(* 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
type mode = Predicate_Compile_Aux.mode
type options = Predicate_Compile_Aux.options
type compilation = Predicate_Compile_Aux.compilation
type compilation_funs = Predicate_Compile_Aux.compilation_funs
val setup : theory -> theory
val code_pred : options -> string -> Proof.context -> Proof.state
val code_pred_cmd : options -> string -> Proof.context -> Proof.state
val values_cmd : string list -> mode option list option
-> ((string option * bool) * (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 : Proof.context -> string -> bool
val function_name_of : compilation -> Proof.context -> string -> mode -> string
val predfun_intro_of: Proof.context -> string -> mode -> thm
val predfun_elim_of: Proof.context -> string -> mode -> thm
val all_preds_of : Proof.context -> string list
val modes_of: compilation -> Proof.context -> string -> mode list
val all_modes_of : compilation -> Proof.context -> (string * mode list) list
val all_random_modes_of : Proof.context -> (string * mode list) list
val intros_of : Proof.context -> string -> thm list
val intros_graph_of : Proof.context -> thm list Graph.T
val add_intro : thm -> theory -> theory
val set_elim : thm -> theory -> theory
val register_alternative_function : string -> mode -> string -> theory -> theory
val alternative_compilation_of_global : theory -> string -> mode ->
(compilation_funs -> typ -> term) option
val alternative_compilation_of : Proof.context -> string -> mode ->
(compilation_funs -> typ -> term) option
val functional_compilation : string -> mode -> compilation_funs -> typ -> term
val force_modes_and_functions : string -> (mode * (string * bool)) list -> theory -> theory
val force_modes_and_compilations : string ->
(mode * ((compilation_funs -> typ -> term) * bool)) list -> theory -> theory
val preprocess_intro : theory -> thm -> thm
val print_stored_rules : Proof.context -> unit
val print_all_modes : compilation -> Proof.context -> unit
val mk_casesrule : Proof.context -> term -> thm list -> term
val put_pred_result : (unit -> term Predicate.pred) -> Proof.context -> Proof.context
val put_pred_random_result : (unit -> int * int -> term Predicate.pred * (int * int)) ->
Proof.context -> Proof.context
val put_dseq_result : (unit -> term DSequence.dseq) -> Proof.context -> Proof.context
val put_dseq_random_result : (unit -> int -> int -> int * int -> term DSequence.dseq * (int * int)) ->
Proof.context -> Proof.context
val put_lseq_random_result :
(unit -> int -> int -> int * int -> int -> term Lazy_Sequence.lazy_sequence) ->
Proof.context -> Proof.context
val put_lseq_random_stats_result :
(unit -> int -> int -> int * int -> int -> (term * int) Lazy_Sequence.lazy_sequence) ->
Proof.context -> Proof.context
val code_pred_intro_attrib : attribute
(* used by Quickcheck_Generator *)
(* temporary for testing of the compilation *)
val add_equations : options -> string list -> theory -> theory
val add_depth_limited_random_equations : options -> string list -> theory -> theory
val add_random_dseq_equations : options -> string list -> theory -> theory
val add_new_random_dseq_equations : options -> string list -> theory -> theory
val mk_tracing : string -> term -> term
val prepare_intrs : options -> Proof.context -> string list -> thm list ->
((string * typ) list * string list * string list * (string * mode list) list *
(string * (Term.term list * Predicate_Compile_Aux.indprem list) list) list)
type mode_analysis_options = {use_random : bool, reorder_premises : bool, infer_pos_and_neg_modes : bool}
datatype mode_derivation = Mode_App of mode_derivation * mode_derivation | Context of mode
| Mode_Pair of mode_derivation * mode_derivation | Term of mode
type moded_clause = term list * (Predicate_Compile_Aux.indprem * mode_derivation) list
type 'a pred_mode_table = (string * ((bool * mode) * 'a) list) list
val infer_modes :
mode_analysis_options -> options ->
(string -> Predicate_Compile_Aux.mode list) * (string -> Predicate_Compile_Aux.mode list)
* (string -> Predicate_Compile_Aux.mode -> bool) -> Proof.context -> (string * typ) list ->
(string * mode list) list ->
string list -> (string * (Term.term list * Predicate_Compile_Aux.indprem list) list) list ->
((moded_clause list pred_mode_table * (string * mode list) list) * string list)
end;
structure Predicate_Compile_Core : PREDICATE_COMPILE_CORE =
struct
open Predicate_Compile_Aux;
(** auxiliary **)
(* debug stuff *)
fun print_tac options s =
if show_proof_trace options then Tactical.print_tac s else Seq.single;
fun assert b = if not b then raise Fail "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 raise Fail ("assert_tac: Numbers of subgoals mismatch at goal state :"
^ "\n" ^ Pretty.string_of (Pretty.chunks
(Goal_Display.pretty_goals_without_context 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_name Product_Type.prod}, [Type (@{type_name Product_Type.prod}, [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 eq_mode (m, mode_of d2) then m' else raise Fail "mode_of: derivation has mismatching modes")
| _ => raise Fail "mode_of: derivation has a non-functional mode")
| 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 * ((bool * mode) * 'a) list) list
(* book-keeping *)
datatype predfun_data = PredfunData of {
definition : thm,
intro : thm,
elim : thm,
neg_intro : thm option
};
fun rep_predfun_data (PredfunData data) = data;
fun mk_predfun_data (definition, ((intro, elim), neg_intro)) =
PredfunData {definition = definition, intro = intro, elim = elim, neg_intro = neg_intro}
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 ctxt name =
Option.map rep_pred_data (try (Graph.get_node (PredData.get (ProofContext.theory_of ctxt))) name)
fun the_pred_data ctxt name = case lookup_pred_data ctxt 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 o ProofContext.theory_of
val intros_of = #intros oo the_pred_data
fun the_elim_of ctxt name = case #elim (the_pred_data ctxt name)
of NONE => error ("No elimination rule for predicate " ^ quote name)
| SOME thm => thm
val has_elim = is_some o #elim oo the_pred_data
fun function_names_of compilation ctxt name =
case AList.lookup (op =) (#function_names (the_pred_data ctxt 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 ctxt name mode =
case AList.lookup eq_mode
(function_names_of compilation ctxt 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 ctxt name = map fst (function_names_of compilation ctxt name)
fun all_modes_of compilation ctxt =
map_filter (fn name => Option.map (pair name) (try (modes_of compilation ctxt) name))
(all_preds_of ctxt)
val all_random_modes_of = all_modes_of Random
fun defined_functions compilation ctxt name = case lookup_pred_data ctxt name of
NONE => false
| SOME data => AList.defined (op =) (#function_names data) compilation
fun needs_random ctxt s m =
member (op =) (#needs_random (the_pred_data ctxt s)) m
fun lookup_predfun_data ctxt name mode =
Option.map rep_predfun_data
(AList.lookup (op =) (#predfun_data (the_pred_data ctxt name)) mode)
fun the_predfun_data ctxt name mode =
case lookup_predfun_data ctxt 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
val predfun_neg_intro_of = #neg_intro ooo the_predfun_data
val intros_graph_of =
Graph.map (K (#intros o rep_pred_data)) o PredData.get o ProofContext.theory_of
(* diagnostic display functions *)
fun print_modes options modes =
if show_modes options then
tracing ("Inferred modes:\n" ^
cat_lines (map (fn (s, ms) => s ^ ": " ^ commas (map
(fn (p, m) => string_of_mode m ^ (if p then "pos" else "neg")) ms)) modes))
else ()
fun print_pred_mode_table string_of_entry pred_mode_table =
let
fun print_mode pred ((pol, 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 ctxt (Prem t) =
(Syntax.string_of_term ctxt t) ^ "(premise)"
| string_of_prem ctxt (Negprem t) =
(Syntax.string_of_term ctxt (HOLogic.mk_not t)) ^ "(negative premise)"
| string_of_prem ctxt (Sidecond t) =
(Syntax.string_of_term ctxt t) ^ "(sidecondition)"
| string_of_prem ctxt _ = raise Fail "string_of_prem: unexpected input"
fun string_of_clause ctxt pred (ts, prems) =
(space_implode " --> "
(map (string_of_prem ctxt) prems)) ^ " --> " ^ pred ^ " "
^ (space_implode " " (map (Syntax.string_of_term ctxt) ts))
fun print_compiled_terms options ctxt =
if show_compilation options then
print_pred_mode_table (fn _ => fn _ => Syntax.string_of_term ctxt)
else K ()
fun print_stored_rules ctxt =
let
val preds = Graph.keys (PredData.get (ProofContext.theory_of ctxt))
fun print pred () = let
val _ = writeln ("predicate: " ^ pred)
val _ = writeln ("introrules: ")
val _ = fold (fn thm => fn u => writeln (Display.string_of_thm ctxt thm))
(rev (intros_of ctxt pred)) ()
in
if (has_elim ctxt pred) then
writeln ("elimrule: " ^ Display.string_of_thm ctxt (the_elim_of ctxt pred))
else
writeln ("no elimrule defined")
end
in
fold print preds ()
end;
fun print_all_modes compilation ctxt =
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 ctxt) ()
end
(* validity checks *)
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' = map snd 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 errors =
map (fn (s, _) => case proposed_modes options s of
SOME ms => (case AList.lookup (op =) modes s of
SOME inferred_ms =>
let
val preds_without_modes = map fst (filter (null o snd) modes)
