# HG changeset patch # User bulwahn # Date 1253715612 -7200 # Node ID 09546e6542224fbf29a80686d0c1d88a3f1b1b96 # Parent fd96d5f49d59dfca317c4c772c8959743ef1bae5 moved predicate compiler to Tools diff -r fd96d5f49d59 -r 09546e654222 src/HOL/IsaMakefile --- a/src/HOL/IsaMakefile Wed Sep 23 16:20:12 2009 +0200 +++ b/src/HOL/IsaMakefile Wed Sep 23 16:20:12 2009 +0200 @@ -6,7 +6,7 @@ default: HOL generate: HOL-Generate-HOL HOL-Generate-HOLLight -images: HOL HOL-Base HOL-Plain HOL-Main HOL-Algebra HOL-Nominal HOL-NSA HOL-Word TLA HOL4 HOL-MicroJava +images: HOL HOL-Base HOL-Plain HOL-Main HOL-Algebra HOL-Nominal HOL-NSA HOL-Word TLA HOL4 #Note: keep targets sorted (except for HOL-Library and HOL-ex) test: \ @@ -909,7 +909,7 @@ ex/Sudoku.thy ex/Tarski.thy \ ex/Termination.thy ex/Transfer_Ex.thy ex/Unification.thy ex/document/root.bib \ ex/document/root.tex ex/set.thy ex/svc_funcs.ML ex/svc_test.thy \ - ex/Predicate_Compile.thy ex/predicate_compile.ML ex/Predicate_Compile_ex.thy + ex/Predicate_Compile.thy Tools/Predicate_Compile/predicate_compile_core.ML ex/Predicate_Compile_ex.thy @$(ISABELLE_TOOL) usedir $(OUT)/HOL ex diff -r fd96d5f49d59 -r 09546e654222 src/HOL/Tools/Predicate_Compile/predicate_compile_core.ML --- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/src/HOL/Tools/Predicate_Compile/predicate_compile_core.ML Wed Sep 23 16:20:12 2009 +0200 @@ -0,0 +1,2400 @@ +(* Author: Lukas Bulwahn, TU Muenchen + +(Prototype of) A compiler from predicates specified by intro/elim rules +to equations. +*) + +signature PREDICATE_COMPILE_CORE = +sig + type smode = (int * int list option) list + type mode = smode option list * smode + datatype tmode = Mode of mode * smode * tmode option list; + (*val add_equations_of: bool -> string list -> theory -> theory *) + val register_predicate : (thm list * thm * int) -> theory -> theory + val is_registered : theory -> string -> bool + (* val fetch_pred_data : theory -> string -> (thm list * thm * int) *) + val predfun_intro_of: theory -> string -> mode -> thm + val predfun_elim_of: theory -> string -> mode -> thm + val strip_intro_concl: int -> term -> term * (term list * term list) + val predfun_name_of: theory -> string -> mode -> string + val all_preds_of : theory -> string list + val modes_of: theory -> string -> mode list + val string_of_mode : mode -> string + val intros_of: theory -> string -> thm list + val nparams_of: theory -> string -> int + val add_intro: thm -> theory -> theory + val set_elim: thm -> theory -> theory + val setup: theory -> theory + val code_pred: string -> Proof.context -> Proof.state + val code_pred_cmd: string -> Proof.context -> Proof.state + val print_stored_rules: theory -> unit + val print_all_modes: theory -> unit + val do_proofs: bool ref + val mk_casesrule : Proof.context -> int -> thm list -> term + val analyze_compr: theory -> term -> term + val eval_ref: (unit -> term Predicate.pred) option ref + val add_equations : string list -> theory -> theory + val code_pred_intros_attrib : attribute + (* used by Quickcheck_Generator *) + (*val funT_of : mode -> typ -> typ + val mk_if_pred : term -> term + val mk_Eval : term * term -> term*) + val mk_tupleT : typ list -> typ +(* val mk_predT : typ -> typ *) + (* temporary for testing of the compilation *) + datatype indprem = Prem of term list * term | Negprem of term list * term | Sidecond of term | + GeneratorPrem of term list * term | Generator of (string * typ); + (* val prepare_intrs: theory -> string list -> + (string * typ) list * int * string list * string list * (string * mode list) list * + (string * (term list * indprem list) list) list * (string * (int option list * int)) list*) + datatype compilation_funs = CompilationFuns of { + mk_predT : typ -> typ, + dest_predT : typ -> typ, + mk_bot : typ -> term, + mk_single : term -> term, + mk_bind : term * term -> term, + mk_sup : term * term -> term, + mk_if : term -> term, + mk_not : term -> term, + mk_map : typ -> typ -> term -> term -> term, + lift_pred : term -> term + }; + type moded_clause = term list * (indprem * tmode) list + type 'a pred_mode_table = (string * (mode * 'a) list) list + val infer_modes : theory -> (string * mode list) list + -> (string * mode list) list + -> string list + -> (string * (term list * indprem list) list) list + -> (moded_clause list) pred_mode_table + val infer_modes_with_generator : theory -> (string * mode list) list + -> (string * mode list) list + -> string list + -> (string * (term list * indprem list) list) list + -> (moded_clause list) pred_mode_table + (*val compile_preds : theory -> compilation_funs -> string list -> string list + -> (string * typ) list -> (moded_clause list) pred_mode_table -> term pred_mode_table + val rpred_create_definitions :(string * typ) list -> string * mode list + -> theory -> theory + val split_smode : int list -> term list -> (term list * term list) *) + val print_moded_clauses : + theory -> (moded_clause list) pred_mode_table -> unit + val print_compiled_terms : theory -> term pred_mode_table -> unit + (*val rpred_prove_preds : theory -> term pred_mode_table -> thm pred_mode_table*) + val rpred_compfuns : compilation_funs + val dest_funT : typ -> typ * typ + (* val depending_preds_of : theory -> thm list -> string list *) + val add_quickcheck_equations : string list -> theory -> theory + val add_sizelim_equations : string list -> theory -> theory + val is_inductive_predicate : theory -> string -> bool + val terms_vs : term list -> string list + val subsets : int -> int -> int list list + val check_mode_clause : bool -> theory -> string list -> + (string * mode list) list -> (string * mode list) list -> mode -> (term list * indprem list) + -> (term list * (indprem * tmode) list) option + val string_of_moded_prem : theory -> (indprem * tmode) -> string + val all_modes_of : theory -> (string * mode list) list + val all_generator_modes_of : theory -> (string * mode list) list + val compile_clause : compilation_funs -> term option -> (term list -> term) -> + theory -> string list -> string list -> mode -> term -> moded_clause -> term + val preprocess_intro : theory -> thm -> thm + val is_constrt : theory -> term -> bool + val is_predT : typ -> bool + val guess_nparams : typ -> int + val cprods_subset : 'a list list -> 'a list list +end; + +structure Predicate_Compile_Core : PREDICATE_COMPILE_CORE = +struct + +(** auxiliary **) + +(* debug stuff *) + +fun tracing s = (if ! Toplevel.debug then Output.tracing s else ()); + +fun print_tac s = Seq.single; (*Tactical.print_tac s;*) (* (if ! Toplevel.debug then Tactical.print_tac s else Seq.single); *) +fun debug_tac msg = Seq.single; (* (fn st => (Output.tracing msg; Seq.single st)); *) + +val do_proofs = ref true; + +fun mycheat_tac thy i st = + (Tactic.rtac (SkipProof.make_thm thy (Var (("A", 0), propT))) i) st + +fun remove_last_goal thy st = + (Tactic.rtac (SkipProof.make_thm thy (Var (("A", 0), propT))) (nprems_of st)) st + +(* reference to preprocessing of InductiveSet package *) + +val ind_set_codegen_preproc = Inductive_Set.codegen_preproc; + +(** fundamentals **) + +(* syntactic operations *) + +fun mk_eq (x, xs) = + let fun mk_eqs _ [] = [] + | mk_eqs a (b::cs) = + HOLogic.mk_eq (Free (a, fastype_of b), b) :: mk_eqs a cs + in mk_eqs x xs end; + +fun mk_tupleT [] = HOLogic.unitT + | mk_tupleT Ts = foldr1 HOLogic.mk_prodT Ts; + +fun dest_tupleT (Type (@{type_name Product_Type.unit}, [])) = [] + | dest_tupleT (Type (@{type_name "*"}, [T1, T2])) = T1 :: (dest_tupleT T2) + | dest_tupleT t = [t] + +fun mk_tuple [] = HOLogic.unit + | mk_tuple ts = foldr1 HOLogic.mk_prod ts; + +fun dest_tuple (Const (@{const_name Product_Type.Unity}, _)) = [] + | dest_tuple (Const (@{const_name Pair}, _) $ t1 $ t2) = t1 :: (dest_tuple t2) + | dest_tuple t = [t] + +fun mk_scomp (t, u) = + let + val T = fastype_of t + val U = fastype_of u + val [A] = binder_types T + val D = body_type U + in + Const (@{const_name "scomp"}, T --> U --> A --> D) $ t $ u + end; + +fun dest_funT (Type ("fun",[S, T])) = (S, T) + | dest_funT T = raise TYPE ("dest_funT", [T], []) + +fun mk_fun_comp (t, u) = + let + val (_, B) = dest_funT (fastype_of t) + val (C, A) = dest_funT (fastype_of u) + in + Const(@{const_name "Fun.comp"}, (A --> B) --> (C --> A) --> C --> B) $ t $ u + end; + +fun dest_randomT (Type ("fun", [@{typ Random.seed}, + Type ("*", [Type ("*", [T, @{typ "unit => Code_Eval.term"}]) ,@{typ Random.seed}])])) = T + | dest_randomT T = raise TYPE ("dest_randomT", [T], []) + +(* destruction of intro rules *) + +(* FIXME: look for other place where this functionality was used before *) +fun strip_intro_concl nparams intro = let + val _ $ u = Logic.strip_imp_concl intro + val (pred, all_args) = strip_comb u + val (params, args) = chop nparams all_args +in (pred, (params, args)) end + +(** data structures **) + +type smode = (int * int list option) list; +type mode = smode option list * smode; +datatype tmode = Mode of mode * smode * tmode option list; + +fun gen_split_smode (mk_tuple, strip_tuple) smode ts = + let + fun split_tuple' _ _ [] = ([], []) + | split_tuple' is i (t::ts) = + (if i mem is then apfst else apsnd) (cons t) + (split_tuple' is (i+1) ts) + fun split_tuple is t = split_tuple' is 1 (strip_tuple t) + fun split_smode' _ _ [] = ([], []) + | split_smode' smode i (t::ts) = + (if i mem (map fst smode) then + case (the (AList.lookup (op =) smode i)) of + NONE => apfst (cons t) + | SOME is => + let + val (ts1, ts2) = split_tuple is t + fun cons_tuple ts = if null ts then I else cons (mk_tuple ts) + in (apfst (cons_tuple ts1)) o (apsnd (cons_tuple ts2)) end + else apsnd (cons t)) + (split_smode' smode (i+1) ts) + in split_smode' smode 1 ts end + +val split_smode = gen_split_smode (HOLogic.mk_tuple, HOLogic.strip_tuple) +val split_smodeT = gen_split_smode (HOLogic.mk_tupleT, HOLogic.strip_tupleT) + +fun gen_split_mode split_smode (iss, is) ts = + let + val (t1, t2) = chop (length iss) ts + in (t1, split_smode is t2) end + +val split_mode = gen_split_mode split_smode +val split_modeT = gen_split_mode split_smodeT + +fun string_of_smode js = + commas (map + (fn (i, is) => + string_of_int i ^ (case is of NONE => "" + | SOME is => "p" ^ enclose "[" "]" (commas (map string_of_int is)))) js) + +fun string_of_mode (iss, is) = space_implode " -> " (map + (fn NONE => "X" + | SOME js => enclose "[" "]" (string_of_smode js)) + (iss @ [SOME is])); + +fun string_of_tmode (Mode (predmode, termmode, param_modes)) = + "predmode: " ^ (string_of_mode predmode) ^ + (if null param_modes then "" else + "; " ^ "params: " ^ commas (map (the_default "NONE" o Option.map string_of_tmode) param_modes)) + +datatype indprem = Prem of term list * term | Negprem of term list * term | Sidecond of term | + GeneratorPrem of term list * term | Generator of (string * typ); + +type moded_clause = term list * (indprem * tmode) list +type 'a pred_mode_table = (string * (mode * 'a) list) list + +datatype predfun_data = PredfunData of { + name : string, + definition : thm, + intro : thm, + elim : thm +}; + +fun rep_predfun_data (PredfunData data) = data; +fun mk_predfun_data (name, definition, intro, elim) = + PredfunData {name = name, definition = definition, intro = intro, elim = elim} + +datatype function_data = FunctionData of { + name : string, + equation : thm option (* is not used at all? *) +}; + +fun rep_function_data (FunctionData data) = data; +fun mk_function_data (name, equation) = + FunctionData {name = name, equation = equation} + +datatype pred_data = PredData of { + intros : thm list, + elim : thm option, + nparams : int, + functions : (mode * predfun_data) list, + generators : (mode * function_data) list, + sizelim_functions : (mode * function_data) list +}; + +fun rep_pred_data (PredData data) = data; +fun mk_pred_data ((intros, elim, nparams), (functions, generators, sizelim_functions)) = + PredData {intros = intros, elim = elim, nparams = nparams, + functions = functions, generators = generators, sizelim_functions = sizelim_functions} +fun map_pred_data f (PredData {intros, elim, nparams, functions, generators, sizelim_functions}) = + mk_pred_data (f ((intros, elim, nparams), (functions, generators, sizelim_functions))) + +fun eq_option eq (NONE, NONE) = true + | eq_option eq (SOME x, SOME y) = eq (x, y) + | eq_option eq _ = false + +fun eq_pred_data (PredData d1, PredData d2) = + eq_list (Thm.eq_thm) (#intros d1, #intros d2) andalso + eq_option (Thm.eq_thm) (#elim d1, #elim d2) andalso + #nparams d1 = #nparams d2 + +structure PredData = TheoryDataFun +( + type T = pred_data Graph.T; + val empty = Graph.empty; + val copy = I; + val extend = I; + fun merge _ = Graph.merge eq_pred_data; +); + +(* queries *) + +fun lookup_pred_data thy name = + Option.map rep_pred_data (try (Graph.get_node (PredData.get thy)) name) + +fun the_pred_data thy name = case lookup_pred_data thy name + of NONE => error ("No such predicate " ^ quote name) + | SOME data => data; + +val is_registered = is_some oo lookup_pred_data + +val all_preds_of = Graph.keys o PredData.get + +fun intros_of thy = map (Thm.transfer thy) o #intros o the_pred_data thy + +fun the_elim_of thy name = case #elim (the_pred_data thy name) + of NONE => error ("No elimination rule for predicate " ^ quote name) + | SOME thm => Thm.transfer thy thm + +val has_elim = is_some o #elim oo the_pred_data; + +val nparams_of = #nparams oo the_pred_data + +val modes_of = (map fst) o #functions oo the_pred_data + +fun all_modes_of thy = map (fn name => (name, modes_of thy name)) (all_preds_of thy) + +val is_compiled = not o null o #functions oo the_pred_data + +fun lookup_predfun_data thy name mode = + Option.map rep_predfun_data (AList.lookup (op =) + (#functions (the_pred_data thy name)) mode) + +fun the_predfun_data thy name mode = case lookup_predfun_data thy name mode + of NONE => error ("No function defined for mode " ^ string_of_mode mode ^ " of predicate " ^ name) + | SOME data => data; + +val predfun_name_of = #name ooo the_predfun_data + +val predfun_definition_of = #definition ooo the_predfun_data + +val predfun_intro_of = #intro ooo the_predfun_data + +val predfun_elim_of = #elim ooo the_predfun_data + +fun lookup_generator_data thy name mode = + Option.map rep_function_data (AList.lookup (op =) + (#generators (the_pred_data thy name)) mode) + +fun the_generator_data thy name mode = case lookup_generator_data thy name mode + of NONE => error ("No generator defined for mode " ^ string_of_mode mode ^ " of predicate " ^ name) + | SOME data => data + +val generator_name_of = #name ooo the_generator_data + +val generator_modes_of = (map fst) o #generators oo the_pred_data + +fun all_generator_modes_of thy = + map (fn name => (name, generator_modes_of thy name)) (all_preds_of thy) + +fun lookup_sizelim_function_data thy name mode = + Option.map rep_function_data (AList.lookup (op =) + (#sizelim_functions (the_pred_data thy name)) mode) + +fun the_sizelim_function_data thy name mode = case lookup_sizelim_function_data thy name mode + of NONE => error ("No size-limited function defined for mode " ^ string_of_mode mode + ^ " of predicate " ^ name) + | SOME data => data + +val sizelim_function_name_of = #name ooo the_sizelim_function_data + +(*val generator_modes_of = (map fst) o #generators oo the_pred_data*) + +(* diagnostic display functions *) + +fun print_modes modes = Output.tracing ("Inferred modes:\n" ^ + cat_lines (map (fn (s, ms) => s ^ ": " ^ commas (map + string_of_mode ms)) modes)); + +fun print_pred_mode_table string_of_entry thy pred_mode_table = + let + fun print_mode pred (mode, entry) = "mode : " ^ (string_of_mode mode) + ^ (string_of_entry pred mode entry) + fun print_pred (pred, modes) = + "predicate " ^ pred ^ ": " ^ cat_lines (map (print_mode pred) modes) + val _ = Output.tracing (cat_lines (map print_pred pred_mode_table)) + in () end; + +fun string_of_moded_prem thy (Prem (ts, p), tmode) = + (Syntax.string_of_term_global thy (list_comb (p, ts))) ^ + "(" ^ (string_of_tmode tmode) ^ ")" + | string_of_moded_prem thy (GeneratorPrem (ts, p), Mode (predmode, is, _)) = + (Syntax.string_of_term_global thy (list_comb (p, ts))) ^ + "(generator_mode: " ^ (string_of_mode predmode) ^ ")" + | string_of_moded_prem thy (Generator (v, T), _) = + "Generator for " ^ v ^ " of Type " ^ (Syntax.string_of_typ_global thy T) + | string_of_moded_prem thy (Negprem (ts, p), Mode (_, is, _)) = + (Syntax.string_of_term_global thy (list_comb (p, ts))) ^ + "(negative mode: " ^ string_of_smode is ^ ")" + | string_of_moded_prem thy (Sidecond t, Mode (_, is, _)) = + (Syntax.string_of_term_global thy t) ^ + "(sidecond mode: " ^ string_of_smode is ^ ")" + | string_of_moded_prem _ _ = error "string_of_moded_prem: unimplemented" + +fun print_moded_clauses thy = + let + fun string_of_clause pred mode clauses = + cat_lines (map (fn (ts, prems) => (space_implode " --> " + (map (string_of_moded_prem thy) prems)) ^ " --> " ^ pred ^ " " + ^ (space_implode " " (map (Syntax.string_of_term_global thy) ts))) clauses) + in print_pred_mode_table string_of_clause thy end; + +fun print_compiled_terms thy = + print_pred_mode_table (fn _ => fn _ => Syntax.string_of_term_global thy) thy + +fun print_stored_rules thy = + let + val preds = (Graph.keys o PredData.get) thy + fun print pred () = let + val _ = writeln ("predicate: " ^ pred) + val _ = writeln ("number of parameters: " ^ string_of_int (nparams_of thy pred)) + val _ = writeln ("introrules: ") + val _ = fold (fn thm => fn u => writeln (Display.string_of_thm_global thy thm)) + (rev (intros_of thy pred)) () + in + if (has_elim thy pred) then + writeln ("elimrule: " ^ Display.string_of_thm_global thy (the_elim_of thy pred)) + else + writeln ("no elimrule defined") + end + in + fold print preds () + end; + +fun print_all_modes thy = + let + val _ = writeln ("Inferred modes:") + fun print (pred, modes) u = + let + val _ = writeln ("predicate: " ^ pred) + val _ = writeln ("modes: " ^ (commas (map string_of_mode modes))) + in u end + in + fold print (all_modes_of thy) () + end + +(** preprocessing rules **) + +fun imp_prems_conv cv ct = + case Thm.term_of ct of + Const ("==>", _) $ _ $ _ => Conv.combination_conv (Conv.arg_conv cv) (imp_prems_conv cv) ct + | _ => Conv.all_conv ct + +fun Trueprop_conv cv ct = + case Thm.term_of ct of + Const ("Trueprop", _) $ _ => Conv.arg_conv cv ct + | _ => error "Trueprop_conv" + +fun preprocess_intro thy rule = + Conv.fconv_rule + (imp_prems_conv + (Trueprop_conv (Conv.try_conv (Conv.rewr_conv (Thm.symmetric @{thm Predicate.eq_is_eq}))))) + (Thm.transfer thy rule) + +fun preprocess_elim thy nparams elimrule = + let + val _ = Output.tracing ("Preprocessing elimination rule " + ^ (Display.string_of_thm_global thy elimrule)) + fun replace_eqs (Const ("Trueprop", _) $ (Const ("op =", T) $ lhs $ rhs)) = + HOLogic.mk_Trueprop (Const (@{const_name Predicate.eq}, T) $ lhs $ rhs) + | replace_eqs t = t + val prems = Thm.prems_of elimrule + val nargs = length (snd (strip_comb (HOLogic.dest_Trueprop (hd prems)))) - nparams + fun preprocess_case t = + let + val params = Logic.strip_params t + val (assums1, assums2) = chop nargs (Logic.strip_assums_hyp t) + val assums_hyp' = assums1 @ (map replace_eqs assums2) + in + list_all (params, Logic.list_implies (assums_hyp', Logic.strip_assums_concl t)) + end + val cases' = map preprocess_case (tl prems) + val elimrule' = Logic.list_implies ((hd prems) :: cases', Thm.concl_of elimrule) + (*val _ = Output.tracing ("elimrule': "^ (Syntax.string_of_term_global thy elimrule'))*) + val bigeq = (Thm.symmetric (Conv.implies_concl_conv + (MetaSimplifier.rewrite true [@{thm Predicate.eq_is_eq}]) + (cterm_of thy elimrule'))) + (* + val _ = Output.tracing ("bigeq:" ^ (Display.string_of_thm_global thy bigeq)) + val res = + Thm.equal_elim bigeq elimrule + *) + (* + val t = (fn {...} => mycheat_tac thy 1) + val eq = Goal.prove (ProofContext.init thy) [] [] (Logic.mk_equals ((Thm.prop_of elimrule), elimrule')) t + *) + val _ = Output.tracing "Preprocessed elimination rule" + in + Thm.equal_elim bigeq elimrule + end; + +(* special case: predicate with no introduction rule *) +fun noclause thy predname elim = let + val T = (Logic.unvarifyT o Sign.the_const_type thy) predname + val Ts = binder_types T + val names = Name.variant_list [] + (map (fn i => "x" ^ (string_of_int i)) (1 upto (length Ts))) + val vs = map2 (curry Free) names Ts + val clausehd = HOLogic.mk_Trueprop (list_comb (Const (predname, T), vs)) + val intro_t = Logic.mk_implies (@{prop False}, clausehd) + val P = HOLogic.mk_Trueprop (Free ("P", HOLogic.boolT)) + val elim_t = Logic.list_implies ([clausehd, Logic.mk_implies (@{prop False}, P)], P) + val intro = Goal.prove (ProofContext.init thy) names [] intro_t + (fn {...} => etac @{thm FalseE} 1) + val elim = Goal.prove (ProofContext.init thy) ("P" :: names) [] elim_t + (fn {...