--- a/etc/components Mon Dec 06 11:41:24 2010 +0100
+++ b/etc/components Mon Dec 06 13:17:26 2010 +0100
@@ -17,3 +17,4 @@
src/HOL/Library/Sum_Of_Squares
src/HOL/Tools/SMT
src/HOL/Tools/Predicate_Compile
+src/HOL/Mutabelle
--- a/etc/isar-keywords.el Mon Dec 06 11:41:24 2010 +0100
+++ b/etc/isar-keywords.el Mon Dec 06 13:17:26 2010 +0100
@@ -248,7 +248,7 @@
"txt"
"txt_raw"
"typ"
- "type_mapper"
+ "type_lifting"
"type_notation"
"typed_print_translation"
"typedecl"
@@ -551,7 +551,7 @@
"sublocale"
"termination"
"theorem"
- "type_mapper"
+ "type_lifting"
"typedef"))
(defconst isar-keywords-qed
--- a/src/HOL/Datatype.thy Mon Dec 06 11:41:24 2010 +0100
+++ b/src/HOL/Datatype.thy Mon Dec 06 13:17:26 2010 +0100
@@ -13,6 +13,12 @@
("Tools/Datatype/datatype_realizer.ML")
begin
+subsection {* Prelude: lifting over function space *}
+
+type_lifting map_fun
+ by (simp_all add: fun_eq_iff)
+
+
subsection {* The datatype universe *}
typedef (Node)
--- a/src/HOL/Fun.thy Mon Dec 06 11:41:24 2010 +0100
+++ b/src/HOL/Fun.thy Mon Dec 06 13:17:26 2010 +0100
@@ -7,6 +7,7 @@
theory Fun
imports Complete_Lattice
+uses ("Tools/type_lifting.ML")
begin
text{*As a simplification rule, it replaces all function equalities by
@@ -126,9 +127,6 @@
"map_fun f g h x = g (h (f x))"
by (simp add: map_fun_def)
-type_mapper map_fun
- by (simp_all add: fun_eq_iff)
-
subsection {* Injectivity and Bijectivity *}
@@ -774,7 +772,9 @@
thus False by best
qed
-subsection {* Proof tool setup *}
+subsection {* Setup *}
+
+subsubsection {* Proof tools *}
text {* simplifies terms of the form
f(...,x:=y,...,x:=z,...) to f(...,x:=z,...) *}
@@ -809,7 +809,7 @@
*}
-subsection {* Code generator setup *}
+subsubsection {* Code generator *}
types_code
"fun" ("(_ ->/ _)")
@@ -840,4 +840,9 @@
code_const "id"
(Haskell "id")
+
+subsubsection {* Functorial structure of types *}
+
+use "Tools/type_lifting.ML"
+
end
--- a/src/HOL/HOL.thy Mon Dec 06 11:41:24 2010 +0100
+++ b/src/HOL/HOL.thy Mon Dec 06 13:17:26 2010 +0100
@@ -32,7 +32,6 @@
"Tools/async_manager.ML"
"Tools/try.ML"
("Tools/cnf_funcs.ML")
- ("Tools/type_mapper.ML")
"~~/src/Tools/subtyping.ML"
begin
@@ -714,7 +713,6 @@
and [Pure.elim?] = iffD1 iffD2 impE
use "Tools/hologic.ML"
-use "Tools/type_mapper.ML"
subsubsection {* Atomizing meta-level connectives *}
--- a/src/HOL/IsaMakefile Mon Dec 06 11:41:24 2010 +0100
+++ b/src/HOL/IsaMakefile Mon Dec 06 13:17:26 2010 +0100
@@ -147,7 +147,6 @@
$(SRC)/Tools/solve_direct.ML \
$(SRC)/Tools/value.ML \
HOL.thy \
- Tools/type_mapper.ML \
Tools/hologic.ML \
Tools/recfun_codegen.ML \
Tools/simpdata.ML
@@ -243,6 +242,7 @@
Tools/split_rule.ML \
Tools/try.ML \
Tools/typedef.ML \
+ Tools/type_lifting.ML \
Transitive_Closure.thy \
Typedef.thy \
Wellfounded.thy
--- a/src/HOL/Library/Cset.thy Mon Dec 06 11:41:24 2010 +0100
+++ b/src/HOL/Library/Cset.thy Mon Dec 06 13:17:26 2010 +0100
@@ -188,7 +188,7 @@
"map f (Cset.set xs) = Cset.set (remdups (List.map f xs))"
by (simp add: set_def)
-type_mapper map
+type_lifting map
by (simp_all add: image_image)
definition filter :: "('a \<Rightarrow> bool) \<Rightarrow> 'a Cset.set \<Rightarrow> 'a Cset.set" where
--- a/src/HOL/Library/Dlist.thy Mon Dec 06 11:41:24 2010 +0100
+++ b/src/HOL/Library/Dlist.thy Mon Dec 06 13:17:26 2010 +0100
@@ -175,7 +175,7 @@
section {* Functorial structure *}
-type_mapper map
+type_lifting map
by (auto intro: dlist_eqI simp add: remdups_map_remdups comp_def)
--- a/src/HOL/Library/Mapping.thy Mon Dec 06 11:41:24 2010 +0100
+++ b/src/HOL/Library/Mapping.thy Mon Dec 06 13:17:26 2010 +0100
@@ -50,7 +50,7 @@
"lookup (map f g m) = Option.map g \<circ> lookup m \<circ> f"
by (simp add: map_def)
-type_mapper map
+type_lifting map
by (auto intro!: mapping_eqI ext simp add: Option.map.compositionality Option.map.identity)
--- a/src/HOL/Library/Multiset.thy Mon Dec 06 11:41:24 2010 +0100
+++ b/src/HOL/Library/Multiset.thy Mon Dec 06 13:17:26 2010 +0100
@@ -1631,7 +1631,7 @@
@{term "{#x+x|x:#M. x<c#}"}.
