTs, outargTs)) = split_modeT (iss, is) Ts
val paramTs' =
map2 (fn SOME is => depth_limited_funT_of compfuns ([], is) | NONE => I) iss paramTs
in
(paramTs' @ inargTs @ [@{typ bool}, @{typ "code_numeral"}])
---> (mk_predT compfuns (HOLogic.mk_tupleT outargTs))
end;
fun random_function_funT_of (iss, is) T =
let
val Ts = binder_types T
val (paramTs, (inargTs, outargTs)) = split_modeT (iss, is) Ts
val paramTs' = map2 (fn SOME is => random_function_funT_of ([], is) | NONE => I) iss paramTs
in
(paramTs' @ inargTs @ [@{typ code_numeral}]) --->
(mk_predT RandomPredCompFuns.compfuns (HOLogic.mk_tupleT outargTs))
end
(* Mode analysis *)
(*** check if a term contains only constructor functions ***)
fun is_constrt thy =
let
val cnstrs = flat (maps
(map (fn (_, (Tname, _, cs)) => map (apsnd (rpair Tname o length)) cs) o #descr o snd)
(Symtab.dest (Datatype.get_all thy)));
fun check t = (case strip_comb t of
(Free _, []) => true
| (Const (s, T), ts) => (case (AList.lookup (op =) cnstrs s, body_type T) of
(SOME (i, Tname), Type (Tname', _)) =>
length ts = i andalso Tname = Tname' andalso forall check ts
| _ => false)
| _ => false)
in check end;
(*** check if a type is an equality type (i.e. doesn't contain fun)
FIXME this is only an approximation ***)
fun is_eqT (Type (s, Ts)) = s <> "fun" andalso forall is_eqT Ts
| is_eqT _ = true;
fun term_vs tm = fold_aterms (fn Free (x, T) => cons x | _ => I) tm [];
val terms_vs = distinct (op =) o maps term_vs;
(** collect all Frees in a term (with duplicates!) **)
fun term_vTs tm =
fold_aterms (fn Free xT => cons xT | _ => I) tm [];
fun subsets i j =
if i <= j then
let
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;
val is = subsets (i+1) j
in merge (map (fn ks => i::ks) is) is end
else [[]];
(* FIXME: should be in library - cprod = map_prod I *)
fun cprod ([], ys) = []
| cprod (x :: xs, ys) = map (pair x) ys @ cprod (xs, ys);
fun cprods xss = List.foldr (map op :: o cprod) [[]] xss;
fun cprods_subset [] = [[]]
| cprods_subset (xs :: xss) =
let
val yss = (cprods_subset xss)
in maps (fn ys => map (fn x => cons x ys) xs) yss @ yss end
fun modes_of_term modes t =
let
val ks = map_index (fn (i, T) => (i + 1, NONE)) (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 = map (rpair NONE) (1 upto k)
in
if not (is_prefix op = prfx is) then [] else
let val is' = map (fn (i, t) => (i - k, t)) (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) @
map_filter (AList.lookup (op =) vTs) vs;
in
subset (op =) (terms_vs (in_ts @ in_ts'), vs) andalso
forall (is_eqT o fastype_of) in_ts' andalso
subset (op =) (term_vs t, 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, _) =>
is = map (rpair NONE) (1 upto length us) andalso
subset (op =) (terms_vs us, vs) andalso
subset (op =) (term_vs t, vs))
(modes_of_term modes t handle Option =>
error ("Bad predicate: " ^ Syntax.string_of_term_global thy t))
| Sidecond t => if subset (op =) (term_vs t, 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 check_mode_clause with_generator thy param_vs modes gen_modes (iss, is) (ts, ps) =
let
val modes' = modes @ map_filter
(fn (_, NONE) => NONE | (v, SOME js) => SOME (v, [([], js)]))
(param_vs ~~ iss);
val gen_modes' = gen_modes @ map_filter
(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 as Prem _, SOME mode) => check_mode_prems ((p, mode) :: acc_ps)
(case p of Prem (us, _) => union (op =) vs (terms_vs us) | _ => vs)
(filter_out (equal p) ps)
| _ =>
let
val all_generator_vs = all_subsets (subtract (op =) vs prem_vs)
|> sort (int_ord o (pairself length))
in
case (find_first (fn generator_vs => is_some
(select_mode_prem thy modes' (union (op =) vs generator_vs) ps))
all_generator_vs) of
SOME generator_vs => check_mode_prems
((map (generator vTs) generator_vs) @ acc_ps)
(union (op =) vs generator_vs) ps
| NONE => NONE
end)
else
NONE)
| SOME (p, SOME mode) => check_mode_prems ((p, mode) :: acc_ps)
(case p of Prem (us, _) => union (op =) vs (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 [] (union (op =) param_vs in_vs) ps of
NONE => NONE
| SOME (acc_ps, vs) =>
if with_generator then
SOME (ts, (rev acc_ps) @ (map (generator vTs) (subtract (op =) vs concl_vs)))
else
if subset (op =) (concl_vs, vs) then SOME (ts, rev acc_ps) else NONE
else NONE
end;
fun print_failed_mode options thy modes p m rs i =
if show_mode_inference options then
let
val _ = tracing ("Clause " ^ string_of_int (i + 1) ^ " of " ^
p ^ " violates mode " ^ string_of_mode thy p m)
in () end
else ()
fun check_modes_pred options with_generator thy param_vs clauses modes gen_modes (p, ms) =
let
val rs = case AList.lookup (op =) clauses p of SOME rs => rs | NONE => []
in (p, 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 => (print_failed_mode options thy modes p m rs i; false)) ms)
end;
fun get_modes_pred with_generator thy param_vs clauses modes gen_modes (p, ms) =
let
val rs = case AList.lookup (op =) clauses p of SOME rs => rs | NONE => []
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 infer_modes options thy extra_modes all_modes param_vs clauses =
let
val modes =
fixp (fn modes =>
map (check_modes_pred options false thy param_vs clauses (modes @ extra_modes) []) modes)
all_modes
in