val modes' = map snd 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"
^ (if show_invalid_clauses options then
("For the following clauses, the following modes could not be inferred: " ^ "\n"
^ cat_lines errors) else "") ^
(if not (null preds_without_modes) then
"\n" ^ "No mode inferred for the predicates " ^ commas preds_without_modes
else ""))
else ()
end
| NONE => ())
| NONE => ()) preds
(* 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_global [] 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
val paramTs = ho_argsT_of_typ (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_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
raise Fail "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_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 (@{type_name Product_Type.prod}, [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
(* TODO: can be simplified if parameters are not treated specially ? *)
val (((pred, params), intros_th), ctxt1) = import_intros pred introrules ctxt
(* TODO: distinct required ? -- test case with more than one parameter! *)
val params = distinct (op aconv) params
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)
(* TODO: can be simplified if parameters are not treated specially ? <-- see uncommented code! *)
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 = map Free (fold Term.add_frees (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;
fun dest_conjunct_prem th =
case HOLogic.dest_Trueprop (prop_of th) of
(Const (@{const_name HOL.conj}, _) $ t $ t') =>
dest_conjunct_prem (th RS @{thm conjunct1})
@ dest_conjunct_prem (th RS @{thm conjunct2})
| _ => [th]
fun prove_casesrule ctxt (pred, (pre_cases_rule, nparams)) cases_rule =
let
val thy = ProofContext.theory_of ctxt
val nargs = length (binder_types (fastype_of pred))
fun PEEK f dependent_tactic st = dependent_tactic (f st) st
fun meta_eq_of th = th RS @{thm eq_reflection}
val tuple_rew_rules = map meta_eq_of [@{thm fst_conv}, @{thm snd_conv}, @{thm Pair_eq}]
fun instantiate i n {context = ctxt, params = p, prems = prems,
asms = a, concl = cl, schematics = s} =
let
fun term_pair_of (ix, (ty,t)) = (Var (ix,ty), t)
fun inst_of_matches tts = fold (Pattern.match thy) tts (Vartab.empty, Vartab.empty)
|> snd |> Vartab.dest |> map (pairself (cterm_of thy) o term_pair_of)
val (cases, (eqs, prems)) = apsnd (chop (nargs - nparams)) (chop n prems)
val case_th = MetaSimplifier.simplify true
(@{thm Predicate.eq_is_eq} :: map meta_eq_of eqs) (nth cases (i - 1))
val prems' = maps (dest_conjunct_prem o MetaSimplifier.simplify true tuple_rew_rules) prems
val pats = map (swap o HOLogic.dest_eq o HOLogic.dest_Trueprop) (take nargs (prems_of case_th))
val case_th' = Thm.instantiate ([], inst_of_matches pats) case_th
OF (replicate nargs @{thm refl})
val thesis =
Thm.instantiate ([], inst_of_matches (prems_of case_th' ~~ map prop_of prems')) case_th'
OF prems'
in
(rtac thesis 1)
end
val tac =
etac pre_cases_rule 1
THEN
(PEEK nprems_of
(fn n =>
ALLGOALS (fn i =>
MetaSimplifier.rewrite_goal_tac [@{thm split_paired_all}] i
THEN (SUBPROOF (instantiate i n) ctxt i))))
in
Goal.prove ctxt (Term.add_free_names cases_rule []) [] cases_rule (fn _ => tac)
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 (@{const_name Trueprop}, _) $ _ => Conv.arg_conv cv ct
| _ => raise Fail "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 ctxt elimrule =
let
fun replace_eqs (Const (@{const_name Trueprop}, _) $ (Const (@{const_name HOL.eq}, T) $ lhs $ rhs)) =
HOLogic.mk_Trueprop (Const (@{const_name Predicate.eq}, T) $ lhs $ rhs)
| replace_eqs t = t
val thy = ProofContext.theory_of ctxt
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 ctxt name =
case try (Inductive.the_inductive ctxt) 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 thy = ProofContext.theory_of ctxt
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 nparams = length (Inductive.params_of (#raw_induct result))
val elim_t = mk_casesrule ctxt pred intros
val elim =
prove_casesrule ctxt (pred, (pre_elim, nparams)) elim_t
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 apsnd o apfst) (cons (mode, mk_predfun_data data))
in PredData.map (Graph.map_node name (map_pred_data add)) end
fun is_inductive_predicate ctxt name =
is_some (try (Inductive.the_inductive ctxt) name)
fun depending_preds_of ctxt (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 ctxt c orelse is_registered ctxt 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 (ProofContext.init_global 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_global 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 apfst) (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 apfst)
(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 apsnd o apsnd) (K modes)
in
PredData.map (Graph.map_node name (map_pred_data set))
end
(* registration of alternative function names *)
structure Alt_Compilations_Data = Theory_Data
(
type T = (mode * (compilation_funs -> typ -> term)) list Symtab.table;
val empty = Symtab.empty;
val extend = I;
fun merge data : T = Symtab.merge (K true) data;
);
fun alternative_compilation_of_global thy pred_name mode =
AList.lookup eq_mode (Symtab.lookup_list (Alt_Compilations_Data.get thy) pred_name) mode
fun alternative_compilation_of ctxt pred_name mode =
AList.lookup eq_mode
(Symtab.lookup_list (Alt_Compilations_Data.get (ProofContext.theory_of ctxt)) pred_name) mode
fun force_modes_and_compilations pred_name compilations =
let
(* thm refl is a dummy thm *)
val modes = map fst compilations
val (needs_random, non_random_modes) = pairself (map fst)
(List.partition (fn (m, (fun_name, random)) => random) compilations)
val non_random_dummys = map (rpair "dummy") non_random_modes
val all_dummys = map (rpair "dummy") modes
val dummy_function_names = map (rpair all_dummys) Predicate_Compile_Aux.random_compilations
@ map (rpair non_random_dummys) Predicate_Compile_Aux.non_random_compilations
val alt_compilations = map (apsnd fst) compilations
in
PredData.map (Graph.new_node
(pred_name, mk_pred_data (([], SOME @{thm refl}), (dummy_function_names, ([], needs_random)))))
#> Alt_Compilations_Data.map (Symtab.insert (K false) (pred_name, alt_compilations))
end
fun functional_compilation fun_name mode compfuns T =
let
val (inpTs, outpTs) = split_map_modeT (fn _ => fn T => (SOME T, NONE))
mode (binder_types T)
val bs = map (pair "x") inpTs
val bounds = map Bound (rev (0 upto (length bs) - 1))
val f = Const (fun_name, inpTs ---> HOLogic.mk_tupleT outpTs)
in list_abs (bs, mk_single compfuns (list_comb (f, bounds))) end
fun register_alternative_function pred_name mode fun_name =
Alt_Compilations_Data.map (Symtab.insert_list (eq_pair eq_mode (K false))
(pred_name, (mode, functional_compilation fun_name mode)))
fun force_modes_and_functions pred_name fun_names =
force_modes_and_compilations pred_name
(map (fn (mode, (fun_name, random)) => (mode, (functional_compilation fun_name mode, random)))
fun_names)
(* compilation modifiers *)
structure Comp_Mod =
struct
datatype comp_modifiers = Comp_Modifiers of
{
compilation : compilation,
function_name_prefix : string,
compfuns : compilation_funs,
mk_random : typ -> term list -> term,
modify_funT : typ -> typ,
additional_arguments : string list -> term list,
wrap_compilation : compilation_funs -> string -> typ -> mode -> term list -> term -> term,
transform_additional_arguments : indprem -> term list -> term list
}
fun dest_comp_modifiers (Comp_Modifiers c) = c
val 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 mk_random = #mk_random o dest_comp_modifiers
val funT_of' = funT_of o compfuns
val modify_funT = #modify_funT o dest_comp_modifiers
fun funT_of comp mode = modify_funT comp o funT_of' comp mode
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;
val depth_limited_comp_modifiers = Comp_Mod.Comp_Modifiers
{
compilation = Depth_Limited,
function_name_prefix = "depth_limited_",
compfuns = PredicateCompFuns.compfuns,
mk_random = (fn _ => error "no random generation"),
additional_arguments = fn names =>
let
val depth_name = Name.variant names "depth"
in [Free (depth_name, @{typ code_numeral})] end,
modify_funT = (fn T => let val (Ts, U) = strip_type T
val Ts' = [@{typ code_numeral}] in (Ts @ Ts') ---> U end),
wrap_compilation =
fn compfuns => fn s => fn T => fn mode => fn additional_arguments => fn compilation =>
let
val [depth] = additional_arguments
val (_, Ts) = split_modeT' mode (binder_types T)
val T' = mk_predT compfuns (HOLogic.mk_tupleT Ts)
val if_const = Const (@{const_name "If"}, @{typ bool} --> T' --> T' --> T')
in
if_const $ HOLogic.mk_eq (depth, @{term "0 :: code_numeral"})
$ mk_bot compfuns (dest_predT compfuns T')
$ compilation
end,
transform_additional_arguments =
fn prem => fn additional_arguments =>
let
val [depth] = additional_arguments
val depth' =
Const (@{const_name Groups.minus}, @{typ "code_numeral => code_numeral => code_numeral"})
$ depth $ Const (@{const_name Groups.one}, @{typ "Code_Numeral.code_numeral"})
in [depth'] end
}
val random_comp_modifiers = Comp_Mod.Comp_Modifiers
{
compilation = Random,
function_name_prefix = "random_",
compfuns = PredicateCompFuns.compfuns,
mk_random = (fn T => fn additional_arguments =>
list_comb (Const(@{const_name Quickcheck.iter},
[@{typ code_numeral}, @{typ code_numeral}, @{typ Random.seed}] --->
