renamed old-style Drule.standard to Drule.export_without_context, to emphasize that this is in no way a standard operation;
(* 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
-> (string option * (Predicate_Compile_Aux.compilation * int list))
-> int -> string -> Toplevel.state -> unit
val register_predicate : (string * thm list * thm) -> theory -> theory
val register_intros : string * thm list -> theory -> theory
val is_registered : theory -> string -> bool
val function_name_of : Predicate_Compile_Aux.compilation -> theory
-> string -> Predicate_Compile_Aux.mode -> string
val predfun_intro_of: theory -> string -> Predicate_Compile_Aux.mode -> thm
val predfun_elim_of: theory -> string -> Predicate_Compile_Aux.mode -> thm
val all_preds_of : theory -> string list
val modes_of: Predicate_Compile_Aux.compilation
-> theory -> string -> Predicate_Compile_Aux.mode list
val all_modes_of : Predicate_Compile_Aux.compilation
-> 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 add_intro : thm -> theory -> theory
val set_elim : thm -> theory -> theory
val preprocess_intro : theory -> thm -> thm
val print_stored_rules : theory -> unit
val print_all_modes : Predicate_Compile_Aux.compilation -> theory -> unit
val mk_casesrule : Proof.context -> term -> 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 dseq_eval_ref : (unit -> term DSequence.dseq) option Unsynchronized.ref
val random_dseq_eval_ref : (unit -> int -> int -> int * int -> term DSequence.dseq * (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_random_dseq_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)); *)
fun assert b = if not b then error "Assertion failed" else warning "Assertion holds"
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)));
(** 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
val strip_intro_concl = (strip_comb o HOLogic.dest_Trueprop o Logic.strip_imp_concl o prop_of)
(* derivation trees for modes of premises *)
datatype mode_derivation = Mode_App of mode_derivation * mode_derivation | Context of mode
| Mode_Pair of mode_derivation * mode_derivation | Term of mode
fun string_of_derivation (Mode_App (m1, m2)) =
"App (" ^ string_of_derivation m1 ^ ", " ^ string_of_derivation m2 ^ ")"
| string_of_derivation (Mode_Pair (m1, m2)) =
"Pair (" ^ string_of_derivation m1 ^ ", " ^ string_of_derivation m2 ^ ")"
| string_of_derivation (Term m) = "Term (" ^ string_of_mode m ^ ")"
| string_of_derivation (Context m) = "Context (" ^ string_of_mode m ^ ")"
fun strip_mode_derivation deriv =
let
fun strip (Mode_App (deriv1, deriv2)) ds = strip deriv1 (deriv2 :: ds)
| strip deriv ds = (deriv, ds)
in
strip deriv []
end
fun mode_of (Context m) = m
| mode_of (Term m) = m
| mode_of (Mode_App (d1, d2)) =
(case mode_of d1 of Fun (m, m') =>
(if m = mode_of d2 then m' else error "mode_of")
| _ => error "mode_of2")
| mode_of (Mode_Pair (d1, d2)) =
Pair (mode_of d1, mode_of d2)
fun head_mode_of deriv = mode_of (fst (strip_mode_derivation deriv))
fun param_derivations_of deriv =
let
val (_, argument_derivs) = strip_mode_derivation deriv
fun param_derivation (Mode_Pair (m1, m2)) =
param_derivation m1 @ param_derivation m2
| param_derivation (Term _) = []
| param_derivation m = [m]
in
maps param_derivation argument_derivs
end
fun collect_context_modes (Mode_App (m1, m2)) =
collect_context_modes m1 @ collect_context_modes m2
| collect_context_modes (Mode_Pair (m1, m2)) =
collect_context_modes m1 @ collect_context_modes m2
| collect_context_modes (Context m) = [m]
| collect_context_modes (Term _) = []
(* representation of inferred clauses with modes *)
type moded_clause = term list * (indprem * mode_derivation) list
type 'a pred_mode_table = (string * (mode * 'a) list) list
(* book-keeping *)
datatype predfun_data = PredfunData of {
definition : thm,
intro : thm,
elim : thm
};
fun rep_predfun_data (PredfunData data) = data;
fun mk_predfun_data (definition, intro, elim) =
PredfunData {definition = definition, intro = intro, elim = elim}
datatype pred_data = PredData of {
intros : thm list,
elim : thm option,
function_names : (compilation * (mode * string) list) list,
predfun_data : (mode * predfun_data) list,
needs_random : mode list
};
fun rep_pred_data (PredData data) = data;
fun mk_pred_data ((intros, elim), (function_names, predfun_data, needs_random)) =
PredData {intros = intros, elim = elim,
function_names = function_names, predfun_data = predfun_data, needs_random = needs_random}
fun map_pred_data f (PredData {intros, elim, function_names, predfun_data, needs_random}) =
mk_pred_data (f ((intros, elim), (function_names, predfun_data, needs_random)))
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)
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;
fun function_names_of compilation thy name =
case AList.lookup (op =) (#function_names (the_pred_data thy name)) compilation of
NONE => error ("No " ^ string_of_compilation compilation
^ "functions defined for predicate " ^ quote name)
| SOME fun_names => fun_names
fun function_name_of compilation thy name mode =
case AList.lookup (op =) (function_names_of compilation thy name) mode of
NONE => error ("No " ^ string_of_compilation compilation
^ "function defined for mode " ^ string_of_mode mode ^ " of predicate " ^ quote name)
| SOME function_name => function_name
fun modes_of compilation thy name = map fst (function_names_of compilation thy name)
fun all_modes_of compilation thy =
map_filter (fn name => Option.map (pair name) (try (modes_of compilation thy) name))
(all_preds_of thy)
val all_random_modes_of = all_modes_of Random
fun defined_functions compilation thy name =
AList.defined (op =) (#function_names (the_pred_data thy name)) compilation
fun lookup_predfun_data thy name mode =
Option.map rep_predfun_data
(AList.lookup (op =) (#predfun_data (the_pred_data thy name)) mode)
fun the_predfun_data thy name mode =
case lookup_predfun_data thy name mode of
NONE => error ("No function defined for mode " ^ string_of_mode mode ^
" of predicate " ^ name)
| SOME data => data;
val predfun_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
(* 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 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 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 t) =
(Syntax.string_of_term_global thy t) ^ "(premise)"
| string_of_prem thy (Negprem t) =
(Syntax.string_of_term_global thy (HOLogic.mk_not t)) ^ "(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_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 ("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 compilation thy =
let
val _ = writeln ("Inferred modes:")
fun print (pred, modes) u =
let
val _ = writeln ("predicate: " ^ pred)
val _ = writeln ("modes: " ^ (commas (map string_of_mode modes)))
in u end
in
fold print (all_modes_of compilation thy) ()
end
(* validity checks *)
(* EXPECTED MODE and PROPOSED_MODE are largely the same; define a clear semantics for those! *)