map (get_modes_pred false thy param_vs clauses (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, subtract (op =) vs' vs))
:: remove_from rem xs
fun infer_modes_with_generator options thy extra_modes all_modes param_vs clauses =
let
val prednames = map fst clauses
val extra_modes' = all_modes_of thy
val gen_modes = all_random_modes_of thy
|> filter_out (fn (name, _) => member (op =) prednames name)
val starting_modes = remove_from extra_modes' all_modes
fun eq_mode (m1, m2) = (m1 = m2)
val modes =
fixp (fn modes =>
map (check_modes_pred options true thy param_vs clauses extra_modes'
(gen_modes @ modes)) modes) starting_modes
in
AList.join (op =)
(fn _ => fn ((mps1, mps2)) =>
merge (fn ((m1, _), (m2, _)) => eq_mode (m1, m2)) (mps1, mps2))
(infer_modes options thy extra_modes all_modes param_vs clauses,
map (get_modes_pred true thy param_vs clauses 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);
(** specific rpred functions -- move them to the correct place in this file *)
fun mk_Eval_of additional_arguments ((x, T), NONE) names = (x, names)
| mk_Eval_of additional_arguments ((x, T), SOME mode) names =
let
val Ts = binder_types T
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;
fun mk_arg (i, T) =
let
val vname = Name.variant names ("x" ^ string_of_int i)
val default = Free (vname, T)
in
case AList.lookup (op =) mode i of
NONE => (([], [default]), [default])
| SOME NONE => (([default], []), [default])
| SOME (SOME pis) =>
case HOLogic.strip_tupleT T of
[] => error "pair mode but unit tuple" (*(([default], []), [default])*)
| [_] => error "pair mode but not a tuple" (*(([default], []), [default])*)
| Ts =>
let
val vnames = Name.variant_list names
(map (fn j => "x" ^ string_of_int i ^ "p" ^ string_of_int j)
(1 upto length Ts))
val args = map2 (curry Free) vnames Ts
fun split_args (i, arg) (ins, outs) =
if member (op =) pis i then
(arg::ins, outs)
else
(ins, arg::outs)
val (inargs, outargs) = fold_rev split_args ((1 upto length Ts) ~~ args) ([], [])
fun tuple args = if null args then [] else [HOLogic.mk_tuple args]
in ((tuple inargs, tuple outargs), args) end
end
val (inoutargs, args) = split_list (map mk_arg (1 upto (length Ts) ~~ Ts))
val (inargs, outargs) = pairself flat (split_list inoutargs)
val r = PredicateCompFuns.mk_Eval
(list_comb (x, inargs @ additional_arguments), HOLogic.mk_tuple outargs)
val t = fold_rev mk_split_lambda args r
in
(t, names)
end;
structure Comp_Mod =
struct
datatype comp_modifiers = Comp_Modifiers of
{
function_name_of : theory -> string -> Predicate_Compile_Aux.mode -> string,
set_function_name : string -> Predicate_Compile_Aux.mode -> string -> theory -> theory,
function_name_prefix : string,
funT_of : compilation_funs -> mode -> typ -> typ,
additional_arguments : string list -> term list,
wrap_compilation : compilation_funs -> string -> typ -> mode -> term list -> term -> term,
transform_additional_arguments : indprem -> term list -> term list
}
fun dest_comp_modifiers (Comp_Modifiers c) = c
val function_name_of = #function_name_of o dest_comp_modifiers
val set_function_name = #set_function_name o dest_comp_modifiers
val function_name_prefix = #function_name_prefix o dest_comp_modifiers
val funT_of = #funT_of o dest_comp_modifiers
val additional_arguments = #additional_arguments o dest_comp_modifiers
val wrap_compilation = #wrap_compilation o dest_comp_modifiers
val transform_additional_arguments = #transform_additional_arguments o dest_comp_modifiers
end;
fun compile_arg compilation_modifiers compfuns additional_arguments thy param_vs iss arg =
let
fun map_params (t as Free (f, T)) =
if member (op =) param_vs f then
case (the (AList.lookup (op =) (param_vs ~~ iss) f)) of
SOME is =>
let
val T' = Comp_Mod.funT_of compilation_modifiers compfuns ([], is) T
in fst (mk_Eval_of additional_arguments ((Free (f, T'), T), SOME is) []) end
| NONE => t
else t
| map_params t = t
in map_aterms map_params arg end
fun compile_match compilation_modifiers compfuns additional_arguments
param_vs iss thy eqs eqs' out_ts success_t =
let
val eqs'' = maps mk_eq eqs @ eqs'
val eqs'' =
map (compile_arg compilation_modifiers compfuns additional_arguments thy param_vs iss) 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 = HOLogic.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) DatatypeCase.Quiet [] v
[(HOLogic.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 = map2 (curry Free)
(Name.variant_list names (replicate (length Ts) "x")) Ts
in
fold_rev lambda vs (f (list_comb (t, vs)))
end;
fun compile_param compilation_modifiers compfuns thy NONE t = t
| compile_param compilation_modifiers compfuns thy (m as SOME (Mode (mode, _, ms))) t =
let
val (f, args) = strip_comb (Envir.eta_contract t)
val (params, args') = chop (length ms) args
val params' = map2 (compile_param compilation_modifiers compfuns thy) ms params
val f' =
case f of
Const (name, T) => Const (Comp_Mod.function_name_of compilation_modifiers thy name mode,
Comp_Mod.funT_of compilation_modifiers compfuns mode T)
| Free (name, T) => Free (name, Comp_Mod.funT_of compilation_modifiers compfuns mode T)
| _ => error ("PredicateCompiler: illegal parameter term")
in
list_comb (f', params' @ args')
end
fun compile_expr compilation_modifiers compfuns thy ((Mode (mode, _, ms)), t)
inargs additional_arguments =