PredicateCompFuns.mk_predT T), additional_arguments)),
modify_funT = (fn T =>
let
val (Ts, U) = strip_type T
val Ts' = [@{typ code_numeral}, @{typ code_numeral}, @{typ "code_numeral * code_numeral"}]
in (Ts @ Ts') ---> U end),
additional_arguments = (fn names =>
let
val [nrandom, size, seed] = Name.variant_list names ["nrandom", "size", "seed"]
in
[Free (nrandom, @{typ code_numeral}), Free (size, @{typ code_numeral}),
Free (seed, @{typ "code_numeral * code_numeral"})]
end),
wrap_compilation = K (K (K (K (K I))))
: (compilation_funs -> string -> typ -> mode -> term list -> term -> term),
transform_additional_arguments = K I : (indprem -> term list -> term list)
}
val depth_limited_random_comp_modifiers = Comp_Mod.Comp_Modifiers
{
compilation = Depth_Limited_Random,
function_name_prefix = "depth_limited_random_",
compfuns = PredicateCompFuns.compfuns,
mk_random = (fn T => fn additional_arguments =>
list_comb (Const(@{const_name Quickcheck.iter},
[@{typ code_numeral}, @{typ code_numeral}, @{typ Random.seed}] --->
PredicateCompFuns.mk_predT T), tl additional_arguments)),
modify_funT = (fn T =>
let
val (Ts, U) = strip_type T
val Ts' = [@{typ code_numeral}, @{typ code_numeral}, @{typ code_numeral},
@{typ "code_numeral * code_numeral"}]
in (Ts @ Ts') ---> U end),
additional_arguments = (fn names =>
let
val [depth, nrandom, size, seed] = Name.variant_list names ["depth", "nrandom", "size", "seed"]
in
[Free (depth, @{typ code_numeral}), Free (nrandom, @{typ code_numeral}),
Free (size, @{typ code_numeral}), Free (seed, @{typ "code_numeral * code_numeral"})]
end),
wrap_compilation =
fn compfuns => fn s => fn T => fn mode => fn additional_arguments => fn compilation =>
let
val depth = hd (additional_arguments)
val (_, Ts) = split_map_modeT (fn m => fn T => (SOME (funT_of compfuns m T), NONE))
mode (binder_types T)
val T' = mk_predT compfuns (HOLogic.mk_tupleT Ts)
val if_const = Const (@{const_name "If"}, @{typ bool} --> T' --> T' --> T')
in
if_const $ HOLogic.mk_eq (depth, @{term "0 :: code_numeral"})
$ mk_bot compfuns (dest_predT compfuns T')
$ compilation
end,
transform_additional_arguments =
fn prem => fn additional_arguments =>
let
val [depth, nrandom, size, seed] = additional_arguments
val depth' =
Const (@{const_name Groups.minus}, @{typ "code_numeral => code_numeral => code_numeral"})
$ depth $ Const (@{const_name Groups.one}, @{typ "Code_Numeral.code_numeral"})
in [depth', nrandom, size, seed] end
}
val predicate_comp_modifiers = Comp_Mod.Comp_Modifiers
{
compilation = Pred,
function_name_prefix = "",
compfuns = PredicateCompFuns.compfuns,
mk_random = (fn _ => error "no random generation"),
modify_funT = I,
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 annotated_comp_modifiers = Comp_Mod.Comp_Modifiers
{
compilation = Annotated,
function_name_prefix = "annotated_",
compfuns = PredicateCompFuns.compfuns,
mk_random = (fn _ => error "no random generation"),
modify_funT = I,
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,
mk_random = (fn _ => error "no random generation"),
modify_funT = I,
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 pos_random_dseq_comp_modifiers = Comp_Mod.Comp_Modifiers
{
compilation = Pos_Random_DSeq,
function_name_prefix = "random_dseq_",
compfuns = Random_Sequence_CompFuns.compfuns,
mk_random = (fn T => fn additional_arguments =>
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),
modify_funT = I,
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 neg_random_dseq_comp_modifiers = Comp_Mod.Comp_Modifiers
{
compilation = Neg_Random_DSeq,
function_name_prefix = "random_dseq_neg_",
compfuns = Random_Sequence_CompFuns.compfuns,
mk_random = (fn _ => error "no random generation"),
modify_funT = I,
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 new_pos_random_dseq_comp_modifiers = Comp_Mod.Comp_Modifiers
{
compilation = New_Pos_Random_DSeq,
function_name_prefix = "new_random_dseq_",
compfuns = New_Pos_Random_Sequence_CompFuns.compfuns,
mk_random = (fn T => fn additional_arguments =>
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 ("New_Random_Sequence.Random", (@{typ code_numeral} --> @{typ Random.seed} -->
HOLogic.mk_prodT (HOLogic.mk_prodT (T, @{typ "unit => term"}), @{typ Random.seed})) -->
New_Pos_Random_Sequence_CompFuns.mk_pos_random_dseqT T) $ random
end),
modify_funT = I,
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 new_neg_random_dseq_comp_modifiers = Comp_Mod.Comp_Modifiers
{
compilation = New_Neg_Random_DSeq,
function_name_prefix = "new_random_dseq_neg_",
compfuns = New_Neg_Random_Sequence_CompFuns.compfuns,
mk_random = (fn _ => error "no random generation"),
modify_funT = I,
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)
}
fun negative_comp_modifiers_of comp_modifiers =
(case Comp_Mod.compilation comp_modifiers of
Pos_Random_DSeq => neg_random_dseq_comp_modifiers
| Neg_Random_DSeq => pos_random_dseq_comp_modifiers
| New_Pos_Random_DSeq => new_neg_random_dseq_comp_modifiers
| New_Neg_Random_DSeq => new_pos_random_dseq_comp_modifiers
| c => comp_modifiers)
(** mode analysis **)
type mode_analysis_options = {use_random : bool, reorder_premises : bool, infer_pos_and_neg_modes : bool}
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 (pol, 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 (pol, 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 (@{type_name Product_Type.prod}, [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
raise Fail "all_input_of: not a predicate"
end
fun find_least ord xs =
let
fun find' x y = (case y of NONE => SOME x | SOME y' => if ord (x, y') = LESS then SOME x else y)
in
fold find' xs NONE
end
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 ctxt (Const (f, _)) = is_constr ctxt f
| is_invertible_function ctxt _ = false
fun non_invertible_subterms ctxt (t as Free _) = []
| non_invertible_subterms ctxt t =
let
val (f, args) = strip_comb t
in
if is_invertible_function ctxt f then
maps (non_invertible_subterms ctxt) args
else
[t]
end
fun collect_non_invertible_subterms ctxt (f as Free _) (names, eqs) = (f, (names, eqs))
| collect_non_invertible_subterms ctxt t (names, eqs) =
case (strip_comb t) of (f, args) =>
if is_invertible_function ctxt f then
let
val (args', (names', eqs')) =
fold_map (collect_non_invertible_subterms ctxt) 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 ctxt vs t =
forall
(fn t => is_eqT (fastype_of t) andalso forall (member (op =) vs) (term_vs t))
(non_invertible_subterms ctxt t)
andalso
(forall (is_eqT o snd)
(inter (fn ((f', _), f) => f = f') vs (Term.add_frees t [])))
fun vars_of_destructable_term ctxt (Free (x, _)) = [x]
| vars_of_destructable_term ctxt t =
let
val (f, args) = strip_comb t
in
if is_invertible_function ctxt f then
maps (vars_of_destructable_term ctxt) args
else
[]
end
fun is_constructable vs t = forall (member (op =) vs) (term_vs t)
fun missing_vars vs t = subtract (op =) vs (term_vs t)
fun output_terms (Const (@{const_name Pair}, _) $ t1 $ t2, Mode_Pair (d1, d2)) =
output_terms (t1, d1) @ output_terms (t2, d2)
| output_terms (t1 $ t2, Mode_App (d1, d2)) =
output_terms (t1, d1) @ output_terms (t2, d2)
| output_terms (t, Term Output) = [t]
| output_terms _ = []
fun lookup_mode modes (Const (s, T)) =
(case (AList.lookup (op =) modes s) of
SOME ms => SOME (map (fn m => (Context m, [])) ms)
| NONE => NONE)
| lookup_mode modes (Free (x, _)) =
(case (AList.lookup (op =) modes x) of
SOME ms => SOME (map (fn m => (Context m , [])) ms)
| NONE => NONE)
fun derivations_of (ctxt : Proof.context) modes vs (Const (@{const_name Pair}, _) $ t1 $ t2) (Pair (m1, m2)) =
map_product
(fn (m1, mvars1) => fn (m2, mvars2) => (Mode_Pair (m1, m2), union (op =) mvars1 mvars2))
(derivations_of ctxt modes vs t1 m1) (derivations_of ctxt modes vs t2 m2)
| derivations_of ctxt modes vs t (m as Fun _) =
(*let
val (p, args) = strip_comb t
in
(case lookup_mode modes p of
SOME ms => map_filter (fn (Context m, []) => let
val ms = strip_fun_mode m
val (argms, restms) = chop (length args) ms
val m' = fold_rev (curry Fun) restms Bool
in
if forall (fn m => eq_mode (Input, m)) argms andalso eq_mode (m', mode) then
SOME (fold (curry Mode_App) (map Term argms) (Context m), missing_vars vs t)
else NONE
end) ms
| NONE => (if is_all_input mode then [(Context mode, [])] else []))
end*)
(case try (all_derivations_of ctxt modes vs) t of
SOME derivs =>
filter (fn (d, mvars) => eq_mode (mode_of d, m) andalso null (output_terms (t, d))) derivs
| NONE => (if is_all_input m then [(Context m, [])] else []))
| derivations_of ctxt modes vs t m =
if eq_mode (m, Input) then
[(Term Input, missing_vars vs t)]
else if eq_mode (m, Output) then
(if is_possible_output ctxt vs t then [(Term Output, [])] else [])
else []
and all_derivations_of ctxt modes vs (Const (@{const_name Pair}, _) $ t1 $ t2) =
let
val derivs1 = all_derivations_of ctxt modes vs t1
val derivs2 = all_derivations_of ctxt 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 ctxt modes vs (t1 $ t2) =
let
val derivs1 = all_derivations_of ctxt 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 ctxt modes vs t2 m')
| _ => raise Fail "all_derivations_of: derivation has an unexpected non-functional mode") derivs1
end
| all_derivations_of _ modes vs (Const (s, T)) = the (lookup_mode modes (Const (s, T)))
| all_derivations_of _ modes vs (Free (x, T)) = the (lookup_mode modes (Free (x, T)))