fun check_expected_modes preds options modes =
case expected_modes options of
SOME (s, ms) => (case AList.lookup (op =) modes s of
SOME modes =>
let
val modes' = 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 => ()
fun check_proposed_modes preds options modes extra_modes errors =
case proposed_modes options of
SOME (s, ms) => (case AList.lookup (op =) modes s of
SOME inferred_ms =>
let
val preds_without_modes = map fst (filter (null o snd) (modes @ extra_modes))
val modes' = inferred_ms
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) ^ "\n"
^ "For the following clauses, the following modes could not be inferred: " ^ "\n"
^ cat_lines errors ^
(if not (null preds_without_modes) then
"\n" ^ "No mode inferred for the predicates " ^ commas preds_without_modes
else ""))
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 [] ctxt =
let
val ([outp_pred], ctxt') = Variable.import_terms true [inp_pred] ctxt
val T = fastype_of outp_pred
(* TODO: put in a function for this next line! *)
val paramTs = ho_argsT_of (hd (all_modes_of_typ T)) (binder_types T)
val (param_names, ctxt'') = Variable.variant_fixes
(map (fn i => "p" ^ (string_of_int i)) (1 upto (length paramTs))) ctxt'
val params = map2 (curry Free) param_names paramTs
in
(((outp_pred, params), []), ctxt')
end
| import_intros inp_pred (th :: ths) ctxt =
let
val ((_, [th']), ctxt') = Variable.import true [th] ctxt
val thy = ProofContext.theory_of ctxt'
val (pred, args) = strip_intro_concl th'
val T = fastype_of pred
val ho_args = ho_args_of (hd (all_modes_of_typ T)) 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 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 (_, args') = (strip_comb o HOLogic.dest_Trueprop o Logic.strip_imp_concl o prop_of) th
val ho_args' = map dest_Var (ho_args_of (hd (all_modes_of_typ T)) args')
in Thm.certify_instantiate ([], ho_args' ~~ ho_args) 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, ho_args), th' :: ths'), ctxt1)
end
(* generation of case rules from user-given introduction rules *)
fun mk_args2 (Type ("*", [T1, T2])) st =
let
val (t1, st') = mk_args2 T1 st
val (t2, st'') = mk_args2 T2 st'
in
(HOLogic.mk_prod (t1, t2), st'')
end
| mk_args2 (T as Type ("fun", _)) (params, ctxt) =
let
val (S, U) = strip_type T
in
if U = HOLogic.boolT then
(hd params, (tl params, ctxt))
else
let
val ([x], ctxt') = Variable.variant_fixes ["x"] ctxt
in
(Free (x, T), (params, ctxt'))
end
end
| mk_args2 T (params, ctxt) =
let
val ([x], ctxt') = Variable.variant_fixes ["x"] ctxt
in
(Free (x, T), (params, ctxt'))
end
fun mk_casesrule ctxt pred introrules =
let
val (((pred, params), intros_th), ctxt1) = import_intros pred 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 = binder_types (fastype_of pred)
val (argvs, _) = fold_map mk_args2 argsT (params, ctxt2)
fun mk_case intro =
let
val (_, args) = (strip_comb o HOLogic.dest_Trueprop o Logic.strip_imp_concl) 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, 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 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))))
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
val no_compilation = ([], [], [])
fun fetch_pred_data thy name =
case try (Inductive.the_inductive (ProofContext.init thy)) name of
SOME (info as (_, result)) =>
let
fun is_intro_of intro =
let
val (const, _) = strip_comb (HOLogic.dest_Trueprop (concl_of intro))
in (fst (dest_Const const) = name) end;
val intros =
(map (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 elim = singleton (Inductive_Set.codegen_preproc thy) (preprocess_elim thy nparams
(expand_tuples_elim pre_elim))*)
val elim =
(Drule.export_without_context o Skip_Proof.make_thm thy)
(mk_casesrule (ProofContext.init thy) pred intros)
in
mk_pred_data ((intros, SOME elim), no_compilation)
end
| NONE => error ("No such predicate: " ^ quote name)
fun add_predfun_data name mode data =
let
val add = (apsnd o apsnd3) (cons (mode, mk_predfun_data data))
in PredData.map (Graph.map_node name (map_pred_data add)) end
fun is_inductive_predicate thy name =
is_some (try (Inductive.the_inductive (ProofContext.init thy)) name)
fun depending_preds_of thy (key, value) =
let
val intros = (#intros o rep_pred_data) value
in
fold Term.add_const_names (map Thm.prop_of intros) []
|> filter (fn c => (not (c = key)) andalso
(is_inductive_predicate thy c orelse is_registered thy c))
end;
fun add_intro thm thy =
let
val (name, T) = dest_Const (fst (strip_intro_concl 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) => (intros @ [thm], elim)))) gr
| NONE => Graph.new_node (name, mk_pred_data (([thm], NONE), no_compilation)) gr
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, _) = (intros, SOME thm)
in PredData.map (Graph.map_node name (map_pred_data (apfst set))) end
fun register_predicate (constname, pre_intros, pre_elim) thy =
let
val intros = map (preprocess_intro thy) pre_intros
val elim = preprocess_elim thy 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), 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 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 pre_elim =
(Drule.export_without_context o Skip_Proof.make_thm thy)
(mk_casesrule (ProofContext.init thy) pred pre_intros)
in register_predicate (constname, pre_intros, pre_elim) thy end
fun defined_function_of compilation pred =
let
val set = (apsnd o apfst3) (cons (compilation, []))
in
PredData.map (Graph.map_node pred (map_pred_data set))
end
fun set_function_name compilation pred mode name =
let
val set = (apsnd o apfst3)
(AList.map_default (op =) (compilation, [(mode, name)]) (cons (mode, name)))
in
PredData.map (Graph.map_node pred (map_pred_data set))
end
fun set_needs_random name modes =
let
val set = (apsnd o aptrd3) (K modes)
in
PredData.map (Graph.map_node name (map_pred_data set))
end
(* datastructures and setup for generic 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
};
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 dest_Eval (Const (@{const_name Predicate.eval}, _) $ f $ x) = (f, x)
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;
structure DSequence_CompFuns =
struct
fun mk_dseqT T = Type ("fun", [@{typ code_numeral}, Type ("fun", [@{typ bool},
Type (@{type_name Option.option}, [Type ("Lazy_Sequence.lazy_sequence", [T])])])])
fun dest_dseqT (Type ("fun", [@{typ code_numeral}, Type ("fun", [@{typ bool},
Type (@{type_name Option.option}, [Type ("Lazy_Sequence.lazy_sequence", [T])])])])) = T
| dest_dseqT T = raise TYPE ("dest_dseqT", [T], []);
fun mk_bot T = Const ("DSequence.empty", mk_dseqT T);
fun mk_single t =
let val T = fastype_of t
in Const("DSequence.single", T --> mk_dseqT T) $ t end;
fun mk_bind (x, f) =
let val T as Type ("fun", [_, U]) = fastype_of f
in
Const ("DSequence.bind", fastype_of x --> T --> U) $ x $ f
end;
val mk_sup = HOLogic.mk_binop "DSequence.union";
fun mk_if cond = Const ("DSequence.if_seq",
HOLogic.boolT --> mk_dseqT HOLogic.unitT) $ cond;