case strip_comb t of
(Const (name, T), params) =>
let
val params' = map2 (compile_param compilation_modifiers compfuns thy) ms params
val name' = Comp_Mod.function_name_of compilation_modifiers thy name mode
val T' = Comp_Mod.funT_of compilation_modifiers compfuns mode T
in
(list_comb (Const (name', T'), params' @ inargs @ additional_arguments))
end
| (Free (name, T), params) =>
list_comb (Free (name, Comp_Mod.funT_of compilation_modifiers compfuns mode T),
params @ inargs @ additional_arguments)
fun compile_clause compilation_modifiers compfuns thy all_vs param_vs additional_arguments
(iss, is) inp (ts, moded_ps) =
let
val compile_match = compile_match compilation_modifiers compfuns
additional_arguments param_vs iss thy
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
compile_match constr_vs (eqs @ eqs') out_ts'''
(mk_single compfuns (HOLogic.mk_tuple 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 additional_arguments' =
Comp_Mod.transform_additional_arguments compilation_modifiers p additional_arguments
val (compiled_clause, rest) = case p of
Prem (us, t) =>
let
val (in_ts, out_ts''') = split_smode is us;
val in_ts = map (compile_arg compilation_modifiers compfuns
additional_arguments thy param_vs iss) in_ts
val u =
compile_expr compilation_modifiers compfuns thy
(mode, t) in_ts additional_arguments'
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 in_ts = map (compile_arg compilation_modifiers compfuns
additional_arguments thy param_vs iss) in_ts
val u = mk_not compfuns
(compile_expr compilation_modifiers compfuns thy
(mode, t) in_ts additional_arguments')
val rest = compile_prems out_ts''' vs' names'' ps
in
(u, rest)
end
| Sidecond t =>
let
val t = compile_arg compilation_modifiers compfuns additional_arguments
thy param_vs iss t
val rest = compile_prems [] vs' names'' ps;
in
(mk_if compfuns t, rest)
end
| Generator (v, T) =>
let
val [size] = additional_arguments
val u = lift_random (HOLogic.mk_random T size)
val rest = compile_prems [Free (v, T)] vs' names'' ps;
in
(u, rest)
end
in
compile_match 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 compilation_modifiers compfuns thy all_vs param_vs s T mode moded_cls =
let
val (Ts1, Ts2) = chop (length (fst mode)) (binder_types T)
val (Us1, Us2) = split_smodeT (snd mode) Ts2
val Ts1' =
map2 (fn NONE => I | SOME is => Comp_Mod.funT_of compilation_modifiers compfuns ([], is))
(fst mode) Ts1
fun mk_input_term (i, NONE) =
[Free (Name.variant (all_vs @ param_vs) ("x" ^ string_of_int i), nth Ts2 (i - 1))]
| mk_input_term (i, SOME pis) = case HOLogic.strip_tupleT (nth Ts2 (i - 1)) of
[] => error "strange unit input"
| [T] => [Free (Name.variant (all_vs @ param_vs)
("x" ^ string_of_int i), nth Ts2 (i - 1))]
| Ts => let
val vnames = Name.variant_list (all_vs @ param_vs)
(map (fn j => "x" ^ string_of_int i ^ "p" ^ string_of_int j)
pis)
in
if null pis then
[]
else
[HOLogic.mk_tuple (map2 (curry Free) vnames (map (fn j => nth Ts (j - 1)) pis))]
end
val in_ts = maps mk_input_term (snd mode)
val params = map2 (fn s => fn T => Free (s, T)) param_vs Ts1'
val additional_arguments = Comp_Mod.additional_arguments compilation_modifiers
(all_vs @ param_vs)
val cl_ts =
map (compile_clause compilation_modifiers compfuns
thy all_vs param_vs additional_arguments mode (HOLogic.mk_tuple in_ts)) moded_cls;
val compilation = Comp_Mod.wrap_compilation compilation_modifiers compfuns
s T mode additional_arguments
(if null cl_ts then
mk_bot compfuns (HOLogic.mk_tupleT Us2)
else foldr1 (mk_sup compfuns) cl_ts)
val fun_const =
Const (Comp_Mod.function_name_of compilation_modifiers thy s mode,
Comp_Mod.funT_of compilation_modifiers compfuns mode T)
in
HOLogic.mk_Trueprop
(HOLogic.mk_eq (list_comb (fun_const, params @ in_ts @ additional_arguments), compilation))
end;
(* special setup for simpset *)
val HOL_basic_ss' = HOL_basic_ss addsimps (@{thms "HOL.simp_thms"} @ [@{thm Pair_eq}])
setSolver (mk_solver "all_tac_solver" (fn _ => fn _ => all_tac))
setSolver (mk_solver "True_solver" (fn _ => rtac @{thm TrueI}))
(* 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 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 (Ts1, Ts2) = chop (length iss) Ts;
val Ts1' =
map2 (fn NONE => I | SOME is => funT_of (PredicateCompFuns.compfuns) ([], is)) iss Ts1
val param_names = Name.variant_list []
(map (fn i => "x" ^ string_of_int i) (1 upto (length Ts1)));
val params = map2 (curry Free) param_names Ts1'
fun mk_args (i, T) argnames =
let
val vname = Name.variant (param_names @ argnames) ("x" ^ string_of_int (length Ts1' + i))
val default = (Free (vname, T), vname :: argnames)
in
case AList.lookup (op =) is i of
NONE => default
| SOME NONE => default
| SOME (SOME pis) =>
case HOLogic.strip_tupleT T of
[] => default
| [_] => default
| Ts =>
let
val vnames = Name.variant_list (param_names @ argnames)
(map (fn j => "x" ^ string_of_int (length Ts1' + i) ^ "p" ^ string_of_int j)
(1 upto (length Ts)))
in (HOLogic.mk_tuple (map2 (curry Free) vnames Ts), vnames @ argnames) end
end
val (args, argnames) = fold_map mk_args (1 upto (length Ts2) ~~ Ts2) []
val (inargs, outargs) = split_smode is args
val param_names' = Name.variant_list (param_names @ argnames)
(map (fn i => "p" ^ string_of_int i) (1 upto (length iss)))