| all_derivations_of _ modes vs _ = raise Fail "all_derivations_of: unexpected term"
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 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 =) (map (fn ((p, m), r) => (m, r)) 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 lexl_ord [] (x, x') = EQUAL
| lexl_ord (ord :: ords') (x, x') =
case ord (x, x') of
EQUAL => lexl_ord ords' (x, x')
| ord => ord
fun deriv_ord' ctxt pol pred modes t1 t2 ((deriv1, mvars1), (deriv2, mvars2)) =
let
(* prefer functional modes if it is a function *)
fun fun_ord ((t1, deriv1, mvars1), (t2, deriv2, mvars2)) =
let
fun is_functional t mode =
case try (fst o dest_Const o fst o strip_comb) t of
NONE => false
| SOME c => is_some (alternative_compilation_of ctxt c mode)
in
case (is_functional t1 (head_mode_of deriv1), is_functional t2 (head_mode_of deriv2)) of
(true, true) => EQUAL
| (true, false) => LESS
| (false, true) => GREATER
| (false, false) => EQUAL
end
(* prefer modes without requirement for generating random values *)
fun mvars_ord ((t1, deriv1, mvars1), (t2, deriv2, mvars2)) =
int_ord (length mvars1, length mvars2)
(* prefer non-random modes *)
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)
(* prefer modes with more input and less output *)
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))
(* prefer recursive calls *)
fun is_rec_premise t =
case fst (strip_comb t) of Const (c, T) => c = pred | _ => false
fun recursive_ord ((t1, deriv1, mvars1), (t2, deriv2, mvars2)) =
int_ord (if is_rec_premise t1 then 0 else 1,
if is_rec_premise t2 then 0 else 1)
val ord = lexl_ord [mvars_ord, fun_ord, random_mode_ord, output_mode_ord, recursive_ord]
in
ord ((t1, deriv1, mvars1), (t2, deriv2, mvars2))
end
fun deriv_ord ctxt pol pred modes t = deriv_ord' ctxt pol pred modes t t
fun premise_ord thy pol pred modes ((prem1, a1), (prem2, a2)) =
rev_option_ord (deriv_ord' thy pol pred modes (dest_indprem prem1) (dest_indprem 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 (mode_analysis_options : mode_analysis_options) (ctxt : Proof.context) pred
pol (modes, (pos_modes, neg_modes)) vs ps =
let
fun choose_mode_of_prem (Prem t) =
find_least (deriv_ord ctxt pol pred modes t) (all_derivations_of ctxt pos_modes vs t)
| choose_mode_of_prem (Sidecond t) = SOME (Context Bool, missing_vars vs t)
| choose_mode_of_prem (Negprem t) = find_least (deriv_ord ctxt (not pol) pred modes t)
(filter (fn (d, missing_vars) => is_all_input (head_mode_of d))
(all_derivations_of ctxt neg_modes vs t))
| choose_mode_of_prem p = raise Fail ("choose_mode_of_prem: unexpected premise " ^ string_of_prem ctxt p)
in
if #reorder_premises mode_analysis_options then
find_least (premise_ord ctxt pol pred modes) (ps ~~ map choose_mode_of_prem ps)
else
SOME (hd ps, choose_mode_of_prem (hd ps))
end
fun check_mode_clause' (mode_analysis_options : mode_analysis_options) ctxt pred param_vs (modes :
(string * ((bool * mode) * bool) list) list) ((pol, mode) : bool * mode) (ts, ps) =
let
val vTs = distinct (op =) (fold Term.add_frees (map dest_indprem ps) (fold Term.add_frees ts []))
val modes' = modes @ (param_vs ~~ map (fn x => [((true, x), false), ((false, x), false)]) (ho_arg_modes_of mode))
fun retrieve_modes_of_pol pol = map (fn (s, ms) =>
(s, map_filter (fn ((p, m), r) => if p = pol then SOME m else NONE | _ => NONE) ms))
val (pos_modes', neg_modes') =
if #infer_pos_and_neg_modes mode_analysis_options then
(retrieve_modes_of_pol pol modes', retrieve_modes_of_pol (not pol) modes')
else
let
val modes = map (fn (s, ms) => (s, map (fn ((p, m), r) => m) ms)) modes'
in (modes, modes) end
val (in_ts, out_ts) = split_mode mode ts
val in_vs = maps (vars_of_destructable_term ctxt) in_ts
val out_vs = terms_vs out_ts
fun known_vs_after p vs = (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)
| _ => raise Fail "unexpected premise")
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 mode_analysis_options ctxt pred pol (modes', (pos_modes', neg_modes')) vs ps) of
SOME (p, SOME (deriv, [])) => check_mode_prems ((p, deriv) :: acc_ps) rnd
(known_vs_after p vs) (filter_out (equal p) ps)
| SOME (p, SOME (deriv, missing_vars)) =>
if #use_random mode_analysis_options andalso pol then
check_mode_prems ((p, deriv) :: (map
(fn v => (Generator (v, the (AList.lookup (op =) vTs v)), Term Output))
(distinct (op =) missing_vars))
@ acc_ps) true (known_vs_after p vs) (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 vs) (in_ts @ out_ts) then
SOME (ts, rev acc_ps, rnd)
else
if #use_random mode_analysis_options andalso pol then
let
val generators = map
(fn v => (Generator (v, the (AList.lookup (op =) vTs v)), Term Output))
(subtract (op =) vs (terms_vs (in_ts @ 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' mode_analysis_options options thy param_vs clauses modes (p, (ms : ((bool * mode) * bool) list)) =
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 : bool * mode), 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 = Output.cond_timeit false "work part of check_mode for one mode" (fn _ =>
map (check_mode_clause' mode_analysis_options thy p param_vs modes m) rs)
in
Output.cond_timeit false "aux part of check_mode for one mode" (fn _ =>
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 _ = if show_mode_inference options then
tracing ("checking " ^ string_of_int (length ms) ^ " modes ...")
else ()
val res = Output.cond_timeit false "check_mode" (fn _ => map (fn (m, _) => (m, check_mode m)) ms)
val (ms', errors) = split res
in
((p, (ms' : ((bool * mode) * bool) list)), errors)
end;
fun get_modes_pred' mode_analysis_options 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' mode_analysis_options thy p param_vs modes m) rs)) ms)
end;
fun fixp f (x : (string * ((bool * mode) * bool) list) list) =
let val y = f x
in if x = y then x else fixp f y end;
fun fixp_with_state f (x : (string * ((bool * mode) * bool) list) list, state) =
let
val (y, state') = f (x, state)
in
if x = y then (y, state') else fixp_with_state f (y, state')
end
fun string_of_ext_mode ((pol, mode), rnd) =
string_of_mode mode ^ "(" ^ (if pol then "pos" else "neg") ^ ", "
^ (if rnd then "rnd" else "nornd") ^ ")"
fun print_extra_modes options modes =
if show_mode_inference options then
tracing ("Modes of inferred predicates: " ^
cat_lines (map (fn (s, ms) => s ^ ": " ^ commas (map string_of_ext_mode ms)) modes))
else ()
fun infer_modes mode_analysis_options options (lookup_mode, lookup_neg_mode, needs_random) ctxt
preds all_modes param_vs clauses =
let
fun appair f (x1, x2) (y1, y2) = (f x1 y1, f x2 y2)
fun add_needs_random s (false, m) = ((false, m), false)
| add_needs_random s (true, m) = ((true, m), needs_random s m)
fun add_polarity_and_random_bit s b ms = map (fn m => add_needs_random s (b, m)) ms
val prednames = map fst preds
(* extramodes contains all modes of all constants, should we only use the necessary ones
- what is the impact on performance? *)
fun predname_of (Prem t) =
(case try dest_Const (fst (strip_comb t)) of SOME (c, _) => insert (op =) c | NONE => I)
| predname_of (Negprem t) =
(case try dest_Const (fst (strip_comb t)) of SOME (c, _) => insert (op =) c | NONE => I)
| predname_of _ = I
val relevant_prednames = fold (fn (_, clauses') =>
fold (fn (_, ps) => fold Term.add_const_names (map dest_indprem ps)) clauses') clauses []
|> filter_out (fn name => member (op =) prednames name)
val extra_modes =
if #infer_pos_and_neg_modes mode_analysis_options then
let
val pos_extra_modes =
map_filter (fn name => Option.map (pair name) (try lookup_mode name))
relevant_prednames
val neg_extra_modes =
map_filter (fn name => Option.map (pair name) (try lookup_neg_mode name))
relevant_prednames
in
map (fn (s, ms) => (s, (add_polarity_and_random_bit s true ms)
@ add_polarity_and_random_bit s false (the (AList.lookup (op =) neg_extra_modes s))))
pos_extra_modes
end
else
map (fn (s, ms) => (s, (add_polarity_and_random_bit s true ms)))
(map_filter (fn name => Option.map (pair name) (try lookup_mode name))
relevant_prednames)
val _ = print_extra_modes options extra_modes
val start_modes =
if #infer_pos_and_neg_modes mode_analysis_options then
map (fn (s, ms) => (s, map (fn m => ((true, m), false)) ms @
(map (fn m => ((false, m), false)) ms))) all_modes
else
map (fn (s, ms) => (s, map (fn m => ((true, m), false)) ms)) all_modes
fun iteration modes = map
(check_modes_pred' mode_analysis_options options ctxt param_vs clauses
(modes @ extra_modes)) modes
val ((modes : (string * ((bool * mode) * bool) list) list), errors) =
Output.cond_timeit false "Fixpount computation of mode analysis" (fn () =>
if show_invalid_clauses options then
fixp_with_state (fn (modes, errors) =>
let
val (modes', new_errors) = split_list (iteration modes)
in (modes', errors @ flat new_errors) end) (start_modes, [])
else
(fixp (fn modes => map fst (iteration modes)) start_modes, []))
val moded_clauses = map (get_modes_pred' mode_analysis_options ctxt param_vs clauses
(modes @ extra_modes)) modes
val need_random = fold (fn (s, ms) => if member (op =) (map fst preds) s then
cons (s, (map_filter (fn ((true, m), true) => SOME m | _ => NONE) ms)) else I)
modes []
in
((moded_clauses, need_random), errors)
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;
(* TODO: uses param_vs -- change necessary for compilation with new modes *)