} => etac elim 1) +in + ([intro], elim) +end + +fun fetch_pred_data thy name = + case try (Inductive.the_inductive (ProofContext.init thy)) name of + SOME (info as (_, result)) => + let + fun is_intro_of intro = + let + val (const, _) = strip_comb (HOLogic.dest_Trueprop (concl_of intro)) + in (fst (dest_Const const) = name) end; + val intros = ind_set_codegen_preproc thy ((map (preprocess_intro thy)) + (filter is_intro_of (#intrs result))) + val pre_elim = nth (#elims result) (find_index (fn s => s = name) (#names (fst info))) + val nparams = length (Inductive.params_of (#raw_induct result)) + val elim = singleton (ind_set_codegen_preproc thy) (preprocess_elim thy nparams pre_elim) + val (intros, elim) = if null intros then noclause thy name elim else (intros, elim) + in + mk_pred_data ((intros, SOME elim, nparams), ([], [], [])) + end + | NONE => error ("No such predicate: " ^ quote name) + +(* updaters *) + +fun apfst3 f (x, y, z) = (f x, y, z) +fun apsnd3 f (x, y, z) = (x, f y, z) +fun aptrd3 f (x, y, z) = (x, y, f z) + +fun add_predfun name mode data = + let + val add = (apsnd o apfst3 o cons) (mode, mk_predfun_data data) + in PredData.map (Graph.map_node name (map_pred_data add)) end + +fun is_inductive_predicate thy name = + is_some (try (Inductive.the_inductive (ProofContext.init thy)) name) + +fun depending_preds_of thy (key, value) = + let + val intros = (#intros o rep_pred_data) value + in + fold Term.add_const_names (map Thm.prop_of intros) [] + |> filter (fn c => (not (c = key)) andalso (is_inductive_predicate thy c orelse is_registered thy c)) + end; + + +(* code dependency graph *) +(* +fun dependencies_of thy name = + let + val (intros, elim, nparams) = fetch_pred_data thy name + val data = mk_pred_data ((intros, SOME elim, nparams), ([], [], [])) + val keys = depending_preds_of thy intros + in + (data, keys) + end; +*) +(* guessing number of parameters *) +fun find_indexes pred xs = + let + fun find is n [] = is + | find is n (x :: xs) = find (if pred x then (n :: is) else is) (n + 1) xs; + in rev (find [] 0 xs) end; + +fun is_predT (T as Type("fun", [_, _])) = (snd (strip_type T) = HOLogic.boolT) + | is_predT _ = false + +fun guess_nparams T = + let + val argTs = binder_types T + val nparams = fold (curry Int.max) + (map (fn x => x + 1) (find_indexes is_predT argTs)) 0 + in nparams end; + +fun add_intro thm thy = let + val (name, T) = dest_Const (fst (strip_intro_concl 0 (prop_of thm))) + fun cons_intro gr = + case try (Graph.get_node gr) name of + SOME pred_data => Graph.map_node name (map_pred_data + (apfst (fn (intro, elim, nparams) => (thm::intro, elim, nparams)))) gr + | NONE => + let + val nparams = the_default (guess_nparams T) (try (#nparams o rep_pred_data o (fetch_pred_data thy)) name) + in Graph.new_node (name, mk_pred_data (([thm], NONE, nparams), ([], [], []))) gr end; + in PredData.map cons_intro thy end + +fun set_elim thm = let + val (name, _) = dest_Const (fst + (strip_comb (HOLogic.dest_Trueprop (hd (prems_of thm))))) + fun set (intros, _, nparams) = (intros, SOME thm, nparams) + in PredData.map (Graph.map_node name (map_pred_data (apfst set))) end + +fun set_nparams name nparams = let + fun set (intros, elim, _ ) = (intros, elim, nparams) + in PredData.map (Graph.map_node name (map_pred_data (apfst set))) end + +fun register_predicate (pre_intros, pre_elim, nparams) thy = let + val (name, _) = dest_Const (fst (strip_intro_concl nparams (prop_of (hd pre_intros)))) + (* preprocessing *) + val intros = ind_set_codegen_preproc thy (map (preprocess_intro thy) pre_intros) + val elim = singleton (ind_set_codegen_preproc thy) (preprocess_elim thy nparams pre_elim) + in + PredData.map + (Graph.new_node (name, mk_pred_data ((intros, SOME elim, nparams), ([], [], [])))) thy + end + +fun set_generator_name pred mode name = + let + val set = (apsnd o apsnd3 o cons) (mode, mk_function_data (name, NONE)) + in + PredData.map (Graph.map_node pred (map_pred_data set)) + end + +fun set_sizelim_function_name pred mode name = + let + val set = (apsnd o aptrd3 o cons) (mode, mk_function_data (name, NONE)) + in + PredData.map (Graph.map_node pred (map_pred_data set)) + end + +(** data structures for generic compilation for different monads **) + +(* maybe rename functions more generic: + mk_predT -> mk_monadT; dest_predT -> dest_monadT + mk_single -> mk_return (?) +*) +datatype compilation_funs = CompilationFuns of { + mk_predT : typ -> typ, + dest_predT : typ -> typ, + mk_bot : typ -> term, + mk_single : term -> term, + mk_bind : term * term -> term, + mk_sup : term * term -> term, + mk_if : term -> term, + mk_not : term -> term, +(* funT_of : mode -> typ -> typ, *) +(* mk_fun_of : theory -> (string * typ) -> mode -> term, *) + mk_map : typ -> typ -> term -> term -> term, + lift_pred : term -> term +}; + +fun mk_predT (CompilationFuns funs) = #mk_predT funs +fun dest_predT (CompilationFuns funs) = #dest_predT funs +fun mk_bot (CompilationFuns funs) = #mk_bot funs +fun mk_single (CompilationFuns funs) = #mk_single funs +fun mk_bind (CompilationFuns funs) = #mk_bind funs +fun mk_sup (CompilationFuns funs) = #mk_sup funs +fun mk_if (CompilationFuns funs) = #mk_if funs +fun mk_not (CompilationFuns funs) = #mk_not funs +(*fun funT_of (CompilationFuns funs) = #funT_of funs*) +(*fun mk_fun_of (CompilationFuns funs) = #mk_fun_of funs*) +fun mk_map (CompilationFuns funs) = #mk_map funs +fun lift_pred (CompilationFuns funs) = #lift_pred funs + +fun funT_of compfuns (iss, is) T = + let + val Ts = binder_types T + val (paramTs, (inargTs, outargTs)) = split_modeT (iss, is) Ts + val paramTs' = map2 (fn NONE => I | SOME is => funT_of compfuns ([], is)) iss paramTs + in + (paramTs' @ inargTs) ---> (mk_predT compfuns (mk_tupleT outargTs)) + end; + +fun sizelim_funT_of compfuns (iss, is) T = + let + val Ts = binder_types T + val (paramTs, (inargTs, outargTs)) = split_modeT (iss, is) Ts + val paramTs' = map2 (fn SOME is => sizelim_funT_of compfuns ([], is) | NONE => I) iss paramTs + in + (paramTs' @ inargTs @ [@{typ "code_numeral"}]) ---> (mk_predT compfuns (mk_tupleT outargTs)) + end; + +fun mk_fun_of compfuns thy (name, T) mode = + Const (predfun_name_of thy name mode, funT_of compfuns mode T) + +fun mk_sizelim_fun_of compfuns thy (name, T) mode = + Const (sizelim_function_name_of thy name mode, sizelim_funT_of compfuns mode T) + +fun mk_generator_of compfuns thy (name, T) mode = + Const (generator_name_of thy name mode, sizelim_funT_of compfuns mode T) + + +structure PredicateCompFuns = +struct + +fun mk_predT T = Type (@{type_name "Predicate.pred"}, [T]) + +fun dest_predT (Type (@{type_name "Predicate.pred"}, [T])) = T + | dest_predT T = raise TYPE ("dest_predT", [T], []); + +fun mk_bot T = Const (@{const_name Orderings.bot}, mk_predT T); + +fun mk_single t = + let val T = fastype_of t + in Const(@{const_name Predicate.single}, T --> mk_predT T) $ t end; + +fun mk_bind (x, f) = + let val T as Type ("fun", [_, U]) = fastype_of f + in + Const (@{const_name Predicate.bind}, fastype_of x --> T --> U) $ x $ f + end; + +val mk_sup = HOLogic.mk_binop @{const_name sup}; + +fun mk_if cond = Const (@{const_name Predicate.if_pred}, + HOLogic.boolT --> mk_predT HOLogic.unitT) $ cond; + +fun mk_not t = let val T = mk_predT HOLogic.unitT + in Const (@{const_name Predicate.not_pred}, T --> T) $ t end + +fun mk_Enum f = + let val T as Type ("fun", [T', _]) = fastype_of f + in + Const (@{const_name Predicate.Pred}, T --> mk_predT T') $ f + end; + +fun mk_Eval (f, x) = + let + val T = fastype_of x + in + Const (@{const_name Predicate.eval}, mk_predT T --> T --> HOLogic.boolT) $ f $ x + end; + +fun mk_map T1 T2 tf tp = Const (@{const_name Predicate.map}, + (T1 --> T2) --> mk_predT T1 --> mk_predT T2) $ tf $ tp; + +val lift_pred = I + +val compfuns = CompilationFuns {mk_predT = mk_predT, dest_predT = dest_predT, mk_bot = mk_bot, + mk_single = mk_single, mk_bind = mk_bind, mk_sup = mk_sup, mk_if = mk_if, mk_not = mk_not, + mk_map = mk_map, lift_pred = lift_pred}; + +end; + +(* termify_code: +val termT = Type ("Code_Eval.term", []); +fun termifyT T = HOLogic.mk_prodT (T, HOLogic.unitT --> termT) +*) +(* +fun lift_random random = + let + val T = dest_randomT (fastype_of random) + in + mk_scomp (random, + mk_fun_comp (HOLogic.pair_const (PredicateCompFuns.mk_predT T) @{typ Random.seed}, + mk_fun_comp (Const (@{const_name Predicate.single}, T --> (PredicateCompFuns.mk_predT T)), + Const (@{const_name "fst"}, HOLogic.mk_prodT (T, @{typ "unit => term"}) --> T)))) + end; +*) + +structure RPredCompFuns = +struct + +fun mk_rpredT T = + @{typ "Random.seed"} --> HOLogic.mk_prodT (PredicateCompFuns.mk_predT T, @{typ "Random.seed"}) + +fun dest_rpredT (Type ("fun", [_, + Type (@{type_name "*"}, [Type (@{type_name "Predicate.pred"}, [T]), _])])) = T + | dest_rpredT T = raise TYPE ("dest_rpredT", [T], []); + +fun mk_bot T = Const(@{const_name RPred.bot}, mk_rpredT T) + +fun mk_single t = + let + val T = fastype_of t + in + Const (@{const_name RPred.return}, T --> mk_rpredT T) $ t + end; + +fun mk_bind (x, f) = + let + val T as (Type ("fun", [_, U])) = fastype_of f + in + Const (@{const_name RPred.bind}, fastype_of x --> T --> U) $ x $ f + end + +val mk_sup = HOLogic.mk_binop @{const_name RPred.supp} + +fun mk_if cond = Const (@{const_name RPred.if_rpred}, + HOLogic.boolT --> mk_rpredT HOLogic.unitT) $ cond; + +fun mk_not t = error "Negation is not defined for RPred" + +fun mk_map t = error "FIXME" (*FIXME*) + +fun lift_pred t = + let + val T = PredicateCompFuns.dest_predT (fastype_of t) + val lift_predT = PredicateCompFuns.mk_predT T --> mk_rpredT T + in + Const (@{const_name "RPred.lift_pred"}, lift_predT) $ t + end; + +val compfuns = CompilationFuns {mk_predT = mk_rpredT, dest_predT = dest_rpredT, mk_bot = mk_bot, + mk_single = mk_single, mk_bind = mk_bind, mk_sup = mk_sup, mk_if = mk_if, mk_not = mk_not, + mk_map = mk_map, lift_pred = lift_pred}; + +end; +(* for external use with interactive mode *) +val rpred_compfuns = RPredCompFuns.compfuns; + +fun lift_random random = + let + val T = dest_randomT (fastype_of random) + in + Const (@{const_name lift_random}, (@{typ Random.seed} --> + HOLogic.mk_prodT (HOLogic.mk_prodT (T, @{typ "unit => term"}), @{typ Random.seed})) --> + RPredCompFuns.mk_rpredT T) $ random + end; + +(* Mode analysis *) + +(*** check if a term contains only constructor functions ***) +fun is_constrt thy = + let + val cnstrs = flat (maps + (map (fn (_, (Tname, _, cs)) => map (apsnd (rpair Tname o length)) cs) o #descr o snd) + (Symtab.dest (Datatype.get_all thy))); + fun check t = (case strip_comb t of + (Free _, []) => true + | (Const (s, T), ts) => (case (AList.lookup (op =) cnstrs s, body_type T) of + (SOME (i, Tname), Type (Tname', _)) => length ts = i andalso Tname = Tname' andalso forall check ts + | _ => false) + | _ => false) + in check end; + +(*** check if a type is an equality type (i.e. doesn't contain fun) + FIXME this is only an approximation ***) +fun is_eqT (Type (s, Ts)) = s <> "fun" andalso forall is_eqT Ts + | is_eqT _ = true; + +fun term_vs tm = fold_aterms (fn Free (x, T) => cons x | _ => I) tm []; +val terms_vs = distinct (op =) o maps term_vs; + +(** collect all Frees in a term (with duplicates!) **) +fun term_vTs tm = + fold_aterms (fn Free xT => cons xT | _ => I) tm []; + +(*FIXME this function should not be named merge... make it local instead*) +fun merge xs [] = xs + | merge [] ys = ys + | merge (x::xs) (y::ys) = if length x >= length y then x::merge xs (y::ys) + else y::merge (x::xs) ys; + +fun subsets i j = if i <= j then + let val is = subsets (i+1) j + in merge (map (fn ks => i::ks) is) is end + else [[]]; + +(* FIXME: should be in library - map_prod *) +fun cprod ([], ys) = [] + | cprod (x :: xs, ys) = map (pair x) ys @ cprod (xs, ys); + +fun cprods xss = foldr (map op :: o cprod) [[]] xss; + +fun cprods_subset [] = [[]] + | cprods_subset (xs :: xss) = + let + val yss = (cprods_subset xss) + in maps (fn ys => map (fn x => cons x ys) xs) yss @ yss end + +(*TODO: cleanup function and put together with modes_of_term *) +(* +fun modes_of_param default modes t = let + val (vs, t') = strip_abs t + val b = length vs + fun mk_modes name args = Option.map (maps (fn (m as (iss, is)) => + let + val (args1, args2) = + if length args < length iss then + error ("Too few arguments for inductive predicate " ^ name) + else chop (length iss) args; + val k = length args2; + val perm = map (fn i => (find_index_eq (Bound (b - i)) args2) + 1) + (1 upto b) + val partial_mode = (1 upto k) \\ perm + in + if not (partial_mode subset is) then [] else + let + val is' = + (fold_index (fn (i, j) => if j mem is then cons (i + 1) else I) perm []) + |> fold (fn i => if i > k then cons (i - k + b) else I) is + + val res = map (fn x => Mode (m, is', x)) (cprods (map + (fn (NONE, _) => [NONE] + | (SOME js, arg) => map SOME (filter + (fn Mode (_, js', _) => js=js') (modes_of_term modes arg))) + (iss ~~ args1))) + in res end + end)) (AList.lookup op = modes name) + in case strip_comb t' of + (Const (name, _), args) => the_default default (mk_modes name args) + | (Var ((name, _), _), args) => the (mk_modes name args) + | (Free (name, _), args) => the (mk_modes name args) + | _ => default end + +and +*) +fun modes_of_term modes t = + let + val ks = map_index (fn (i, T) => (i, NONE)) (binder_types (fastype_of t)); + val default = [Mode (([], ks), ks, [])]; + fun mk_modes name args = Option.map (maps (fn (m as (iss, is)) => + let + val (args1, args2) = + if length args < length iss then + error ("Too few arguments for inductive predicate " ^ name) + else chop (length iss) args; + val k = length args2; + val prfx = map (rpair NONE) (1 upto k) + in + if not (is_prefix op = prfx is) then [] else + let val is' = List.drop (is, k) + in map (fn x => Mode (m, is', x)) (cprods (map + (fn (NONE, _) => [NONE] + | (SOME js, arg) => map SOME (filter + (fn Mode (_, js', _) => js=js') (modes_of_term modes arg))) + (iss ~~ args1))) + end + end)) (AList.lookup op = modes name) + + in + case strip_comb (Envir.eta_contract t) of + (Const (name, _), args) => the_default default (mk_modes name args) + | (Var ((name, _), _), args) => the (mk_modes name args) + | (Free (name, _), args) => the (mk_modes name args) + | (Abs _, []) => error "Abs at param position" (* modes_of_param default modes t *) + | _ => default + end + +fun select_mode_prem thy modes vs ps = + find_first (is_some o snd) (ps ~~ map + (fn Prem (us, t) => find_first (fn Mode (_, is, _) => + let + val (in_ts, out_ts) = split_smode is us; + val (out_ts', in_ts') = List.partition (is_constrt thy) out_ts; + val vTs = maps term_vTs out_ts'; + val dupTs = map snd (duplicates (op =) vTs) @ + List.mapPartial (AList.lookup (op =) vTs) vs; + in + terms_vs (in_ts @ in_ts') subset vs andalso + forall (is_eqT o fastype_of) in_ts' andalso + term_vs t subset vs andalso + forall is_eqT dupTs + end) + (modes_of_term modes t handle Option => + error ("Bad predicate: " ^ Syntax.string_of_term_global thy t)) + | Negprem (us, t) => find_first (fn Mode (_, is, _) => + length us = length is andalso + terms_vs us subset vs andalso + term_vs t subset vs) + (modes_of_term modes t handle Option => + error ("Bad predicate: " ^ Syntax.string_of_term_global thy t)) + | Sidecond t => if term_vs t subset vs then SOME (Mode (([], []), [], [])) + else NONE + ) ps); + +fun fold_prem f (Prem (args, _)) = fold f args + | fold_prem f (Negprem (args, _)) = fold f args + | fold_prem f (Sidecond t) = f t + +fun all_subsets [] = [[]] + | all_subsets (x::xs) = let val xss' = all_subsets xs in xss' @ (map (cons x) xss') end + +fun generator vTs v = + let + val T = the (AList.lookup (op =) vTs v) + in + (Generator (v, T), Mode (([], []), [], [])) + end; + +fun gen_prem (Prem (us, t)) = GeneratorPrem (us, t) + | gen_prem _ = error "gen_prem : invalid input for gen_prem" + +fun param_gen_prem param_vs (p as Prem (us, t as Free (v, _))) = + if member (op =) param_vs v then + GeneratorPrem (us, t) + else p + | param_gen_prem param_vs p = p + +fun check_mode_clause with_generator thy param_vs modes gen_modes (iss, is) (ts, ps) = + let + val modes' = modes @ List.mapPartial + (fn (_, NONE) => NONE | (v, SOME js) => SOME (v, [([], js)])) + (param_vs ~~ iss); + val gen_modes' = gen_modes @ List.mapPartial + (fn (_, NONE) => NONE | (v, SOME js) => SOME (v, [([], js)])) + (param_vs ~~ iss); + val vTs = distinct (op =) ((fold o fold_prem) Term.add_frees ps (fold Term.add_frees ts [])) + val prem_vs = distinct (op =) ((fold o fold_prem) Term.add_free_names ps []) + fun check_mode_prems acc_ps vs [] = SOME (acc_ps, vs) + | check_mode_prems acc_ps vs ps = (case select_mode_prem thy modes' vs ps of + NONE => + (if with_generator then + (case select_mode_prem thy gen_modes' vs ps of + SOME (p, SOME mode) => check_mode_prems ((gen_prem p, mode) :: acc_ps) + (case p of Prem (us, _) => vs union terms_vs us | _ => vs) + (filter_out (equal p) ps) + | NONE => + let + val all_generator_vs = all_subsets (prem_vs \\ vs) |> sort (int_ord o (pairself length)) + in + case (find_first (fn generator_vs => is_some + (select_mode_prem thy modes' (vs union generator_vs) ps)) all_generator_vs) of + SOME generator_vs => check_mode_prems ((map (generator vTs) generator_vs) @ acc_ps) + (vs union generator_vs) ps + | NONE => NONE + end) + else + NONE) + | SOME (p, SOME mode) => check_mode_prems ((if with_generator then param_gen_prem param_vs p else p, mode) :: acc_ps) + (case p of Prem (us, _) => vs union terms_vs us | _ => vs) + (filter_out (equal p) ps)) + val (in_ts, in_ts') = List.partition (is_constrt thy) (fst (split_smode is ts)); + val in_vs = terms_vs in_ts; + val concl_vs = terms_vs ts + in + if forall is_eqT (map snd (duplicates (op =) (maps term_vTs in_ts))) andalso + forall (is_eqT o fastype_of) in_ts' then + case check_mode_prems [] (param_vs union in_vs) ps of + NONE => NONE + | SOME (acc_ps, vs) => + if with_generator then + SOME (ts, (rev acc_ps) @ (map (generator vTs) (concl_vs \\ vs))) + else + if concl_vs subset vs then SOME (ts, rev acc_ps) else NONE + else NONE + end; + +fun check_modes_pred with_generator thy param_vs clauses modes gen_modes (p, ms) = + let val SOME rs = AList.lookup (op =) clauses p + in (p, List.filter (fn m => case find_index + (is_none o check_mode_clause with_generator thy param_vs modes gen_modes m) rs of + ~1 => true + | i => (Output.tracing ("Clause " ^ string_of_int (i + 1) ^ " of " ^ + p ^ " violates mode " ^ string_of_mode m); + Output.tracing (commas (map (Syntax.string_of_term_global thy) (fst (nth rs i)))); false)) ms) + end; + +fun get_modes_pred with_generator thy param_vs clauses modes gen_modes (p, ms) = + let + val SOME rs = AList.lookup (op =) clauses p + in + (p, map (fn m => + (m, map (the o check_mode_clause with_generator thy param_vs modes gen_modes m) rs)) ms) + end; + +fun fixp f (x : (string * mode list) list) = + let val y = f x + in if x = y then x else fixp f y end; + +fun infer_modes thy extra_modes all_modes param_vs clauses = + let + val modes = + fixp (fn modes => + map (check_modes_pred false thy param_vs clauses (modes @ extra_modes) []) modes) + all_modes + in + map (get_modes_pred false thy param_vs clauses (modes @ extra_modes) []) modes + end; + +fun remove_from rem [] = [] + | remove_from rem ((k, vs) :: xs) = + (case AList.lookup (op =) rem k of + NONE => (k, vs) + | SOME vs' => (k, vs \\ vs')) + :: remove_from rem xs + +fun infer_modes_with_generator thy extra_modes all_modes param_vs clauses = + let + val prednames = map fst clauses + val extra_modes = all_modes_of thy + val gen_modes = all_generator_modes_of thy + |> filter_out (fn (name, _) => member (op =) prednames name) + val starting_modes = remove_from extra_modes all_modes + val modes = + fixp (fn modes => + map (check_modes_pred true thy param_vs clauses extra_modes (gen_modes @ modes)) modes) + starting_modes + in + map (get_modes_pred true thy param_vs clauses extra_modes (gen_modes @ modes)) modes + end; + +(* term construction *) + +fun mk_v (names, vs) s T = (case AList.lookup (op =) vs s of + NONE => (Free (s, T), (names, (s, [])::vs)) + | SOME xs => + let + val s' = Name.variant names s; + val v = Free (s', T) + in + (v, (s'::names, AList.update (op =) (s, v::xs) vs)) + end); + +fun distinct_v (Free (s, T)) nvs = mk_v nvs s T + | distinct_v (t $ u) nvs = + let + val (t', nvs') = distinct_v t nvs; + val (u', nvs'') = distinct_v u nvs'; + in (t' $ u', nvs'') end + | distinct_v x nvs = (x, nvs); + +fun compile_match thy compfuns eqs eqs' out_ts success_t = + let + val eqs'' = maps mk_eq eqs @ eqs' + val names = fold Term.add_free_names (success_t :: eqs'' @ out_ts) []; + val name = Name.variant names "x"; + val name' = Name.variant (name :: names) "y"; + val T = mk_tupleT (map fastype_of out_ts); + val U = fastype_of success_t; + val U' = dest_predT compfuns U; + val v = Free (name, T); + val v' = Free (name', T); + in + lambda v (fst (Datatype.make_case + (ProofContext.init thy) false [] v + [(mk_tuple out_ts, + if null eqs'' then success_t + else Const (@{const_name HOL.If}, HOLogic.boolT --> U --> U --> U) $ + foldr1 HOLogic.mk_conj eqs'' $ success_t $ + mk_bot compfuns U'), + (v', mk_bot compfuns U')])) + end; + +(*FIXME function can be removed*) +fun mk_funcomp f t = + let + val names = Term.add_free_names t []; + val Ts = binder_types (fastype_of t); + val vs = map Free + (Name.variant_list names (replicate (length Ts) "x") ~~ Ts) + in + fold_rev lambda vs (f (list_comb (t, vs))) + end; +(* +fun compile_param_ext thy compfuns modes (NONE, t) = t + | compile_param_ext thy compfuns modes (m as SOME (Mode ((iss, is'), is, ms)), t) = + let + val (vs, u) = strip_abs t + val (ivs, ovs) = split_mode is vs + val (f, args) = strip_comb u + val (params, args') = chop (length ms) args + val (inargs, outargs) = split_mode is' args' + val b = length vs + val perm = map (fn i => (find_index_eq (Bound (b - i)) args') + 1) (1 upto b) + val outp_perm = + snd (split_mode is perm) + |> map (fn i => i - length (filter (fn x => x < i) is')) + val names = [] -- TODO + val out_names = Name.variant_list names (replicate (length outargs) "x") + val f' = case f of + Const (name, T) => + if AList.defined op = modes name then + mk_predfun_of thy compfuns (name, T) (iss, is') + else error "compile param: Not an inductive predicate with correct mode" + | Free (name, T) => Free (name, param_funT_of compfuns T (SOME is')) + val outTs = dest_tupleT (dest_predT compfuns (body_type (fastype_of f'))) + val out_vs = map Free (out_names ~~ outTs) + val params' = map (compile_param thy modes) (ms ~~ params) + val f_app = list_comb (f', params' @ inargs) + val single_t = (mk_single compfuns (mk_tuple (map (fn i => nth out_vs (i - 1)) outp_perm))) + val match_t = compile_match thy compfuns [] [] out_vs single_t + in list_abs (ivs, + mk_bind compfuns (f_app, match_t)) + end + | compile_param_ext _ _ _ _ = error "compile params" +*) + +fun compile_param size thy compfuns (NONE, t) = t + | compile_param size thy compfuns (m as SOME (Mode ((iss, is'), is, ms)), t) = + let + val (f, args) = strip_comb (Envir.eta_contract t) + val (params, args') = chop (length ms) args + val params' = map (compile_param size thy compfuns) (ms ~~ params) + val mk_fun_of = case