val param_vs = map2 (curry 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 @ args))
val predpropE = HOLogic.mk_Trueprop (list_comb (pred, params' @ args))
val param_eqs = map2 (HOLogic.mk_Trueprop oo (curry 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 HOLogic.mk_tuple outargs))
val funpropI = HOLogic.mk_Trueprop (PredicateCompFuns.mk_Eval (list_comb (funtrm, funargs),
HOLogic.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"}, @{thm pair_collapse}]
val unfolddef_tac = Simplifier.asm_full_simp_tac (HOL_basic_ss addsimps simprules) 1
val introthm = Goal.prove (ProofContext.init thy)
(argnames @ param_names @ 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 @ param_names' @ ["y", "P"]) [] elimtrm (fn _ => unfolddef_tac)
in
(introthm, elimthm)
end;
fun create_constname_of_mode options thy prefix name T mode =
let
val system_proposal = prefix ^ (Long_Name.base_name name)
^ "_" ^ ascii_string_of_mode' (translate_mode T mode)
val name = the_default system_proposal (proposed_names options name (translate_mode T mode))
in
Sign.full_bname thy name
end;
fun split_tupleT is T =
let
fun split_tuple' _ _ [] = ([], [])
| split_tuple' is i (T::Ts) =
(if member (op =) is i then apfst else apsnd) (cons T)
(split_tuple' is (i+1) Ts)
in
split_tuple' is 1 (HOLogic.strip_tupleT T)
end
fun mk_arg xin xout pis T =
let
val n = length (HOLogic.strip_tupleT T)
val ni = length pis
fun mk_proj i j t =
(if i = j then I else HOLogic.mk_fst)
(funpow (i - 1) HOLogic.mk_snd t)
fun mk_arg' i (si, so) =
if member (op =) pis i then
(mk_proj si ni xin, (si+1, so))
else
(mk_proj so (n - ni) xout, (si, so+1))
val (args, _) = fold_map mk_arg' (1 upto n) (1, 1)
in
HOLogic.mk_tuple args
end
fun create_definitions options 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 options thy "" name T 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_smodeT is Ts2
val Ts1' = map2 (fn NONE => I | SOME is => funT_of compfuns ([], is)) iss Ts1
val funT = (Ts1' @ Us1) ---> (mk_predT compfuns (HOLogic.mk_tupleT Us2))
val names = Name.variant_list []
(map (fn i => "x" ^ string_of_int i) (1 upto (length Ts)));
val param_names = Name.variant_list []
(map (fn i => "x" ^ string_of_int i) (1 upto (length Ts1')))
val xparams = map2 (curry Free) param_names Ts1'
fun mk_vars (i, T) names =
let
val vname = Name.variant names ("x" ^ string_of_int (length Ts1' + i))
in
case AList.lookup (op =) is i of
NONE => ((([], [Free (vname, T)]), Free (vname, T)), vname :: names)
| SOME NONE => ((([Free (vname, T)], []), Free (vname, T)), vname :: names)
| SOME (SOME pis) =>
let
val (Tins, Touts) = split_tupleT pis T
val name_in = Name.variant names ("x" ^ string_of_int (length Ts1' + i) ^ "in")
val name_out = Name.variant names ("x" ^ string_of_int (length Ts1' + i) ^ "out")
val xin = Free (name_in, HOLogic.mk_tupleT Tins)
val xout = Free (name_out, HOLogic.mk_tupleT Touts)
val xarg = mk_arg xin xout pis T
in
(((if null Tins then [] else [xin],
if null Touts then [] else [xout]), xarg), name_in :: name_out :: names) end
end
val (xinoutargs, names) = fold_map mk_vars ((1 upto (length Ts2)) ~~ Ts2) param_names
val (xinout, xargs) = split_list xinoutargs
val (xins, xouts) = pairself flat (split_list xinout)
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 define_functions comp_modifiers compfuns options preds (name, modes) thy =
let
val T = AList.lookup (op =) preds name |> the
fun create_definition mode thy =
let
val function_name_prefix = Comp_Mod.function_name_prefix comp_modifiers
val mode_cname = create_constname_of_mode options thy function_name_prefix name T mode
val funT = Comp_Mod.funT_of comp_modifiers compfuns mode T
in
thy |> Sign.add_consts_i [(Binding.name (Long_Name.base_name mode_cname), funT, NoSyn)]
|> Comp_Mod.set_function_name comp_modifiers 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 "split_eta"}, @{thm "split_beta"}, @{thm "fst_conv"},
@{thm "snd_conv"}, @{thm pair_collapse}, @{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 (map2 (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 (map2 (prove_param thy) ms args1))
THEN (REPEAT_DETERM (atac 1))
end
| _ => rtac @{thm bindI} 1
THEN asm_full_simp_tac
(HOL_basic_ss' addsimps [@{thm "split_eta"}, @{thm "split_beta"}, @{thm "fst_conv"},
@{thm "snd_conv"}, @{thm pair_collapse}]) 1
THEN (atac 1)
THEN print_tac "after prove parameter call"
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 @ maps get_case_rewrite (snd (strip_comb t)) end
else []
val simprules = @{thm "unit.cases"} :: @{thm "prod.cases"} :: maps 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_full_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
([], map (rpair NONE) (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
(@{thms "HOL.simp_thms"} @ (@{thm not_False_eq_True} :: @{thm eval_pred} :: defs))) 1
(* need better control here! *)
end
fun prove_clause options 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 print_tac "before simplifying assumptions"
THEN asm_full_simp_tac HOL_basic_ss' 1
THEN print_tac "before single intro rule"
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))
THEN (EVERY (map2 (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
print_tac' options "Proving clause..."