fun mk_not t = let val T = mk_dseqT HOLogic.unitT
in Const ("DSequence.not_seq", T --> T) $ t end
fun mk_map T1 T2 tf tp = Const ("DSequence.map",
(T1 --> T2) --> mk_dseqT T1 --> mk_dseqT T2) $ tf $ tp
val compfuns = CompilationFuns {mk_predT = mk_dseqT, dest_predT = dest_dseqT,
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 Random_Sequence_CompFuns =
struct
fun mk_random_dseqT T =
@{typ code_numeral} --> @{typ code_numeral} --> @{typ Random.seed} -->
HOLogic.mk_prodT (DSequence_CompFuns.mk_dseqT T, @{typ Random.seed})
fun dest_random_dseqT (Type ("fun", [@{typ code_numeral}, Type ("fun", [@{typ code_numeral},
Type ("fun", [@{typ Random.seed},
Type (@{type_name "*"}, [T, @{typ Random.seed}])])])])) = DSequence_CompFuns.dest_dseqT T
| dest_random_dseqT T = raise TYPE ("dest_random_dseqT", [T], []);
fun mk_bot T = Const ("Random_Sequence.empty", mk_random_dseqT T);
fun mk_single t =
let val T = fastype_of t
in Const("Random_Sequence.single", T --> mk_random_dseqT T) $ t end;
fun mk_bind (x, f) =
let
val T as Type ("fun", [_, U]) = fastype_of f
in
Const ("Random_Sequence.bind", fastype_of x --> T --> U) $ x $ f
end;
val mk_sup = HOLogic.mk_binop "Random_Sequence.union";
fun mk_if cond = Const ("Random_Sequence.if_random_dseq",
HOLogic.boolT --> mk_random_dseqT HOLogic.unitT) $ cond;
fun mk_not t = let val T = mk_random_dseqT HOLogic.unitT
in Const ("Random_Sequence.not_random_dseq", T --> T) $ t end
fun mk_map T1 T2 tf tp = Const ("Random_Sequence.map",
(T1 --> T2) --> mk_random_dseqT T1 --> mk_random_dseqT T2) $ tf $ tp
val compfuns = CompilationFuns {mk_predT = mk_random_dseqT, dest_predT = dest_random_dseqT,
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;
fun mk_random T =
let
val random = Const ("Quickcheck.random_class.random",
@{typ code_numeral} --> @{typ Random.seed} -->
HOLogic.mk_prodT (HOLogic.mk_prodT (T, @{typ "unit => term"}), @{typ Random.seed}))
in
Const ("Random_Sequence.Random", (@{typ code_numeral} --> @{typ Random.seed} -->
HOLogic.mk_prodT (HOLogic.mk_prodT (T, @{typ "unit => term"}), @{typ Random.seed})) -->
Random_Sequence_CompFuns.mk_random_dseqT T) $ random
end;
(* for external use with interactive mode *)
val pred_compfuns = PredicateCompFuns.compfuns
val randompred_compfuns = Random_Sequence_CompFuns.compfuns;
(* function types and names of different compilations *)
fun funT_of compfuns mode T =
let
val Ts = binder_types T
val (inTs, outTs) = split_map_modeT (fn m => fn T => (SOME (funT_of compfuns m T), NONE)) mode Ts
in
inTs ---> (mk_predT compfuns (HOLogic.mk_tupleT outTs))
end;
(** mode analysis **)
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 [[]];
fun print_failed_mode options thy modes p m rs is =
if show_mode_inference options then
let
val _ = tracing ("Clauses " ^ commas (map (fn i => string_of_int (i + 1)) is) ^ " of " ^
p ^ " violates mode " ^ string_of_mode m)
in () end
else ()
fun error_of p m is =
(" Clauses " ^ commas (map (fn i => string_of_int (i + 1)) is) ^ " of " ^
p ^ " violates mode " ^ string_of_mode m)
fun is_all_input mode =
let
fun is_all_input' (Fun _) = true
| is_all_input' (Pair (m1, m2)) = is_all_input' m1 andalso is_all_input' m2
| is_all_input' Input = true
| is_all_input' Output = false
in
forall is_all_input' (strip_fun_mode mode)
end
fun all_input_of T =
let
val (Ts, U) = strip_type T
fun input_of (Type ("*", [T1, T2])) = Pair (input_of T1, input_of T2)
| input_of _ = Input
in
if U = HOLogic.boolT then
fold_rev (curry Fun) (map input_of Ts) Bool
else
error "all_input_of: not a predicate"
end
fun partial_hd [] = NONE
| partial_hd (x :: xs) = SOME x
fun term_vs tm = fold_aterms (fn Free (x, T) => cons x | _ => I) tm [];
val terms_vs = distinct (op =) o maps term_vs;
fun input_mode T =
let
val (Ts, U) = strip_type T
in
fold_rev (curry Fun) (map (K Input) Ts) Input
end
fun output_mode T =
let
val (Ts, U) = strip_type T
in
fold_rev (curry Fun) (map (K Output) Ts) Output
end
fun is_invertible_function thy (Const (f, _)) = is_constr thy f
| is_invertible_function thy _ = false
fun non_invertible_subterms thy (Free _) = []
| non_invertible_subterms thy t =
case (strip_comb t) of (f, args) =>
if is_invertible_function thy f then
maps (non_invertible_subterms thy) args
else
[t]
fun collect_non_invertible_subterms thy (f as Free _) (names, eqs) = (f, (names, eqs))
| collect_non_invertible_subterms thy t (names, eqs) =
case (strip_comb t) of (f, args) =>
if is_invertible_function thy f then
let
val (args', (names', eqs')) =
fold_map (collect_non_invertible_subterms thy) args (names, eqs)
in
(list_comb (f, args'), (names', eqs'))
end
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
(*
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;
*)
fun is_possible_output thy vs t =
forall
(fn t => is_eqT (fastype_of t) andalso forall (member (op =) vs) (term_vs t))
(non_invertible_subterms thy t)
fun vars_of_destructable_term thy (Free (x, _)) = [x]
| vars_of_destructable_term thy t =
case (strip_comb t) of (f, args) =>
if is_invertible_function thy f then
maps (vars_of_destructable_term thy) args
else
[]
fun is_constructable thy vs t = forall (member (op =) vs) (term_vs t)
fun missing_vars vs t = subtract (op =) vs (term_vs t)
fun derivations_of thy modes vs t Input =
[(Term Input, missing_vars vs t)]
| derivations_of thy modes vs t Output =
if is_possible_output thy vs t then [(Term Output, [])] else []
| derivations_of thy modes vs (Const ("Pair", _) $ t1 $ t2) (Pair (m1, m2)) =
map_product
(fn (m1, mvars1) => fn (m2, mvars2) => (Mode_Pair (m1, m2), union (op =) mvars1 mvars2))
(derivations_of thy modes vs t1 m1) (derivations_of thy modes vs t2 m2)
| derivations_of thy modes vs t m =
(case try (all_derivations_of thy modes vs) t of
SOME derivs => filter (fn (d, mvars) => mode_of d = m) derivs
| NONE => (if is_all_input m then [(Context m, [])] else []))
and all_derivations_of thy modes vs (Const ("Pair", _) $ t1 $ t2) =
let
val derivs1 = all_derivations_of thy modes vs t1
val derivs2 = all_derivations_of thy modes vs t2
in
map_product
(fn (m1, mvars1) => fn (m2, mvars2) => (Mode_Pair (m1, m2), union (op =) mvars1 mvars2))
derivs1 derivs2
end
| all_derivations_of thy modes vs (t1 $ t2) =
let
val derivs1 = all_derivations_of thy modes vs t1
in
maps (fn (d1, mvars1) =>
case mode_of d1 of
Fun (m', _) => map (fn (d2, mvars2) =>
(Mode_App (d1, d2), union (op =) mvars1 mvars2)) (derivations_of thy modes vs t2 m')
| _ => error "Something went wrong") derivs1
end
| all_derivations_of thy modes vs (Const (s, T)) =
(case (AList.lookup (op =) modes s) of
SOME ms => map (fn m => (Context m, [])) ms
| NONE => error ("No mode for constant " ^ s))
| all_derivations_of _ modes vs (Free (x, _)) =
(case (AList.lookup (op =) modes x) of
SOME ms => map (fn m => (Context m , [])) ms
| NONE => error ("No mode for parameter variable " ^ x))
| all_derivations_of _ modes vs _ = error "all_derivations_of"
fun rev_option_ord ord (NONE, NONE) = EQUAL
| rev_option_ord ord (NONE, SOME _) = GREATER