size of NONE => mk_fun_of | SOME _ => mk_sizelim_fun_of + val funT_of = case size of NONE => funT_of | SOME _ => sizelim_funT_of + val f' = + case f of + Const (name, T) => + mk_fun_of compfuns thy (name, T) (iss, is') + | Free (name, T) => Free (name, funT_of compfuns (iss, is') T) + | _ => error ("PredicateCompiler: illegal parameter term") + in list_comb (f', params' @ args') end + +fun compile_expr size thy ((Mode (mode, is, ms)), t) = + case strip_comb t of + (Const (name, T), params) => + let + val params' = map (compile_param size thy PredicateCompFuns.compfuns) (ms ~~ params) + val mk_fun_of = case size of NONE => mk_fun_of | SOME _ => mk_sizelim_fun_of + in + list_comb (mk_fun_of PredicateCompFuns.compfuns thy (name, T) mode, params') + end + | (Free (name, T), args) => + let + val funT_of = case size of NONE => funT_of | SOME _ => sizelim_funT_of + in + list_comb (Free (name, funT_of PredicateCompFuns.compfuns ([], is) T), args) + end; + +fun compile_gen_expr size thy compfuns ((Mode (mode, is, ms)), t) = + case strip_comb t of + (Const (name, T), params) => + let + val params' = map (compile_param size thy compfuns) (ms ~~ params) + in + list_comb (mk_generator_of compfuns thy (name, T) mode, params') + end + | (Free (name, T), args) => + list_comb (Free (name, sizelim_funT_of RPredCompFuns.compfuns ([], is) T), args) + +(** specific rpred functions -- move them to the correct place in this file *) + +(* uncommented termify code; causes more trouble than expected at first *) +(* +fun mk_valtermify_term (t as Const (c, T)) = HOLogic.mk_prod (t, Abs ("u", HOLogic.unitT, HOLogic.reflect_term t)) + | mk_valtermify_term (Free (x, T)) = Free (x, termifyT T) + | mk_valtermify_term (t1 $ t2) = + let + val T = fastype_of t1 + val (T1, T2) = dest_funT T + val t1' = mk_valtermify_term t1 + val t2' = mk_valtermify_term t2 + in + Const ("Code_Eval.valapp", termifyT T --> termifyT T1 --> termifyT T2) $ t1' $ t2' + end + | mk_valtermify_term _ = error "Not a valid term for mk_valtermify_term" +*) + +fun compile_clause compfuns size final_term thy all_vs param_vs (iss, is) inp (ts, moded_ps) = + let + fun check_constrt t (names, eqs) = + if is_constrt thy t then (t, (names, eqs)) else + let + val s = Name.variant names "x"; + val v = Free (s, fastype_of t) + in (v, (s::names, HOLogic.mk_eq (v, t)::eqs)) end; + + val (in_ts, out_ts) = split_smode is ts; + val (in_ts', (all_vs', eqs)) = + fold_map check_constrt in_ts (all_vs, []); + + fun compile_prems out_ts' vs names [] = + let + val (out_ts'', (names', eqs')) = + fold_map check_constrt out_ts' (names, []); + val (out_ts''', (names'', constr_vs)) = fold_map distinct_v + out_ts'' (names', map (rpair []) vs); + in + (* termify code: + compile_match thy compfuns constr_vs (eqs @ eqs') out_ts''' + (mk_single compfuns (mk_tuple (map mk_valtermify_term out_ts))) + *) + compile_match thy compfuns constr_vs (eqs @ eqs') out_ts''' + (final_term out_ts) + end + | compile_prems out_ts vs names ((p, mode as Mode ((_, is), _, _)) :: ps) = + let + val vs' = distinct (op =) (flat (vs :: map term_vs out_ts)); + val (out_ts', (names', eqs)) = + fold_map check_constrt out_ts (names, []) + val (out_ts'', (names'', constr_vs')) = fold_map distinct_v + out_ts' ((names', map (rpair []) vs)) + val (compiled_clause, rest) = case p of + Prem (us, t) => + let + val (in_ts, out_ts''') = split_smode is us; + val args = case size of + NONE => in_ts + | SOME size_t => in_ts @ [size_t] + val u = lift_pred compfuns + (list_comb (compile_expr size thy (mode, t), args)) + val rest = compile_prems out_ts''' vs' names'' ps + in + (u, rest) + end + | Negprem (us, t) => + let + val (in_ts, out_ts''') = split_smode is us + val u = lift_pred compfuns + (mk_not PredicateCompFuns.compfuns (list_comb (compile_expr NONE thy (mode, t), in_ts))) + val rest = compile_prems out_ts''' vs' names'' ps + in + (u, rest) + end + | Sidecond t => + let + val rest = compile_prems [] vs' names'' ps; + in + (mk_if compfuns t, rest) + end + | GeneratorPrem (us, t) => + let + val (in_ts, out_ts''') = split_smode is us; + val args = case size of + NONE => in_ts + | SOME size_t => in_ts @ [size_t] + val u = list_comb (compile_gen_expr size thy compfuns (mode, t), args) + val rest = compile_prems out_ts''' vs' names'' ps + in + (u, rest) + end + | Generator (v, T) => + let + val u = lift_random (HOLogic.mk_random T @{term "1::code_numeral"}) + val rest = compile_prems [Free (v, T)] vs' names'' ps; + in + (u, rest) + end + in + compile_match thy compfuns constr_vs' eqs out_ts'' + (mk_bind compfuns (compiled_clause, rest)) + end + val prem_t = compile_prems in_ts' param_vs all_vs' moded_ps; + in + mk_bind compfuns (mk_single compfuns inp, prem_t) + end + +fun compile_pred compfuns mk_fun_of use_size thy all_vs param_vs s T mode moded_cls = + let + val (Ts1, Ts2) = chop (length (fst mode)) (binder_types T) + val (Us1, Us2) = split_smodeT (snd mode) Ts2 + val funT_of = if use_size then sizelim_funT_of else funT_of + val Ts1' = map2 (fn NONE => I | SOME is => funT_of compfuns ([], is)) (fst mode) Ts1 + val size_name = Name.variant (all_vs @ param_vs) "size" + fun mk_input_term (i, NONE) = + [Free (Name.variant (all_vs @ param_vs) ("x" ^ string_of_int i), nth Ts2 (i - 1))] + | mk_input_term (i, SOME pis) = case HOLogic.strip_tupleT (nth Ts2 (i - 1)) of + [] => error "strange unit input" + | [T] => [Free (Name.variant (all_vs @ param_vs) ("x" ^ string_of_int i), nth Ts2 (i - 1))] + | Ts => let + val vnames = Name.variant_list (all_vs @ param_vs) + (map (fn j => "x" ^ string_of_int i ^ "p" ^ string_of_int j) + pis) + in if null pis then [] + else [HOLogic.mk_tuple (map Free (vnames ~~ map (fn j => nth Ts (j - 1)) pis))] end + val in_ts = maps mk_input_term (snd mode) + val params = map2 (fn s => fn T => Free (s, T)) param_vs Ts1' + val size = Free (size_name, @{typ "code_numeral"}) + val decr_size = + if use_size then + SOME (Const ("HOL.minus_class.minus", @{typ "code_numeral => code_numeral => code_numeral"}) + $ size $ Const ("HOL.one_class.one", @{typ "Code_Numeral.code_numeral"})) + else + NONE + val cl_ts = + map (compile_clause compfuns decr_size (fn out_ts => mk_single compfuns (mk_tuple out_ts)) + thy all_vs param_vs mode (mk_tuple in_ts)) moded_cls; + val t = foldr1 (mk_sup compfuns) cl_ts + val T' = mk_predT compfuns (mk_tupleT Us2) + val size_t = Const (@{const_name "If"}, @{typ bool} --> T' --> T' --> T') + $ HOLogic.mk_eq (size, @{term "0 :: code_numeral"}) + $ mk_bot compfuns (dest_predT compfuns T') $ t + val fun_const = mk_fun_of compfuns thy (s, T) mode + val eq = if use_size then + (list_comb (fun_const, params @ in_ts @ [size]), size_t) + else + (list_comb (fun_const, params @ in_ts), t) + in + HOLogic.mk_Trueprop (HOLogic.mk_eq eq) + 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 mk_Eval_of ((x, T), NONE) names = (x, names) + | mk_Eval_of ((x, T), SOME mode) names = + let + val Ts = binder_types T + (*val argnames = Name.variant_list names + (map (fn i => "x" ^ string_of_int i) (1 upto (length Ts))); + val args = map Free (argnames ~~ Ts) + val (inargs, outargs) = split_smode mode args*) + 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 = map 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), mk_tuple outargs) + val t = fold_rev mk_split_lambda args r + in + (t, names) + end; + +fun create_intro_elim_rule (mode as (iss, is)) defthm mode_id funT pred thy = +let + val Ts = binder_types (fastype_of pred) + val funtrm = Const (mode_id, funT) + val (Ts1, Ts2) = chop (length iss) Ts; + val Ts1' = map2 (fn NONE => I | SOME is => funT_of (PredicateCompFuns.compfuns) ([], is)) iss Ts1 + val param_names = Name.variant_list [] + (map (fn i => "x" ^ string_of_int i) (1 upto (length Ts1))); + val params = map Free (param_names ~~ Ts1') + fun mk_args (i, T) argnames = + let + val vname = Name.variant (param_names @ argnames) ("x" ^ string_of_int (length Ts1' + i)) + val default = (Free (vname, T), vname :: argnames) + in + case AList.lookup (op =) is i of + NONE => default + | SOME NONE => default + | SOME (SOME pis) => + case HOLogic.strip_tupleT T of + [] => default + | [_] => default + | Ts => + let + val vnames = Name.variant_list (param_names @ argnames) + (map (fn j => "x" ^ string_of_int (length Ts1' + i) ^ "p" ^ string_of_int j) + (1 upto (length Ts))) + in (HOLogic.mk_tuple (map Free (vnames ~~ Ts)), vnames @ argnames) end + end + val (args, argnames) = fold_map mk_args (1 upto (length Ts2) ~~ Ts2) [] + val (inargs, outargs) = split_smode is args + val param_names' = Name.variant_list (param_names @ argnames) + (map (fn i => "p" ^ string_of_int i) (1 upto (length iss))) + val param_vs = map Free (param_names' ~~ Ts1) + val (params', names) = fold_map mk_Eval_of ((params ~~ Ts1) ~~ iss) [] + val predpropI = HOLogic.mk_Trueprop (list_comb (pred, param_vs @ args)) + val predpropE = HOLogic.mk_Trueprop (list_comb (pred, params' @ args)) + val param_eqs = map (HOLogic.mk_Trueprop o HOLogic.mk_eq) (param_vs ~~ params') + val funargs = params @ inargs + val funpropE = HOLogic.mk_Trueprop (PredicateCompFuns.mk_Eval (list_comb (funtrm, funargs), + if null outargs then Free("y", HOLogic.unitT) else mk_tuple outargs)) + val funpropI = HOLogic.mk_Trueprop (PredicateCompFuns.mk_Eval (list_comb (funtrm, funargs), + mk_tuple outargs)) + val introtrm = Logic.list_implies (predpropI :: param_eqs, funpropI) + val simprules = [defthm, @{thm eval_pred}, + @{thm "split_beta"}, @{thm "fst_conv"}, @{thm "snd_conv"}, @{thm pair_collapse}] + val unfolddef_tac = Simplifier.asm_full_simp_tac (HOL_basic_ss addsimps simprules) 1 + val introthm = Goal.prove (ProofContext.init thy) (argnames @ param_names @ param_names' @ ["y"]) [] introtrm (fn {...} => unfolddef_tac) + val P = HOLogic.mk_Trueprop (Free ("P", HOLogic.boolT)); + val elimtrm = Logic.list_implies ([funpropE, Logic.mk_implies (predpropE, P)], P) + val elimthm = Goal.prove (ProofContext.init thy) (argnames @ param_names @ param_names' @ ["y", "P"]) [] elimtrm (fn {...} => unfolddef_tac) + val _ = Output.tracing (Display.string_of_thm_global thy elimthm) + val _ = Output.tracing (Display.string_of_thm_global thy introthm) + +in + (introthm, elimthm) +end; + +fun create_constname_of_mode thy prefix name mode = + let + fun string_of_mode mode = if null mode then "0" + else space_implode "_" (map (fn (i, NONE) => string_of_int i | (i, SOME pis) => string_of_int i ^ "p" + ^ space_implode "p" (map string_of_int pis)) mode) + val HOmode = space_implode "_and_" + (fold (fn NONE => I | SOME mode => cons (string_of_mode mode)) (fst mode) []) + in + (Sign.full_bname thy (prefix ^ (Long_Name.base_name name))) ^ + (if HOmode = "" then "_" else "_for_" ^ HOmode ^ "_yields_") ^ (string_of_mode (snd mode)) + end; + +fun split_tupleT is T = + let + fun split_tuple' _ _ [] = ([], []) + | split_tuple' is i (T::Ts) = + (if i mem is then apfst else apsnd) (cons T) + (split_tuple' is (i+1) Ts) + in + split_tuple' is 1 (HOLogic.strip_tupleT T) + end + +fun mk_arg xin xout pis T = + let + val n = length (HOLogic.strip_tupleT T) + val ni = length pis + fun mk_proj i j t = + (if i = j then I else HOLogic.mk_fst) + (funpow (i - 1) HOLogic.mk_snd t) + fun mk_arg' i (si, so) = if i mem pis then + (mk_proj si ni xin, (si+1, so)) + else + (mk_proj so (n - ni) xout, (si, so+1)) + val (args, _) = fold_map mk_arg' (1 upto n) (1, 1) + in + HOLogic.mk_tuple args + end + +fun create_definitions preds (name, modes) thy = + let + val compfuns = PredicateCompFuns.compfuns + val T = AList.lookup (op =) preds name |> the + fun create_definition (mode as (iss, is)) thy = let + val mode_cname = create_constname_of_mode thy "" name mode + val mode_cbasename = Long_Name.base_name mode_cname + val Ts = binder_types T + val (Ts1, Ts2) = chop (length iss) Ts + val (Us1, Us2) = split_smodeT is Ts2 + val Ts1' = map2 (fn NONE => I | SOME is => funT_of compfuns ([], is)) iss Ts1 + val funT = (Ts1' @ Us1) ---> (mk_predT compfuns (mk_tupleT Us2)) + val names = Name.variant_list [] + (map (fn i => "x" ^ string_of_int i) (1 upto (length Ts))); + (* old *) + (* + val xs = map Free (names ~~ (Ts1' @ Ts2)) + val (xparams, xargs) = chop (length iss) xs + val (xins, xouts) = split_smode is xargs + *) + (* new *) + val param_names = Name.variant_list [] + (map (fn i => "x" ^ string_of_int i) (1 upto (length Ts1'))) + val xparams = map Free (param_names ~~ Ts1') + fun mk_vars (i, T) names = + let + val vname = Name.variant names ("x" ^ string_of_int (length Ts1' + i)) + in + case AList.lookup (op =) is i of + NONE => ((([], [Free (vname, T)]), Free (vname, T)), vname :: names) + | SOME NONE => ((([Free (vname, T)], []), Free (vname, T)), vname :: names) + | SOME (SOME pis) => + let + val (Tins, Touts) = split_tupleT pis T + val name_in = Name.variant names ("x" ^ string_of_int (length Ts1' + i) ^ "in") + val name_out = Name.variant names ("x" ^ string_of_int (length Ts1' + i) ^ "out") + val xin = Free (name_in, HOLogic.mk_tupleT Tins) + val xout = Free (name_out, HOLogic.mk_tupleT Touts) + val xarg = mk_arg xin xout pis T + in (((if null Tins then [] else [xin], if null Touts then [] else [xout]), xarg), name_in :: name_out :: names) end + (* HOLogic.strip_tupleT T of + [] => + in (Free (vname, T), vname :: names) end + | [_] => let val vname = Name.variant names ("x" ^ string_of_int (length Ts1' + i)) + in (Free (vname, T), vname :: names) end + | Ts => + let + val vnames = Name.variant_list names + (map (fn j => "x" ^ string_of_int (length Ts1' + i) ^ "p" ^ string_of_int j) + (1 upto (length Ts))) + in (HOLogic.mk_tuple (map Free (vnames ~~ Ts)), vnames @ names) end *) + end + val (xinoutargs, names) = fold_map mk_vars ((1 upto (length Ts2)) ~~ Ts2) param_names + val (xinout, xargs) = split_list xinoutargs + val (xins, xouts) = pairself flat (split_list xinout) + (*val (xins, xouts) = split_smode is xargs*) + val (xparams', names') = fold_map mk_Eval_of ((xparams ~~ Ts1) ~~ iss) names + val _ = Output.tracing ("xargs:" ^ commas (map (Syntax.string_of_term_global thy) xargs)) + fun mk_split_lambda [] t = lambda (Free (Name.variant names' "x", HOLogic.unitT)) t + | mk_split_lambda [x] t = lambda x t + | mk_split_lambda xs t = + let + fun mk_split_lambda' (x::y::[]) t = HOLogic.mk_split (lambda x (lambda y t)) + | mk_split_lambda' (x::xs) t = HOLogic.mk_split (lambda x (mk_split_lambda' xs t)) + in + mk_split_lambda' xs t + end; + val predterm = PredicateCompFuns.mk_Enum (mk_split_lambda xouts + (list_comb (Const (name, T), xparams' @ xargs))) + val lhs = list_comb (Const (mode_cname, funT), xparams @ xins) + val def = Logic.mk_equals (lhs, predterm) + val _ = Output.tracing ("def:" ^ (Syntax.string_of_term_global thy def)) + val ([definition], thy') = thy |> + Sign.add_consts_i [(Binding.name mode_cbasename, funT, NoSyn)] |> + PureThy.add_defs false [((Binding.name (mode_cbasename ^ "_def"), def), [])] + val (intro, elim) = + create_intro_elim_rule mode definition mode_cname funT (Const (name, T)) thy' + val _ = Output.tracing (Display.string_of_thm_global thy' definition) + in thy' + |> add_predfun name mode (mode_cname, definition, intro, elim) + |> PureThy.store_thm (Binding.name (mode_cbasename ^ "I"), intro) |> snd + |> PureThy.store_thm (Binding.name (mode_cbasename ^ "E"), elim) |> snd + |> Theory.checkpoint + end; + in + fold create_definition modes thy + end; + +fun sizelim_create_definitions preds (name, modes) thy = + let + val T = AList.lookup (op =) preds name |> the + fun create_definition mode thy = + let + val mode_cname = create_constname_of_mode thy "sizelim_" name mode + val funT = sizelim_funT_of PredicateCompFuns.compfuns mode T + in + thy |> Sign.add_consts_i [(Binding.name (Long_Name.base_name mode_cname), funT, NoSyn)] + |> set_sizelim_function_name name mode mode_cname + end; + in + fold create_definition modes thy + end; + +fun rpred_create_definitions preds (name, modes) thy = + let + val T = AList.lookup (op =) preds name |> the + fun create_definition mode thy = + let + val mode_cname = create_constname_of_mode thy "gen_" name mode + val funT = sizelim_funT_of RPredCompFuns.compfuns mode T + in + thy |> Sign.add_consts_i [(Binding.name (Long_Name.base_name mode_cname), funT, NoSyn)] + |> set_generator_name name mode mode_cname + end; + in + fold create_definition modes thy + end; + +(* Proving equivalence of term *) + +fun is_Type (Type _) = true + | is_Type _ = false + +(* returns true if t is an application of an datatype constructor *) +(* which then consequently would be splitted *) +(* else false *) +fun is_constructor thy t = + if (is_Type (fastype_of t)) then + (case Datatype.get_info thy ((fst o dest_Type o fastype_of) t) of + NONE => false + | SOME info => (let + val constr_consts = maps (fn (_, (_, _, constrs)) => map fst constrs) (#descr info) + val (c, _) = strip_comb t + in (case c of + Const (name, _) => name mem_string constr_consts + | _ => false) end)) + else false + +(* MAJOR FIXME: prove_params should be simple + - different form of introrule for parameters ? *) +fun prove_param thy (NONE, t) = TRY (rtac @{thm refl} 1) + | prove_param thy (m as SOME (Mode (mode, is, ms)), t) = + let + val (f, args) = strip_comb (Envir.eta_contract t) + val (params, _) = chop (length ms) args + val f_tac = case f of + Const (name, T) => simp_tac (HOL_basic_ss addsimps + ([@{thm eval_pred}, (predfun_definition_of thy name mode), + @{thm "split_eta"}, @{thm "split_beta"}, @{thm "fst_conv"}, + @{thm "snd_conv"}, @{thm pair_collapse}, @{thm "Product_Type.split_conv"}])) 1 + | Free _ => TRY (rtac @{thm refl} 1) + | Abs _ => error "prove_param: No valid parameter term" + in + REPEAT_DETERM (etac @{thm thin_rl} 1) + THEN REPEAT_DETERM (rtac @{thm ext} 1) + THEN print_tac "prove_param" + THEN f_tac + THEN print_tac "after simplification in prove_args" + THEN (EVERY (map (prove_param thy) (ms ~~ params))) + THEN (REPEAT_DETERM (atac 1)) + end + +fun prove_expr thy (Mode (mode, is, ms), t, us) (premposition : int) = + case strip_comb t of + (Const (name, T), args) => + let + val introrule = predfun_intro_of thy name mode + val (args1, args2) = chop (length ms) args + in + rtac @{thm bindI} 1 + THEN print_tac "before intro rule:" + (* for the right assumption in first position *) + THEN rotate_tac premposition 1 + THEN debug_tac (Display.string_of_thm (ProofContext.init thy) introrule) + THEN rtac introrule 1 + THEN print_tac "after intro rule" + (* work with parameter arguments *) + THEN (atac 1) + THEN (print_tac "parameter goal") + THEN (EVERY (map (prove_param thy) (ms ~~ args1))) + THEN (REPEAT_DETERM (atac 1)) + end + | _ => rtac @{thm bindI} 1 + THEN asm_full_simp_tac + (HOL_basic_ss' addsimps [@{thm "split_eta"}, @{thm "split_beta"}, @{thm "fst_conv"}, + @{thm "snd_conv"}, @{thm pair_collapse}]) 1 + THEN (atac 1) + THEN print_tac "after prove parameter call" + + +fun SOLVED tac st = FILTER (fn st' => nprems_of st' = nprems_of st - 1) tac st; + +fun SOLVEDALL tac st = FILTER (fn st' => nprems_of st' = 0) tac st + +fun prove_match thy (out_ts : term list) = let + fun get_case_rewrite t = + if (is_constructor thy t) then let + val case_rewrites = (#case_rewrites (Datatype.the_info thy + ((fst o dest_Type o fastype_of) t))) + in case_rewrites @ (flat (map get_case_rewrite (snd (strip_comb t)))) end + else [] + val simprules = @{thm "unit.cases"} :: @{thm "prod.cases"} :: (flat (map get_case_rewrite out_ts)) +(* replace TRY by determining if it necessary - are there equations when calling compile match? *) +in + (* make this simpset better! *) + asm_full_simp_tac (HOL_basic_ss' addsimps simprules) 1 + THEN print_tac "after prove_match:" + THEN (DETERM (TRY (EqSubst.eqsubst_tac (ProofContext.init thy) [0] [@{thm "HOL.if_P"}] 1 + THEN (REPEAT_DETERM (rtac @{thm conjI} 1 THEN (SOLVED (asm_simp_tac HOL_basic_ss 1)))) + THEN (SOLVED (asm_simp_tac HOL_basic_ss 1))))) + THEN print_tac "after if simplification" +end; + +(* corresponds to compile_fun -- maybe call that also compile_sidecond? *) + +fun prove_sidecond thy modes t = + let + fun preds_of t nameTs = case strip_comb t of + (f as Const (name, T), args) => + if AList.defined (op =) modes name then (name, T) :: nameTs + else fold preds_of args nameTs + | _ => nameTs + val preds = preds_of t [] + val defs = map + (fn (pred, T) => predfun_definition_of thy pred + ([], map (rpair NONE) (1 upto (length (binder_types T))))) + preds + in + (* remove not_False_eq_True when simpset in prove_match is better *) + simp_tac (HOL_basic_ss addsimps + (@{thms "HOL.simp_thms"} @ (@{thm not_False_eq_True} :: @{thm eval_pred} :: defs))) 1 + (* need better control here! *) + end + +fun prove_clause thy nargs modes (iss, is) (_, clauses) (ts, moded_ps) = + let + val (in_ts, clause_out_ts) = split_smode is ts; + fun prove_prems out_ts [] = + (prove_match thy out_ts) + THEN print_tac "before simplifying assumptions" + THEN asm_full_simp_tac HOL_basic_ss' 1 + THEN print_tac "before single intro rule" + THEN (rtac (if null clause_out_ts then @{thm singleI_unit} else @{thm singleI}) 1) + | prove_prems out_ts ((p, mode as Mode ((iss, is), _, param_modes)) :: ps) = + let + val premposition = (find_index (equal p) clauses) + nargs + val rest_tac = (case p of Prem (us, t) => + let + val (_, out_ts''') = split_smode is us + val rec_tac = prove_prems out_ts''' ps + in + print_tac "before clause:" + THEN asm_simp_tac HOL_basic_ss 1 + THEN print_tac "before prove_expr:" + THEN prove_expr thy (mode, t, us) premposition + THEN print_tac "after prove_expr:" + THEN rec_tac + end + | Negprem (us, t) => + let + val (_, out_ts''') = split_smode is us + val rec_tac = prove_prems out_ts''' ps + val name = (case strip_comb t of (Const (c, _), _) => SOME c | _ => NONE) + val (_, params) = strip_comb t + in + rtac @{thm bindI} 1 + THEN (if (is_some name) then + simp_tac (HOL_basic_ss addsimps [predfun_definition_of thy (the name) (iss, is)]) 1 + THEN rtac @{thm not_predI} 1 + THEN simp_tac (HOL_basic_ss addsimps [@{thm not_False_eq_True}]) 1 + THEN (REPEAT_DETERM (atac 1)) + (* FIXME: work with parameter arguments *) + THEN (EVERY (map (prove_param thy) (param_modes ~~ params))) + else + rtac @{thm not_predI'} 1) + THEN simp_tac (HOL_basic_ss addsimps [@{thm not_False_eq_True}]) 1 + THEN rec_tac + end + | Sidecond t => + rtac @{thm bindI} 1 + THEN rtac @{thm if_predI} 1 + THEN print_tac "before sidecond:" + THEN prove_sidecond thy modes t + THEN print_tac "after sidecond:" + THEN prove_prems [] ps) + in (prove_match thy out_ts) + THEN rest_tac + end; + val prems_tac = prove_prems in_ts moded_ps + in + rtac @{thm bindI} 1 + THEN rtac @{thm singleI} 1 + THEN prems_tac + end; + +fun select_sup 1 1 = [] + | select_sup _ 1 = [rtac @{thm supI1}] + | select_sup n i = (rtac @{thm supI2})::(select_sup (n - 1) (i - 1)); + +fun prove_one_direction thy clauses preds modes pred mode moded_clauses = + let + val T = the (AList.lookup (op =) preds pred) + val nargs = length (binder_types T) - nparams_of thy pred + val pred_case_rule = the_elim_of thy pred + in + REPEAT_DETERM (CHANGED (rewtac @{thm "split_paired_all"})) + THEN print_tac "before applying elim rule" + THEN etac (predfun_elim_of thy pred mode) 1 + THEN etac pred_case_rule 1 + THEN (EVERY (map + (fn i => EVERY' (select_sup (length moded_clauses) i) i) + (1 upto (length moded_clauses)))) + THEN (EVERY (map2 (prove_clause thy nargs modes mode) clauses moded_clauses)) + THEN print_tac "proved one direction" + end; + +(** Proof in the other direction **) + +fun prove_match2 thy out_ts = let + fun split_term_tac (Free _) = all_tac + | split_term_tac t = + if (is_constructor thy t) then let + val info = Datatype.the_info thy ((fst o dest_Type o fastype_of) t) + val num_of_constrs = length (#case_rewrites info) + (* special treatment of pairs -- because of fishing *) + val split_rules = case (fst o dest_Type o fastype_of) t of + "*" => [@{thm prod.split_asm}] + | _ => PureThy.get_thms thy (((fst o dest_Type o fastype_of) t) ^ ".split_asm") + val (_, ts) = strip_comb t + in + (Splitter.split_asm_tac split_rules 1) +(* THEN (Simplifier.asm_full_simp_tac HOL_basic_ss 1) + THEN (DETERM (TRY (etac @{thm Pair_inject} 1))) *) + THEN (REPEAT_DETERM_N (num_of_constrs - 1) (etac @{thm botE} 1 ORELSE etac @{thm botE} 2)) + THEN (EVERY (map split_term_tac ts)) + end + else all_tac + in + split_term_tac (mk_tuple out_ts) + THEN (DETERM (TRY ((Splitter.split_asm_tac [@{thm "split_if_asm"}] 1) THEN (etac @{thm botE} 2)))) + end + +(* VERY LARGE SIMILIRATIY to function prove_param +-- join both functions +*) +(* TODO: remove function *) + +fun prove_param2 thy (NONE, t) = all_tac + | prove_param2 thy (m as SOME (Mode (mode, is, ms)), t) = let + val (f, args) = strip_comb (Envir.eta_contract t) + val (params, _) = chop (length ms) args + val f_tac = case f of + Const (name, T) => full_simp_tac (HOL_basic_ss addsimps + (@{thm eval_pred}::(predfun_definition_of thy name mode) + :: @{thm "Product_Type.split_conv"}::[])) 1 + | Free _ => all_tac + | _ => error "prove_param2: illegal parameter term" + in + print_tac "before simplification in prove_args:" + THEN f_tac + THEN print_tac "after simplification in prove_args" + THEN (EVERY (map (prove_param2 thy) (ms ~~ params))) + end + + +fun prove_expr2 thy (Mode (mode, is, ms), t) = + (case strip_comb t of + (Const (name, T), args) => + etac @{thm bindE} 1 + THEN (REPEAT_DETERM (CHANGED (rewtac @{thm "split_paired_all"}))) + THEN print_tac "prove_expr2-before" + THEN (debug_tac (Syntax.string_of_term_global thy + (prop_of (predfun_elim_of thy name mode)))) + THEN (etac (predfun_elim_of thy name mode) 1) + THEN print_tac "prove_expr2" + THEN (EVERY (map (prove_param2 thy) (ms ~~ args))) + THEN print_tac "finished prove_expr2" + | _ => etac @{thm bindE} 1) + +(* FIXME: what is this for? *) +(* replace defined by has_mode thy pred *) +(* TODO: rewrite function *) +fun prove_sidecond2 thy modes t = let + fun preds_of t nameTs = case strip_comb t of + (f as Const (name, T), args) => + if AList.defined (op =) modes name then (name, T) :: nameTs + else fold preds_of args nameTs + | _ => nameTs + val preds = preds_of t [] + val defs = map + (fn (pred, T) => predfun_definition_of thy pred + ([], map (rpair NONE) (1 upto (length (binder_types T))))) + preds + in + (* only simplify the one assumption *) + full_simp_tac (HOL_basic_ss' addsimps @{thm eval_pred} :: defs) 1 + (* need better control here! *) + THEN print_tac "after sidecond2 simplification" + end + +fun prove_clause2 thy modes pred (iss, is) (ts, ps) i = + let + val pred_intro_rule = nth (intros_of thy pred) (i - 1) + val (in_ts, clause_out_ts) = split_smode is ts; + fun prove_prems2 out_ts [] = + print_tac "before prove_match2 - last call:" + THEN prove_match2 thy out_ts + THEN print_tac "after prove_match2 - last call:" + THEN (etac @{thm singleE} 1) + THEN (REPEAT_DETERM (etac @{thm Pair_inject} 1)) + THEN (asm_full_simp_tac HOL_basic_ss' 1) + THEN (REPEAT_DETERM (etac @{thm Pair_inject} 1)) + THEN (asm_full_simp_tac HOL_basic_ss' 1) + THEN SOLVED (print_tac "state before applying intro rule:" + THEN (rtac pred_intro_rule 1) + (* How to handle equality correctly? *) + THEN (print_tac "state before assumption matching") + THEN (REPEAT (atac 1 ORELSE + (CHANGED (asm_full_simp_tac (HOL_basic_ss' addsimps + [@{thm split_eta}, @{thm "split_beta"}, @{thm "fst_conv"}, @{thm "snd_conv"}, @{thm pair_collapse}]) 1) + THEN print_tac "state after simp_tac:")))) + | prove_prems2 out_ts ((p, mode as Mode ((iss, is), _, param_modes)) :: ps) = + let + val rest_tac = (case p of + Prem (us, t) => + let + val (_, out_ts''') = split_smode is us + val rec_tac = prove_prems2 out_ts''' ps + in + (prove_expr2 thy (mode, t)) THEN rec_tac + end + | Negprem (us, t) => + let + val (_, out_ts''') = split_smode is us + val rec_tac = prove_prems2 out_ts''' ps + val name = (case strip_comb t of (Const (c, _), _) => SOME c | _ => NONE) + val (_, params) = strip_comb t + in + print_tac "before neg prem 2" + THEN etac @{thm bindE} 1 + THEN (if is_some name then + full_simp_tac (HOL_basic_ss addsimps [predfun_definition_of thy (the name) (iss, is)]) 1 + THEN etac @{thm not_predE} 1 + THEN simp_tac (HOL_basic_ss addsimps [@{thm not_False_eq_True}]) 1 + THEN (EVERY (map (prove_param2 thy) (param_modes ~~ params))) + else + etac @{thm not_predE'} 1) + THEN rec_tac + end + | Sidecond t => + etac @{thm bindE} 1 + THEN etac @{thm if_predE} 1 + THEN prove_sidecond2 thy modes t + THEN prove_prems2 [] ps) + in print_tac "before prove_match2:" + THEN prove_match2 thy out_ts + THEN print_tac "after prove_match2:" + THEN rest_tac + end; + val prems_tac = prove_prems2 in_ts ps + in + print_tac "starting prove_clause2" + THEN etac @{thm bindE} 1 + THEN (etac @{thm singleE'} 1) + THEN (TRY (etac @{thm Pair_inject} 1)) + THEN print_tac "after singleE':" + THEN prems_tac + end; + +fun prove_other_direction thy modes pred mode moded_clauses = + let + fun prove_clause clause i = + (if i < length moded_clauses then etac @{thm supE} 1 else all_tac) + THEN (prove_clause2 thy modes pred mode clause i) + in + (DETERM (TRY (rtac @{thm unit.induct} 1))) + THEN (REPEAT_DETERM (CHANGED (rewtac @{thm split_paired_all}))) + THEN (rtac (predfun_intro_of thy pred mode) 1) + THEN (REPEAT_DETERM (rtac @{thm refl} 2)) + THEN (EVERY (map2 prove_clause moded_clauses (1 upto (length moded_clauses)))) + end; + +(** proof procedure **) + +fun prove_pred thy clauses preds modes pred mode (moded_clauses, compiled_term) = + let + val ctxt = ProofContext.init thy + val clauses = the (AList.lookup (op =) clauses pred) + in + Goal.prove ctxt (Term.add_free_names compiled_term []) [] compiled_term + (if !do_proofs then + (fn _ => + rtac @{thm pred_iffI} 1 + THEN print_tac "after pred_iffI" + THEN prove_one_direction thy clauses preds modes pred mode moded_clauses + THEN print_tac "proved one direction" + THEN prove_other_direction thy modes pred mode moded_clauses + THEN print_tac "proved other direction") + else (fn _ => mycheat_tac thy 1)) + end; + +(* composition of mode inference, definition, compilation and proof *) + +(** auxillary combinators for table of preds and modes **) + +fun map_preds_modes f preds_modes_table = + map (fn (pred, modes) => + (pred, map (fn (mode, value) => (mode, f pred mode value)) modes)) preds_modes_table + +fun join_preds_modes table1 table2 = + map_preds_modes (fn pred => fn mode => fn value => + (value, the (AList.lookup (op =) (the (AList.lookup (op =) table2 pred)) mode))) table1 + +fun maps_modes preds_modes_table = + map (fn (pred, modes) => + (pred, map (fn (mode, value) => value) modes)) preds_modes_table + +fun compile_preds compfuns mk_fun_of use_size thy all_vs param_vs preds moded_clauses = + map_preds_modes (fn pred => compile_pred compfuns mk_fun_of use_size thy all_vs param_vs pred + (the (AList.lookup (op =) preds pred))) moded_clauses + +fun prove thy clauses preds modes moded_clauses compiled_terms = + map_preds_modes (prove_pred thy clauses preds modes) + (join_preds_modes moded_clauses compiled_terms) + +fun prove_by_skip thy _ _ _ _ compiled_terms = + map_preds_modes (fn pred => fn mode => fn t => Drule.standard (SkipProof.make_thm thy t)) + compiled_terms + +fun prepare_intrs thy prednames = + let + val intrs = maps (intros_of thy) prednames + |> map (Logic.unvarify o prop_of) + val nparams = nparams_of thy (hd prednames) + val extra_modes = all_modes_of thy |> filter_out (fn (name, _) => member (op =) prednames name) + val preds = distinct (op =) (map (dest_Const o fst o (strip_intro_concl nparams)) intrs) + val _ $ u = Logic.strip_imp_concl (hd intrs); + val params = List.take (snd (strip_comb u), nparams); + val param_vs = maps term_vs params + val all_vs = terms_vs intrs + fun dest_prem t = + (case strip_comb t of + (v as Free _, ts) => if v mem params then Prem (ts, v) else Sidecond t + | (c as Const (@{const_name Not}, _), [t]) => (case dest_prem t of + Prem (ts, t) => Negprem (ts, t) + | Negprem _ => error ("Double negation not allowed in premise: " ^ (Syntax.string_of_term_global thy (c $ t))) + | Sidecond t => Sidecond (c $ t)) + | (c as Const (s, _), ts) => + if is_registered thy s then + let val (ts1, ts2) = chop (nparams_of thy s) ts + in Prem (ts2, list_comb (c, ts1)) end + else Sidecond t + | _ => Sidecond t) + fun add_clause intr (clauses, arities) = + let + val _ $ t = Logic.strip_imp_concl intr; + val (Const (name, T), ts) = strip_comb t; + val (ts1, ts2) = chop nparams ts; + val prems = map (dest_prem o HOLogic.dest_Trueprop) (Logic.strip_imp_prems intr); + val (Ts, Us) = chop nparams (binder_types T) + in + (AList.update op = (name, these (AList.lookup op = clauses name) @ + [(ts2, prems)]) clauses, + AList.update op = (name, (map (fn U => (case strip_type U of + (Rs as _ :: _, Type ("bool", [])) => SOME (length Rs) + | _ => NONE)) Ts, + length Us)) arities) + end; + val (clauses, arities) = fold add_clause intrs ([], []); + fun modes_of_arities arities = + (map (fn (s, (ks, k)) => (s, cprod (cprods (map + (fn NONE => [NONE] + | SOME k' => map SOME (map (map (rpair NONE)) (subsets 1 k'))) ks), + map (map (rpair NONE)) (subsets 1 k)))) arities) + fun modes_of_typ T = + let + val (Ts, Us) = chop nparams (binder_types T) + fun all_smodes_of_typs Ts = cprods_subset ( + map_index (fn (i, U) => + case HOLogic.strip_tupleT U of + [] => [(i + 1, NONE)] + | [U] => [(i + 1, NONE)] + | Us => map (pair (i + 1) o SOME) ((subsets 1 (length Us)) \\ [[], 1 upto (length Us)])) + Ts) + in + cprod (cprods (map (fn T => case strip_type T of + (Rs as _ :: _, Type ("bool", [])) => map SOME (all_smodes_of_typs Rs) | _ => [NONE]) Ts), + all_smodes_of_typs Us) + end + val all_modes = map (fn (s, T) => (s, modes_of_typ T)) preds + in (preds, nparams, all_vs, param_vs, extra_modes, clauses, all_modes) end; + +(** main function of predicate compiler **) + +fun add_equations_of steps prednames thy = + let + val _ = Output.tracing ("Starting predicate compiler for predicates " ^ commas prednames ^ "...") + val (preds, nparams, all_vs, param_vs, extra_modes, clauses, all_modes) = + prepare_intrs thy prednames + val _ = Output.tracing "Infering modes..." + val moded_clauses = #infer_modes steps thy extra_modes all_modes param_vs clauses + val modes = map (fn (p, mps) => (p, map fst mps)) moded_clauses + val _ = print_modes modes + val _ = print_moded_clauses thy moded_clauses + val _ = Output.tracing "Defining executable functions..." + val thy' = fold (#create_definitions steps preds) modes thy + |> Theory.checkpoint + val _ = Output.tracing "Compiling equations..." + val compiled_terms = + (#compile_preds steps) thy' all_vs param_vs preds moded_clauses + val _ = print_compiled_terms thy' compiled_terms + val _ = Output.tracing "Proving equations..." + val result_thms = #prove steps thy' clauses preds (extra_modes @ modes) + moded_clauses compiled_terms + val qname = #qname steps + (* val attrib = gn thy => Attrib.attribute_i thy Code.add_eqn_attrib *) + val attrib = fn thy => Attrib.attribute_i thy (Attrib.internal (K (Thm.declaration_attribute + (fn thm => Context.mapping (Code.add_eqn thm) I)))) + val thy'' = fold (fn (name, result_thms) => fn thy => snd (PureThy.add_thmss + [((Binding.qualify true (Long_Name.base_name name) (Binding.name qname), result_thms), + [attrib thy ])] thy)) + (maps_modes result_thms) thy' + |> Theory.checkpoint + in + thy'' + end + +fun extend' value_of edges_of key (G, visited) = + let + val (G', v) = case try (Graph.get_node G) key of + SOME v => (G, v) + | NONE => (Graph.new_node (key, value_of key) G, value_of key) + val (G'', visited') = fold (extend' value_of edges_of) (edges_of (key, v) \\ visited) + (G', key :: visited) + in + (fold (Graph.add_edge o (pair key)) (edges_of (key, v)) G'', visited') + end; + +fun extend value_of edges_of key G = fst (extend' value_of edges_of key (G, [])) + +fun gen_add_equations steps names thy = + let + val thy' = PredData.map (fold (extend (fetch_pred_data thy) (depending_preds_of thy)) names) thy + |> Theory.checkpoint; + fun strong_conn_of gr keys = + Graph.strong_conn (Graph.subgraph (member (op =) (Graph.all_succs gr keys)) gr) + val scc = strong_conn_of (PredData.get thy') names + val thy'' = fold_rev + (fn preds => fn thy => + if #are_not_defined steps thy preds then add_equations_of steps preds thy else thy) + scc thy' |> Theory.checkpoint + in thy'' end + +(* different instantiantions of the predicate compiler *) + +val add_equations = gen_add_equations + {infer_modes = infer_modes, + create_definitions = create_definitions, + compile_preds = compile_preds PredicateCompFuns.compfuns mk_fun_of false, + prove = prove, + are_not_defined = (fn thy => forall (null o modes_of thy)), + qname = "equation"} + +val add_sizelim_equations = gen_add_equations + {infer_modes = infer_modes, + create_definitions = sizelim_create_definitions, + compile_preds = compile_preds PredicateCompFuns.compfuns mk_sizelim_fun_of true, + prove = prove_by_skip, + are_not_defined = (fn thy => fn preds => true), (* TODO *) + qname = "sizelim_equation" + } + +val add_quickcheck_equations = gen_add_equations + {infer_modes = infer_modes_with_generator, + create_definitions = rpred_create_definitions, + compile_preds = compile_preds RPredCompFuns.compfuns mk_generator_of true, + prove = prove_by_skip, + are_not_defined = (fn thy => fn preds => true), (* TODO *) + qname = "rpred_equation"} + +(** user interface **) + +(* generation of case rules from user-given introduction rules *) + +fun mk_casesrule ctxt nparams introrules = + let + val intros = map (Logic.unvarify o prop_of) introrules + val (pred, (params, args)) = strip_intro_concl nparams (hd intros) + val ([propname], ctxt1) = Variable.variant_fixes ["thesis"] ctxt + val prop = HOLogic.mk_Trueprop (Free (propname, HOLogic.boolT)) + val (argnames, ctxt2) = Variable.variant_fixes + (map (fn i => "a" ^ string_of_int i) (1 upto (length args))) ctxt1 + val argvs = map2 (curry Free) argnames (map fastype_of args) + fun mk_case intro = + let + val (_, (_, args)) = strip_intro_concl nparams intro + val prems = Logic.strip_imp_prems intro + val eqprems = map (HOLogic.mk_Trueprop o HOLogic.mk_eq) (argvs ~~ args) + val frees = (fold o fold_aterms) + (fn t as Free _ => + if member (op aconv) params t then I else insert (op aconv) t + | _ => I) (args @ prems) [] + in fold Logic.all frees (Logic.list_implies (eqprems @ prems, prop)) end + val assm = HOLogic.mk_Trueprop (list_comb (pred, params @ argvs)) + val cases = map mk_case intros + in Logic.list_implies (assm :: cases, prop) end; + +(* code_pred_intro attribute *) + +fun attrib f = Thm.declaration_attribute (fn thm => Context.mapping (f thm) I); + +val code_pred_intros_attrib = attrib add_intro; + +local + +(* TODO: make TheoryDataFun to GenericDataFun & remove duplication of local theory and theory *) +fun generic_code_pred prep_const raw_const lthy = + let + val thy = ProofContext.theory_of lthy + val const = prep_const thy raw_const + val lthy' = LocalTheory.theory (PredData.map + (extend (fetch_pred_data thy) (depending_preds_of thy) const)) lthy + |> LocalTheory.checkpoint + val thy' = ProofContext.theory_of lthy' + val preds = Graph.all_preds (PredData.get thy') [const] |> filter_out (has_elim thy') + fun mk_cases const = + let + val nparams = nparams_of thy' const + val intros = intros_of thy' const + in mk_casesrule lthy' nparams intros end + val cases_rules = map mk_cases preds + val cases = + map (fn case_rule => RuleCases.Case {fixes = [], + assumes = [("", Logic.strip_imp_prems case_rule)], + binds = [], cases = []}) cases_rules + val case_env = map2 (fn p => fn c => (Long_Name.base_name p, SOME c)) preds cases + val lthy'' = lthy' + |> fold Variable.auto_fixes cases_rules + |> ProofContext.add_cases true case_env + fun after_qed thms goal_ctxt = + let + val global_thms = ProofContext.export goal_ctxt + (ProofContext.init (ProofContext.theory_of goal_ctxt)) (map the_single thms) + in + goal_ctxt |> LocalTheory.theory (fold set_elim global_thms #> add_equations [const]) + end + in + Proof.theorem_i NONE after_qed (map (single o (rpair [])) cases_rules) lthy'' + end; + +structure P = OuterParse + +in + +val code_pred = generic_code_pred (K I); +val code_pred_cmd = generic_code_pred Code.read_const + +val setup = PredData.put (Graph.empty) #> + Attrib.setup @{binding code_pred_intros} (Scan.succeed (attrib add_intro)) + "adding alternative introduction rules for code generation of inductive predicates" +(* Attrib.setup @{binding code_ind_cases} (Scan.succeed add_elim_attrib) + "adding alternative elimination rules for code generation of inductive predicates"; + *) + (*FIXME name discrepancy in attribs and ML code*) + (*FIXME intros should be better named intro*) + (*FIXME why distinguished attribute for cases?*) + +val _ = OuterSyntax.local_theory_to_proof "code_pred" + "prove equations for predicate specified by intro/elim rules" + OuterKeyword.thy_goal (P.term_group >> code_pred_cmd) + +end + +(*FIXME +- Naming of auxiliary rules necessary? +- add default code equations P x y z = P_i_i_i x y z +*) + +(* transformation for code generation *) + +val eval_ref = ref (NONE : (unit -> term Predicate.pred) option); + +(*FIXME turn this into an LCF-guarded preprocessor for comprehensions*) +fun analyze_compr thy t_compr = + let + val split = case t_compr of (Const (@{const_name Collect}, _) $ t) => t + | _ => error ("Not a set comprehension: " ^ Syntax.string_of_term_global thy t_compr); + val (body, Ts, fp) = HOLogic.strip_psplits split; + val (pred as Const (name, T), all_args) = strip_comb body; + val (params, args) = chop (nparams_of thy name) all_args; + val user_mode = map_filter I (map_index + (fn (i, t) => case t of Bound j => if j < length Ts then NONE + else SOME (i+1) | _ => SOME (i+1)) args); (*FIXME dangling bounds should not occur*) + val user_mode' = map (rpair NONE) user_mode + val modes = filter (fn Mode (_, is, _) => is = user_mode') + (modes_of_term (all_modes_of thy) (list_comb (pred, params))); + val m = case modes + of [] => error ("No mode possible for comprehension " + ^ Syntax.string_of_term_global thy t_compr) + | [m] => m + | m :: _ :: _ => (warning ("Multiple modes possible for comprehension " + ^ Syntax.string_of_term_global thy t_compr); m); + val (inargs, outargs) = split_smode user_mode' args; + val t_pred = list_comb (compile_expr NONE thy (m, list_comb (pred, params)), inargs); + val t_eval = if null outargs then t_pred else let + val outargs_bounds = map (fn Bound i => i) outargs; + val outargsTs = map (nth Ts) outargs_bounds; + val T_pred = HOLogic.mk_tupleT outargsTs; + val T_compr = HOLogic.mk_ptupleT fp Ts; + val arrange_bounds = map_index I outargs_bounds + |> sort (prod_ord (K EQUAL) int_ord) + |> map fst; + val arrange = funpow (length outargs_bounds - 1) HOLogic.mk_split + (Term.list_abs (map (pair "") outargsTs, + HOLogic.mk_ptuple fp T_compr (map Bound arrange_bounds))) + in mk_map PredicateCompFuns.compfuns T_pred T_compr arrange t_pred end + in t_eval end; + +fun eval thy t_compr = + let + val t = analyze_compr thy t_compr; + val T = dest_predT PredicateCompFuns.compfuns (fastype_of t); + val t' = mk_map PredicateCompFuns.compfuns T HOLogic.termT (HOLogic.term_of_const T) t; + in (T, Code_ML.eval NONE ("Predicate_Compile.eval_ref", eval_ref) Predicate.map thy t' []) end; + +fun values ctxt k t_compr = + let + val thy = ProofContext.theory_of ctxt; + val (T, t) = eval thy t_compr; + val setT = HOLogic.mk_setT T; + val (ts, _) = Predicate.yieldn k t; + val elemsT = HOLogic.mk_set T ts; + in if k = ~1 orelse length ts < k then elemsT + else Const (@{const_name Set.union}, setT --> setT --> setT) $ elemsT $ t_compr + end; + +fun values_cmd modes k raw_t state = + let + val ctxt = Toplevel.context_of state; + val t = Syntax.read_term ctxt raw_t; + val t' = values ctxt k t; + val ty' = Term.type_of t'; + val ctxt' = Variable.auto_fixes t' ctxt; + val p = PrintMode.with_modes modes (fn () => + Pretty.block [Pretty.quote (Syntax.pretty_term ctxt' t'), Pretty.fbrk, + Pretty.str "::", Pretty.brk 1, Pretty.quote (Syntax.pretty_typ ctxt' ty')]) (); + in Pretty.writeln p end; + +local structure P = OuterParse in + +val opt_modes = Scan.optional (P.