THEN 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 options 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 print_tac' options "before applying elim rule"
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 options 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
(print_tac ("Term " ^ (Syntax.string_of_term_global thy t) ^
"splitting with rules \n" ^
commas (map (Display.string_of_thm_global thy) split_rules)))
THEN TRY ((Splitter.split_asm_tac split_rules 1)
THEN (print_tac "after splitting with split_asm rules")
(* 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 (assert_tac (Max_number_of_subgoals 2))
THEN (EVERY (map split_term_tac ts))
end
else all_tac
in
split_term_tac (HOLogic.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 (map2 (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 (map2 (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
([], map (rpair NONE) (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' addsimps
[@{thm split_eta}, @{thm "split_beta"}, @{thm "fst_conv"},
@{thm "snd_conv"}, @{thm pair_collapse}]) 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 (map2 (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 options 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 (if null moded_clauses then
etac @{thm botE} 1
else EVERY (map2 prove_clause moded_clauses (1 upto (length moded_clauses))))
end;
(** proof procedure **)
fun prove_pred options thy clauses preds modes pred mode (moded_clauses, compiled_term) =
let
val ctxt = ProofContext.init thy
val clauses = case AList.lookup (op =) clauses pred of SOME rs => rs | NONE => []
in
Goal.prove ctxt (Term.add_free_names compiled_term []) [] compiled_term
(if not (skip_proof options) then
(fn _ =>
rtac @{thm pred_iffI} 1
THEN print_tac' options "after pred_iffI"
THEN prove_one_direction options thy clauses preds modes pred mode moded_clauses
THEN print_tac' options "proved one direction"
THEN prove_other_direction options thy modes pred mode moded_clauses
THEN print_tac' options "proved other direction")
else (fn _ => Skip_Proof.cheat_tac thy))
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 comp_modifiers compfuns thy all_vs param_vs preds moded_clauses =
map_preds_modes (fn pred => compile_pred comp_modifiers compfuns thy all_vs param_vs pred
(the (AList.lookup (op =) preds pred))) moded_clauses
fun prove options thy clauses preds modes moded_clauses compiled_terms =
map_preds_modes (prove_pred options thy clauses preds modes)
(join_preds_modes moded_clauses compiled_terms)
fun prove_by_skip options thy _ _ _ _ compiled_terms =
map_preds_modes (fn pred => fn mode => fn t => Drule.standard (Skip_Proof.make_thm thy t))
compiled_terms
(* preparation of introduction rules into special datastructures *)
fun dest_prem thy params t =
(case strip_comb t of
(v as Free _, ts) => if member (op =) params v then Prem (ts, v) else Sidecond t
| (c as Const (@{const_name Not}, _), [t]) => (case dest_prem thy params 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 prepare_intrs options thy prednames intros =
let
val intrs = map prop_of intros
val nparams = nparams_of thy (hd prednames)
val preds = map (fn c => Const (c, Sign.the_const_type thy c)) prednames
val (preds, intrs) = unify_consts thy preds intrs
val ([preds, intrs], _) = fold_burrow (Variable.import_terms false) [preds, intrs]
(ProofContext.init thy)
val preds = map dest_Const preds
val extra_modes = all_modes_of thy
|> filter_out (fn (name, _) => member (op =) prednames name)
val params = case intrs of
[] =>
let
val (paramTs, _) = chop nparams (binder_types (snd (hd preds)))
val param_names = Name.variant_list [] (map (fn i => "p" ^ string_of_int i)
(1 upto length paramTs))
in map2 (curry Free) param_names paramTs end
| intr :: _ => fst (chop nparams
(snd (strip_comb (HOLogic.dest_Trueprop (Logic.strip_imp_concl intr)))))
val param_vs = maps term_vs params
val all_vs = terms_vs intrs
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 thy params 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 ([], []);
fun modes_of_arities arities =
(map (fn (s, (ks, k)) => (s, cprod (cprods (map
(fn NONE => [NONE]
| SOME k' => map SOME (map (map (rpair NONE)) (subsets 1 k'))) ks),
map (map (rpair NONE)) (subsets 1 k)))) arities)
fun modes_of_typ T =
let
val (Ts, Us) = chop nparams (binder_types T)
fun all_smodes_of_typs Ts = cprods_subset (
map_index (fn (i, U) =>
case HOLogic.strip_tupleT U of
[] => [(i + 1, NONE)]
| [U] => [(i + 1, NONE)]
| Us => (i + 1, NONE) ::
(map (pair (i + 1) o SOME)
(subtract (op =) [[], 1 upto (length Us)] (subsets 1 (length Us)))))
Ts)
in
cprod (cprods (map (fn T => case strip_type T of
(Rs as _ :: _, Type ("bool", [])) =>
map SOME (all_smodes_of_typs Rs) | _ => [NONE]) Ts), all_smodes_of_typs Us)
end
val all_modes = map (fn (s, T) =>
case proposed_modes options s of
NONE => (s, modes_of_typ T)
| SOME modes' => (s, map (translate_mode' nparams) modes'))
preds
in (preds, nparams, all_vs, param_vs, extra_modes, clauses, all_modes) end;
(* sanity check of introduction rules *)
fun check_format_of_intro_rule thy intro =
let
val concl = Logic.strip_imp_concl (prop_of intro)
val (p, args) = strip_comb (HOLogic.dest_Trueprop concl)
val params = fst (chop (nparams_of thy (fst (dest_Const p))) args)
fun check_arg arg = case HOLogic.strip_tupleT (fastype_of arg) of
(Ts as _ :: _ :: _) =>
if length (HOLogic.strip_tuple arg) = length Ts then
true
else
error ("Format of introduction rule is invalid: tuples must be expanded:"
^ (Syntax.string_of_term_global thy arg) ^ " in " ^
(Display.string_of_thm_global thy intro))
| _ => true
val prems = Logic.strip_imp_prems (prop_of intro)
fun check_prem (Prem (args, _)) = forall check_arg args
| check_prem (Negprem (args, _)) = forall check_arg args
| check_prem _ = true
in
forall check_arg args andalso
forall (check_prem o dest_prem thy params o HOLogic.dest_Trueprop) prems
end
(*
fun check_intros_elim_match thy prednames =
let
fun check predname =
let
val intros = intros_of thy predname
val elim = the_elim_of thy predname
val nparams = nparams_of thy predname
val elim' =
(Drule.standard o (Skip_Proof.make_thm thy))
(mk_casesrule (ProofContext.init thy) nparams intros)
in
if not (Thm.equiv_thm (elim, elim')) then
error "Introduction and elimination rules do not match!"