| rev_option_ord ord (SOME _, NONE) = LESS
| rev_option_ord ord (SOME x, SOME y) = ord (x, y)
fun term_of_prem (Prem t) = t
| term_of_prem (Negprem t) = t
| term_of_prem (Sidecond t) = t
fun random_mode_in_deriv modes t deriv =
case try dest_Const (fst (strip_comb t)) of
SOME (s, _) =>
(case AList.lookup (op =) modes s of
SOME ms =>
(case AList.lookup (op =) ms (head_mode_of deriv) of
SOME r => r
| NONE => false)
| NONE => false)
| NONE => false
fun number_of_output_positions mode =
let
val args = strip_fun_mode mode
fun contains_output (Fun _) = false
| contains_output Input = false
| contains_output Output = true
| contains_output (Pair (m1, m2)) = contains_output m1 orelse contains_output m2
in
length (filter contains_output args)
end
fun lex_ord ord1 ord2 (x, x') =
case ord1 (x, x') of
EQUAL => ord2 (x, x')
| ord => ord
fun deriv_ord2' thy modes t1 t2 ((deriv1, mvars1), (deriv2, mvars2)) =
let
fun mvars_ord ((t1, deriv1, mvars1), (t2, deriv2, mvars2)) =
int_ord (length mvars1, length mvars2)
fun random_mode_ord ((t1, deriv1, mvars1), (t2, deriv2, mvars2)) =
int_ord (if random_mode_in_deriv modes t1 deriv1 then 1 else 0,
if random_mode_in_deriv modes t1 deriv1 then 1 else 0)
fun output_mode_ord ((t1, deriv1, mvars1), (t2, deriv2, mvars2)) =
int_ord (number_of_output_positions (head_mode_of deriv1),
number_of_output_positions (head_mode_of deriv2))
in
lex_ord mvars_ord (lex_ord random_mode_ord output_mode_ord)
((t1, deriv1, mvars1), (t2, deriv2, mvars2))
end
fun deriv_ord2 thy modes t = deriv_ord2' thy modes t t
fun deriv_ord ((deriv1, mvars1), (deriv2, mvars2)) =
int_ord (length mvars1, length mvars2)
fun premise_ord thy modes ((prem1, a1), (prem2, a2)) =
rev_option_ord (deriv_ord2' thy modes (term_of_prem prem1) (term_of_prem prem2)) (a1, a2)
fun print_mode_list modes =
tracing ("modes: " ^ (commas (map (fn (s, ms) => s ^ ": " ^
commas (map (fn (m, r) => string_of_mode m ^ (if r then " random " else " not ")) ms)) modes)))
fun select_mode_prem' thy modes vs ps =
let
val modes' = map (fn (s, ms) => (s, map fst ms)) modes
in
partial_hd (sort (premise_ord thy modes) (ps ~~ map
(fn Prem t =>
partial_hd
(sort (deriv_ord2 thy modes t) (all_derivations_of thy modes' vs t))
| Sidecond t => SOME (Context Bool, missing_vars vs t)
| Negprem t =>
partial_hd
(sort (deriv_ord2 thy modes t) (filter (fn (d, missing_vars) => is_all_input (head_mode_of d))
(all_derivations_of thy modes' vs t)))
| p => error (string_of_prem thy p))
ps))
end
fun check_mode_clause' use_random thy param_vs modes mode (ts, ps) =
let
val vTs = distinct (op =) (fold Term.add_frees (map term_of_prem ps) (fold Term.add_frees ts []))
val modes' = modes @ (param_vs ~~ map (fn x => [(x, false)]) (ho_arg_modes_of mode))
val (in_ts, out_ts) = split_mode mode ts
val in_vs = maps (vars_of_destructable_term thy) in_ts
val out_vs = terms_vs out_ts
fun check_mode_prems acc_ps rnd vs [] = SOME (acc_ps, vs, rnd)
| check_mode_prems acc_ps rnd vs ps =
(case select_mode_prem' thy modes' vs ps of
SOME (p, SOME (deriv, [])) => check_mode_prems ((p, deriv) :: acc_ps) rnd (*TODO: uses random? *)
(case p of
Prem t => union (op =) vs (term_vs t)
| Sidecond t => vs
| Negprem t => union (op =) vs (term_vs t)
| _ => error "I do not know")
(filter_out (equal p) ps)
| SOME (p, SOME (deriv, missing_vars)) =>
if use_random then
check_mode_prems ((p, deriv) :: (map
(fn v => (Generator (v, the (AList.lookup (op =) vTs v)), Term Output)) missing_vars)
@ acc_ps) true
(case p of
Prem t => union (op =) vs (term_vs t)
| Sidecond t => union (op =) vs (term_vs t)
| Negprem t => union (op =) vs (term_vs t)
| _ => error "I do not know")
(filter_out (equal p) ps)
else NONE
| SOME (p, NONE) => NONE
| NONE => NONE)
in
case check_mode_prems [] false in_vs ps of
NONE => NONE
| SOME (acc_ps, vs, rnd) =>
if forall (is_constructable thy vs) (in_ts @ out_ts) then
SOME (ts, rev acc_ps, rnd)
else
if use_random then
let
val generators = map
(fn v => (Generator (v, the (AList.lookup (op =) vTs v)), Term Output))
(subtract (op =) vs (terms_vs out_ts))
in
SOME (ts, rev (generators @ acc_ps), true)
end
else
NONE
end
datatype result = Success of bool | Error of string
fun check_modes_pred' use_random options thy param_vs clauses modes (p, ms) =
let
fun split xs =
let
fun split' [] (ys, zs) = (rev ys, rev zs)
| split' ((m, Error z) :: xs) (ys, zs) = split' xs (ys, z :: zs)
| split' ((m, Success rnd) :: xs) (ys, zs) = split' xs ((m, rnd) :: ys, zs)
in
split' xs ([], [])
end
val rs = these (AList.lookup (op =) clauses p)
fun check_mode m =
let
val res = map (check_mode_clause' use_random thy param_vs modes m) rs
in
case find_indices is_none res of
[] => Success (exists (fn SOME (_, _, true) => true | _ => false) res)
| is => (print_failed_mode options thy modes p m rs is; Error (error_of p m is))
end
val res = map (fn (m, _) => (m, check_mode m)) ms
val (ms', errors) = split res
in
((p, ms'), errors)
end;
fun get_modes_pred' use_random thy param_vs clauses modes (p, ms) =
let
val rs = these (AList.lookup (op =) clauses p)
in
(p, map (fn (m, rnd) =>
(m, map ((fn (ts, ps, rnd) => (ts, ps)) o the o check_mode_clause' use_random thy param_vs modes m) rs)) ms)
end;
fun fixp f x =
let val y = f x
in if x = y then x else fixp f y end;
fun fixp_with_state f (x, state) =
let
val (y, state') = f (x, state)
in
if x = y then (y, state') else fixp_with_state f (y, state')
end
fun infer_modes use_random options preds extra_modes param_vs clauses thy =
let
val all_modes = map (fn (s, T) => (s, map (rpair false) (all_modes_of_typ T))) preds
fun needs_random s m = (m, member (op =) (#needs_random (the_pred_data thy s)) m)
val extra_modes = map (fn (s, ms) => (s, map (needs_random s) ms)) extra_modes
val (modes, errors) =
fixp_with_state (fn (modes, errors) =>
let
val res = map
(check_modes_pred' use_random options thy param_vs clauses (modes @ extra_modes)) modes
in (map fst res, errors @ maps snd res) end)
(all_modes, [])
val thy' = fold (fn (s, ms) => if member (op =) (map fst preds) s then
set_needs_random s (map fst (filter (fn (_, rnd) => rnd = true) ms)) else I) modes thy
in
((map (get_modes_pred' use_random thy param_vs clauses (modes @ extra_modes)) modes, errors), thy')
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
{
compilation : compilation,
function_name_prefix : string,
compfuns : compilation_funs,
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 compilation = #compilation o dest_comp_modifiers
val function_name_prefix = #function_name_prefix o dest_comp_modifiers
val compfuns = #compfuns o dest_comp_modifiers
val funT_of = funT_of o compfuns
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;
(* TODO: uses param_vs -- change necessary for compilation with new modes *)
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 (AList.lookup (op =) (param_vs ~~ iss) f) of
SOME is =>
let
val _ = error "compile_arg: A parameter in a input position -- do we have a test case?"