fun compile_arg compilation_modifiers additional_arguments ctxt 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 additional_arguments
param_vs iss ctxt eqs eqs' out_ts success_t =
let
val compfuns = Comp_Mod.compfuns compilation_modifiers
val eqs'' = maps mk_eq eqs @ eqs'
val eqs'' =
map (compile_arg compilation_modifiers additional_arguments ctxt 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 ctxt 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 string_of_tderiv ctxt (t, deriv) =
(case (t, deriv) of
(t1 $ t2, Mode_App (deriv1, deriv2)) =>
string_of_tderiv ctxt (t1, deriv1) ^ " $ " ^ string_of_tderiv ctxt (t2, deriv2)
| (Const (@{const_name Pair}, _) $ t1 $ t2, Mode_Pair (deriv1, deriv2)) =>
"(" ^ string_of_tderiv ctxt (t1, deriv1) ^ ", " ^ string_of_tderiv ctxt (t2, deriv2) ^ ")"
| (t, Term Input) => Syntax.string_of_term ctxt t ^ "[Input]"
| (t, Term Output) => Syntax.string_of_term ctxt t ^ "[Output]"
| (t, Context m) => Syntax.string_of_term ctxt t ^ "[" ^ string_of_mode m ^ "]")
fun compile_expr compilation_modifiers ctxt (t, deriv) additional_arguments =
let
val compfuns = Comp_Mod.compfuns compilation_modifiers
fun expr_of (t, deriv) =
(case (t, deriv) of
(t, Term Input) => SOME t
| (t, Term Output) => NONE
| (Const (name, T), Context mode) =>
(case alternative_compilation_of ctxt name mode of
SOME alt_comp => SOME (alt_comp compfuns T)
| NONE =>
SOME (Const (function_name_of (Comp_Mod.compilation compilation_modifiers)
ctxt 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 (@{const_name 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
list_comb (the (expr_of (t, deriv)), additional_arguments)
end
fun compile_clause compilation_modifiers ctxt all_vs param_vs additional_arguments
mode inp (in_ts, out_ts) moded_ps =
let
val compfuns = Comp_Mod.compfuns compilation_modifiers
val iss = ho_arg_modes_of mode (* FIXME! *)
val compile_match = compile_match compilation_modifiers
additional_arguments param_vs iss ctxt
val (in_ts', (all_vs', eqs)) =
fold_map (collect_non_invertible_subterms ctxt) in_ts (all_vs, []);
fun compile_prems out_ts' vs names [] =
let
val (out_ts'', (names', eqs')) =
fold_map (collect_non_invertible_subterms ctxt) 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 ctxt) 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 ctxt (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 neg_compilation_modifiers =
negative_comp_modifiers_of compilation_modifiers
val u = mk_not compfuns
(compile_expr neg_compilation_modifiers ctxt (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 additional_arguments
ctxt param_vs iss t
val rest = compile_prems [] vs' names'' ps;
in
(mk_if compfuns t, rest)
end
| Generator (v, T) =>
let
val u = Comp_Mod.mk_random compilation_modifiers T additional_arguments
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
(* switch detection *)
(** argument position of an inductive predicates and the executable functions **)
type position = int * int list
fun input_positions_pair Input = [[]]
| input_positions_pair Output = []
| input_positions_pair (Fun _) = []
| input_positions_pair (Pair (m1, m2)) =
map (cons 1) (input_positions_pair m1) @ map (cons 2) (input_positions_pair m2)
fun input_positions_of_mode mode = flat (map_index
(fn (i, Input) => [(i, [])]
| (_, Output) => []
| (_, Fun _) => []
| (i, m as Pair (m1, m2)) => map (pair i) (input_positions_pair m))
(Predicate_Compile_Aux.strip_fun_mode mode))
fun argument_position_pair mode [] = []
| argument_position_pair (Pair (Fun _, m2)) (2 :: is) = argument_position_pair m2 is
| argument_position_pair (Pair (m1, m2)) (i :: is) =
(if eq_mode (m1, Output) andalso i = 2 then
argument_position_pair m2 is
else if eq_mode (m2, Output) andalso i = 1 then
argument_position_pair m1 is
else (i :: argument_position_pair (if i = 1 then m1 else m2) is))
fun argument_position_of mode (i, is) =
(i - (length (filter (fn Output => true | Fun _ => true | _ => false)
(List.take (strip_fun_mode mode, i)))),
argument_position_pair (nth (strip_fun_mode mode) i) is)
fun nth_pair [] t = t
| nth_pair (1 :: is) (Const (@{const_name Pair}, _) $ t1 $ _) = nth_pair is t1
| nth_pair (2 :: is) (Const (@{const_name Pair}, _) $ _ $ t2) = nth_pair is t2
| nth_pair _ _ = raise Fail "unexpected input for nth_tuple"
(** switch detection analysis **)
fun find_switch_test ctxt (i, is) (ts, prems) =
let
val t = nth_pair is (nth ts i)
val T = fastype_of t
in
case T of
TFree _ => NONE
| Type (Tcon, _) =>
(case Datatype_Data.get_constrs (ProofContext.theory_of ctxt) Tcon of
NONE => NONE
| SOME cs =>
(case strip_comb t of
(Var _, []) => NONE
| (Free _, []) => NONE
| (Const (c, T), _) => if AList.defined (op =) cs c then SOME (c, T) else NONE))
end
fun partition_clause ctxt pos moded_clauses =
let
fun insert_list eq (key, value) = AList.map_default eq (key, []) (cons value)
fun find_switch_test' moded_clause (cases, left) =
case find_switch_test ctxt pos moded_clause of
SOME (c, T) => (insert_list (op =) ((c, T), moded_clause) cases, left)
| NONE => (cases, moded_clause :: left)
in
fold find_switch_test' moded_clauses ([], [])
end
datatype switch_tree =
Atom of moded_clause list | Node of (position * ((string * typ) * switch_tree) list) * switch_tree
fun mk_switch_tree ctxt mode moded_clauses =
let
fun select_best_switch moded_clauses input_position best_switch =
let
val ord = option_ord (rev_order o int_ord o (pairself (length o snd o snd)))
val partition = partition_clause ctxt input_position moded_clauses
val switch = if (length (fst partition) > 1) then SOME (input_position, partition) else NONE
in
case ord (switch, best_switch) of LESS => best_switch
| EQUAL => best_switch | GREATER => switch
end
fun detect_switches moded_clauses =
case fold (select_best_switch moded_clauses) (input_positions_of_mode mode) NONE of
SOME (best_pos, (switched_on, left_clauses)) =>
Node ((best_pos, map (apsnd detect_switches) switched_on),
detect_switches left_clauses)
| NONE => Atom moded_clauses
in
detect_switches moded_clauses
end
(** compilation of detected switches **)
fun destruct_constructor_pattern (pat, obj) =
(case strip_comb pat of
(f as Free _, []) => cons (pat, obj)
| (Const (c, T), pat_args) =>
(case strip_comb obj of
(Const (c', T'), obj_args) =>
(if c = c' andalso T = T' then
fold destruct_constructor_pattern (pat_args ~~ obj_args)
else raise Fail "pattern and object mismatch")
| _ => raise Fail "unexpected object")
| _ => raise Fail "unexpected pattern")
fun compile_switch compilation_modifiers ctxt all_vs param_vs additional_arguments mode
in_ts' outTs switch_tree =
let
val compfuns = Comp_Mod.compfuns compilation_modifiers
val thy = ProofContext.theory_of ctxt
fun compile_switch_tree _ _ (Atom []) = NONE
| compile_switch_tree all_vs ctxt_eqs (Atom moded_clauses) =
let
val in_ts' = map (Pattern.rewrite_term thy ctxt_eqs []) in_ts'
fun compile_clause' (ts, moded_ps) =
let
val (ts, out_ts) = split_mode mode ts
val subst = fold destruct_constructor_pattern (in_ts' ~~ ts) []
val (fsubst, pat') = List.partition (fn (_, Free _) => true | _ => false) subst
val moded_ps' = (map o apfst o map_indprem)
(Pattern.rewrite_term thy (map swap fsubst) []) moded_ps
val inp = HOLogic.mk_tuple (map fst pat')
val in_ts' = map (Pattern.rewrite_term thy (map swap fsubst) []) (map snd pat')
val out_ts' = map (Pattern.rewrite_term thy (map swap fsubst) []) out_ts
in
compile_clause compilation_modifiers ctxt all_vs param_vs additional_arguments
mode inp (in_ts', out_ts') moded_ps'
end
in SOME (foldr1 (mk_sup compfuns) (map compile_clause' moded_clauses)) end
| compile_switch_tree all_vs ctxt_eqs (Node ((position, switched_clauses), left_clauses)) =
let
val (i, is) = argument_position_of mode position
val inp_var = nth_pair is (nth in_ts' i)
val x = Name.variant all_vs "x"
val xt = Free (x, fastype_of inp_var)
fun compile_single_case ((c, T), switched) =
let
val Ts = binder_types T
val argnames = Name.variant_list (x :: all_vs)
(map (fn i => "c" ^ string_of_int i) (1 upto length Ts))
val args = map2 (curry Free) argnames Ts
val pattern = list_comb (Const (c, T), args)
val ctxt_eqs' = (inp_var, pattern) :: ctxt_eqs
val compilation = the_default (mk_bot compfuns (HOLogic.mk_tupleT outTs))
(compile_switch_tree (argnames @ x :: all_vs) ctxt_eqs' switched)
in
(pattern, compilation)
end
val switch = fst (Datatype.make_case ctxt Datatype_Case.Quiet [] inp_var
((map compile_single_case switched_clauses) @
[(xt, mk_bot compfuns (HOLogic.mk_tupleT outTs))]))
in
case compile_switch_tree all_vs ctxt_eqs left_clauses of
NONE => SOME switch
| SOME left_comp => SOME (mk_sup compfuns (switch, left_comp))
end
in
compile_switch_tree all_vs [] switch_tree
end
(* compilation of predicates *)
fun compile_pred options compilation_modifiers ctxt all_vs param_vs s T (pol, mode) moded_cls =
let
val compilation_modifiers = if pol then compilation_modifiers else
negative_comp_modifiers_of compilation_modifiers
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 (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 compilation =
if detect_switches options then
the_default (mk_bot compfuns (HOLogic.mk_tupleT outTs))
(compile_switch compilation_modifiers ctxt all_vs param_vs additional_arguments
mode in_ts' outTs (mk_switch_tree ctxt mode moded_cls))
else
let
val cl_ts =
map (fn (ts, moded_prems) =>