$$$ "(" |-- P.!!! (Scan.repeat1 P.xname --| P.$$$ ")")) []; + +val _ = OuterSyntax.improper_command "values" "enumerate and print comprehensions" OuterKeyword.diag + (opt_modes -- Scan.optional P.nat ~1 -- P.term + >> (fn ((modes, k), t) => Toplevel.no_timing o Toplevel.keep + (values_cmd modes k t))); + +end; + +end; diff -r fd96d5f49d59 -r 09546e654222 src/HOL/ex/Predicate_Compile.thy --- a/src/HOL/ex/Predicate_Compile.thy Wed Sep 23 16:20:12 2009 +0200 +++ b/src/HOL/ex/Predicate_Compile.thy Wed Sep 23 16:20:12 2009 +0200 @@ -1,6 +1,6 @@ theory Predicate_Compile imports Complex_Main RPred -uses "predicate_compile.ML" +uses "../Tools/Predicate_Compile/predicate_compile_core.ML" begin setup {* Predicate_Compile.setup *} diff -r fd96d5f49d59 -r 09546e654222 src/HOL/ex/predicate_compile.ML --- a/src/HOL/ex/predicate_compile.ML Wed Sep 23 16:20:12 2009 +0200 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,2399 +0,0 @@ -(* Author: Lukas Bulwahn, TU Muenchen - -(Prototype of) A compiler from predicates specified by intro/elim rules -to equations. -*) - -signature PREDICATE_COMPILE = -sig - type smode = (int * int list option) list - type mode = smode option list * smode - datatype tmode = Mode of mode * smode * tmode option list; - (*val add_equations_of: bool -> string list -> theory -> theory *) - val register_predicate : (thm list * thm * int) -> theory -> theory - val is_registered : theory -> string -> bool - (* val fetch_pred_data : theory -> string -> (thm list * thm * int) *) - val predfun_intro_of: theory -> string -> mode -> thm - val predfun_elim_of: theory -> string -> mode -> thm - val strip_intro_concl: int -> term -> term * (term list * term list) - val predfun_name_of: theory -> string -> mode -> string - val all_preds_of : theory -> string list - val modes_of: theory -> string -> mode list - val string_of_mode : mode -> string - val intros_of: theory -> string -> thm list - val nparams_of: theory -> string -> int - val add_intro: thm -> theory -> theory - val set_elim: thm -> theory -> theory - val setup: theory -> theory - val code_pred: string -> Proof.context -> Proof.state - val code_pred_cmd: string -> Proof.context -> Proof.state - val print_stored_rules: theory -> unit - val print_all_modes: theory -> unit - val do_proofs: bool ref - val mk_casesrule : Proof.context -> int -> thm list -> term - val analyze_compr: theory -> term -> term - val eval_ref: (unit -> term Predicate.pred) option ref - val add_equations : string list -> theory -> theory - val code_pred_intros_attrib : attribute - (* used by Quickcheck_Generator *) - (*val funT_of : mode -> typ -> typ - val mk_if_pred : term -> term - val mk_Eval : term * term -> term*) - val mk_tupleT : typ list -> typ -(* val mk_predT : typ -> typ *) - (* temporary for testing of the compilation *) - datatype indprem = Prem of term list * term | Negprem of term list * term | Sidecond of term | - GeneratorPrem of term list * term | Generator of (string * typ); - (* val prepare_intrs: theory -> string list -> - (string * typ) list * int * string list * string list * (string * mode list) list * - (string * (term list * indprem list) list) list * (string * (int option list * int)) list*) - datatype compilation_funs = CompilationFuns of { - mk_predT : typ -> typ, - dest_predT : typ -> typ, - mk_bot : typ -> term, - mk_single : term -> term, - mk_bind : term * term -> term, - mk_sup : term * term -> term, - mk_if : term -> term, - mk_not : term -> term, - mk_map : typ -> typ -> term -> term -> term, - lift_pred : term -> term - }; - type moded_clause = term list * (indprem * tmode) list - type 'a pred_mode_table = (string * (mode * 'a) list) list - val infer_modes : theory -> (string * mode list) list - -> (string * mode list) list - -> string list - -> (string * (term list * indprem list) list) list - -> (moded_clause list) pred_mode_table - val infer_modes_with_generator : theory -> (string * mode list) list - -> (string * mode list) list - -> string list - -> (string * (term list * indprem list) list) list - -> (moded_clause list) pred_mode_table - (*val compile_preds : theory -> compilation_funs -> string list -> string list - -> (string * typ) list -> (moded_clause list) pred_mode_table -> term pred_mode_table - val rpred_create_definitions :(string * typ) list -> string * mode list - -> theory -> theory - val split_smode : int list -> term list -> (term list * term list) *) - val print_moded_clauses : - theory -> (moded_clause list) pred_mode_table -> unit - val print_compiled_terms : theory -> term pred_mode_table -> unit - (*val rpred_prove_preds : theory -> term pred_mode_table -> thm pred_mode_table*) - val rpred_compfuns : compilation_funs - val dest_funT : typ -> typ * typ - (* val depending_preds_of : theory -> thm list -> string list *) - val add_quickcheck_equations : string list -> theory -> theory - val add_sizelim_equations : string list -> theory -> theory - val is_inductive_predicate : theory -> string -> bool - val terms_vs : term list -> string list - val subsets : int -> int -> int list list - val check_mode_clause : bool -> theory -> string list -> - (string * mode list) list -> (string * mode list) list -> mode -> (term list * indprem list) - -> (term list * (indprem * tmode) list) option - val string_of_moded_prem : theory -> (indprem * tmode) -> string - val all_modes_of : theory -> (string * mode list) list - val all_generator_modes_of : theory -> (string * mode list) list - val compile_clause : compilation_funs -> term option -> (term list -> term) -> - theory -> string list -> string list -> mode -> term -> moded_clause -> term - val preprocess_intro : theory -> thm -> thm - val is_constrt : theory -> term -> bool - val is_predT : typ -> bool - val guess_nparams : typ -> int - val cprods_subset : 'a list list -> 'a list list -end; - -structure Predicate_Compile : PREDICATE_COMPILE = -struct - -(** auxiliary **) - -(* debug stuff *) - -fun tracing s = (if ! Toplevel.debug then Output.tracing s else ()); - -fun print_tac s = Seq.single; (*Tactical.print_tac s;*) (* (if ! Toplevel.debug then Tactical.print_tac s else Seq.single); *) -fun debug_tac msg = Seq.single; (* (fn st => (Output.tracing msg; Seq.single st)); *) - -val do_proofs = ref true; - -fun mycheat_tac thy i st = - (Tactic.rtac (SkipProof.make_thm thy (Var (("A", 0), propT))) i) st - -fun remove_last_goal thy st = - (Tactic.rtac (SkipProof.make_thm thy (Var (("A", 0), propT))) (nprems_of st)) st - -(* reference to preprocessing of InductiveSet package *) - -val ind_set_codegen_preproc = Inductive_Set.codegen_preproc; - -(** fundamentals **) - -(* syntactic operations *) - -fun mk_eq (x, xs) = - let fun mk_eqs _ [] = [] - | mk_eqs a (b::cs) = - HOLogic.mk_eq (Free (a, fastype_of b), b) :: mk_eqs a cs - in mk_eqs x xs end; - -fun mk_tupleT [] = HOLogic.unitT - | mk_tupleT Ts = foldr1 HOLogic.mk_prodT Ts; - -fun dest_tupleT (Type (@{type_name Product_Type.unit}, [])) = [] - | dest_tupleT (Type (@{type_name "*"}, [T1, T2])) = T1 :: (dest_tupleT T2) - | dest_tupleT t = [t] - -fun mk_tuple [] = HOLogic.unit - | mk_tuple ts = foldr1 HOLogic.mk_prod ts; - -fun dest_tuple (Const (@{const_name Product_Type.Unity}, _)) = [] - | dest_tuple (Const (@{const_name Pair}, _) $ t1 $ t2) = t1 :: (dest_tuple t2) - | dest_tuple t = [t] - -fun mk_scomp (t, u) = - let - val T = fastype_of t - val U = fastype_of u - val [A] = binder_types T - val D = body_type U - in - Const (@{const_name "scomp"}, T --> U --> A --> D) $ t $ u - end; - -fun dest_funT (Type ("fun",[S, T])) = (S, T) - | dest_funT T = raise TYPE ("dest_funT", [T], []) - -fun mk_fun_comp (t, u) = - let - val (_, B) = dest_funT (fastype_of t) - val (C, A) = dest_funT (fastype_of u) - in - Const(@{const_name "Fun.comp"}, (A --> B) --> (C --> A) --> C --> B) $ t $ u - end; - -fun dest_randomT (Type ("fun", [@{typ Random.seed}, - Type ("*", [Type ("*", [T, @{typ "unit => Code_Eval.term"}]) ,@{typ Random.seed}])])) = T - | dest_randomT T = raise TYPE ("dest_randomT", [T], []) - -(* destruction of intro rules *) - -(* FIXME: look for other place where this functionality was used before *) -fun strip_intro_concl nparams intro = let - val _ $ u = Logic.strip_imp_concl intro - val (pred, all_args) = strip_comb u - val (params, args) = chop nparams all_args -in (pred, (params, args)) end - -(** data structures **) - -type smode = (int * int list option) list; -type mode = smode option list * smode; -datatype tmode = Mode of mode * smode * tmode option list; - -fun gen_split_smode (mk_tuple, strip_tuple) smode ts = - let - fun split_tuple' _ _ [] = ([], []) - | split_tuple' is i (t::ts) = - (if i mem is then apfst else apsnd) (cons t) - (split_tuple' is (i+1) ts) - fun split_tuple is t = split_tuple' is 1 (strip_tuple t) - fun split_smode' _ _ [] = ([], []) - | split_smode' smode i (t::ts) = - (if i mem (map fst smode) then - case (the (AList.lookup (op =) smode i)) of - NONE => apfst (cons t) - | SOME is => - let - val (ts1, ts2) = split_tuple is t - fun cons_tuple ts = if null ts then I else cons (mk_tuple ts) - in (apfst (cons_tuple ts1)) o (apsnd (cons_tuple ts2)) end - else apsnd (cons t)) - (split_smode' smode (i+1) ts) - in split_smode' smode 1 ts end - -val split_smode = gen_split_smode (HOLogic.mk_tuple, HOLogic.strip_tuple) -val split_smodeT = gen_split_smode (HOLogic.mk_tupleT, HOLogic.strip_tupleT) - -fun gen_split_mode split_smode (iss, is) ts = - let - val (t1, t2) = chop (length iss) ts - in (t1, split_smode is t2) end - -val split_mode = gen_split_mode split_smode -val split_modeT = gen_split_mode split_smodeT - -fun string_of_smode js = - commas (map - (fn (i, is) => - string_of_int i ^ (case is of NONE => "" - | SOME is => "p" ^ enclose "[" "]" (commas (map string_of_int is)))) js) - -fun string_of_mode (iss, is) = space_implode " -> " (map - (fn NONE => "X" - | SOME js => enclose "[" "]" (string_of_smode js)) - (iss @ [SOME is])); - -fun string_of_tmode (Mode (predmode, termmode, param_modes)) = - "predmode: " ^ (string_of_mode predmode) ^ - (if null param_modes then "" else - "; " ^ "params: " ^ commas (map (the_default "NONE" o Option.map string_of_tmode) param_modes)) - -datatype indprem = Prem of term list * term | Negprem of term list * term | Sidecond of term | - GeneratorPrem of term list * term | Generator of (string * typ); - -type moded_clause = term list * (indprem * tmode) list -type 'a pred_mode_table = (string * (mode * 'a) list) list - -datatype predfun_data = PredfunData of { - name : string, - definition : thm, - intro : thm, - elim : thm -}; - -fun rep_predfun_data (PredfunData data) = data; -fun mk_predfun_data (name, definition, intro, elim) = - PredfunData {name = name, definition = definition, intro = intro, elim = elim} - -datatype function_data = FunctionData of { - name : string, - equation : thm option (* is not used at all? *) -}; - -fun rep_function_data (FunctionData data) = data; -fun mk_function_data (name, equation) = - FunctionData {name = name, equation = equation} - -datatype pred_data = PredData of { - intros : thm list, - elim : thm option, - nparams : int, - functions : (mode * predfun_data) list, - generators : (mode * function_data) list, - sizelim_functions : (mode * function_data) list -}; - -fun rep_pred_data (PredData data) = data; -fun mk_pred_data ((intros, elim, nparams), (functions, generators, sizelim_functions)) = - PredData {intros = intros, elim = elim, nparams = nparams, - functions = functions, generators = generators, sizelim_functions = sizelim_functions} -fun map_pred_data f (PredData {intros, elim, nparams, functions, generators, sizelim_functions}) = - mk_pred_data (f ((intros, elim, nparams), (functions, generators, sizelim_functions))) - -fun eq_option eq (NONE, NONE) = true - | eq_option eq (SOME x, SOME y) = eq (x, y) - | eq_option eq _ = false - -fun eq_pred_data (PredData d1, PredData d2) = - eq_list (Thm.eq_thm) (#intros d1, #intros d2) andalso - eq_option (Thm.eq_thm) (#elim d1, #elim d2) andalso - #nparams d1 = #nparams d2 - -structure PredData = TheoryDataFun -( - type T = pred_data Graph.T; - val empty = Graph.empty; - val copy = I; - val extend = I; - fun merge _ = Graph.merge eq_pred_data; -); - -(* queries *) - -fun lookup_pred_data thy name = - Option.map rep_pred_data (try (Graph.get_node (PredData.get thy)) name) - -fun the_pred_data thy name = case lookup_pred_data thy name - of NONE => error ("No such predicate " ^ quote name) - | SOME data => data; - -val is_registered = is_some oo lookup_pred_data - -val all_preds_of = Graph.keys o PredData.get - -fun intros_of thy = map (Thm.transfer thy) o #intros o the_pred_data thy - -fun the_elim_of thy name = case #elim (the_pred_data thy name) - of NONE => error ("No elimination rule for predicate " ^ quote name) - | SOME thm => Thm.transfer thy thm - -val has_elim = is_some o #elim oo the_pred_data; - -val nparams_of = #nparams oo the_pred_data - -val modes_of = (map fst) o #functions oo the_pred_data - -fun all_modes_of thy = map (fn name => (name, modes_of thy name)) (all_preds_of thy) - -val is_compiled = not o null o #functions oo the_pred_data - -fun lookup_predfun_data thy name mode = - Option.map rep_predfun_data (AList.lookup (op =) - (#functions (the_pred_data thy name)) mode) - -fun the_predfun_data thy name mode = case lookup_predfun_data thy name mode - of NONE => error ("No function defined for mode " ^ string_of_mode mode ^ " of predicate " ^ name) - | SOME data => data; - -val predfun_name_of = #name ooo the_predfun_data - -val predfun_definition_of = #definition ooo the_predfun_data - -val predfun_intro_of = #intro ooo the_predfun_data - -val predfun_elim_of = #elim ooo the_predfun_data - -fun lookup_generator_data thy name mode = - Option.map rep_function_data (AList.lookup (op =) - (#generators (the_pred_data thy name)) mode) - -fun the_generator_data thy name mode = case lookup_generator_data thy name mode - of NONE => error ("No generator defined for mode " ^ string_of_mode mode ^ " of predicate " ^ name) - | SOME data => data - -val generator_name_of = #name ooo the_generator_data - -val generator_modes_of = (map fst) o #generators oo the_pred_data - -fun all_generator_modes_of thy = - map (fn name => (name, generator_modes_of thy name)) (all_preds_of thy) - -fun lookup_sizelim_function_data thy name mode = - Option.map rep_function_data (AList.lookup (op =) - (#sizelim_functions (the_pred_data thy name)) mode) - -fun the_sizelim_function_data thy name mode = case lookup_sizelim_function_data thy name mode - of NONE => error ("No size-limited function defined for mode " ^ string_of_mode mode - ^ " of predicate " ^ name) - | SOME data => data - -val sizelim_function_name_of = #name ooo the_sizelim_function_data - -(*val generator_modes_of = (map fst) o #generators oo the_pred_data*) - -(* diagnostic display functions *) - -fun print_modes modes = Output.tracing ("Inferred modes:\n" ^ - cat_lines (map (fn (s, ms) => s ^ ": " ^ commas (map - string_of_mode ms)) modes)); - -fun print_pred_mode_table string_of_entry thy pred_mode_table = - let - fun print_mode pred (mode, entry) = "mode : " ^ (string_of_mode mode) - ^ (string_of_entry pred mode entry) - fun print_pred (pred, modes) = - "predicate " ^ pred ^ ": " ^ cat_lines (map (print_mode pred) modes) - val _ = Output.tracing (cat_lines (map print_pred pred_mode_table)) - in () end; - -fun string_of_moded_prem thy (Prem (ts, p), tmode) = - (Syntax.string_of_term_global thy (list_comb (p, ts))) ^ - "(" ^ (string_of_tmode tmode) ^ ")" - | string_of_moded_prem thy (GeneratorPrem (ts, p), Mode (predmode, is, _)) = - (Syntax.string_of_term_global thy (list_comb (p, ts))) ^ - "(generator_mode: " ^ (string_of_mode predmode) ^ ")" - | string_of_moded_prem thy (Generator (v, T), _) = - "Generator for " ^ v ^ " of Type " ^ (Syntax.string_of_typ_global thy T) - | string_of_moded_prem thy (Negprem (ts, p), Mode (_, is, _)) = - (Syntax.string_of_term_global thy (list_comb (p, ts))) ^ - "(negative mode: " ^ string_of_smode is ^ ")" - | string_of_moded_prem thy (Sidecond t, Mode (_, is, _)) = - (Syntax.string_of_term_global thy t) ^ - "(sidecond mode: " ^ string_of_smode is ^ ")" - | string_of_moded_prem _ _ = error "string_of_moded_prem: unimplemented" - -fun print_moded_clauses thy = - let - fun string_of_clause pred mode clauses = - cat_lines (map (fn (ts, prems) => (space_implode " --> " - (map (string_of_moded_prem thy) prems)) ^ " --> " ^ pred ^ " " - ^ (space_implode " " (map (Syntax.string_of_term_global thy) ts))) clauses) - in print_pred_mode_table string_of_clause thy end; - -fun print_compiled_terms thy = - print_pred_mode_table (fn _ => fn _ => Syntax.string_of_term_global thy) thy - -fun print_stored_rules thy = - let - val preds = (Graph.keys o PredData.get) thy - fun print pred () = let - val _ = writeln ("predicate: " ^ pred) - val _ = writeln ("number of parameters: " ^ string_of_int (nparams_of thy pred)) - val _ = writeln ("introrules: ") - val _ = fold (fn thm => fn u => writeln (Display.string_of_thm_global thy thm)) - (rev (intros_of thy pred)) () - in - if (has_elim thy pred) then - writeln ("elimrule: " ^ Display.string_of_thm_global thy (the_elim_of thy pred)) - else - writeln ("no elimrule defined") - end - in - fold print preds () - end; - -fun print_all_modes thy = - let - val _ = writeln ("Inferred modes:") - fun print (pred, modes) u = - let - val _ = writeln ("predicate: " ^ pred) - val _ = writeln ("modes: " ^ (commas (map string_of_mode modes))) - in u end - in - fold print (all_modes_of thy) () - end - -(** preprocessing rules **) - -fun imp_prems_conv cv ct = - case Thm.term_of ct of - Const ("==>", _) $ _ $ _ => Conv.combination_conv (Conv.arg_conv cv) (imp_prems_conv cv) ct - | _ => Conv.all_conv ct - -fun Trueprop_conv cv ct = - case Thm.term_of ct of - Const ("Trueprop", _) $ _ => Conv.arg_conv cv ct - | _ => error "Trueprop_conv" - -fun preprocess_intro thy rule = - Conv.fconv_rule - (imp_prems_conv - (Trueprop_conv (Conv.try_conv (Conv.rewr_conv (Thm.symmetric @{thm Predicate.eq_is_eq}))))) - (Thm.transfer thy rule) - -fun preprocess_elim thy nparams elimrule = - let - val _ = Output.tracing ("Preprocessing elimination rule " - ^ (Display.string_of_thm_global thy elimrule)) - fun replace_eqs (Const ("Trueprop", _) $ (Const ("op =", T) $ lhs $ rhs)) = - HOLogic.mk_Trueprop (Const (@{const_name Predicate.eq}, T) $ lhs $ rhs) - | replace_eqs t = t - val prems = Thm.prems_of elimrule - val nargs = length (snd (strip_comb (HOLogic.dest_Trueprop (hd prems)))) - nparams - fun preprocess_case t = - let - val params = Logic.strip_params t - val (assums1, assums2) = chop nargs (Logic.strip_assums_hyp t) - val assums_hyp' = assums1 @ (map replace_eqs assums2) - in - list_all (params, Logic.list_implies (assums_hyp', Logic.strip_assums_concl t)) - end - val cases' = map preprocess_case (tl prems) - val elimrule' = Logic.list_implies ((hd prems) :: cases', Thm.concl_of elimrule) - (* - (*val _ = Output.tracing ("elimrule': "^ (Syntax.string_of_term_global thy elimrule'))*) - val bigeq = (Thm.symmetric (Conv.implies_concl_conv (MetaSimplifier.rewrite true [@{thm Predicate.eq_is_eq}]) - (cterm_of thy elimrule'))) - val _ = Output.tracing ("bigeq:" ^ (Display.string_of_thm_global thy bigeq)) - val res = - Thm.equal_elim bigeq - - elimrule - *) - val t = (fn {...} => mycheat_tac thy 1) - val eq = Goal.prove (ProofContext.init thy) [] [] (Logic.mk_equals ((Thm.prop_of elimrule), elimrule')) t - val _ = Output.tracing "Preprocessed elimination rule" - in - Thm.equal_elim eq elimrule - end; - -(* special case: predicate with no introduction rule *) -fun noclause thy predname elim = let - val T = (Logic.unvarifyT o Sign.the_const_type thy) predname - val Ts = binder_types T - val names = Name.variant_list [] - (map (fn i => "x" ^ (string_of_int i)) (1 upto (length Ts))) - val vs = map2 (curry Free) names Ts - val clausehd = HOLogic.mk_Trueprop (list_comb (Const (predname, T), vs)) - val intro_t = Logic.mk_implies (@{prop False}, clausehd) - val P = HOLogic.mk_Trueprop (Free ("P", HOLogic.boolT)) - val elim_t = Logic.list_implies ([clausehd, Logic.mk_implies (@{prop False}, P)], P) - val intro = Goal.prove (ProofContext.init thy) names [] intro_t - (fn {...} => etac @{thm FalseE} 1) - val elim = Goal.prove (ProofContext.init thy) ("P" :: names) [] elim_t - (fn {...