val T' = Comp_Mod.funT_of compilation_modifiers is T
in t(*fst (mk_Eval_of additional_arguments ((Free (f, T'), T), 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) Datatype_Case.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;
fun compile_expr compilation_modifiers compfuns thy (t, deriv) additional_arguments =
let
fun expr_of (t, deriv) =
(case (t, deriv) of
(t, Term Input) => SOME t
| (t, Term Output) => NONE
| (Const (name, T), Context mode) =>
SOME (Const (function_name_of (Comp_Mod.compilation compilation_modifiers) thy name mode,
Comp_Mod.funT_of compilation_modifiers mode T))
| (Free (s, T), Context m) =>
SOME (Free (s, Comp_Mod.funT_of compilation_modifiers m T))
| (t, Context m) =>
let
val bs = map (pair "x") (binder_types (fastype_of t))
val bounds = map Bound (rev (0 upto (length bs) - 1))
in SOME (list_abs (bs, mk_if compfuns (list_comb (t, bounds)))) end
| (Const ("Pair", _) $ t1 $ t2, Mode_Pair (d1, d2)) =>
(case (expr_of (t1, d1), expr_of (t2, d2)) of
(NONE, NONE) => NONE
| (NONE, SOME t) => SOME t
| (SOME t, NONE) => SOME t
| (SOME t1, SOME t2) => SOME (HOLogic.mk_prod (t1, t2)))
| (t1 $ t2, Mode_App (deriv1, deriv2)) =>
(case (expr_of (t1, deriv1), expr_of (t2, deriv2)) of
(SOME t, NONE) => SOME t
| (SOME t, SOME u) => SOME (t $ u)
| _ => error "something went wrong here!"))
in
the (expr_of (t, deriv))
end
fun compile_clause compilation_modifiers compfuns thy all_vs param_vs additional_arguments
mode inp (ts, moded_ps) =
let
val iss = ho_arg_modes_of mode
val compile_match = compile_match compilation_modifiers compfuns
additional_arguments param_vs iss thy
val (in_ts, out_ts) = split_mode mode ts;
val (in_ts', (all_vs', eqs)) =
fold_map (collect_non_invertible_subterms thy) in_ts (all_vs, []);
fun compile_prems out_ts' vs names [] =
let
val (out_ts'', (names', eqs')) =
fold_map (collect_non_invertible_subterms thy) 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, deriv) :: ps) =
let
val vs' = distinct (op =) (flat (vs :: map term_vs out_ts));
val (out_ts', (names', eqs)) =
fold_map (collect_non_invertible_subterms thy) out_ts (names, [])
val (out_ts'', (names'', constr_vs')) = fold_map distinct_v
out_ts' ((names', map (rpair []) vs))
val mode = head_mode_of deriv
val additional_arguments' =
Comp_Mod.transform_additional_arguments compilation_modifiers p additional_arguments
val (compiled_clause, rest) = case p of
Prem t =>
let
val u =
compile_expr compilation_modifiers compfuns thy
(t, deriv) additional_arguments'
val (_, out_ts''') = split_mode mode (snd (strip_comb t))
val rest = compile_prems out_ts''' vs' names'' ps
in
(u, rest)
end
| Negprem t =>
let
val u = mk_not compfuns
(compile_expr compilation_modifiers compfuns thy
(t, deriv) additional_arguments')
val (_, out_ts''') = split_mode mode (snd (strip_comb t))
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 u = mk_random T
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 thy all_vs param_vs s T mode moded_cls =
let
(* TODO: val additional_arguments = Comp_Mod.additional_arguments compilation_modifiers
(all_vs @ param_vs)
*)
val compfuns = Comp_Mod.compfuns compilation_modifiers
fun is_param_type (T as Type ("fun",[_ , T'])) =
is_some (try (dest_predT compfuns) T) orelse is_param_type T'
| is_param_type T = is_some (try (dest_predT compfuns) T)
val additional_arguments = []
val (inpTs, outTs) = split_map_modeT (fn m => fn T => (SOME (funT_of compfuns m T), NONE)) mode
(binder_types T)
val predT = mk_predT compfuns (HOLogic.mk_tupleT outTs)
val funT = Comp_Mod.funT_of compilation_modifiers mode T
val (in_ts, _) = fold_map (fold_map_aterms_prodT (curry HOLogic.mk_prod)
(fn T => fn (param_vs, names) =>
if is_param_type T then
(Free (hd param_vs, T), (tl param_vs, names))
else
let
val new = Name.variant names "x"
in (Free (new, T), (param_vs, new :: names)) end)) inpTs
(param_vs, (all_vs @ param_vs))
val in_ts' = map_filter (map_filter_prod
(fn t as Free (x, _) => if member (op =) param_vs x then NONE else SOME t | t => SOME t)) in_ts
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 outTs)
else foldr1 (mk_sup compfuns) cl_ts)
val fun_const =
Const (function_name_of (Comp_Mod.compilation compilation_modifiers) thy s mode, funT)
in
HOLogic.mk_Trueprop
(HOLogic.mk_eq (list_comb (fun_const, 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 split_lambda (x as Free _) t = lambda x t
| split_lambda (Const ("Pair", _) $ t1 $ t2) t =
HOLogic.mk_split (split_lambda t1 (split_lambda t2 t))
| split_lambda (Const ("Product_Type.Unity", _)) t = Abs ("x", HOLogic.unitT, t)
| split_lambda t _ = raise (TERM ("split_lambda", [t]))
fun strip_split_abs (Const ("split", _) $ t) = strip_split_abs t
| strip_split_abs (Abs (_, _, t)) = strip_split_abs t
| strip_split_abs t = t
fun mk_args is_eval (Pair (m1, m2), Type ("*", [T1, T2])) names =
let
val (t1, names') = mk_args is_eval (m1, T1) names
val (t2, names'') = mk_args is_eval (m2, T2) names'
in
(HOLogic.mk_prod (t1, t2), names'')
end
| mk_args is_eval ((m as Fun _), T) names =
let
val funT = funT_of PredicateCompFuns.compfuns m T
val x = Name.variant names "x"
val (args, _) = fold_map (mk_args is_eval) (strip_fun_mode m ~~ binder_types T) (x :: names)
val (inargs, outargs) = split_map_mode (fn _ => fn t => (SOME t, NONE)) m args
val t = fold_rev split_lambda args (PredicateCompFuns.mk_Eval
(list_comb (Free (x, funT), inargs), HOLogic.mk_tuple outargs))
in
(if is_eval then t else Free (x, funT), x :: names)
end
| mk_args is_eval (_, T) names =
let
val x = Name.variant names "x"
in
(Free (x, T), x :: names)
end
fun create_intro_elim_rule mode defthm mode_id funT pred thy =
let
val funtrm = Const (mode_id, funT)
val Ts = binder_types (fastype_of pred)
val (args, argnames) = fold_map (mk_args true) (strip_fun_mode mode ~~ Ts) []
fun strip_eval _ t =
let
val t' = strip_split_abs t
val (r, _) = PredicateCompFuns.dest_Eval t'
in (SOME (fst (strip_comb r)), NONE) end
val (inargs, outargs) = split_map_mode strip_eval mode args
val eval_hoargs = ho_args_of mode args
val hoargTs = ho_argsT_of mode Ts
val hoarg_names' =
Name.variant_list argnames ((map (fn i => "x" ^ string_of_int i)) (1 upto (length hoargTs)))
val hoargs' = map2 (curry Free) hoarg_names' hoargTs
val args' = replace_ho_args mode hoargs' args
val predpropI = HOLogic.mk_Trueprop (list_comb (pred, args'))
val predpropE = HOLogic.mk_Trueprop (list_comb (pred, args))
val param_eqs = map2 (HOLogic.mk_Trueprop oo (curry HOLogic.mk_eq)) eval_hoargs hoargs'
val funpropE = HOLogic.mk_Trueprop (PredicateCompFuns.mk_Eval (list_comb (funtrm, inargs),
if null outargs then Free("y", HOLogic.unitT) else HOLogic.mk_tuple outargs))
val funpropI = HOLogic.mk_Trueprop (PredicateCompFuns.mk_Eval (list_comb (funtrm, inargs),
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 @ hoarg_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 @ ["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 mode