else true
end
in forall check prednames end
*)
(* create code equation *)
fun add_code_equations thy nparams preds result_thmss =
let
fun add_code_equation (predname, T) (pred, result_thms) =
let
val full_mode = (replicate nparams NONE,
map (rpair NONE) (1 upto (length (binder_types T) - nparams)))
in
if member (op =) (modes_of thy predname) full_mode then
let
val Ts = binder_types T
val arg_names = Name.variant_list []
(map (fn i => "x" ^ string_of_int i) (1 upto length Ts))
val args = map2 (curry Free) arg_names Ts
val predfun = Const (predfun_name_of thy predname full_mode,
Ts ---> PredicateCompFuns.mk_predT @{typ unit})
val rhs = PredicateCompFuns.mk_Eval (list_comb (predfun, args), @{term "Unity"})
val eq_term = HOLogic.mk_Trueprop
(HOLogic.mk_eq (list_comb (Const (predname, T), args), rhs))
val def = predfun_definition_of thy predname full_mode
val tac = fn _ => Simplifier.simp_tac
(HOL_basic_ss addsimps [def, @{thm eval_pred}]) 1
val eq = Goal.prove (ProofContext.init thy) arg_names [] eq_term tac
in
(pred, result_thms @ [eq])
end
else
(pred, result_thms)
end
in
map2 add_code_equation preds result_thmss
end
(** main function of predicate compiler **)
datatype steps = Steps of
{
compile_preds : theory -> string list -> string list -> (string * typ) list
-> (moded_clause list) pred_mode_table -> term pred_mode_table,
define_functions : options -> (string * typ) list -> string * mode list -> theory -> theory,
infer_modes : options -> theory -> (string * mode list) list -> (string * mode list) list
-> string list -> (string * (term list * indprem list) list) list
-> moded_clause list pred_mode_table,
prove : options -> theory -> (string * (term list * indprem list) list) list
-> (string * typ) list -> (string * mode list) list
-> moded_clause list pred_mode_table -> term pred_mode_table -> thm pred_mode_table,
add_code_equations : theory -> int -> (string * typ) list
-> (string * thm list) list -> (string * thm list) list,
defined : theory -> string -> bool,
qname : bstring
}
fun add_equations_of steps options prednames thy =
let
fun dest_steps (Steps s) = s
val _ = print_step options
("Starting predicate compiler for predicates " ^ commas prednames ^ "...")
(*val _ = check_intros_elim_match thy prednames*)
(*val _ = map (check_format_of_intro_rule thy) (maps (intros_of thy) prednames)*)
val (preds, nparams, all_vs, param_vs, extra_modes, clauses, all_modes) =
prepare_intrs options thy prednames (maps (intros_of thy) prednames)
val _ = print_step options "Infering modes..."
val moded_clauses =
#infer_modes (dest_steps steps) options thy extra_modes all_modes param_vs clauses
val modes = map (fn (p, mps) => (p, map fst mps)) moded_clauses
val _ = check_expected_modes preds options modes
val _ = print_modes options thy modes
(*val _ = print_moded_clauses thy moded_clauses*)
val _ = print_step options "Defining executable functions..."
val thy' = fold (#define_functions (dest_steps steps) options preds) modes thy
|> Theory.checkpoint
val _ = print_step options "Compiling equations..."
val compiled_terms =
#compile_preds (dest_steps steps) thy' all_vs param_vs preds moded_clauses
val _ = print_compiled_terms options thy' compiled_terms
val _ = print_step options "Proving equations..."