} => etac elim 1) -in - ([intro], elim) -end - -fun fetch_pred_data thy name = - case try (Inductive.the_inductive (ProofContext.init thy)) name of - SOME (info as (_, result)) => - let - fun is_intro_of intro = - let - val (const, _) = strip_comb (HOLogic.dest_Trueprop (concl_of intro)) - in (fst (dest_Const const) = name) end; - val intros = ind_set_codegen_preproc thy ((map (preprocess_intro thy)) - (filter is_intro_of (#intrs result))) - val pre_elim = nth (#elims result) (find_index (fn s => s = name) (#names (fst info))) - val nparams = length (Inductive.params_of (#raw_induct result)) - val elim = singleton (ind_set_codegen_preproc thy) (preprocess_elim thy nparams pre_elim) - val (intros, elim) = if null intros then noclause thy name elim else (intros, elim) - in - mk_pred_data ((intros, SOME elim, nparams), ([], [], [])) - end - | NONE => error ("No such predicate: " ^ quote name) - -(* updaters *) - -fun apfst3 f (x, y, z) = (f x, y, z) -fun apsnd3 f (x, y, z) = (x, f y, z) -fun aptrd3 f (x, y, z) = (x, y, f z) - -fun add_predfun name mode data = - let - val add = (apsnd o apfst3 o cons) (mode, mk_predfun_data data) - in PredData.map (Graph.map_node name (map_pred_data add)) end - -fun is_inductive_predicate thy name = - is_some (try (Inductive.the_inductive (ProofContext.init thy)) name) - -fun depending_preds_of thy (key, value) = - let - val intros = (#intros o rep_pred_data) value - in - fold Term.add_const_names (map Thm.prop_of intros) [] - |> filter (fn c => (not (c = key)) andalso (is_inductive_predicate thy c orelse is_registered thy c)) - end; - - -(* code dependency graph *) -(* -fun dependencies_of thy name = - let - val (intros, elim, nparams) = fetch_pred_data thy name - val data = mk_pred_data ((intros, SOME elim, nparams), ([], [], [])) - val keys = depending_preds_of thy intros - in - (data, keys) - end; -*) -(* guessing number of parameters *) -fun find_indexes pred xs = - let - fun find is n [] = is - | find is n (x :: xs) = find (if pred x then (n :: is) else is) (n + 1) xs; - in rev (find [] 0 xs) end; - -fun is_predT (T as Type("fun", [_, _])) = (snd (strip_type T) = HOLogic.boolT) - | is_predT _ = false - -fun guess_nparams T = - let - val argTs = binder_types T - val nparams = fold (curry Int.max) - (map (fn x => x + 1) (find_indexes is_predT argTs)) 0 - in nparams end; - -fun add_intro thm thy = let - val (name, T) = dest_Const (fst (strip_intro_concl 0 (prop_of thm))) - fun cons_intro gr = - case try (Graph.get_node gr) name of - SOME pred_data => Graph.map_node name (map_pred_data - (apfst (fn (intro, elim, nparams) => (thm::intro, elim, nparams)))) gr - | NONE => - let - val nparams = the_default (guess_nparams T) (try (#nparams o rep_pred_data o (fetch_pred_data thy)) name) - in Graph.new_node (name, mk_pred_data (([thm], NONE, nparams), ([], [], []))) gr end; - in PredData.map cons_intro thy end - -fun set_elim thm = let - val (name, _) = dest_Const (fst - (strip_comb (HOLogic.dest_Trueprop (hd (prems_of thm))))) - fun set (intros, _, nparams) = (intros, SOME thm, nparams) - in PredData.map (Graph.map_node name (map_pred_data (apfst set))) end - -fun set_nparams name nparams = let - fun set (intros, elim, _ ) = (intros, elim, nparams) - in PredData.map (Graph.map_node name (map_pred_data (apfst set))) end - -fun register_predicate (pre_intros, pre_elim, nparams) thy = let - val (name, _) = dest_Const (fst (strip_intro_concl nparams (prop_of (hd pre_intros)))) - (* preprocessing *) - val intros = ind_set_codegen_preproc thy (map (preprocess_intro thy) pre_intros) - val elim = singleton (ind_set_codegen_preproc thy) (preprocess_elim thy nparams pre_elim) - in - PredData.map - (Graph.new_node (name, mk_pred_data ((intros, SOME elim, nparams), ([], [], [])))) thy - end - -fun set_generator_name pred mode name = - let - val set = (apsnd o apsnd3 o cons) (mode, mk_function_data (name, NONE)) - in - PredData.map (Graph.map_node pred (map_pred_data set)) - end - -fun set_sizelim_function_name pred mode name = - let - val set = (apsnd o aptrd3 o cons) (mode, mk_function_data (name, NONE)) - in - PredData.map (Graph.map_node pred (map_pred_data set)) - end - -(** data structures for generic compilation for different monads **) - -(* maybe rename functions more generic: - mk_predT -> mk_monadT; dest_predT -> dest_monadT - mk_single -> mk_return (?) -*) -datatype compilation_funs = CompilationFuns of { - mk_predT : typ -> typ, - dest_predT : typ -> typ, - mk_bot : typ -> term, - mk_single : term -> term, - mk_bind : term * term -> term, - mk_sup : term * term -> term, - mk_if : term -> term, - mk_not : term -> term, -(* funT_of : mode -> typ -> typ, *) -(* mk_fun_of : theory -> (string * typ) -> mode -> term, *) - mk_map : typ -> typ -> term -> term -> term, - lift_pred : term -> term -}; - -fun mk_predT (CompilationFuns funs) = #mk_predT funs -fun dest_predT (CompilationFuns funs) = #dest_predT funs -fun mk_bot (CompilationFuns funs) = #mk_bot funs -fun mk_single (CompilationFuns funs) = #mk_single funs -fun mk_bind (CompilationFuns funs) = #mk_bind funs -fun mk_sup (CompilationFuns funs) = #mk_sup funs -fun mk_if (CompilationFuns funs) = #mk_if funs -fun mk_not (CompilationFuns funs) = #mk_not funs -(*fun funT_of (CompilationFuns funs) = #funT_of funs*) -(*fun mk_fun_of (CompilationFuns funs) = #mk_fun_of funs*) -fun mk_map (CompilationFuns funs) = #mk_map funs -fun lift_pred (CompilationFuns funs) = #lift_pred funs - -fun funT_of compfuns (iss, is) T = - let - val Ts = binder_types T - val (paramTs, (inargTs, outargTs)) = split_modeT (iss, is) Ts - val paramTs' = map2 (fn NONE => I | SOME is => funT_of compfuns ([], is)) iss paramTs - in - (paramTs' @ inargTs) ---> (mk_predT compfuns (mk_tupleT outargTs)) - end; - -fun sizelim_funT_of compfuns (iss, is) T = - let - val Ts = binder_types T - val (paramTs, (inargTs, outargTs)) = split_modeT (iss, is) Ts - val paramTs' = map2 (fn SOME is => sizelim_funT_of compfuns ([], is) | NONE => I) iss paramTs - in - (paramTs' @ inargTs @ [@{typ "code_numeral"}]) ---> (mk_predT compfuns (mk_tupleT outargTs)) - end; - -fun mk_fun_of compfuns thy (name, T) mode = - Const (predfun_name_of thy name mode, funT_of compfuns mode T) - -fun mk_sizelim_fun_of compfuns thy (name, T) mode = - Const (sizelim_function_name_of thy name mode, sizelim_funT_of compfuns mode T) - -fun mk_generator_of compfuns thy (name, T) mode = - Const (generator_name_of thy name mode, sizelim_funT_of compfuns mode T) - - -structure PredicateCompFuns = -struct - -fun mk_predT T = Type (@{type_name "Predicate.pred"}, [T]) - -fun dest_predT (Type (@{type_name "Predicate.pred"}, [T])) = T - | dest_predT T = raise TYPE ("dest_predT", [T], []); - -fun mk_bot T = Const (@{const_name Orderings.bot}, mk_predT T); - -fun mk_single t = - let val T = fastype_of t - in Const(@{const_name Predicate.single}, T --> mk_predT T) $ t end; - -fun mk_bind (x, f) = - let val T as Type ("fun", [_, U]) = fastype_of f - in - Const (@{const_name Predicate.bind}, fastype_of x --> T --> U) $ x $ f - end; - -val mk_sup = HOLogic.mk_binop @{const_name sup}; - -fun mk_if cond = Const (@{const_name Predicate.if_pred}, - HOLogic.boolT --> mk_predT HOLogic.unitT) $ cond; - -fun mk_not t = let val T = mk_predT HOLogic.unitT - in Const (@{const_name Predicate.not_pred}, T --> T) $ t end - -fun mk_Enum f = - let val T as Type ("fun", [T', _]) = fastype_of f - in - Const (@{const_name Predicate.Pred}, T --> mk_predT T') $ f - end; - -fun mk_Eval (f, x) = - let - val T = fastype_of x - in - Const (@{const_name Predicate.eval}, mk_predT T --> T --> HOLogic.boolT) $ f $ x - end; - -fun mk_map T1 T2 tf tp = Const (@{const_name Predicate.map}, - (T1 --> T2) --> mk_predT T1 --> mk_predT T2) $ tf $ tp; - -val lift_pred = I - -val compfuns = CompilationFuns {mk_predT = mk_predT, dest_predT = dest_predT, mk_bot = mk_bot, - mk_single = mk_single, mk_bind = mk_bind, mk_sup = mk_sup, mk_if = mk_if, mk_not = mk_not, - mk_map = mk_map, lift_pred = lift_pred}; - -end; - -(* termify_code: -val termT = Type ("Code_Eval.term", []); -fun termifyT T = HOLogic.mk_prodT (T, HOLogic.unitT --> termT) -*) -(* -fun lift_random random = - let - val T = dest_randomT (fastype_of random) - in - mk_scomp (random, - mk_fun_comp (HOLogic.pair_const (PredicateCompFuns.mk_predT T) @{typ Random.seed}, - mk_fun_comp (Const (@{const_name Predicate.single}, T --> (PredicateCompFuns.mk_predT T)), - Const (@{const_name "fst"}, HOLogic.mk_prodT (T, @{typ "unit => term"}) --> T)))) - end; -*) - -structure RPredCompFuns = -struct - -fun mk_rpredT T = - @{typ "Random.seed"} --> HOLogic.mk_prodT (PredicateCompFuns.mk_predT T, @{typ "Random.seed"}) - -fun dest_rpredT (Type ("fun", [_, - Type (@{type_name "*"}, [Type (@{type_name "Predicate.pred"}, [T]), _])])) = T - | dest_rpredT T = raise TYPE ("dest_rpredT", [T], []); - -fun mk_bot T = Const(@{const_name RPred.bot}, mk_rpredT T) - -fun mk_single t = - let - val T = fastype_of t - in - Const (@{const_name RPred.return}, T --> mk_rpredT T) $ t - end; - -fun mk_bind (x, f) = - let - val T as (Type ("fun", [_, U])) = fastype_of f - in - Const (@{const_name RPred.bind}, fastype_of x --> T --> U) $ x $ f - end - -val mk_sup = HOLogic.mk_binop @{const_name RPred.supp} - -fun mk_if cond = Const (@{const_name RPred.if_rpred}, - HOLogic.boolT --> mk_rpredT HOLogic.unitT) $ cond; - -fun mk_not t = error "Negation is not defined for RPred" - -fun mk_map t = error "FIXME" (*FIXME*) - -fun lift_pred t = - let - val T = PredicateCompFuns.dest_predT (fastype_of t) - val lift_predT = PredicateCompFuns.mk_predT T --> mk_rpredT T - in - Const (@{const_name "RPred.lift_pred"}, lift_predT) $ t - end; - -val compfuns = CompilationFuns {mk_predT = mk_rpredT, dest_predT = dest_rpredT, mk_bot = mk_bot, - mk_single = mk_single, mk_bind = mk_bind, mk_sup = mk_sup, mk_if = mk_if, mk_not = mk_not, - mk_map = mk_map, lift_pred = lift_pred}; - -end; -(* for external use with interactive mode *) -val rpred_compfuns = RPredCompFuns.compfuns; - -fun lift_random random = - let - val T = dest_randomT (fastype_of random) - in - Const (@{const_name lift_random}, (@{typ Random.seed} --> - HOLogic.mk_prodT (HOLogic.mk_prodT (T, @{typ "unit => term"}), @{typ Random.seed})) --> - RPredCompFuns.mk_rpredT T) $ random - end; - -(* Mode analysis *) - -(*** check if a term contains only constructor functions ***) -fun is_constrt thy = - let - val cnstrs = flat (maps - (map (fn (_, (Tname, _, cs)) => map (apsnd (rpair Tname o length)) cs) o #descr o snd) - (Symtab.dest (Datatype.get_all thy))); - fun check t = (case strip_comb t of - (Free _, []) => true - | (Const (s, T), ts) => (case (AList.lookup (op =) cnstrs s, body_type T) of - (SOME (i, Tname), Type (Tname', _)) => length ts = i andalso Tname = Tname' andalso forall check ts - | _ => false) - | _ => false) - in check end; - -(*** check if a type is an equality type (i.e. doesn't contain fun) - FIXME this is only an approximation ***) -fun is_eqT (Type (s, Ts)) = s <> "fun" andalso forall is_eqT Ts - | is_eqT _ = true; - -fun term_vs tm = fold_aterms (fn Free (x, T) => cons x | _ => I) tm []; -val terms_vs = distinct (op =) o maps term_vs; - -(** collect all Frees in a term (with duplicates!) **) -fun term_vTs tm = - fold_aterms (fn Free xT => cons xT | _ => I) tm []; - -(*FIXME this function should not be named merge... make it local instead*) -fun merge xs [] = xs - | merge [] ys = ys - | merge (x::xs) (y::ys) = if length x >= length y then x::merge xs (y::ys) - else y::merge (x::xs) ys; - -fun subsets i j = if i <= j then - let val is = subsets (i+1) j - in merge (map (fn ks => i::ks) is) is end - else [[]]; - -(* FIXME: should be in library - map_prod *) -fun cprod ([], ys) = [] - | cprod (x :: xs, ys) = map (pair x) ys @ cprod (xs, ys); - -fun cprods xss = foldr (map op :: o cprod) [[]] xss; - -fun cprods_subset [] = [[]] - | cprods_subset (xs :: xss) = - let - val yss = (cprods_subset xss) - in maps (fn ys => map (fn x => cons x ys) xs) yss @ yss end - -(*TODO: cleanup function and put together with modes_of_term *) -(* -fun modes_of_param default modes t = let - val (vs, t') = strip_abs t - val b = length vs - fun mk_modes name args = Option.map (maps (fn (m as (iss, is)) => - let - val (args1, args2) = - if length args < length iss then - error ("Too few arguments for inductive predicate " ^ name) - else chop (length iss) args; - val k = length args2; - val perm = map (fn i => (find_index_eq (Bound (b - i)) args2) + 1) - (1 upto b) - val partial_mode = (1 upto k) \\ perm - in - if not (partial_mode subset is) then [] else - let - val is' = - (fold_index (fn (i, j) => if j mem is then cons (i + 1) else I) perm []) - |> fold (fn i => if i > k then cons (i - k + b) else I) is - - val res = map (fn x => Mode (m, is', x)) (cprods (map - (fn (NONE, _) => [NONE] - | (SOME js, arg) => map SOME (filter - (fn Mode (_, js', _) => js=js') (modes_of_term modes arg))) - (iss ~~ args1))) - in res end - end)) (AList.lookup op = modes name) - in case strip_comb t' of - (Const (name, _), args) => the_default default (mk_modes name args) - | (Var ((name, _), _), args) => the (mk_modes name args) - | (Free (name, _), args) => the (mk_modes name args) - | _ => default end - -and -*) -fun modes_of_term modes t = - let - val ks = map_index (fn (i, T) => (i, NONE)) (binder_types (fastype_of t)); - val default = [Mode (([], ks), ks, [])]; - fun mk_modes name args = Option.map (maps (fn (m as (iss, is)) => - let - val (args1, args2) = - if length args < length iss then - error ("Too few arguments for inductive predicate " ^ name) - else chop (length iss) args; - val k = length args2; - val prfx = map (rpair NONE) (1 upto k) - in - if not (is_prefix op = prfx is) then [] else - let val is' = List.drop (is, k) - in map (fn x => Mode (m, is', x)) (cprods (map - (fn (NONE, _) => [NONE] - | (SOME js, arg) => map SOME (filter - (fn Mode (_, js', _) => js=js') (modes_of_term modes arg))) - (iss ~~ args1))) - end - end)) (AList.lookup op = modes name) - - in - case strip_comb (Envir.eta_contract t) of - (Const (name, _), args) => the_default default (mk_modes name args) - | (Var ((name, _), _), args) => the (mk_modes name args) - | (Free (name, _), args) => the (mk_modes name args) - | (Abs _, []) => error "Abs at param position" (* modes_of_param default modes t *) - | _ => default - end - -fun select_mode_prem thy modes vs ps = - find_first (is_some o snd) (ps ~~ map - (fn Prem (us, t) => find_first (fn Mode (_, is, _) => - let - val (in_ts, out_ts) = split_smode is us; - val (out_ts', in_ts') = List.partition (is_constrt thy) out_ts; - val vTs = maps term_vTs out_ts'; - val dupTs = map snd (duplicates (op =) vTs) @ - List.mapPartial (AList.lookup (op =) vTs) vs; - in - terms_vs (in_ts @ in_ts') subset vs andalso - forall (is_eqT o fastype_of) in_ts' andalso - term_vs t subset vs andalso - forall is_eqT dupTs - end) - (modes_of_term modes t handle Option => - error ("Bad predicate: " ^ Syntax.string_of_term_global thy t)) - | Negprem (us, t) => find_first (fn Mode (_, is, _) => - length us = length is andalso - terms_vs us subset vs andalso - term_vs t subset vs) - (modes_of_term modes t handle Option => - error ("Bad predicate: " ^ Syntax.string_of_term_global thy t)) - | Sidecond t => if term_vs t subset vs then SOME (Mode (([], []), [], [])) - else NONE - ) ps); - -fun fold_prem f (Prem (args, _)) = fold f args - | fold_prem f (Negprem (args, _)) = fold f args - | fold_prem f (Sidecond t) = f t - -fun all_subsets [] = [[]] - | all_subsets (x::xs) = let val xss' = all_subsets xs in xss' @ (map (cons x) xss') end - -fun generator vTs v = - let - val T = the (AList.lookup (op =) vTs v) - in - (Generator (v, T), Mode (([], []), [], [])) - end; - -fun gen_prem (Prem (us, t)) = GeneratorPrem (us, t) - | gen_prem _ = error "gen_prem : invalid input for gen_prem" - -fun param_gen_prem param_vs (p as Prem (us, t as Free (v, _))) = - if member (op =) param_vs v then - GeneratorPrem (us, t) - else p - | param_gen_prem param_vs p = p - -fun check_mode_clause with_generator thy param_vs modes gen_modes (iss, is) (ts, ps) = - let - val modes' = modes @ List.mapPartial - (fn (_, NONE) => NONE | (v, SOME js) => SOME (v, [([], js)])) - (param_vs ~~ iss); - val gen_modes' = gen_modes @ List.mapPartial - (fn (_, NONE) => NONE | (v, SOME js) => SOME (v, [([], js)])) - (param_vs ~~ iss); - val vTs = distinct (op =) ((fold o fold_prem) Term.add_frees ps (fold Term.add_frees ts [])) - val prem_vs = distinct (op =) ((fold o fold_prem) Term.add_free_names ps []) - fun check_mode_prems acc_ps vs [] = SOME (acc_ps, vs) - | check_mode_prems acc_ps vs ps = (case select_mode_prem thy modes' vs ps of - NONE => - (if with_generator then - (case select_mode_prem thy gen_modes' vs ps of - SOME (p, SOME mode) => check_mode_prems ((gen_prem p, mode) :: acc_ps) - (case p of Prem (us, _) => vs union terms_vs us | _ => vs) - (filter_out (equal p) ps) - | NONE => - let - val all_generator_vs = all_subsets (prem_vs \\ vs) |> sort (int_ord o (pairself length)) - in - case (find_first (fn generator_vs => is_some - (select_mode_prem thy modes' (vs union generator_vs) ps)) all_generator_vs) of - SOME generator_vs => check_mode_prems ((map (generator vTs) generator_vs) @ acc_ps) - (vs union generator_vs) ps - | NONE => NONE - end) - else - NONE) - | SOME (p, SOME mode) => check_mode_prems ((if with_generator then param_gen_prem param_vs p else p, mode) :: acc_ps) - (case p of Prem (us, _) => vs union terms_vs us | _ => vs) - (filter_out (equal p) ps)) - val (in_ts, in_ts') = List.partition (is_constrt thy) (fst (split_smode is ts)); - val in_vs = terms_vs in_ts; - val concl_vs = terms_vs ts - in - if forall is_eqT (map snd (duplicates (op =) (maps term_vTs in_ts))) andalso - forall (is_eqT o fastype_of) in_ts' then - case check_mode_prems [] (param_vs union in_vs) ps of - NONE => NONE - | SOME (acc_ps, vs) => - if with_generator then - SOME (ts, (rev acc_ps) @ (map (generator vTs) (concl_vs \\ vs))) - else - if concl_vs subset vs then SOME (ts, rev acc_ps) else NONE - else NONE - end; - -fun check_modes_pred with_generator thy param_vs clauses modes gen_modes (p, ms) = - let val SOME rs = AList.lookup (op =) clauses p - in (p, List.filter (fn m => case find_index - (is_none o check_mode_clause with_generator thy param_vs modes gen_modes m) rs of - ~1 => true - | i => (Output.tracing ("Clause " ^ string_of_int (i + 1) ^ " of " ^ - p ^ " violates mode " ^ string_of_mode m); - Output.tracing (commas (map (Syntax.string_of_term_global thy) (fst (nth rs i)))); false)) ms) - end; - -fun get_modes_pred with_generator thy param_vs clauses modes gen_modes (p, ms) = - let - val SOME rs = AList.lookup (op =) clauses p - in - (p, map (fn m => - (m, map (the o check_mode_clause with_generator thy param_vs modes gen_modes m) rs)) ms) - end; - -fun fixp f (x : (string * mode list) list) = - let val y = f x - in if x = y then x else fixp f y end; - -fun infer_modes thy extra_modes all_modes param_vs clauses = - let - val modes = - fixp (fn modes => - map (check_modes_pred false thy param_vs clauses (modes @ extra_modes) []) modes) - all_modes - in - map (get_modes_pred false thy param_vs clauses (modes @ extra_modes) []) modes - end; - -fun remove_from rem [] = [] - | remove_from rem ((k, vs) :: xs) = - (case AList.lookup (op =) rem k of - NONE => (k, vs) - | SOME vs' => (k, vs \\ vs')) - :: remove_from rem xs - -fun infer_modes_with_generator thy extra_modes all_modes param_vs clauses = - let - val prednames = map fst clauses - val extra_modes = all_modes_of thy - val gen_modes = all_generator_modes_of thy - |> filter_out (fn (name, _) => member (op =) prednames name) - val starting_modes = remove_from extra_modes all_modes - val modes = - fixp (fn modes => - map (check_modes_pred true thy param_vs clauses extra_modes (gen_modes @ modes)) modes) - starting_modes - in - map (get_modes_pred true thy param_vs clauses extra_modes (gen_modes @ modes)) modes - end; - -(* term construction *) - -fun mk_v (names, vs) s T = (case AList.lookup (op =) vs s of - NONE => (Free (s, T), (names, (s, [])::vs)) - | SOME xs => - let - val s' = Name.variant names s; - val v = Free (s', T) - in - (v, (s'::names, AList.update (op =) (s, v::xs) vs)) - end); - -fun distinct_v (Free (s, T)) nvs = mk_v nvs s T - | distinct_v (t $ u) nvs = - let - val (t', nvs') = distinct_v t nvs; - val (u', nvs'') = distinct_v u nvs'; - in (t' $ u', nvs'') end - | distinct_v x nvs = (x, nvs); - -fun compile_match thy compfuns eqs eqs' out_ts success_t = - let - val eqs'' = maps mk_eq eqs @ eqs' - val names = fold Term.add_free_names (success_t :: eqs'' @ out_ts) []; - val name = Name.variant names "x"; - val name' = Name.variant (name :: names) "y"; - val T = mk_tupleT (map fastype_of out_ts); - val U = fastype_of success_t; - val U' = dest_predT compfuns U; - val v = Free (name, T); - val v' = Free (name', T); - in - lambda v (fst (Datatype.make_case - (ProofContext.init thy) false [] v - [(mk_tuple out_ts, - if null eqs'' then success_t - else Const (@{const_name HOL.If}, HOLogic.boolT --> U --> U --> U) $ - foldr1 HOLogic.mk_conj eqs'' $ success_t $ - mk_bot compfuns U'), - (v', mk_bot compfuns U')])) - end; - -(*FIXME function can be removed*) -fun mk_funcomp f t = - let - val names = Term.add_free_names t []; - val Ts = binder_types (fastype_of t); - val vs = map Free - (Name.variant_list names (replicate (length Ts) "x") ~~ Ts) - in - fold_rev lambda vs (f (list_comb (t, vs))) - end; -(* -fun compile_param_ext thy compfuns modes (NONE, t) = t - | compile_param_ext thy compfuns modes (m as SOME (Mode ((iss, is'), is, ms)), t) = - let - val (vs, u) = strip_abs t - val (ivs, ovs) = split_mode is vs - val (f, args) = strip_comb u - val (params, args') = chop (length ms) args - val (inargs, outargs) = split_mode is' args' - val b = length vs - val perm = map (fn i => (find_index_eq (Bound (b - i)) args') + 1) (1 upto b) - val outp_perm = - snd (split_mode is perm) - |> map (fn i => i - length (filter (fn x => x < i) is')) - val names = [] -- TODO - val out_names = Name.variant_list names (replicate (length outargs) "x") - val f' = case f of - Const (name, T) => - if AList.defined op = modes name then - mk_predfun_of thy compfuns (name, T) (iss, is') - else error "compile param: Not an inductive predicate with correct mode" - | Free (name, T) => Free (name, param_funT_of compfuns T (SOME is')) - val outTs = dest_tupleT (dest_predT compfuns (body_type (fastype_of f'))) - val out_vs = map Free (out_names ~~ outTs) - val params' = map (compile_param thy modes) (ms ~~ params) - val f_app = list_comb (f', params' @ inargs) - val single_t = (mk_single compfuns (mk_tuple (map (fn i => nth out_vs (i - 1)) outp_perm))) - val match_t = compile_match thy compfuns [] [] out_vs single_t - in list_abs (ivs, - mk_bind compfuns (f_app, match_t)) - end - | compile_param_ext _ _ _ _ = error "compile params" -*) - -fun compile_param size thy compfuns (NONE, t) = t - | compile_param size thy compfuns (m as SOME (Mode ((iss, is'), is, ms)), t) = - let - val (f, args) = strip_comb (Envir.eta_contract t) - val (params, args') = chop (length ms) args - val params' = map (compile_param size thy compfuns) (ms ~~ params) - val mk_fun_of = case size of NONE => mk_fun_of | SOME _ => mk_sizelim_fun_of - val funT_of = case size of NONE => funT_of | SOME _ => sizelim_funT_of - val f' = - case f of - Const (name, T) => - mk_fun_of compfuns thy (name, T) (iss, is') - | Free (name, T) => Free (name, funT_of compfuns (iss, is') T) - | _ => error ("PredicateCompiler: illegal parameter term") - in list_comb (f', params' @ args') end - -fun compile_expr