val name = the_default system_proposal (proposed_names options name mode)
in
Sign.full_bname thy name
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 thy =
let
val mode_cname = create_constname_of_mode options thy "" name T mode
val mode_cbasename = Long_Name.base_name mode_cname
val funT = funT_of compfuns mode T
val (args, _) = fold_map (mk_args true) ((strip_fun_mode mode) ~~ (binder_types T)) []
fun strip_eval m t =
let
val t' = strip_split_abs t
val (r, _) = PredicateCompFuns.dest_Eval t'
in (SOME (fst (strip_comb r)), NONE) end
val (inargs, outargs) = split_map_mode strip_eval mode args
val predterm = fold_rev split_lambda inargs
(PredicateCompFuns.mk_Enum (split_lambda (HOLogic.mk_tuple outargs)
(list_comb (Const (name, T), args))))
val lhs = Const (mode_cname, funT)
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'
|> set_function_name Pred name mode mode_cname
|> add_predfun_data name mode (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
thy |> defined_function_of Pred name |> fold create_definition modes
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 mode T
in
thy |> Sign.add_consts_i [(Binding.name (Long_Name.base_name mode_cname), funT, NoSyn)]
|> set_function_name (Comp_Mod.compilation comp_modifiers) name mode mode_cname
end;
in
thy
|> defined_function_of (Comp_Mod.compilation comp_modifiers) name
|> fold create_definition modes
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 options thy t deriv =
let
val (f, args) = strip_comb (Envir.eta_contract t)
val mode = head_mode_of deriv
val param_derivations = param_derivations_of deriv
val ho_args = ho_args_of mode 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 (rtac @{thm ext} 1)
THEN print_tac' options "prove_param"
THEN f_tac
THEN print_tac' options "after simplification in prove_args"
THEN (REPEAT_DETERM (atac 1))
THEN (EVERY (map2 (prove_param options thy) ho_args param_derivations))
end
fun prove_expr options thy (premposition : int) (t, deriv) =
case strip_comb t of
(Const (name, T), args) =>
let
val mode = head_mode_of deriv
val introrule = predfun_intro_of thy name mode
val param_derivations = param_derivations_of deriv
val ho_args = ho_args_of mode args
in
print_tac' options "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' options "after intro rule"
(* work with parameter arguments *)
THEN atac 1
THEN print_tac' options "parameter goal"
THEN (EVERY (map2 (prove_param options thy) ho_args param_derivations))
THEN (REPEAT_DETERM (atac 1))
end
| _ =>
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' options "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 check_format thy st =
let
val concl' = Logic.strip_assums_concl (hd (prems_of st))
val concl = HOLogic.dest_Trueprop concl'
val expr = fst (strip_comb (fst (PredicateCompFuns.dest_Eval concl)))
fun valid_expr (Const (@{const_name Predicate.bind}, _)) = true
| valid_expr (Const (@{const_name Predicate.single}, _)) = true
| valid_expr _ = false
in
if valid_expr expr then
((*tracing "expression is valid";*) Seq.single st)
else
((*tracing "expression is not valid";*) Seq.empty) (*error "check_format: wrong format"*)
end
fun prove_match options 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' options "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 print_tac' options "if condition to be solved:"
THEN (SOLVED (asm_simp_tac HOL_basic_ss' 1 THEN print_tac' options "after if simp; in SOLVED:"))
THEN check_format thy
THEN print_tac' options "after if simplification - a TRY block")))
THEN print_tac' options "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
(all_input_of 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 mode (_, clauses) (ts, moded_ps) =
let
val (in_ts, clause_out_ts) = split_mode mode ts;
fun prove_prems out_ts [] =
(prove_match options thy out_ts)
THEN print_tac' options "before simplifying assumptions"
THEN asm_full_simp_tac HOL_basic_ss' 1
THEN print_tac' options "before single intro rule"
THEN (rtac (if null clause_out_ts then @{thm singleI_unit} else @{thm singleI}) 1)
| prove_prems out_ts ((p, deriv) :: ps) =
let
val premposition = (find_index (equal p) clauses) + nargs
val mode = head_mode_of deriv
val rest_tac =
rtac @{thm bindI} 1
THEN (case p of Prem t =>
let
val (_, us) = strip_comb t
val (_, out_ts''') = split_mode mode us
val rec_tac = prove_prems out_ts''' ps
in
print_tac' options "before clause:"
(*THEN asm_simp_tac HOL_basic_ss 1*)
THEN print_tac' options "before prove_expr:"
THEN prove_expr options thy premposition (t, deriv)
THEN print_tac' options "after prove_expr:"
THEN rec_tac
end
| Negprem t =>
let
val (t, args) = strip_comb t
val (_, out_ts''') = split_mode mode args
val rec_tac = prove_prems out_ts''' ps
val name = (case strip_comb t of (Const (c, _), _) => SOME c | _ => NONE)
val param_derivations = param_derivations_of deriv
val params = ho_args_of mode args
in
print_tac' options "before prove_neg_expr:"
THEN full_simp_tac (HOL_basic_ss addsimps
[@{thm split_eta}, @{thm split_beta}, @{thm fst_conv},
@{thm snd_conv}, @{thm pair_collapse}, @{thm Product_Type.split_conv}]) 1
THEN (if (is_some name) then
print_tac' options ("before unfolding definition " ^
(Display.string_of_thm_global thy
(predfun_definition_of thy (the name) mode)))
THEN simp_tac (HOL_basic_ss addsimps
[predfun_definition_of thy (the name) mode]) 1
THEN rtac @{thm not_predI} 1
THEN print_tac' options "after applying rule not_predI"
THEN full_simp_tac (HOL_basic_ss addsimps [@{thm not_False_eq_True},
@{thm split_eta}, @{thm split_beta}, @{thm fst_conv},
@{thm snd_conv}, @{thm pair_collapse}, @{thm Product_Type.split_conv}]) 1
THEN (REPEAT_DETERM (atac 1))
THEN (EVERY (map2 (prove_param options thy) params param_derivations))
THEN (REPEAT_DETERM (atac 1))
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 if_predI} 1
THEN print_tac' options "before sidecond:"
THEN prove_sidecond thy modes t
THEN print_tac' options "after sidecond:"
THEN prove_prems [] ps)
in (prove_match options 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)
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' options "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 t deriv =
let
val (f, args) = strip_comb (Envir.eta_contract t)
val mode = head_mode_of deriv
val param_derivations = param_derivations_of deriv
val ho_args = ho_args_of mode 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) ho_args param_derivations)
end
fun prove_expr2 thy (t, deriv) =
(case strip_comb t of
(Const (name, T), args) =>
let
val mode = head_mode_of deriv
val param_derivations = param_derivations_of deriv
val ho_args = ho_args_of mode args
in
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) ho_args param_derivations))
THEN print_tac "finished prove_expr2"
end
| _ => 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