compile_clause compilation_modifiers ctxt all_vs param_vs additional_arguments
mode (HOLogic.mk_tuple in_ts') (split_mode mode ts) moded_prems) moded_cls;
in
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)
end
val fun_const =
Const (function_name_of (Comp_Mod.compilation compilation_modifiers)
ctxt 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 (@{const_name 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 (@{const_name prod_case}, _) $ t) = strip_split_abs t
| strip_split_abs (Abs (_, _, t)) = strip_split_abs t
| strip_split_abs t = t
fun mk_args is_eval (m as Pair (m1, m2), T as Type (@{type_name Product_Type.prod}, [T1, T2])) names =
if eq_mode (m, Input) orelse eq_mode (m, Output) then
let
val x = Name.variant names "x"
in
(Free (x, T), x :: names)
end
else
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 ctxt mode defthm mode_id funT pred =
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 ctxt
(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 ctxt
(argnames @ ["y", "P"]) [] elimtrm (fn _ => unfolddef_tac)
val opt_neg_introthm =
if is_all_input mode then
let
val neg_predpropI = HOLogic.mk_Trueprop (HOLogic.mk_not (list_comb (pred, args')))
val neg_funpropI =
HOLogic.mk_Trueprop (PredicateCompFuns.mk_Eval
(PredicateCompFuns.mk_not (list_comb (funtrm, inargs)), HOLogic.unit))
val neg_introtrm = Logic.list_implies (neg_predpropI :: param_eqs, neg_funpropI)
val tac =
Simplifier.asm_full_simp_tac (HOL_basic_ss addsimps
(@{thm if_False} :: @{thm Predicate.not_pred_eq} :: simprules)) 1
THEN rtac @{thm Predicate.singleI} 1
in SOME (Goal.prove ctxt (argnames @ hoarg_names') []
neg_introtrm (fn _ => tac))
end
else NONE
in
((introthm, elimthm), opt_neg_introthm)
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 ctxt' = ProofContext.init_global thy'
val rules as ((intro, elim), _) =
create_intro_elim_rule ctxt' mode definition mode_cname funT (Const (name, T))
in thy'
|> set_function_name Pred name mode mode_cname
|> add_predfun_data name mode (definition, rules)
|> 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, _) => member (op =) constr_consts name
| _ => false) end))
else false
(* MAJOR FIXME: prove_params should be simple
- different form of introrule for parameters ? *)
fun prove_param options ctxt nargs 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 ctxt name mode,
@{thm split_eta}, @{thm split_beta}, @{thm fst_conv},
@{thm snd_conv}, @{thm pair_collapse}, @{thm Product_Type.split_conv}]) 1
| Free _ =>
Subgoal.FOCUS_PREMS (fn {context = ctxt, params = params, prems, asms, concl, schematics} =>
let
val prems' = maps dest_conjunct_prem (take nargs prems)
in
MetaSimplifier.rewrite_goal_tac
(map (fn th => th RS @{thm sym} RS @{thm eq_reflection}) prems') 1
end) ctxt 1
| Abs _ => raise Fail "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 prove_param"
THEN (REPEAT_DETERM (atac 1))
THEN (EVERY (map2 (prove_param options ctxt nargs) ho_args param_derivations))
THEN REPEAT_DETERM (rtac @{thm refl} 1)
end
fun prove_expr options ctxt nargs (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 ctxt name mode
val param_derivations = param_derivations_of deriv
val ho_args = ho_args_of mode args
in
print_tac options "before intro rule:"
THEN rtac introrule 1
THEN print_tac options "after intro rule"
(* for the right assumption in first position *)
THEN rotate_tac premposition 1
THEN atac 1
THEN print_tac options "parameter goal"
(* work with parameter arguments *)
THEN (EVERY (map2 (prove_param options ctxt nargs) ho_args param_derivations))
THEN (REPEAT_DETERM (atac 1))
end
| (Free _, _) =>
print_tac options "proving parameter call.."
THEN Subgoal.FOCUS_PREMS (fn {context = ctxt, params, prems, asms, concl, schematics} =>
let
val param_prem = nth prems premposition
val (param, _) = strip_comb (HOLogic.dest_Trueprop (prop_of param_prem))
val prems' = maps dest_conjunct_prem (take nargs prems)
fun param_rewrite prem =
param = snd (HOLogic.dest_eq (HOLogic.dest_Trueprop (prop_of prem)))
val SOME rew_eq = find_first param_rewrite prems'
val param_prem' = MetaSimplifier.rewrite_rule
(map (fn th => th RS @{thm eq_reflection})
[rew_eq RS @{thm sym}, @{thm split_beta}, @{thm fst_conv}, @{thm snd_conv}])
param_prem
in
rtac param_prem' 1
end) ctxt 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 ctxt 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 ctxt out_ts =
let
val thy = ProofContext.theory_of ctxt
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 fold (union Thm.eq_thm) (case_rewrites :: map get_case_rewrite (snd (strip_comb t))) [] end
else []
val simprules = insert Thm.eq_thm @{thm "unit.cases"} (insert Thm.eq_thm @{thm "prod.cases"}
(fold (union Thm.eq_thm) (map get_case_rewrite out_ts) []))
(* replace TRY by determining if it necessary - are there equations when calling compile match? *)
in
(* make this simpset better! *)
asm_full_simp_tac (HOL_basic_ss' addsimps simprules) 1
THEN print_tac options "after prove_match:"
THEN (DETERM (TRY (EqSubst.eqsubst_tac ctxt [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 ctxt t =
let
fun preds_of t nameTs = case strip_comb t of
(f as Const (name, T), args) =>
if is_registered ctxt 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 ctxt 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 ctxt nargs mode (_, clauses) (ts, moded_ps) =
let
val (in_ts, clause_out_ts) = split_mode mode ts;
fun prove_prems out_ts [] =
(prove_match options ctxt 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 ctxt nargs 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 neg_intro_rule =
Option.map (fn name =>
the (predfun_neg_intro_of ctxt name mode)) name
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 applying not introduction rule"
THEN rotate_tac premposition 1
THEN etac (the neg_intro_rule) 1
THEN rotate_tac (~premposition) 1
THEN print_tac options "after applying not introduction rule"
THEN (EVERY (map2 (prove_param options ctxt nargs) params param_derivations))
THEN (REPEAT_DETERM (atac 1))
else
rtac @{thm not_predI'} 1
(* test: *)
THEN dtac @{thm sym} 1
THEN asm_full_simp_tac (HOL_basic_ss addsimps [@{thm not_False_eq_True}]) 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 ctxt t
THEN print_tac options "after sidecond:"
THEN prove_prems [] ps)
in (prove_match options ctxt 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 ctxt clauses preds 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 ctxt pred
in
REPEAT_DETERM (CHANGED (rewtac @{thm "split_paired_all"}))
THEN print_tac options "before applying elim rule"
THEN etac (predfun_elim_of ctxt pred mode) 1
THEN etac pred_case_rule 1
THEN print_tac options "after applying elim rule"
THEN (EVERY (map
(fn i => EVERY' (select_sup (length moded_clauses) i) i)
(1 upto (length moded_clauses))))
THEN (EVERY (map2 (prove_clause options ctxt nargs mode) clauses moded_clauses))
THEN print_tac options "proved one direction"
end;
(** Proof in the other direction **)
fun prove_match2 options ctxt out_ts =
let
val thy = ProofContext.theory_of ctxt
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)
val (_, ts) = strip_comb t
in
print_tac options ("Term " ^ (Syntax.string_of_term ctxt t) ^
"splitting with rules \n" ^ Display.string_of_thm ctxt (#split_asm info))
THEN TRY ((Splitter.split_asm_tac [#split_asm info] 1)
THEN (print_tac options "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 options ctxt 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 ctxt name mode)
:: @{thm "Product_Type.split_conv"}::[])) 1
| Free _ => all_tac
| _ => error "prove_param2: illegal parameter term"
in
print_tac options "before simplification in prove_args:"
THEN f_tac
THEN print_tac options "after simplification in prove_args"
THEN EVERY (map2 (prove_param2 options ctxt) ho_args param_derivations)
end
fun prove_expr2 options ctxt (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 options "prove_expr2-before"
THEN etac (predfun_elim_of ctxt name mode) 1
THEN print_tac options "prove_expr2"
THEN (EVERY (map2 (prove_param2 options ctxt) ho_args param_derivations))
THEN print_tac options "finished prove_expr2"
end
| _ => etac @{thm bindE} 1)
fun prove_sidecond2 options ctxt t = let
fun preds_of t nameTs = case strip_comb t of
(f as Const (name, T), args) =>
if is_registered ctxt 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 ctxt 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 options "after sidecond2 simplification"
end
fun prove_clause2 options ctxt pred mode (ts, ps) i =
let
val pred_intro_rule = nth (intros_of ctxt pred) (i - 1)
val (in_ts, clause_out_ts) = split_mode mode ts;
val split_ss = HOL_basic_ss' addsimps [@{thm split_eta}, @{thm split_beta},
@{thm fst_conv}, @{thm snd_conv}, @{thm pair_collapse}]
fun prove_prems2 out_ts [] =
print_tac options "before prove_match2 - last call:"
THEN prove_match2 options ctxt out_ts
THEN print_tac options "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 options "state before applying intro rule:"
THEN (rtac pred_intro_rule
(* How to handle equality correctly? *)
THEN_ALL_NEW (K (print_tac options "state before assumption matching")
THEN' (atac ORELSE' ((CHANGED o asm_full_simp_tac split_ss) THEN' (TRY o atac)))
THEN' (K (print_tac options "state after pre-simplification:"))
THEN' (K (print_tac options "state after assumption matching:")))) 1)