size thy ((Mode (mode, is, ms)), t) = - case strip_comb t of - (Const (name, T), params) => - let - val params' = map (compile_param size thy PredicateCompFuns.compfuns) (ms ~~ params) - val mk_fun_of = case size of NONE => mk_fun_of | SOME _ => mk_sizelim_fun_of - in - list_comb (mk_fun_of PredicateCompFuns.compfuns thy (name, T) mode, params') - end - | (Free (name, T), args) => - let - val funT_of = case size of NONE => funT_of | SOME _ => sizelim_funT_of - in - list_comb (Free (name, funT_of PredicateCompFuns.compfuns ([], is) T), args) - end; - -fun compile_gen_expr size thy compfuns ((Mode (mode, is, ms)), t) = - case strip_comb t of - (Const (name, T), params) => - let - val params' = map (compile_param size thy compfuns) (ms ~~ params) - in - list_comb (mk_generator_of compfuns thy (name, T) mode, params') - end - | (Free (name, T), args) => - list_comb (Free (name, sizelim_funT_of RPredCompFuns.compfuns ([], is) T), args) - -(** specific rpred functions -- move them to the correct place in this file *) - -(* uncommented termify code; causes more trouble than expected at first *) -(* -fun mk_valtermify_term (t as Const (c, T)) = HOLogic.mk_prod (t, Abs ("u", HOLogic.unitT, HOLogic.reflect_term t)) - | mk_valtermify_term (Free (x, T)) = Free (x, termifyT T) - | mk_valtermify_term (t1 $ t2) = - let - val T = fastype_of t1 - val (T1, T2) = dest_funT T - val t1' = mk_valtermify_term t1 - val t2' = mk_valtermify_term t2 - in - Const ("Code_Eval.valapp", termifyT T --> termifyT T1 --> termifyT T2) $ t1' $ t2' - end - | mk_valtermify_term _ = error "Not a valid term for mk_valtermify_term" -*) - -fun compile_clause compfuns size final_term thy all_vs param_vs (iss, is) inp (ts, moded_ps) = - let - fun check_constrt t (names, eqs) = - if is_constrt thy t then (t, (names, eqs)) else - let - val s = Name.variant names "x"; - val v = Free (s, fastype_of t) - in (v, (s::names, HOLogic.mk_eq (v, t)::eqs)) end; - - val (in_ts, out_ts) = split_smode is ts; - val (in_ts', (all_vs', eqs)) = - fold_map check_constrt in_ts (all_vs, []); - - fun compile_prems out_ts' vs names [] = - let - val (out_ts'', (names', eqs')) = - fold_map check_constrt out_ts' (names, []); - val (out_ts''', (names'', constr_vs)) = fold_map distinct_v - out_ts'' (names', map (rpair []) vs); - in - (* termify code: - compile_match thy compfuns constr_vs (eqs @ eqs') out_ts''' - (mk_single compfuns (mk_tuple (map mk_valtermify_term out_ts))) - *) - compile_match thy compfuns constr_vs (eqs @ eqs') out_ts''' - (final_term out_ts) - end - | compile_prems out_ts vs names ((p, mode as Mode ((_, is), _, _)) :: ps) = - let - val vs' = distinct (op =) (flat (vs :: map term_vs out_ts)); - val (out_ts', (names', eqs)) = - fold_map check_constrt out_ts (names, []) - val (out_ts'', (names'', constr_vs')) = fold_map distinct_v - out_ts' ((names', map (rpair []) vs)) - val (compiled_clause, rest) = case p of - Prem (us, t) => - let - val (in_ts, out_ts''') = split_smode is us; - val args = case size of - NONE => in_ts - | SOME size_t => in_ts @ [size_t] - val u = lift_pred compfuns - (list_comb (compile_expr size thy (mode, t), args)) - val rest = compile_prems out_ts''' vs' names'' ps - in - (u, rest) - end - | Negprem (us, t) => - let - val (in_ts, out_ts''') = split_smode is us - val u = lift_pred compfuns - (mk_not PredicateCompFuns.compfuns (list_comb (compile_expr NONE thy (mode, t), in_ts))) - val rest = compile_prems out_ts''' vs' names'' ps - in - (u, rest) - end - | Sidecond t => - let - val rest = compile_prems [] vs' names'' ps; - in - (mk_if compfuns t, rest) - end - | GeneratorPrem (us, t) => - let - val (in_ts, out_ts''') = split_smode is us; - val args = case size of - NONE => in_ts - | SOME size_t => in_ts @ [size_t] - val u = list_comb (compile_gen_expr size thy compfuns (mode, t), args) - val rest = compile_prems out_ts''' vs' names'' ps - in - (u, rest) - end - | Generator (v, T) => - let - val u = lift_random (HOLogic.mk_random T @{term "1::code_numeral"}) - val rest = compile_prems [Free (v, T)] vs' names'' ps; - in - (u, rest) - end - in - compile_match thy compfuns constr_vs' eqs out_ts'' - (mk_bind compfuns (compiled_clause, rest)) - end - val prem_t = compile_prems in_ts' param_vs all_vs' moded_ps; - in - mk_bind compfuns (mk_single compfuns inp, prem_t) - end - -fun compile_pred compfuns mk_fun_of use_size thy all_vs param_vs s T mode moded_cls = - let - val (Ts1, Ts2) = chop (length (fst mode)) (binder_types T) - val (Us1, Us2) = split_smodeT (snd mode) Ts2 - val funT_of = if use_size then sizelim_funT_of else funT_of - val Ts1' = map2 (fn NONE => I | SOME is => funT_of compfuns ([], is)) (fst mode) Ts1 - val size_name = Name.variant (all_vs @ param_vs) "size" - fun mk_input_term (i, NONE) = - [Free (Name.variant (all_vs @ param_vs) ("x" ^ string_of_int i), nth Ts2 (i - 1))] - | mk_input_term (i, SOME pis) = case HOLogic.strip_tupleT (nth Ts2 (i - 1)) of - [] => error "strange unit input" - | [T] => [Free (Name.variant (all_vs @ param_vs) ("x" ^ string_of_int i), nth Ts2 (i - 1))] - | Ts => let - val vnames = Name.variant_list (all_vs @ param_vs) - (map (fn j => "x" ^ string_of_int i ^ "p" ^ string_of_int j) - pis) - in if null pis then [] - else [HOLogic.mk_tuple (map Free (vnames ~~ map (fn j => nth Ts (j - 1)) pis))] end - val in_ts = maps mk_input_term (snd mode) - val params = map2 (fn s => fn T => Free (s, T)) param_vs Ts1' - val size = Free (size_name, @{typ "code_numeral"}) - val decr_size = - if use_size then - SOME (Const ("HOL.minus_class.minus", @{typ "code_numeral => code_numeral => code_numeral"}) - $ size $ Const ("HOL.one_class.one", @{typ "Code_Numeral.code_numeral"})) - else - NONE - val cl_ts = - map (compile_clause compfuns decr_size (fn out_ts => mk_single compfuns (mk_tuple out_ts)) - thy all_vs param_vs mode (mk_tuple in_ts)) moded_cls; - val t = foldr1 (mk_sup compfuns) cl_ts - val T' = mk_predT compfuns (mk_tupleT Us2) - val size_t = Const (@{const_name "If"}, @{typ bool} --> T' --> T' --> T') - $ HOLogic.mk_eq (size, @{term "0 :: code_numeral"}) - $ mk_bot compfuns (dest_predT compfuns T') $ t - val fun_const = mk_fun_of compfuns thy (s, T) mode - val eq = if use_size then - (list_comb (fun_const, params @ in_ts @ [size]), size_t) - else - (list_comb (fun_const, params @ in_ts), t) - in - HOLogic.mk_Trueprop (HOLogic.mk_eq eq) - 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 mk_Eval_of ((x, T), NONE) names = (x, names) - | mk_Eval_of ((x, T), SOME mode) names = - let - val Ts = binder_types T - (*val argnames = Name.variant_list names - (map (fn i => "x" ^ string_of_int i) (1 upto (length Ts))); - val args = map Free (argnames ~~ Ts) - val (inargs, outargs) = split_smode mode args*) - 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 = map 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), mk_tuple outargs) - val t = fold_rev mk_split_lambda args r - in - (t, names) - end; - -fun create_intro_elim_rule (mode as (iss, is)) defthm mode_id funT pred thy = -let - val Ts = binder_types (fastype_of pred) - val funtrm = Const (mode_id, funT) - val (Ts1, Ts2) = chop (length iss) Ts; - val Ts1' = map2 (fn NONE => I | SOME is => funT_of (PredicateCompFuns.compfuns) ([], is)) iss Ts1 - val param_names = Name.variant_list [] - (map (fn i => "x" ^ string_of_int i) (1 upto (length Ts1))); - val params = map Free (param_names ~~ Ts1') - fun mk_args (i, T) argnames = - let - val vname = Name.variant (param_names @ argnames) ("x" ^ string_of_int (length Ts1' + i)) - val default = (Free (vname, T), vname :: argnames) - in - case AList.lookup (op =) is i of - NONE => default - | SOME NONE => default - | SOME (SOME pis) => - case HOLogic.strip_tupleT T of - [] => default - | [_] => default - | Ts => - let - val vnames = Name.variant_list (param_names @ argnames) - (map (fn j => "x" ^ string_of_int (length Ts1' + i) ^ "p" ^ string_of_int j) - (1 upto (length Ts))) - in (HOLogic.mk_tuple (map Free (vnames ~~ Ts)), vnames @ argnames) end - end - val (args, argnames) = fold_map mk_args (1 upto (length Ts2) ~~ Ts2) [] - val (inargs, outargs) = split_smode is args - val param_names' = Name.variant_list (param_names @ argnames) - (map (fn i => "p" ^ string_of_int i) (1 upto (length iss))) - val param_vs = map Free (param_names' ~~ Ts1) - val (params', names) = fold_map mk_Eval_of ((params ~~ Ts1) ~~ iss) [] - val predpropI = HOLogic.mk_Trueprop (list_comb (pred, param_vs @ args)) - val predpropE = HOLogic.mk_Trueprop (list_comb (pred, params' @ args)) - val param_eqs = map (HOLogic.mk_Trueprop o HOLogic.mk_eq) (param_vs ~~ params') - val funargs = params @ inargs - val funpropE = HOLogic.mk_Trueprop (PredicateCompFuns.mk_Eval (list_comb (funtrm, funargs), - if null outargs then Free("y", HOLogic.unitT) else mk_tuple outargs)) - val funpropI = HOLogic.mk_Trueprop (PredicateCompFuns.mk_Eval (list_comb (funtrm, funargs), - mk_tuple outargs)) - val introtrm = Logic.list_implies (predpropI :: param_eqs, funpropI) - val simprules = [defthm, @{thm eval_pred}, - @{thm "split_beta"}, @{thm "fst_conv"}, @{thm "snd_conv"}, @{thm pair_collapse}] - val unfolddef_tac = Simplifier.asm_full_simp_tac (HOL_basic_ss addsimps simprules) 1 - val introthm = Goal.prove (ProofContext.init thy) (argnames @ param_names @ param_names' @ ["y"]) [] introtrm (fn {...} => unfolddef_tac) - val P = HOLogic.mk_Trueprop (Free ("P", HOLogic.boolT)); - val elimtrm = Logic.list_implies ([funpropE, Logic.mk_implies (predpropE, P)], P) - val elimthm = Goal.prove (ProofContext.init thy) (argnames @ param_names @ param_names' @ ["y", "P"]) [] elimtrm (fn {...} => unfolddef_tac) - val _ = Output.tracing (Display.string_of_thm_global thy elimthm) - val _ = Output.tracing (Display.string_of_thm_global thy introthm) - -in - (introthm, elimthm) -end; - -fun create_constname_of_mode thy prefix name mode = - let - fun string_of_mode mode = if null mode then "0" - else space_implode "_" (map (fn (i, NONE) => string_of_int i | (i, SOME pis) => string_of_int i ^ "p" - ^ space_implode "p" (map string_of_int pis)) mode) - val HOmode = space_implode "_and_" - (fold (fn NONE => I | SOME mode => cons (string_of_mode mode)) (fst mode) []) - in - (Sign.full_bname thy (prefix ^ (Long_Name.base_name name))) ^ - (if HOmode = "" then "_" else "_for_" ^ HOmode ^ "_yields_") ^ (string_of_mode (snd mode)) - end; - -fun split_tupleT is T = - let - fun split_tuple' _ _ [] = ([], []) - | split_tuple' is i (T::Ts) = - (if i mem is then apfst else apsnd) (cons T) - (split_tuple' is (i+1) Ts) - in - split_tuple' is 1 (HOLogic.strip_tupleT T) - end - -fun mk_arg xin xout pis T = - let - val n = length (HOLogic.strip_tupleT T) - val ni = length pis - fun mk_proj i j t = - (if i = j then I else HOLogic.mk_fst) - (funpow (i - 1) HOLogic.mk_snd t) - fun mk_arg' i (si, so) = if i mem pis then - (mk_proj si ni xin, (si+1, so)) - else - (mk_proj so (n - ni) xout, (si, so+1)) - val (args, _) = fold_map mk_arg' (1 upto n) (1, 1) - in - HOLogic.mk_tuple args - end - -fun create_definitions preds (name, modes) thy = - let - val compfuns = PredicateCompFuns.compfuns - val T = AList.lookup (op =) preds name |> the - fun create_definition (mode as (iss, is)) thy = let - val mode_cname = create_constname_of_mode thy "" name mode - val mode_cbasename = Long_Name.base_name mode_cname - val Ts = binder_types T - val (Ts1, Ts2) = chop (length iss) Ts - val (Us1, Us2) = split_smodeT is Ts2 - val Ts1' = map2 (fn NONE => I | SOME is => funT_of compfuns ([], is)) iss Ts1 - val funT = (Ts1' @ Us1) ---> (mk_predT compfuns (mk_tupleT Us2)) - val names = Name.variant_list [] - (map (fn i => "x" ^ string_of_int i) (1 upto (length Ts))); - (* old *) - (* - val xs = map Free (names ~~ (Ts1' @ Ts2)) - val (xparams, xargs) = chop (length iss) xs - val (xins, xouts) = split_smode is xargs - *) - (* new *) - val param_names = Name.variant_list [] - (map (fn i => "x" ^ string_of_int i) (1 upto (length Ts1'))) - val xparams = map Free (param_names ~~ Ts1') - fun mk_vars (i, T) names = - let - val vname = Name.variant names ("x" ^ string_of_int (length Ts1' + i)) - in - case AList.lookup (op =) is i of - NONE => ((([], [Free (vname, T)]), Free (vname, T)), vname :: names) - | SOME NONE => ((([Free (vname, T)], []), Free (vname, T)), vname :: names) - | SOME (SOME pis) => - let - val (Tins, Touts) = split_tupleT pis T - val name_in = Name.variant names ("x" ^ string_of_int (length Ts1' + i) ^ "in") - val name_out = Name.variant names ("x" ^ string_of_int (length Ts1' + i) ^ "out") - val xin = Free (name_in, HOLogic.mk_tupleT Tins) - val xout = Free (name_out, HOLogic.mk_tupleT Touts) - val xarg = mk_arg xin xout pis T - in (((if null Tins then [] else [xin], if null Touts then [] else [xout]), xarg), name_in :: name_out :: names) end - (* HOLogic.strip_tupleT T of - [] => - in (Free (vname, T), vname :: names) end - | [_] => let val vname = Name.variant names ("x" ^ string_of_int (length Ts1' + i)) - in (Free (vname, T), vname :: names) end - | Ts => - let - val vnames = Name.variant_list names - (map (fn j => "x" ^ string_of_int (length Ts1' + i) ^ "p" ^ string_of_int j) - (1 upto (length Ts))) - in (HOLogic.mk_tuple (map Free (vnames ~~ Ts)), vnames @ names) end *) - end - val (xinoutargs, names) = fold_map mk_vars ((1 upto (length Ts2)) ~~ Ts2) param_names - val (xinout, xargs) = split_list xinoutargs - val (xins, xouts) = pairself flat (split_list xinout) - (*val (xins, xouts) = split_smode is xargs*) - val (xparams', names') = fold_map mk_Eval_of ((xparams ~~ Ts1) ~~ iss) names - val _ = Output.tracing ("xargs:" ^ commas (map (Syntax.string_of_term_global thy) xargs)) - fun mk_split_lambda [] t = lambda (Free (Name.variant names' "x", HOLogic.unitT)) t - | mk_split_lambda [x] t = lambda x t - | mk_split_lambda xs t = - let - fun mk_split_lambda' (x::y::[]) t = HOLogic.mk_split (lambda x (lambda y t)) - | mk_split_lambda' (x::xs) t = HOLogic.mk_split (lambda x (mk_split_lambda' xs t)) - in - mk_split_lambda' xs t - end; - val predterm = PredicateCompFuns.mk_Enum (mk_split_lambda xouts - (list_comb (Const (name, T), xparams' @ xargs))) - val lhs = list_comb (Const (mode_cname, funT), xparams @ xins) - val def = Logic.mk_equals (lhs, predterm) - val _ = Output.tracing ("def:" ^ (Syntax.string_of_term_global thy def)) - val ([definition], thy') = thy |> - Sign.add_consts_i [(Binding.name mode_cbasename, funT, NoSyn)] |> - PureThy.add_defs false [((Binding.name (mode_cbasename ^ "_def"), def), [])] - val (intro, elim) = - create_intro_elim_rule mode definition mode_cname funT (Const (name, T)) thy' - val _ = Output.tracing (Display.string_of_thm_global thy' definition) - in thy' - |> add_predfun name mode (mode_cname, definition, intro, elim) - |> PureThy.store_thm (Binding.name (mode_cbasename ^ "I"), intro) |> snd - |> PureThy.store_thm (Binding.name (mode_cbasename ^ "E"), elim) |> snd - |> Theory.checkpoint - end; - in - fold create_definition modes thy - end; - -fun sizelim_create_definitions preds (name, modes) thy = - let - val T = AList.lookup (op =) preds name |> the - fun create_definition mode thy = - let - val mode_cname = create_constname_of_mode thy "sizelim_" name mode - val funT = sizelim_funT_of PredicateCompFuns.compfuns mode T - in - thy |> Sign.add_consts_i [(Binding.name (Long_Name.base_name mode_cname), funT, NoSyn)] - |> set_sizelim_function_name name mode mode_cname - end; - in - fold create_definition modes thy - end; - -fun rpred_create_definitions preds (name, modes) thy = - let - val T = AList.lookup (op =) preds name |> the - fun create_definition mode thy = - let - val mode_cname = create_constname_of_mode thy "gen_" name mode - val funT = sizelim_funT_of RPredCompFuns.compfuns mode T - in - thy |> Sign.add_consts_i [(Binding.name (Long_Name.base_name mode_cname), funT, NoSyn)] - |> set_generator_name name mode mode_cname - end; - in - fold create_definition modes thy - end; - -(* Proving equivalence of term *) - -fun is_Type (Type _) = true - | is_Type _ = false - -(* returns true if t is an application of an datatype constructor *) -(* which then consequently would be splitted *) -(* else false *) -fun is_constructor thy t = - if (is_Type (fastype_of t)) then - (case Datatype.get_info thy ((fst o dest_Type o fastype_of) t) of - NONE => false - | SOME info => (let - val constr_consts = maps (fn (_, (_, _, constrs)) => map fst constrs) (#descr info) - val (c, _) = strip_comb t - in (case c of - Const (name, _) => name mem_string constr_consts - | _ => false) end)) - else false - -(* MAJOR FIXME: prove_params should be simple - - different form of introrule for parameters ? *) -fun prove_param thy (NONE, t) = TRY (rtac @{thm refl} 1) - | prove_param thy (m as SOME (Mode (mode, is, ms)), t) = - let - val (f, args) = strip_comb (Envir.eta_contract t) - val (params, _) = chop (length ms) args - val f_tac = case f of - Const (name, T) => simp_tac (HOL_basic_ss addsimps - ([@{thm eval_pred}, (predfun_definition_of thy name mode), - @{thm "split_eta"}, @{thm "split_beta"}, @{thm "fst_conv"}, - @{thm "snd_conv"}, @{thm pair_collapse}, @{thm "Product_Type.split_conv"}])) 1 - | Free _ => TRY (rtac @{thm refl} 1) - | Abs _ => error "prove_param: No valid parameter term" - in - REPEAT_DETERM (etac @{thm thin_rl} 1) - THEN REPEAT_DETERM (rtac @{thm ext} 1) - THEN print_tac "prove_param" - THEN f_tac - THEN print_tac "after simplification in prove_args" - THEN (EVERY (map (prove_param thy) (ms ~~ params))) - THEN (REPEAT_DETERM (atac 1)) - end - -fun prove_expr thy (Mode (mode, is, ms), t, us) (premposition : int) = - case strip_comb t of - (Const (name, T), args) => - let - val introrule = predfun_intro_of thy name mode - val (args1, args2) = chop (length ms) args - in - rtac @{thm bindI} 1 - THEN print_tac "before intro rule:" - (* for the right assumption in first position *) - THEN rotate_tac premposition 1 - THEN debug_tac (Display.string_of_thm (ProofContext.init thy) introrule) - THEN rtac introrule 1 - THEN print_tac "after intro rule" - (* work with parameter arguments *) - THEN (atac 1) - THEN (print_tac "parameter goal") - THEN (EVERY (map (prove_param thy) (ms ~~ args1))) - THEN (REPEAT_DETERM (atac 1)) - end - | _ => rtac @{thm bindI} 1 - THEN asm_full_simp_tac - (HOL_basic_ss' addsimps [@{thm "split_eta"}, @{thm "split_beta"}, @{thm "fst_conv"}, - @{thm "snd_conv"}, @{thm pair_collapse}]) 1 - THEN (atac 1) - THEN print_tac "after prove parameter call" - - -fun SOLVED tac st = FILTER (fn st' => nprems_of st' = nprems_of st - 1) tac st; - -fun SOLVEDALL tac st = FILTER (fn st' => nprems_of st' = 0) tac st - -fun prove_match thy (out_ts : term list) = let - fun get_case_rewrite t = - if (is_constructor thy t) then let - val case_rewrites = (#case_rewrites (Datatype.the_info thy - ((fst o dest_Type o fastype_of) t))) - in case_rewrites @ (flat (map get_case_rewrite (snd (strip_comb t)))) end - else [] - val simprules = @{thm "unit.cases"} :: @{thm "prod.cases"} :: (flat (map get_case_rewrite out_ts)) -(* replace TRY by determining if it necessary - are there equations when calling compile match? *) -in - (* make this simpset better! *) - asm_full_simp_tac (HOL_basic_ss' addsimps simprules) 1 - THEN print_tac "after prove_match:" - THEN (DETERM (TRY (EqSubst.eqsubst_tac (ProofContext.init thy) [0] [@{thm "HOL.if_P"}] 1 - THEN (REPEAT_DETERM (rtac @{thm conjI} 1 THEN (SOLVED (asm_simp_tac HOL_basic_ss 1)))) - THEN (SOLVED (asm_simp_tac HOL_basic_ss 1))))) - THEN print_tac "after if simplification" -end; - -(* corresponds to compile_fun -- maybe call that also compile_sidecond? *) - -fun prove_sidecond thy modes t = - let - fun preds_of t nameTs = case strip_comb t of - (f as Const (name, T), args) => - if AList.defined (op =) modes name then (name, T) :: nameTs - else fold preds_of args nameTs - | _ => nameTs - val preds = preds_of t [] - val defs = map - (fn (pred, T) => predfun_definition_of thy pred - ([], map (rpair NONE) (1 upto (length (binder_types T))))) - preds - in - (* remove not_False_eq_True when simpset in prove_match is better *) - simp_tac (HOL_basic_ss addsimps - (@{thms "HOL.simp_thms"} @ (@{thm not_False_eq_True} :: @{thm eval_pred} :: defs))) 1 - (* need better control here! *) - end - -fun prove_clause thy nargs modes (iss, is) (_, clauses) (ts, moded_ps) = - let - val (in_ts, clause_out_ts) = split_smode is ts; - fun prove_prems out_ts [] = - (prove_match thy out_ts) - THEN print_tac "before simplifying assumptions" - THEN asm_full_simp_tac HOL_basic_ss' 1 - THEN print_tac "before single intro rule" - THEN (rtac (if null clause_out_ts then @{thm singleI_unit} else @{thm singleI}) 1) - | prove_prems out_ts ((p, mode as Mode ((iss, is), _, param_modes)) :: ps) = - let - val premposition = (find_index (equal p) clauses) + nargs - val rest_tac = (case p of Prem (us, t) => - let - val (_, out_ts''') = split_smode is us - val rec_tac = prove_prems out_ts''' ps - in - print_tac "before clause:" - THEN asm_simp_tac HOL_basic_ss 1 - THEN print_tac "before prove_expr:" - THEN prove_expr thy (mode, t, us) premposition - THEN print_tac "after prove_expr:" - THEN rec_tac - end - | Negprem (us, t) => - let - val (_, out_ts''') = split_smode is us - val rec_tac = prove_prems out_ts''' ps - val name = (case strip_comb t of (Const (c, _), _) => SOME c | _ => NONE) - val (_, params) = strip_comb t - in - rtac @{thm bindI} 1 - THEN (if (is_some name) then - simp_tac (HOL_basic_ss addsimps [predfun_definition_of thy (the name) (iss, is)]) 1 - THEN rtac @{thm not_predI} 1 - THEN simp_tac (HOL_basic_ss addsimps [@{thm not_False_eq_True}]) 1 - THEN (REPEAT_DETERM (atac 1)) - (* FIXME: work with parameter arguments *) - THEN (EVERY (map (prove_param thy) (param_modes ~~ params))) - else - rtac @{thm not_predI'} 1) - THEN simp_tac (HOL_basic_ss addsimps [@{thm not_False_eq_True}]) 1 - THEN rec_tac - end - | Sidecond t => - rtac @{thm bindI} 1 - THEN rtac @{thm if_predI} 1 - THEN print_tac "before sidecond:" - THEN prove_sidecond thy modes t - THEN print_tac "after sidecond:" - THEN prove_prems [] ps) - in (prove_match thy out_ts) - THEN rest_tac - end; - val prems_tac = prove_prems in_ts moded_ps - in - rtac @{thm bindI} 1 - THEN rtac @{thm singleI} 1 - THEN prems_tac - end; - -fun select_sup 1 1 = [] - | select_sup _ 1 = [rtac @{thm supI1}] - | select_sup n i = (rtac @{thm supI2})::(select_sup (n - 1) (i - 1)); - -fun prove_one_direction thy clauses preds modes pred mode moded_clauses = - let - val T = the (AList.lookup (op =) preds pred) - val nargs = length (binder_types T) - nparams_of thy pred - val pred_case_rule = the_elim_of thy pred - in - REPEAT_DETERM (CHANGED (rewtac @{thm "split_paired_all"})) - THEN print_tac "before applying elim rule" - THEN etac (predfun_elim_of thy pred mode) 1 - THEN etac pred_case_rule 1 - THEN (EVERY (map - (fn i => EVERY' (select_sup (length moded_clauses) i) i) - (1 upto (length moded_clauses)))) - THEN (EVERY (map2 (prove_clause thy nargs modes mode) clauses moded_clauses)) - THEN print_tac "proved one direction" - end; - -(** Proof in the other direction **) - -fun prove_match2 thy out_ts = let - fun split_term_tac (Free _) = all_tac - | split_term_tac t = - if (is_constructor thy t) then let - val info = Datatype.the_info thy ((fst o dest_Type o fastype_of) t) - val num_of_constrs = length (#case_rewrites info) - (* special treatment of pairs -- because of fishing *) - val split_rules = case (fst o dest_Type o fastype_of) t of - "*" => [@{thm prod.split_asm}] - | _ => PureThy.get_thms thy (((fst o dest_Type o fastype_of) t) ^ ".split_asm") - val (_, ts) = strip_comb t - in - (Splitter.split_asm_tac split_rules 1) -(* THEN (Simplifier.asm_full_simp_tac HOL_basic_ss 1) - THEN (DETERM (TRY (etac @{thm Pair_inject} 1))) *) - THEN (REPEAT_DETERM_N (num_of_constrs - 1) (etac @{thm botE} 1 ORELSE etac @{thm botE} 2)) - THEN (EVERY (map split_term_tac ts)) - end - else all_tac - in - split_term_tac (mk_tuple out_ts) - THEN (DETERM (TRY ((Splitter.split_asm_tac [@{thm "split_if_asm"}] 1) THEN (etac @{thm botE} 2)))) - end - -(* VERY LARGE SIMILIRATIY to function prove_param --- join both functions -*) -(* TODO: remove function *) - -fun prove_param2 thy (NONE, t) = all_tac - | prove_param2 thy (m as SOME (Mode (mode, is, ms)), t) = let - val (f, args) = strip_comb (Envir.eta_contract t) - val (params, _) = chop (length ms) args - val f_tac = case f of - Const (name, T) => full_simp_tac (HOL_basic_ss addsimps - (@{thm eval_pred}::(predfun_definition_of thy name mode) - :: @{thm "Product_Type.split_conv"}::[])) 1 - | Free _ => all_tac - | _ => error "prove_param2: illegal parameter term" - in - print_tac "before simplification in prove_args:" - THEN f_tac - THEN print_tac "after simplification in prove_args" - THEN (EVERY (map (prove_param2 thy) (ms ~~ params))) - end - - -fun prove_expr2 thy (Mode (mode, is, ms), t) = - (case strip_comb t of - (Const (name, T), args) => - etac @{thm bindE} 1 - THEN (REPEAT_DETERM (CHANGED (rewtac @{thm "split_paired_all"}))) - THEN print_tac "prove_expr2-before" - THEN (debug_tac (Syntax.string_of_term_global thy - (prop_of (predfun_elim_of thy name mode)))) - THEN (etac (predfun_elim_of thy name mode) 1) - THEN print_tac "prove_expr2" - THEN (EVERY (map (prove_param2 thy) (ms ~~ args))) - THEN print_tac "finished prove_expr2" - | _ => etac @{thm bindE} 1) - -(* FIXME: what is this for? *) -(* replace defined by has_mode thy pred *) -(* TODO: rewrite function *) -fun prove_sidecond2 thy modes t = let - fun preds_of t nameTs = case strip_comb t of - (f as Const (name, T), args) => - if AList.defined (op =) modes name then (name, T) :: nameTs - else fold preds_of args nameTs - | _ => nameTs - val preds = preds_of t [] - val defs = map - (fn (pred, T) => predfun_definition_of thy pred - ([], map (rpair NONE) (1 upto (length (binder_types T))))) - preds - in - (* only simplify the one assumption *) - full_simp_tac (HOL_basic_ss' addsimps @{thm eval_pred} :: defs) 1 - (* need better control here! *) - THEN print_tac "after sidecond2 simplification" - end - -fun prove_clause2 thy modes pred (iss, is) (ts, ps) i = - let - val pred_intro_rule = nth (intros_of thy pred) (i - 1) - val (in_ts, clause_out_ts) = split_smode is ts; - fun prove_prems2 out_ts [] = - print_tac "before prove_match2 - last call:" - THEN prove_match2 thy out_ts - THEN print_tac "after prove_match2 - last call:" - THEN (etac @{thm singleE} 1) - THEN (REPEAT_DETERM (etac @{thm Pair_inject} 1)) - THEN (asm_full_simp_tac HOL_basic_ss' 1) - THEN (REPEAT_DETERM (etac @{thm Pair_inject} 1)) - THEN (asm_full_simp_tac HOL_basic_ss' 1) - THEN SOLVED (print_tac "state before applying intro rule:" - THEN (rtac pred_intro_rule 1) - (* How to handle equality correctly? *) - THEN (print_tac "state before assumption matching") - THEN (REPEAT (atac 1 ORELSE - (CHANGED (asm_full_simp_tac (HOL_basic_ss' addsimps - [@{thm split_eta}, @{thm "split_beta"}, @{thm "fst_conv"}, @{thm "snd_conv"}, @{thm pair_collapse}]) 1) - THEN print_tac "state after simp_tac:")))) - | prove_prems2 out_ts ((p, mode as Mode ((iss, is), _, param_modes)) :: ps) = - let - val rest_tac = (case p of - Prem (us, t) => - let - val (_, out_ts''') = split_smode is us - val rec_tac = prove_prems2 out_ts''' ps - in - (prove_expr2 thy (mode, t)) THEN rec_tac - end - | Negprem (us, t) => - let - val (_, out_ts''') = split_smode is us - val rec_tac = prove_prems2 out_ts''' ps - val name = (case strip_comb t of (Const (c, _), _) => SOME c | _ => NONE) - val (_, params) = strip_comb t - in - print_tac "before neg prem 2" - THEN etac @{thm bindE} 1 - THEN (if is_some name then - full_simp_tac (HOL_basic_ss addsimps [predfun_definition_of thy (the name) (iss, is)]) 1 - THEN etac @{thm not_predE} 1 - THEN simp_tac (HOL_basic_ss addsimps [@{thm not_False_eq_True}]) 1 - THEN (EVERY (map (prove_param2 thy) (param_modes ~~ params))) - else - etac @{thm not_predE'} 1) - THEN rec_tac - end - | Sidecond t => - etac @{thm bindE} 1 - THEN etac @{thm if_predE} 1 - THEN prove_sidecond2 thy modes t - THEN prove_prems2 [] ps) - in print_tac "before prove_match2:" - THEN prove_match2 thy out_ts - THEN print_tac "after prove_match2:" - THEN rest_tac - end; - val prems_tac = prove_prems2 in_ts ps - in - print_tac "starting prove_clause2" - THEN etac @{thm bindE} 1 - THEN (etac @{thm singleE'} 1) - THEN (TRY (etac @{thm Pair_inject} 1)) - THEN print_tac "after singleE':" - THEN prems_tac - end; - -fun prove_other_direction thy modes pred mode moded_clauses = - let - fun prove_clause clause i = - (if i < length moded_clauses then etac @{thm supE} 1 else all_tac) - THEN (prove_clause2 thy modes pred mode clause i) - in - (DETERM (TRY (rtac @{thm unit.induct} 1))) - THEN (REPEAT_DETERM (CHANGED (rewtac @{thm split_paired_all}))) - THEN (rtac (predfun_intro_of thy pred mode) 1) - THEN (REPEAT_DETERM (rtac @{thm refl} 2)) - THEN (EVERY (map2 prove_clause moded_clauses (1 upto (length moded_clauses)))) - end; - -(** proof procedure **) - -fun prove_pred thy clauses preds modes pred mode (moded_clauses, compiled_term) = - let - val ctxt = ProofContext.init thy - val clauses = the (AList.lookup (op =) clauses pred) - in - Goal.prove ctxt (Term.add_free_names compiled_term []) [] compiled_term - (if !do_proofs then - (fn _ => - rtac @{thm pred_iffI} 1 - THEN print_tac "after pred_iffI" - THEN prove_one_direction thy clauses preds modes pred mode moded_clauses - THEN print_tac "proved one direction" - THEN prove_other_direction thy modes pred mode moded_clauses - THEN print_tac "proved other direction") - else (fn _ => mycheat_tac thy 1)) - end; - -(* composition of mode inference, definition, compilation and proof *) - -(** auxillary combinators for table of preds and modes **) - -fun map_preds_modes f preds_modes_table = - map (fn (pred, modes) => - (pred, map (fn (mode, value) => (mode, f pred mode value)) modes)) preds_modes_table - -fun join_preds_modes table1 table2 = - map_preds_modes (fn pred => fn mode => fn value => - (value, the (AList.lookup (op =) (the (AList.lookup (op =) table2 pred)) mode))) table1 - -fun maps_modes preds_modes_table = - map (fn (pred, modes) => - (pred, map (fn (mode, value) => value) modes)) preds_modes_table - -fun compile_preds compfuns mk_fun_of use_size thy all_vs param_vs preds moded_clauses = - map_preds_modes (fn pred => compile_pred compfuns mk_fun_of use_size thy all_vs param_vs pred - (the (AList.lookup (op =) preds pred))) moded_clauses - -fun prove thy clauses preds modes moded_clauses compiled_terms = - map_preds_modes (prove_pred thy clauses preds modes) - (join_preds_modes moded_clauses compiled_terms) - -fun prove_by_skip thy _ _ _ _ compiled_terms = - map_preds_modes (fn pred => fn mode => fn t => Drule.standard (SkipProof.make_thm thy t)) - compiled_terms - -fun prepare_intrs thy prednames = - let - val intrs = maps (intros_of thy) prednames - |> map (Logic.unvarify o prop_of) - val nparams = nparams_of thy (hd prednames) - val extra_modes = all_modes_of thy |> filter_out (fn (name, _) => member (op =) prednames name) - val preds = distinct (op =) (map (dest_Const o fst o (strip_intro_concl nparams)) intrs) - val _ $ u = Logic.strip_imp_concl (hd intrs); - val params = List.take (snd (strip_comb u), nparams); - val param_vs = maps term_vs params - val all_vs = terms_vs intrs - fun dest_prem t = - (case strip_comb t of - (v as Free _, ts) => if v mem params then Prem (ts, v) else Sidecond t - | (c as Const (@{const_name Not}, _), [t]) => (case dest_prem t of - Prem (ts, t) => Negprem (ts, t) - | Negprem _ => error ("Double negation not allowed in premise: " ^ (Syntax.string_of_term_global thy (c $ t))) - | Sidecond t => Sidecond (c $ t)) - | (c as Const (s, _), ts) => - if is_registered thy s then - let val (ts1, ts2) = chop (nparams_of thy s) ts - in Prem (ts2, list_comb (c, ts1)) end - else Sidecond t - | _ => Sidecond t) - fun add_clause intr (clauses, arities) = - let - val _ $ t = Logic.strip_imp_concl intr; - val (Const (name, T), ts) = strip_comb t; - val (ts1, ts2) = chop nparams ts; - val prems = map (dest_prem o HOLogic.dest_Trueprop) (Logic.strip_imp_prems intr); - val (Ts, Us) = chop nparams (binder_types T) - in - (AList.update op = (name, these (AList.lookup op = clauses name) @ - [(ts2, prems)]) clauses, - AList.update op = (name, (map (fn U => (case strip_type U of - (Rs as _ :: _, Type ("bool", [])) => SOME (length Rs) - | _ => NONE)) Ts, - length Us)) arities) - end; - val (clauses, arities) = fold add_clause intrs ([], []); - fun modes_of_arities arities = - (map (fn (s, (ks, k)) => (s, cprod (cprods (map - (fn NONE => [NONE] - | SOME k' => map SOME (map (map (rpair NONE)) (subsets 1 k'))) ks), - map (map (rpair NONE)) (subsets 1 k)))) arities) - fun modes_of_typ T = - let - val (Ts, Us) = chop nparams (binder_types T) - fun all_smodes_of_typs Ts = cprods_subset ( - map_index (fn (i, U) => - case HOLogic.strip_tupleT U of - [] => [(i + 1, NONE)] - | [U] => [(i + 1, NONE)] - | Us => map (pair (i + 1) o SOME) ((subsets 1 (length Us)) \\ [[], 1 upto (length Us)])) - Ts) - in - cprod (cprods (map (fn T => case strip_type T of - (Rs as _ :: _, Type ("bool", [])) => map SOME (all_smodes_of_typs Rs) | _ => [NONE]) Ts), - all_smodes_of_typs Us) - end - val all_modes = map (fn (s, T) => (s, modes_of_typ T)) preds - in (preds, nparams, all_vs, param_vs, extra_modes, clauses, all_modes) end; - -(** main function of predicate compiler **) - -fun add_equations_of steps prednames thy = - let - val _ = Output.tracing ("Starting predicate compiler for predicates " ^ commas prednames ^ "...") - val (preds, nparams, all_vs, param_vs, extra_modes, clauses, all_modes) = - prepare_intrs thy prednames - val _ = Output.tracing "Infering modes..." - val moded_clauses = #infer_modes steps thy extra_modes all_modes param_vs clauses - val modes = map (fn (p, mps) => (p, map fst mps)) moded_clauses - val _ = print_modes modes - val _ = print_moded_clauses thy moded_clauses - val _ = Output.tracing "Defining executable functions..." - val thy' = fold (#create_definitions steps preds) modes thy - |> Theory.checkpoint - val _ = Output.tracing "Compiling equations..." - val compiled_terms = - (#compile_preds steps) thy' all_vs param_vs preds moded_clauses - val _ = print_compiled_terms thy' compiled_terms - val _ = Output.tracing "Proving equations..." - val result_thms = #prove steps thy' clauses preds (extra_modes @ modes) - moded_clauses compiled_terms - val qname = #qname steps - (* val attrib = gn thy => Attrib.attribute_i thy Code.add_eqn_attrib *) - val attrib = fn thy => Attrib.attribute_i thy (Attrib.internal (K (Thm.declaration_attribute - (fn thm => Context.mapping (Code.add_eqn thm) I)))) - val thy'' = fold (fn (name, result_thms) => fn thy => snd (PureThy.add_thmss - [((Binding.qualify true (Long_Name.base_name name) (Binding.name qname), result_thms), - [attrib thy ])] thy)) - (maps_modes result_thms) thy' - |> Theory.checkpoint - in - thy'' - end - -fun extend' value_of edges_of key (G, visited) = - let - val (G', v) = case try (Graph.get_node G) key of - SOME v => (G, v) - | NONE => (Graph.new_node (key, value_of key) G, value_of key) - val (G'', visited') = fold (extend' value_of edges_of) (edges_of (key, v) \\ visited) - (G', key :: visited) - in - (fold (Graph.add_edge o (pair key)) (edges_of (key, v)) G'', visited') - end; - -fun extend value_of edges_of key G = fst (extend' value_of edges_of key (G, [])) - -fun gen_add_equations steps names thy = - let - val thy' = PredData.map (fold (extend (fetch_pred_data thy) (depending_preds_of thy)) names) thy - |> Theory.checkpoint; - fun strong_conn_of gr keys = - Graph.strong_conn (Graph.subgraph (member (op =) (Graph.all_succs gr keys)) gr) - val scc = strong_conn_of (PredData.get thy') names - val thy'' = fold_rev - (fn preds => fn thy => - if #are_not_defined steps thy preds then add_equations_of steps preds thy else thy) - scc thy' |> Theory.checkpoint - in thy'' end - -(* different instantiantions of the predicate compiler *) - -val add_equations = gen_add_equations - {infer_modes = infer_modes, - create_definitions = create_definitions, - compile_preds = compile_preds PredicateCompFuns.compfuns mk_fun_of false, - prove = prove, - are_not_defined = (fn thy => forall (null o modes_of thy)), - qname = "equation"} - -val add_sizelim_equations = gen_add_equations - {infer_modes = infer_modes, - create_definitions = sizelim_create_definitions, - compile_preds = compile_preds PredicateCompFuns.compfuns mk_sizelim_fun_of true, - prove = prove_by_skip, - are_not_defined = (fn thy => fn preds => true), (* TODO *) - qname = "sizelim_equation" - } - -val add_quickcheck_equations = gen_add_equations - {infer_modes = infer_modes_with_generator, - create_definitions = rpred_create_definitions, - compile_preds = compile_preds RPredCompFuns.compfuns mk_generator_of true, - prove = prove_by_skip, - are_not_defined = (fn thy => fn preds => true), (* TODO *) - qname = "rpred_equation"} - -(** user interface **) - -(* generation of case rules from user-given introduction rules *) - -fun mk_casesrule ctxt nparams introrules = - let - val intros = map (Logic.unvarify o prop_of) introrules - val (pred, (params, args)) = strip_intro_concl nparams (hd intros) - val ([propname], ctxt1) = Variable.variant_fixes ["thesis"] ctxt - val prop = HOLogic.mk_Trueprop (Free (propname, HOLogic.boolT)) - val (argnames, ctxt2) = Variable.variant_fixes - (map (fn i => "a" ^ string_of_int i) (1 upto (length args))) ctxt1 - val argvs = map2 (curry Free) argnames (map fastype_of args) - fun mk_case intro = - let - val (_, (_, args)) = strip_intro_concl nparams intro - val prems = Logic.strip_imp_prems intro - val eqprems = map (HOLogic.mk_Trueprop o HOLogic.mk_eq) (argvs ~~ args) - val frees = (fold o fold_aterms) - (fn t as Free _ => - if member (op aconv) params t then I else insert (op aconv) t - | _ => I) (args @ prems) [] - in fold Logic.all frees (Logic.list_implies (eqprems @ prems, prop)) end - val assm = HOLogic.mk_Trueprop (list_comb (pred, params @ argvs)) - val cases = map mk_case intros - in Logic.list_implies (assm :: cases, prop) end; - -(* code_pred_intro attribute *) - -fun attrib f = Thm.declaration_attribute (fn thm => Context.mapping (f thm) I); - -val code_pred_intros_attrib = attrib add_intro; - -local - -(* TODO: make TheoryDataFun to GenericDataFun & remove duplication of local theory and theory *) -fun generic_code_pred prep_const raw_const lthy = - let - val thy = ProofContext.theory_of lthy - val const = prep_const thy raw_const - val lthy' = LocalTheory.theory (PredData.map - (extend (fetch_pred_data thy) (depending_preds_of thy) const)) lthy - |> LocalTheory.checkpoint - val thy' = ProofContext.theory_of lthy' - val preds = Graph.all_preds (PredData.get thy') [const] |> filter_out (has_elim thy') - fun mk_cases const = - let - val nparams = nparams_of thy' const - val intros = intros_of thy' const - in mk_casesrule lthy' nparams intros end - val cases_rules = map mk_cases preds - val cases = - map (fn case_rule => RuleCases.Case {fixes = [], - assumes = [("", Logic.strip_imp_prems case_rule)], - binds = [], cases = []}) cases_rules - val case_env = map2 (fn p => fn c => (Long_Name.base_name p, SOME c)) preds cases - val lthy'' = lthy' - |> fold Variable.auto_fixes cases_rules - |> ProofContext.add_cases true case_env - fun after_qed thms goal_ctxt = - let - val global_thms = ProofContext.export goal_ctxt - (ProofContext.init (ProofContext.theory_of goal_ctxt)) (map the_single thms) - in - goal_ctxt |> LocalTheory.theory (fold set_elim global_thms #> add_equations [const]) - end - in - Proof.theorem_i NONE after_qed (map (single o (rpair [])) cases_rules) lthy'' - end; - -structure P = OuterParse - -in - -val code_pred = generic_code_pred (K I); -val code_pred_cmd = generic_code_pred Code.read_const - -val setup = PredData.put (Graph.empty) #> - Attrib.setup @{binding code_pred_intros} (Scan.succeed (attrib add_intro)) - "adding alternative introduction rules for code generation of inductive predicates" -(* Attrib.setup @{binding code_ind_cases} (Scan.succeed add_elim_attrib) - "adding alternative elimination rules for code generation of inductive predicates"; - *) - (*FIXME name discrepancy in attribs and ML code*) - (*FIXME intros should be better named intro*) - (*FIXME why distinguished attribute for cases?*) - -val _ = OuterSyntax.local_theory_to_proof "code_pred" - "prove equations for predicate specified by intro/elim rules" - OuterKeyword.thy_goal (P.term_group >> code_pred_cmd) - -end - -(*FIXME -- Naming of auxiliary rules necessary? -- add default code equations P x y z = P_i_i_i x y z -*) - -(* transformation for code generation *) - -val eval_ref = ref (NONE : (unit -> term Predicate.pred) option); - -(*FIXME turn this into an LCF-guarded preprocessor for comprehensions*) -fun analyze_compr thy t_compr = - let - val split = case t_compr of (Const (@{const_name Collect}, _) $ t) => t - | _ => error ("Not a set comprehension: " ^ Syntax.string_of_term_global thy t_compr); - val (body, Ts, fp) = HOLogic.strip_psplits split; - val (pred as Const (name, T), all_args) = strip_comb body; - val (params, args) = chop (nparams_of thy name) all_args; - val user_mode = map_filter I (map_index - (fn (i, t) => case t of Bound j => if j < length Ts then NONE - else SOME (i+1) | _ => SOME (i+1)) args); (*FIXME dangling bounds should not occur*) - val user_mode' = map (rpair NONE) user_mode - val modes = filter (fn Mode (_, is, _) => is = user_mode') - (modes_of_term (all_modes_of thy) (list_comb (pred, params))); - val m = case modes - of [] => error ("No mode possible for comprehension " - ^ Syntax.string_of_term_global thy t_compr) - | [m] => m - | m :: _ :: _ => (warning ("Multiple modes possible for comprehension " - ^ Syntax.string_of_term_global thy t_compr); m); - val (inargs, outargs) = split_smode user_mode' args; - val t_pred = list_comb (compile_expr NONE thy (m, list_comb (pred, params)), inargs); - val t_eval = if null outargs then t_pred else let - val outargs_bounds = map (fn Bound i => i) outargs; - val outargsTs = map (nth Ts) outargs_bounds; - val T_pred = HOLogic.mk_tupleT outargsTs; - val T_compr = HOLogic.mk_ptupleT fp Ts; - val arrange_bounds = map_index I outargs_bounds - |> sort (prod_ord (K EQUAL) int_ord) - |> map fst; - val arrange = funpow (length outargs_bounds - 1) HOLogic.mk_split - (Term.list_abs (map (pair "") outargsTs, - HOLogic.mk_ptuple fp T_compr (map Bound arrange_bounds))) - in mk_map PredicateCompFuns.compfuns T_pred T_compr arrange t_pred end - in t_eval end; - -fun eval thy t_compr = - let - val t = analyze_compr thy t_compr; - val T = dest_predT PredicateCompFuns.compfuns (fastype_of t); - val t' = mk_map PredicateCompFuns.compfuns T HOLogic.termT (HOLogic.term_of_const T) t; - in (T, Code_ML.eval NONE ("Predicate_Compile.eval_ref", eval_ref) Predicate.map thy t' []) end; - -fun values ctxt k t_compr = - let - val thy = ProofContext.theory_of ctxt; - val (T, t) = eval thy t_compr; - val setT = HOLogic.mk_setT T; - val (ts, _) = Predicate.yieldn k t; - val elemsT = HOLogic.mk_set T ts; - in if k = ~1 orelse length ts < k then elemsT - else Const (@{const_name Set.union}, setT --> setT --> setT) $ elemsT $ t_compr - end; - -fun values_cmd modes k raw_t state = - let - val ctxt = Toplevel.context_of state; - val t = Syntax.read_term ctxt raw_t; - val t' = values ctxt k t; - val ty' = Term.type_of t'; - val ctxt' = Variable.auto_fixes t' ctxt; - val p = PrintMode.with_modes modes (fn () => - Pretty.block [Pretty.quote (Syntax.pretty_term ctxt' t'), Pretty.fbrk, - Pretty.str "::", Pretty.brk 1, Pretty.quote (Syntax.pretty_typ ctxt' ty')]) (); - in Pretty.writeln p end; - -local structure P = OuterParse in - -val opt_modes = Scan.optional (P.$$$ "(" |-- P.!!! (Scan.repeat1 P.xname --| P.$$$ ")")) []; - -val _ = OuterSyntax.improper_command "values" "enumerate and print comprehensions" OuterKeyword.diag - (opt_modes -- Scan.optional P.nat ~1 -- P.term - >> (fn ((modes, k), t) => Toplevel.no_timing o Toplevel.keep - (values_cmd modes k t))); - -end; - -end;