val result_thms = #prove (dest_steps steps) options thy' clauses preds (extra_modes @ modes)
moded_clauses compiled_terms
val result_thms' = #add_code_equations (dest_steps steps) thy' nparams preds
(maps_modes result_thms)
val qname = #qname (dest_steps steps)
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))
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)
(subtract (op =) visited (edges_of (key, v)))
(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 options names thy =
let
fun dest_steps (Steps s) = s
val thy' = thy
|> PredData.map (fold (extend (fetch_pred_data thy) (depending_preds_of thy)) names)
|> 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 not (forall (#defined (dest_steps steps) thy) preds) then
add_equations_of steps options preds thy
else thy)
scc thy' |> Theory.checkpoint
in thy'' end
(* different instantiantions of the predicate compiler *)
val predicate_comp_modifiers = Comp_Mod.Comp_Modifiers
{function_name_of = predfun_name_of : (theory -> string -> mode -> string),
set_function_name = (fn _ => fn _ => fn _ => I),
function_name_prefix = "",
funT_of = funT_of : (compilation_funs -> mode -> typ -> typ),
additional_arguments = K [],
wrap_compilation = K (K (K (K (K I))))
: (compilation_funs -> string -> typ -> mode -> term list -> term -> term),
transform_additional_arguments = K I : (indprem -> term list -> term list)
}
val depth_limited_comp_modifiers = Comp_Mod.Comp_Modifiers
{function_name_of = depth_limited_function_name_of,
set_function_name = set_depth_limited_function_name,
funT_of = depth_limited_funT_of : (compilation_funs -> mode -> typ -> typ),
function_name_prefix = "depth_limited_",
additional_arguments = fn names =>
let
val [depth_name, polarity_name] = Name.variant_list names ["depth", "polarity"]
in [Free (polarity_name, @{typ "bool"}), Free (depth_name, @{typ "code_numeral"})] end,
wrap_compilation =
fn compfuns => fn s => fn T => fn mode => fn additional_arguments => fn compilation =>
let
val [polarity, depth] = additional_arguments
val (_, Ts2) = chop (length (fst mode)) (binder_types T)
val (_, Us2) = split_smodeT (snd mode) Ts2
val T' = mk_predT compfuns (HOLogic.mk_tupleT Us2)
val if_const = Const (@{const_name "If"}, @{typ bool} --> T' --> T' --> T')
val full_mode = null Us2
in
if_const $ HOLogic.mk_eq (depth, @{term "0 :: code_numeral"})
$ (if_const $ polarity $ mk_bot compfuns (dest_predT compfuns T')
$ (if full_mode then mk_single compfuns HOLogic.unit else
Const (@{const_name undefined}, T')))
$ compilation
end,
transform_additional_arguments =
fn prem => fn additional_arguments =>
let
val [polarity, depth] = additional_arguments
val polarity' = (case prem of Prem _ => I | Negprem _ => HOLogic.mk_not | _ => I) polarity
val depth' =
Const ("HOL.minus_class.minus", @{typ "code_numeral => code_numeral => code_numeral"})
$ depth $ Const ("HOL.one_class.one", @{typ "Code_Numeral.code_numeral"})
in [polarity', depth'] end
}
val random_comp_modifiers = Comp_Mod.Comp_Modifiers
{function_name_of = random_function_name_of,
set_function_name = set_random_function_name,
function_name_prefix = "random_",
funT_of = K random_function_funT_of : (compilation_funs -> mode -> typ -> typ),
additional_arguments = fn names => [Free (Name.variant names "size", @{typ code_numeral})],
wrap_compilation = K (K (K (K (K I))))
: (compilation_funs -> string -> typ -> mode -> term list -> term -> term),
transform_additional_arguments = K I : (indprem -> term list -> term list)
}
val annotated_comp_modifiers = Comp_Mod.Comp_Modifiers
{function_name_of = annotated_function_name_of,
set_function_name = set_annotated_function_name,
function_name_prefix = "annotated_",
funT_of = funT_of : (compilation_funs -> mode -> typ -> typ),
additional_arguments = K [],
wrap_compilation =
fn compfuns => fn s => fn T => fn mode => fn additional_arguments => fn compilation =>
mk_tracing ("calling predicate " ^ s ^
" with mode " ^ string_of_mode' (translate_mode T mode)) compilation,
transform_additional_arguments = K I : (indprem -> term list -> term list)
}
val add_equations = gen_add_equations
(Steps {infer_modes = infer_modes,
define_functions = create_definitions,
compile_preds = compile_preds predicate_comp_modifiers PredicateCompFuns.compfuns,
prove = prove,
add_code_equations = add_code_equations,
defined = defined_functions,
qname = "equation"})
val add_depth_limited_equations = gen_add_equations
(Steps {infer_modes = infer_modes,
define_functions = define_functions depth_limited_comp_modifiers PredicateCompFuns.compfuns,
compile_preds = compile_preds depth_limited_comp_modifiers PredicateCompFuns.compfuns,
prove = prove_by_skip,
add_code_equations = K (K (K I)),
defined = defined_depth_limited_functions,
qname = "depth_limited_equation"})
val add_annotated_equations = gen_add_equations
(Steps {infer_modes = infer_modes,
define_functions = define_functions annotated_comp_modifiers PredicateCompFuns.compfuns,
compile_preds = compile_preds annotated_comp_modifiers PredicateCompFuns.compfuns,
prove = prove_by_skip,
add_code_equations = K (K (K I)),
defined = defined_annotated_functions,
qname = "annotated_equation"})
val add_quickcheck_equations = gen_add_equations
(Steps {infer_modes = infer_modes_with_generator,
define_functions = define_functions random_comp_modifiers RandomPredCompFuns.compfuns,
compile_preds = compile_preds random_comp_modifiers RandomPredCompFuns.compfuns,
prove = prove_by_skip,
add_code_equations = K (K (K I)),
defined = defined_random_functions,
qname = "random_equation"})
(** user interface **)
(* code_pred_intro attribute *)
fun attrib f = Thm.declaration_attribute (fn thm => Context.mapping (f thm) I);
val code_pred_intro_attrib = attrib add_intro;
(*FIXME
- Naming of auxiliary rules necessary?