| 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 options ctxt (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 options "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 ctxt (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 options ctxt) 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 options ctxt t
THEN prove_prems2 [] ps)
in print_tac options "before prove_match2:"
THEN prove_match2 options ctxt out_ts
THEN print_tac options "after prove_match2:"
THEN rest_tac
end;
val prems_tac = prove_prems2 in_ts ps
in
print_tac options "starting prove_clause2"
THEN etac @{thm bindE} 1
THEN (etac @{thm singleE'} 1)
THEN (TRY (etac @{thm Pair_inject} 1))
THEN print_tac options "after singleE':"
THEN prems_tac
end;
fun prove_other_direction options ctxt 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 options ctxt 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 ctxt 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 pred (pol, mode) (moded_clauses, compiled_term) =
let
val ctxt = ProofContext.init_global 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 ctxt clauses preds pred mode moded_clauses
THEN print_tac options "proved one direction"
THEN prove_other_direction options ctxt 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 options comp_modifiers ctxt all_vs param_vs preds moded_clauses =
map_preds_modes (fn pred => compile_pred options comp_modifiers ctxt all_vs param_vs pred
(the (AList.lookup (op =) preds pred))) moded_clauses
fun prove options thy clauses preds moded_clauses compiled_terms =
map_preds_modes (prove_pred options thy clauses preds)
(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 ctxt 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 ctxt params t of
Prem t => Negprem t
| Negprem _ => error ("Double negation not allowed in premise: " ^
Syntax.string_of_term ctxt (c $ t))
| Sidecond t => Sidecond (c $ t))
| (c as Const (s, _), ts) =>
if is_registered ctxt s then Prem t else Sidecond t
| _ => Sidecond t)
fun prepare_intrs options ctxt prednames intros =
let
val thy = ProofContext.theory_of ctxt
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] ctxt
val preds = map dest_Const preds
val all_vs = terms_vs intrs
fun generate_modes s T =
if member (op =) (no_higher_order_predicate options) s then
all_smodes_of_typ T
else
all_modes_of_typ T
val all_modes =
map (fn (s, T) =>
(s, case proposed_modes options s of
SOME ms => ms
| NONE => generate_modes s T)) preds
val params =
case intrs of
[] =>
let
val T = snd (hd preds)
val paramTs =
ho_argsT_of_typ (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 :: _) =>
let
val (p, args) = strip_comb (HOLogic.dest_Trueprop (Logic.strip_imp_concl intr))
in
ho_args_of_typ (snd (dest_Const p)) args
end
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 ctxt 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, all_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_global 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 ctxt 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 ctxt 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 ctxt 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 ctxt 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 ctxt 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 * (bool * mode) list -> theory -> theory,
prove : options -> theory -> (string * (term list * indprem list) list) list -> (string * typ) list
-> moded_clause list pred_mode_table -> term pred_mode_table -> thm pred_mode_table,
add_code_equations : Proof.context -> (string * typ) list
-> (string * thm list) list -> (string * thm list) list,
comp_modifiers : Comp_Mod.comp_modifiers,
use_random : bool,
qname : bstring
}
fun add_equations_of steps mode_analysis_options options prednames thy =
let
fun dest_steps (Steps s) = s
val compilation = Comp_Mod.compilation (#comp_modifiers (dest_steps steps))
val ctxt = ProofContext.init_global thy
val _ = print_step options
("Starting predicate compiler (compilation: " ^ string_of_compilation compilation
^ ") 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 _ =
if show_intermediate_results options then
tracing (commas (map (Display.string_of_thm ctxt) (maps (intros_of ctxt) prednames)))
else ()
val (preds, all_vs, param_vs, all_modes, clauses) =
prepare_intrs options ctxt prednames (maps (intros_of ctxt) prednames)
val _ = print_step options "Infering modes..."
val (lookup_mode, lookup_neg_mode, needs_random) = (modes_of compilation ctxt,
modes_of (negative_compilation_of compilation) ctxt, needs_random ctxt)
val ((moded_clauses, needs_random), errors) =
Output.cond_timeit (!Quickcheck.timing) "Infering modes"
(fn _ => infer_modes mode_analysis_options
options (lookup_mode, lookup_neg_mode, needs_random) ctxt preds all_modes param_vs clauses)
val thy' = fold (fn (s, ms) => set_needs_random s ms) needs_random 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 errors
val _ = print_modes options modes
val _ = print_step options "Defining executable functions..."
val thy'' =
Output.cond_timeit (!Quickcheck.timing) "Defining executable functions..."
(fn _ => fold (#define_functions (dest_steps steps) options preds) modes thy'
|> Theory.checkpoint)
val ctxt'' = ProofContext.init_global thy''
val _ = print_step options "Compiling equations..."
val compiled_terms =
Output.cond_timeit (!Quickcheck.timing) "Compiling equations...." (fn _ =>
compile_preds options
(#comp_modifiers (dest_steps steps)) ctxt'' all_vs param_vs preds moded_clauses)
val _ = print_compiled_terms options ctxt'' compiled_terms
val _ = print_step options "Proving equations..."
val result_thms =
Output.cond_timeit (!Quickcheck.timing) "Proving equations...." (fn _ =>
#prove (dest_steps steps) options thy'' clauses preds moded_clauses compiled_terms)
val result_thms' = #add_code_equations (dest_steps steps) ctxt'' 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''' =
Output.cond_timeit (!Quickcheck.timing) "Setting code equations...." (fn _ =>
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 ctxt = ProofContext.init_global thy
val thy' = thy
|> PredData.map (fold (extend (fetch_pred_data ctxt) (depending_preds_of ctxt)) 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 (ProofContext.init_global thy)) preds) then
let
val mode_analysis_options = {use_random = #use_random (dest_steps steps),
reorder_premises =
not (no_topmost_reordering options andalso not (null (inter (op =) preds names))),
infer_pos_and_neg_modes = #use_random (dest_steps steps)}
in
add_equations_of steps mode_analysis_options options preds thy
end
else thy)
scc thy' |> Theory.checkpoint
in thy'' end
val add_equations = gen_add_equations
(Steps {
define_functions =
fn options => fn preds => fn (s, modes) =>
create_definitions
options preds (s, map_filter (fn (true, m) => SOME m | _ => NONE) modes),
prove = prove,
add_code_equations = add_code_equations,
comp_modifiers = predicate_comp_modifiers,
use_random = false,
qname = "equation"})
val add_depth_limited_equations = gen_add_equations
(Steps {
define_functions =
fn options => fn preds => fn (s, modes) =>
define_functions depth_limited_comp_modifiers PredicateCompFuns.compfuns
options preds (s, map_filter (fn (true, m) => SOME m | _ => NONE) modes),
prove = prove_by_skip,
add_code_equations = K (K I),
comp_modifiers = depth_limited_comp_modifiers,
use_random = false,
qname = "depth_limited_equation"})
val add_annotated_equations = gen_add_equations
(Steps {
define_functions =
fn options => fn preds => fn (s, modes) =>
define_functions annotated_comp_modifiers PredicateCompFuns.compfuns options preds
(s, map_filter (fn (true, m) => SOME m | _ => NONE) modes),
prove = prove_by_skip,
add_code_equations = K (K I),
comp_modifiers = annotated_comp_modifiers,
use_random = false,
qname = "annotated_equation"})
val add_random_equations = gen_add_equations
(Steps {
define_functions =
fn options => fn preds => fn (s, modes) =>
define_functions random_comp_modifiers PredicateCompFuns.compfuns options preds
(s, map_filter (fn (true, m) => SOME m | _ => NONE) modes),
comp_modifiers = random_comp_modifiers,
prove = prove_by_skip,
add_code_equations = K (K I),
use_random = true,
qname = "random_equation"})
val add_depth_limited_random_equations = gen_add_equations
(Steps {
define_functions =
fn options => fn preds => fn (s, modes) =>
define_functions depth_limited_random_comp_modifiers PredicateCompFuns.compfuns options preds
(s, map_filter (fn (true, m) => SOME m | _ => NONE) modes),
comp_modifiers = depth_limited_random_comp_modifiers,
prove = prove_by_skip,
add_code_equations = K (K I),
use_random = true,
qname = "depth_limited_random_equation"})
val add_dseq_equations = gen_add_equations
(Steps {
define_functions =
fn options => fn preds => fn (s, modes) =>
define_functions dseq_comp_modifiers DSequence_CompFuns.compfuns
options preds (s, map_filter (fn (true, m) => SOME m | _ => NONE) modes),
prove = prove_by_skip,
add_code_equations = K (K I),
comp_modifiers = dseq_comp_modifiers,
use_random = false,
qname = "dseq_equation"})
val add_random_dseq_equations = gen_add_equations
(Steps {
define_functions =
fn options => fn preds => fn (s, modes) =>
let
val pos_modes = map_filter (fn (true, m) => SOME m | _ => NONE) modes
val neg_modes = map_filter (fn (false, m) => SOME m | _ => NONE) modes