(all_input_of 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 mode (ts, ps) i =
let
val pred_intro_rule = nth (intros_of thy pred) (i - 1)
val (in_ts, clause_out_ts) = split_mode mode 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, deriv) :: ps) =
let
val mode = head_mode_of deriv
val rest_tac = (case p of
Prem t =>
let
val (_, us) = strip_comb t
val (_, out_ts''') = split_mode mode us
val rec_tac = prove_prems2 out_ts''' ps
in
(prove_expr2 thy (t, deriv)) THEN rec_tac
end
| Negprem t =>
let
val (_, args) = strip_comb t
val (_, out_ts''') = split_mode mode args
val rec_tac = prove_prems2 out_ts''' ps
val name = (case strip_comb t of (Const (c, _), _) => SOME c | _ => NONE)
val param_derivations = param_derivations_of deriv
val ho_args = ho_args_of mode args
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) mode]) 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) ho_args param_derivations))
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 thy all_vs param_vs preds moded_clauses =
map_preds_modes (fn pred => compile_pred comp_modifiers 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.export_without_context (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 t else Sidecond t
| (c as Const (@{const_name Not}, _), [t]) => (case dest_prem thy params t of
Prem t => Negprem 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 Prem t else Sidecond t
| _ => Sidecond t)
fun prepare_intrs options compilation thy prednames intros =
let
val intrs = map prop_of intros
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 compilation thy |> filter_out (fn (name, _) => member (op =) prednames name)
val all_vs = terms_vs intrs
val params =
case intrs of
[] =>
let
val T = snd (hd preds)
val paramTs =
ho_argsT_of (hd (all_modes_of_typ T)) (binder_types T)
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 :: _) => maps extract_params
(snd (strip_comb (HOLogic.dest_Trueprop (Logic.strip_imp_concl intr))))
val param_vs = map (fst o dest_Free) params
fun add_clause intr clauses =
let
val (Const (name, T), ts) = strip_comb (HOLogic.dest_Trueprop (Logic.strip_imp_concl intr))
val prems = map (dest_prem thy params o HOLogic.dest_Trueprop) (Logic.strip_imp_prems intr)
in
AList.update op = (name, these (AList.lookup op = clauses name) @
[(ts, prems)]) clauses
end;
val clauses = fold add_clause intrs []
in
(preds, all_vs, param_vs, extra_modes, clauses)
end;
(* sanity check of introduction rules *)
(* TODO: rethink check with new modes *)
(*
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 t) = forall check_arg args
| check_prem (Negprem t) = 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.export_without_context 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 preds result_thmss =
let
fun add_code_equation (predname, T) (pred, result_thms) =
let
val full_mode = fold_rev (curry Fun) (map (K Input) (binder_types T)) Bool
in
if member (op =) (modes_of Pred 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 (function_name_of Pred thy predname full_mode,
Ts ---> PredicateCompFuns.mk_predT @{typ unit})
val rhs = @{term Predicate.holds} $ (list_comb (predfun, args))
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 holds_eq}, @{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
{
define_functions : options -> (string * typ) list -> string * mode list -> theory -> theory,
infer_modes : options -> (string * typ) list -> (string * mode list) list
-> string list -> (string * (term list * indprem list) list) list
-> theory -> ((moded_clause list pred_mode_table * string list) * theory),
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 -> (string * typ) list
-> (string * thm list) list -> (string * thm list) list,
comp_modifiers : Comp_Mod.comp_modifiers,
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 compilation = Comp_Mod.compilation (#comp_modifiers (dest_steps steps))
val (preds, all_vs, param_vs, extra_modes, clauses) =
prepare_intrs options compilation thy prednames (maps (intros_of thy) prednames)
val _ = print_step options "Infering modes..."
val ((moded_clauses, errors), thy') =
#infer_modes (dest_steps steps) options preds extra_modes param_vs clauses thy
val modes = map (fn (p, mps) => (p, map fst mps)) moded_clauses
val _ = check_expected_modes preds options modes
val _ = check_proposed_modes preds options modes extra_modes errors
val _ = print_modes options thy' modes
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 (#comp_modifiers (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'' 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 defined = defined_functions (Comp_Mod.compilation (#comp_modifiers (dest_steps steps)))
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 thy) preds) then
add_equations_of steps options preds thy
else thy)
scc thy' |> Theory.checkpoint
in thy'' end
(*
val depth_limited_comp_modifiers = Comp_Mod.Comp_Modifiers
{
compilation = Depth_Limited,
function_name_of = function_name_of Depth_Limited,
set_function_name = set_function_name Depth_Limited,
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 ("Algebras.minus", @{typ "code_numeral => code_numeral => code_numeral"})
$ depth $ Const ("Algebras.one", @{typ "Code_Numeral.code_numeral"})
in [polarity', depth'] end
}
val random_comp_modifiers = Comp_Mod.Comp_Modifiers
{
compilation = Random,
function_name_of = function_name_of Random,
set_function_name = set_function_name Random,
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)
}
*)
(* different instantiantions of the predicate compiler *)
val predicate_comp_modifiers = Comp_Mod.Comp_Modifiers
{
compilation = Pred,
function_name_prefix = "",
compfuns = PredicateCompFuns.compfuns,
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 add_equations = gen_add_equations
(Steps {infer_modes = infer_modes false,
define_functions = create_definitions,
prove = prove,
add_code_equations = add_code_equations,
comp_modifiers = predicate_comp_modifiers,
qname = "equation"})
val annotated_comp_modifiers = Comp_Mod.Comp_Modifiers
{
compilation = Annotated,
function_name_prefix = "annotated_",
compfuns = PredicateCompFuns.compfuns,
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 mode) compilation,
transform_additional_arguments = K I : (indprem -> term list -> term list)
}
val dseq_comp_modifiers = Comp_Mod.Comp_Modifiers
{
compilation = DSeq,
function_name_prefix = "dseq_",
compfuns = DSequence_CompFuns.compfuns,
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 random_dseq_comp_modifiers = Comp_Mod.Comp_Modifiers
{
compilation = Random_DSeq,
function_name_prefix = "random_dseq_",
compfuns = Random_Sequence_CompFuns.compfuns,
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 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 I),
defined = defined_functions Depth_Limited,
qname = "depth_limited_equation"})
*)
val add_annotated_equations = gen_add_equations
(Steps {infer_modes = infer_modes false,