*)
val setup = PredData.put (Graph.empty) #>
Attrib.setup @{binding code_pred_intro} (Scan.succeed (attrib add_intro))
"adding alternative introduction rules for code generation of inductive predicates"
(* TODO: make Theory_Data to Generic_Data & remove duplication of local theory and theory *)
fun generic_code_pred prep_const options raw_const lthy =
let
val thy = ProofContext.theory_of lthy
val const = prep_const thy raw_const
val lthy' = Local_Theory.theory (PredData.map
(extend (fetch_pred_data thy) (depending_preds_of thy) const)) lthy
|> Local_Theory.checkpoint
val thy' = ProofContext.theory_of lthy'
val preds = Graph.all_succs (PredData.get thy') [const] |> filter_out (has_elim thy')
fun mk_cases const =
let
val T = Sign.the_const_type thy const
val pred = Const (const, T)
val nparams = nparams_of thy' const
val intros = intros_of thy' const
in mk_casesrule lthy' pred nparams intros end
val cases_rules = map mk_cases preds
val cases =
map (fn case_rule => Rule_Cases.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 |> Local_Theory.theory (fold set_elim global_thms #>
(if is_random options then
(add_equations options [const] #>
add_quickcheck_equations options [const])
else if is_depth_limited options then
add_depth_limited_equations options [const]
else if is_annotated options then
add_annotated_equations options [const]
else
add_equations options [const]))
end
in
Proof.theorem_i NONE after_qed (map (single o (rpair [])) cases_rules) lthy''
end;
val code_pred = generic_code_pred (K I);
val code_pred_cmd = generic_code_pred Code.read_const
(* transformation for code generation *)
val eval_ref = Unsynchronized.ref (NONE : (unit -> term Predicate.pred) option);
val random_eval_ref =
Unsynchronized.ref (NONE : (unit -> int * int -> term Predicate.pred * (int * int)) option);
(*FIXME turn this into an LCF-guarded preprocessor for comprehensions*)
(* TODO: make analyze_compr generic with respect to the compilation modifiers*)
fun analyze_compr thy compfuns param_user_modes (depth_limit, (random, annotated)) 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_psplits split;
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 user_mode' = map (rpair NONE) user_mode
val all_modes_of = if random then all_random_modes_of else all_modes_of
fun fits_to is NONE = true
| fits_to is (SOME pm) = (is = (snd (translate_mode' 0 pm)))
fun valid ((SOME (Mode (_, is, ms))) :: ms') (pm :: pms) =
fits_to is pm andalso valid (ms @ ms') pms
| valid (NONE :: ms') pms = valid ms' pms
| valid [] [] = true
| valid [] _ = error "Too many mode annotations"
| valid (SOME _ :: _) [] = error "Not enough mode annotations"
val modes = filter (fn Mode (_, is, ms) => is = user_mode'
andalso (the_default true (Option.map (valid ms) param_user_modes)))
(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 (inargs, outargs) = split_smode user_mode' args;
val additional_arguments =
case depth_limit of
NONE => (if random then [@{term "5 :: code_numeral"}] else [])
| SOME d => [@{term "True"}, HOLogic.mk_number @{typ "code_numeral"} d]
val comp_modifiers =
case depth_limit of
NONE =>
(if random then random_comp_modifiers else
if annotated then annotated_comp_modifiers else predicate_comp_modifiers)
| SOME _ => depth_limited_comp_modifiers
val t_pred = compile_expr comp_modifiers compfuns thy
(m, list_comb (pred, params)) inargs additional_arguments;
val t_eval = if null outargs then t_pred else
let
val outargs_bounds = map (fn Bound i => i) outargs;
val outargsTs = map (nth Ts) outargs_bounds;
val T_pred = HOLogic.mk_tupleT outargsTs;
val T_compr = HOLogic.mk_ptupleT fp (rev Ts);
val k = length outargs - 1;
val arrange_bounds = map_index (fn (i, j) => (k-i, k-j)) outargs_bounds
|> sort (prod_ord (K EQUAL) int_ord)
|> map fst;
val (outargsTs', outargsT) = split_last outargsTs;
val (arrange, _) = fold_rev (fn U => fn (t, T) =>
(HOLogic.split_const (U, T, T_compr) $ Abs ("", U, t),
HOLogic.mk_prodT (U, T)))
outargsTs' (Abs ("", outargsT,
HOLogic.mk_ptuple fp T_compr (map Bound arrange_bounds)), outargsT)
in mk_map compfuns T_pred T_compr arrange t_pred end
in t_eval end;
fun eval thy param_user_modes (options as (depth_limit, (random, annotated))) t_compr =
let
val compfuns = if random then RandomPredCompFuns.compfuns else PredicateCompFuns.compfuns
val t = analyze_compr thy compfuns param_user_modes options t_compr;
val T = dest_predT compfuns (fastype_of t);
val t' = mk_map compfuns T HOLogic.termT (HOLogic.term_of_const T) t;
val eval =
if random then
Code_ML.eval NONE ("Predicate_Compile_Core.random_eval_ref", random_eval_ref)
(fn proc => fn g => fn s => g s |>> Predicate.map proc) thy t' []
|> Random_Engine.run
else
Code_ML.eval NONE ("Predicate_Compile_Core.eval_ref", eval_ref) Predicate.map thy t' []
in (T, eval) end;
fun values ctxt param_user_modes options k t_compr =
let
val thy = ProofContext.theory_of ctxt;
val (T, ts) = eval thy param_user_modes options t_compr;
val (ts, _) = Predicate.yieldn k ts;
val setT = HOLogic.mk_setT T;
val elemsT = HOLogic.mk_set T ts;
val cont = Free ("...", setT)
in if k = ~1 orelse length ts < k then elemsT
else Const (@{const_name Set.union}, setT --> setT --> setT) $ elemsT $ cont
end;
fun values_cmd print_modes param_user_modes options k raw_t state =
let
val ctxt = Toplevel.context_of state;
val t = Syntax.read_term ctxt raw_t;
val t' = values ctxt param_user_modes options k t;
val ty' = Term.type_of t';
val ctxt' = Variable.auto_fixes t' ctxt;
val p = PrintMode.with_modes print_modes (fn () =>
Pretty.block [Pretty.quote (Syntax.pretty_term ctxt' t'), Pretty.fbrk,
Pretty.str "::", Pretty.brk 1, Pretty.quote (Syntax.pretty_typ ctxt' ty')]) ();
in Pretty.writeln p end;
end;