in define_functions pos_random_dseq_comp_modifiers Random_Sequence_CompFuns.compfuns
options preds (s, pos_modes)
#> define_functions neg_random_dseq_comp_modifiers Random_Sequence_CompFuns.compfuns
options preds (s, neg_modes)
end,
prove = prove_by_skip,
add_code_equations = K (K I),
comp_modifiers = pos_random_dseq_comp_modifiers,
use_random = true,
qname = "random_dseq_equation"})
val add_new_random_dseq_equations = gen_add_equations
(Steps {
define_functions =
fn options => fn preds => fn (s, modes) =>
let
val pos_modes = map_filter (fn (true, m) => SOME m | _ => NONE) modes
val neg_modes = map_filter (fn (false, m) => SOME m | _ => NONE) modes
in define_functions new_pos_random_dseq_comp_modifiers New_Pos_Random_Sequence_CompFuns.compfuns
options preds (s, pos_modes)
#> define_functions new_neg_random_dseq_comp_modifiers New_Neg_Random_Sequence_CompFuns.compfuns
options preds (s, neg_modes)
end,
prove = prove_by_skip,
add_code_equations = K (K I),
comp_modifiers = new_pos_random_dseq_comp_modifiers,
use_random = true,
qname = "new_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 *)
(* FIXME ... this is important to avoid changing the background theory below *)
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 ctxt = ProofContext.init_global thy
val lthy' = Local_Theory.background_theory (PredData.map
(extend (fetch_pred_data ctxt) (depending_preds_of ctxt) const)) lthy
val thy' = ProofContext.theory_of lthy'
val ctxt' = ProofContext.init_global thy'
val preds = Graph.all_succs (PredData.get thy') [const] |> filter_out (has_elim ctxt')
fun mk_cases const =
let
val T = Sign.the_const_type thy' const
val pred = Const (const, T)
val intros = intros_of ctxt' 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_global (ProofContext.theory_of goal_ctxt)) (map the_single thms)
in
goal_ctxt |> Local_Theory.background_theory (fold set_elim global_thms #>
((case compilation options of
Pred => add_equations
| DSeq => add_dseq_equations
| Pos_Random_DSeq => add_random_dseq_equations
| Depth_Limited => add_depth_limited_equations
| Random => add_random_equations
| Depth_Limited_Random => add_depth_limited_random_equations
| New_Pos_Random_DSeq => add_new_random_dseq_equations
| compilation => error ("Compilation not supported")
) options [const]))
end
in
Proof.theorem 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 *)
structure Pred_Result = Proof_Data (
type T = unit -> term Predicate.pred
fun init _ () = error "Pred_Result"
);
val put_pred_result = Pred_Result.put;
structure Pred_Random_Result = Proof_Data (
type T = unit -> int * int -> term Predicate.pred * (int * int)
fun init _ () = error "Pred_Random_Result"
);
val put_pred_random_result = Pred_Random_Result.put;
structure Dseq_Result = Proof_Data (
type T = unit -> term DSequence.dseq
fun init _ () = error "Dseq_Result"
);
val put_dseq_result = Dseq_Result.put;
structure Dseq_Random_Result = Proof_Data (
type T = unit -> int -> int -> int * int -> term DSequence.dseq * (int * int)
fun init _ () = error "Dseq_Random_Result"
);
val put_dseq_random_result = Dseq_Random_Result.put;
structure Lseq_Random_Result = Proof_Data (
type T = unit -> int -> int -> int * int -> int -> term Lazy_Sequence.lazy_sequence
fun init _ () = error "Lseq_Random_Result"
);
val put_lseq_random_result = Lseq_Random_Result.put;
structure Lseq_Random_Stats_Result = Proof_Data (
type T = unit -> int -> int -> int * int -> int -> (term * int) Lazy_Sequence.lazy_sequence
fun init _ () = error "Lseq_Random_Stats_Result"
);
val put_lseq_random_stats_result = Lseq_Random_Stats_Result.put;
(*FIXME turn this into an LCF-guarded preprocessor for comprehensions*)
fun analyze_compr ctxt 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 ctxt 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) =
case strip_comb body of
(Const (name, T), all_args) => (Const (name, T), all_args)
| (head, _) => error ("Not a constant: " ^ Syntax.string_of_term ctxt head)
in
if defined_functions compilation ctxt name then
let
fun extract_mode (Const (@{const_name 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 (Input, Pair (m1, m2)) =
instance_of (Input, m1) andalso instance_of (Input, m2)
| instance_of (Output, Pair (m1, m2)) =
instance_of (Output, m1) andalso instance_of (Output, m2)
| instance_of _ = false
in forall instance_of (strip_fun_mode m1 ~~ strip_fun_mode m2) end
val derivs = all_derivations_of ctxt (all_modes_of ctxt) [] 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 ctxt t_compr)
| [d] => d
| d :: _ :: _ => (warning ("Multiple modes possible for comprehension "
^ Syntax.string_of_term ctxt t_compr); d);
val (_, outargs) = split_mode (head_mode_of deriv) all_args
val additional_arguments =
case compilation of
Pred => []
| Random => map (HOLogic.mk_number @{typ "code_numeral"}) arguments @
[@{term "(1, 1) :: code_numeral * code_numeral"}]
| Annotated => []
| Depth_Limited => [HOLogic.mk_number @{typ "code_numeral"} (hd arguments)]
| Depth_Limited_Random => map (HOLogic.mk_number @{typ "code_numeral"}) arguments @
[@{term "(1, 1) :: code_numeral * code_numeral"}]
| DSeq => []
| Pos_Random_DSeq => []
| New_Pos_Random_DSeq => []
val comp_modifiers =
case compilation of
Pred => predicate_comp_modifiers
| Random => random_comp_modifiers
| Depth_Limited => depth_limited_comp_modifiers
| Depth_Limited_Random => depth_limited_random_comp_modifiers
(*| Annotated => annotated_comp_modifiers*)
| DSeq => dseq_comp_modifiers
| Pos_Random_DSeq => pos_random_dseq_comp_modifiers
| New_Pos_Random_DSeq => new_pos_random_dseq_comp_modifiers
val t_pred = compile_expr comp_modifiers ctxt
(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 ctxt stats param_user_modes (options as (compilation, arguments)) k t_compr =
let
fun count xs x =
let
fun count' i [] = i
| count' i (x' :: xs) = if x = x' then count' (i + 1) xs else count' i xs
in count' 0 xs end
fun accumulate xs = map (fn x => (x, count xs x)) (sort int_ord (distinct (op =) xs))
val compfuns =
case compilation of
Random => PredicateCompFuns.compfuns
| DSeq => DSequence_CompFuns.compfuns
| Pos_Random_DSeq => Random_Sequence_CompFuns.compfuns
| New_Pos_Random_DSeq => New_Pos_Random_Sequence_CompFuns.compfuns
| _ => PredicateCompFuns.compfuns
val t = analyze_compr ctxt compfuns param_user_modes options t_compr;
val T = dest_predT compfuns (fastype_of t);
val t' =
if stats andalso compilation = New_Pos_Random_DSeq then
mk_map compfuns T (HOLogic.mk_prodT (HOLogic.termT, @{typ code_numeral}))
(absdummy (T, HOLogic.mk_prod (HOLogic.term_of_const T $ Bound 0,
@{term Code_Numeral.of_nat} $ (HOLogic.size_const T $ Bound 0)))) t
else
mk_map compfuns T HOLogic.termT (HOLogic.term_of_const T) t
val thy = ProofContext.theory_of ctxt
val (ts, statistics) =
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))*)
Pos_Random_DSeq =>
let
val [nrandom, size, depth] = arguments
in
rpair NONE (fst (DSequence.yieldn k
(Code_Runtime.eval NONE (Dseq_Random_Result.get, put_dseq_random_result, "Predicate_Compile_Core.put_dseq_random_result")
(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 =>
rpair NONE (fst (DSequence.yieldn k
(Code_Runtime.eval NONE (Dseq_Result.get, put_dseq_result, "Predicate_Compile_Core.put_dseq_result")
DSequence.map thy t' []) (the_single arguments) true))
| New_Pos_Random_DSeq =>
let
val [nrandom, size, depth] = arguments
val seed = Random_Engine.next_seed ()
in
if stats then
apsnd (SOME o accumulate) (split_list
(fst (Lazy_Sequence.yieldn k
(Code_Runtime.eval NONE
(Lseq_Random_Stats_Result.get, put_lseq_random_stats_result, "Predicate_Compile_Core.put_lseq_random_stats_result")
(fn proc => fn g => fn nrandom => fn size => fn s => fn depth => g nrandom size s depth
|> Lazy_Sequence.mapa (apfst proc))
thy t' [] nrandom size seed depth))))
else rpair NONE
(fst (Lazy_Sequence.yieldn k
(Code_Runtime.eval NONE
(Lseq_Random_Result.get, put_lseq_random_result, "Predicate_Compile_Core.put_lseq_random_result")
(fn proc => fn g => fn nrandom => fn size => fn s => fn depth => g nrandom size s depth
|> Lazy_Sequence.mapa proc)
thy t' [] nrandom size seed depth)))
end
| _ =>
rpair NONE (fst (Predicate.yieldn k
(Code_Runtime.eval NONE (Pred_Result.get, put_pred_result, "Predicate_Compile_Core.put_pred_result")
Predicate.map thy t' [])))
in ((T, ts), statistics) end;
fun values ctxt param_user_modes ((raw_expected, stats), comp_options) k t_compr =
let
val ((T, ts), statistics) = eval ctxt stats 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_abbrev Set.union}, setT --> setT --> setT) $ elems $ cont, statistics)
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', stats) = values ctxt param_user_modes options k t
val ty' = Term.type_of t'
val ctxt' = Variable.auto_fixes t' ctxt
val pretty_stat =
case stats of
NONE => []
| SOME xs =>
let
val total = fold (curry (op +)) (map snd xs) 0
fun pretty_entry (s, n) =
[Pretty.str "size", Pretty.brk 1,
Pretty.str (string_of_int s), Pretty.str ":", Pretty.brk 1,
Pretty.str (string_of_int n), Pretty.fbrk]
in
[Pretty.fbrk, Pretty.str "Statistics:", Pretty.fbrk,
Pretty.str "total:", Pretty.brk 1, Pretty.str (string_of_int total), Pretty.fbrk]
@ maps pretty_entry xs
end
val p = Print_Mode.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')]
@ pretty_stat)) ();
in Pretty.writeln p end;
end;