define_functions = define_functions annotated_comp_modifiers PredicateCompFuns.compfuns,
prove = prove_by_skip,
add_code_equations = K (K I),
comp_modifiers = annotated_comp_modifiers,
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 I),
defined = defined_functions Random,
qname = "random_equation"})
*)
val add_dseq_equations = gen_add_equations
(Steps {infer_modes = infer_modes false,
define_functions = define_functions dseq_comp_modifiers DSequence_CompFuns.compfuns,
prove = prove_by_skip,
add_code_equations = K (K I),
comp_modifiers = dseq_comp_modifiers,
qname = "dseq_equation"})
val add_random_dseq_equations = gen_add_equations
(Steps {infer_modes = infer_modes true,
define_functions = define_functions random_dseq_comp_modifiers Random_Sequence_CompFuns.compfuns,
prove = prove_by_skip,
add_code_equations = K (K I),
comp_modifiers = random_dseq_comp_modifiers,
qname = "random_dseq_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 intros = intros_of thy' const
in mk_casesrule lthy' pred 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 #>
((case compilation options of
Pred => add_equations
| DSeq => add_dseq_equations
| Random_DSeq => add_random_dseq_equations
| compilation => error ("Compilation not supported")
(*| Random => (fn opt => fn cs => add_equations opt cs #> add_quickcheck_equations opt cs)
| Depth_Limited => add_depth_limited_equations
| Annotated => add_annotated_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);
val dseq_eval_ref = Unsynchronized.ref (NONE : (unit -> term DSequence.dseq) option);
val random_dseq_eval_ref =
Unsynchronized.ref (NONE : (unit -> int -> int -> int * int -> term DSequence.dseq * (int * int)) option);
(*FIXME turn this into an LCF-guarded preprocessor for comprehensions*)
fun analyze_compr thy compfuns param_user_modes (compilation, arguments) t_compr =
let
val all_modes_of = all_modes_of compilation
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 output_names = Name.variant_list (Term.add_free_names body [])
(map (fn i => "x" ^ string_of_int i) (1 upto length Ts))
val output_frees = map2 (curry Free) output_names (rev Ts)
val body = subst_bounds (output_frees, body)
val T_compr = HOLogic.mk_ptupleT fp Ts
val output_tuple = HOLogic.mk_ptuple fp T_compr (rev output_frees)
val (pred as Const (name, T), all_args) = strip_comb body
in
if defined_functions compilation thy name then
let
fun extract_mode (Const ("Pair", _) $ t1 $ t2) = Pair (extract_mode t1, extract_mode t2)
| extract_mode (Free (x, _)) = if member (op =) output_names x then Output else Input
| extract_mode _ = Input
val user_mode = fold_rev (curry Fun) (map extract_mode all_args) Bool
fun valid modes1 modes2 =
case int_ord (length modes1, length modes2) of
GREATER => error "Not enough mode annotations"
| LESS => error "Too many mode annotations"
| EQUAL => forall (fn (m, NONE) => true | (m, SOME m2) => eq_mode (m, m2))
(modes1 ~~ modes2)
fun mode_instance_of (m1, m2) =
let
fun instance_of (Fun _, Input) = true
| instance_of (Input, Input) = true
| instance_of (Output, Output) = true
| instance_of (Pair (m1, m2), Pair (m1', m2')) =
instance_of (m1, m1') andalso instance_of (m2, m2')
| instance_of (Pair (m1, m2), Input) =
instance_of (m1, Input) andalso instance_of (m2, Input)
| instance_of (Pair (m1, m2), Output) =
instance_of (m1, Output) andalso instance_of (m2, Output)
| instance_of _ = false
in forall instance_of (strip_fun_mode m1 ~~ strip_fun_mode m2) end
val derivs = all_derivations_of thy (all_modes_of thy) [] body
|> filter (fn (d, missing_vars) =>
let
val (p_mode :: modes) = collect_context_modes d
in
null missing_vars andalso
mode_instance_of (p_mode, user_mode) andalso
the_default true (Option.map (valid modes) param_user_modes)
end)
|> map fst
val deriv = case derivs of
[] => error ("No mode possible for comprehension "
^ Syntax.string_of_term_global thy t_compr)
| [d] => d
| d :: _ :: _ => (warning ("Multiple modes possible for comprehension "
^ Syntax.string_of_term_global thy t_compr); d);
val (_, outargs) = split_mode (head_mode_of deriv) all_args
val additional_arguments =
case compilation of
Pred => []
| Random => [@{term "5 :: code_numeral"}]
| Annotated => []
| Depth_Limited => [@{term "True"}, HOLogic.mk_number @{typ "code_numeral"} (hd arguments)]
| DSeq => []
| Random_DSeq => []
val comp_modifiers =
case compilation of
Pred => predicate_comp_modifiers
(*| Random => random_comp_modifiers
| Depth_Limited => depth_limited_comp_modifiers
| Annotated => annotated_comp_modifiers*)
| DSeq => dseq_comp_modifiers
| Random_DSeq => random_dseq_comp_modifiers
val t_pred = compile_expr comp_modifiers compfuns thy (body, deriv) additional_arguments;
val T_pred = dest_predT compfuns (fastype_of t_pred)
val arrange = split_lambda (HOLogic.mk_tuple outargs) output_tuple
in
if null outargs then t_pred else mk_map compfuns T_pred T_compr arrange t_pred
end
else
error "Evaluation with values is not possible because compilation with code_pred was not invoked"
end
fun eval thy param_user_modes (options as (compilation, arguments)) k t_compr =
let
val compfuns =
case compilation of
Random => RandomPredCompFuns.compfuns
| DSeq => DSequence_CompFuns.compfuns
| Random_DSeq => Random_Sequence_CompFuns.compfuns
| _ => 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 ts =
case compilation of
Random =>
fst (Predicate.yieldn k
(Code_Eval.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))
| Random_DSeq =>
let
val [nrandom, size, depth] = arguments
in
fst (DSequence.yieldn k
(Code_Eval.eval NONE ("Predicate_Compile_Core.random_dseq_eval_ref", random_dseq_eval_ref)
(fn proc => fn g => fn nrandom => fn size => fn s => g nrandom size s |>> DSequence.map proc)
thy t' [] nrandom size
|> Random_Engine.run)
depth true)
end
| DSeq =>
fst (DSequence.yieldn k
(Code_Eval.eval NONE ("Predicate_Compile_Core.dseq_eval_ref", dseq_eval_ref)
DSequence.map thy t' []) (the_single arguments) true)
| _ =>
fst (Predicate.yieldn k
(Code_Eval.eval NONE ("Predicate_Compile_Core.eval_ref", eval_ref)
Predicate.map thy t' []))
in (T, ts) end;
fun values ctxt param_user_modes (raw_expected, comp_options) k t_compr =
let
val thy = ProofContext.theory_of ctxt
val (T, ts) = eval thy param_user_modes comp_options k t_compr
val setT = HOLogic.mk_setT T
val elems = HOLogic.mk_set T ts
val cont = Free ("...", setT)
(* check expected values *)
val () =
case raw_expected of
NONE => ()
| SOME s =>
if eq_set (op =) (HOLogic.dest_set (Syntax.read_term ctxt s), ts) then ()
else
error ("expected and computed values do not match:\n" ^
"expected values: " ^ Syntax.string_of_term ctxt (Syntax.read_term ctxt s) ^ "\n" ^
"computed values: " ^ Syntax.string_of_term ctxt elems ^ "\n")
in
if k = ~1 orelse length ts < k then elems
else Const (@{const_name Set.union}, setT --> setT --> setT) $ elems $ 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;