*}
-type_mapper image_mset proof -
+type_lifting image_mset proof -
fix f g A show "image_mset f (image_mset g A) = image_mset (\<lambda>x. f (g x)) A"
by (induct A) simp_all
next
--- a/src/HOL/List.thy Mon Dec 06 11:41:24 2010 +0100
+++ b/src/HOL/List.thy Mon Dec 06 13:17:26 2010 +0100
@@ -881,7 +881,7 @@
"length xs = length ys \<Longrightarrow> map snd (zip xs ys) = ys"
by (induct rule:list_induct2, simp_all)
-type_mapper map
+type_lifting map
by simp_all
--- a/src/HOL/Mirabelle/lib/Tools/mirabelle Mon Dec 06 11:41:24 2010 +0100
+++ b/src/HOL/Mirabelle/lib/Tools/mirabelle Mon Dec 06 13:17:26 2010 +0100
@@ -22,7 +22,7 @@
echo "Usage: isabelle $PRG [OPTIONS] ACTIONS FILES"
echo
echo " Options are:"
- echo " -L LOGIC parent logic to use (default $ISABELLE_LOGIC)"
+ echo " -L LOGIC parent logic to use (default $MIRABELLE_LOGIC)"
echo " -T THEORY parent theory to use (default $MIRABELLE_THEORY)"
echo " -O DIR output directory for test data (default $out)"
echo " -t TIMEOUT timeout for each action in seconds (default $timeout)"
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Mutabelle/etc/settings Mon Dec 06 13:17:26 2010 +0100
@@ -0,0 +1,7 @@
+MUTABELLE_HOME="$COMPONENT"
+
+MUTABELLE_LOGIC=HOL
+MUTABELLE_IMPORT_THEORY=Complex_Main
+MUTABELLE_OUTPUT_PATH=/tmp/mutabelle
+
+ISABELLE_TOOLS="$ISABELLE_TOOLS:$COMPONENT/lib/Tools"
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Mutabelle/lib/Tools/mutabelle Mon Dec 06 13:17:26 2010 +0100
@@ -0,0 +1,107 @@
+#!/usr/bin/env bash
+#
+# Author: Lukas Bulwahn
+#
+# DESCRIPTION: mutant-testing tool for counterexample generators and automated proof tools
+
+
+PRG="$(basename "$0")"
+
+function usage() {
+ echo
+ echo "Usage: isabelle $PRG [OPTIONS] THEORY"
+ echo
+ echo " Options are:"
+ echo " -L LOGIC parent logic to use (default $MUTABELLE_LOGIC)"
+ echo " -T THEORY parent theory to use (default $MUTABELLE_IMPORT_THEORY)"
+ echo " -O DIR output directory for test data (default $MUTABELLE_OUTPUT_PATH)"
+ echo
+ echo " THEORY is the name of the theory of which all theorems should be mutated and tested"
+ exit 1
+}
+
+
+## process command line
+
+# options
+
+while getopts "L:T:O:t:q?" OPT
+do
+ case "$OPT" in
+ L)
+ MIRABELLE_LOGIC="$OPTARG"
+ ;;
+ T)
+ MIRABELLE_IMPORT_THEORY="$OPTARG"
+ ;;
+ O)
+ MIRABELLE_OUTPUT_PATH="$OPTARG"
+ ;;
+ \?)
+ usage
+ ;;
+ esac
+done
+
+shift $(($OPTIND - 1))
+
+[ "$#" -ne 1 ] && usage
+
+MUTABELLE_TEST_THEORY="$1"
+
+## main
+
+echo "Starting Mutabelle..."
+
+# setup
+
+mkdir -p "$MIRABELLE_OUTPUT_PATH"
+
+echo "theory Mutabelle_Test
+imports $MUTABELLE_IMPORT_THEORY
+uses
+ \"$MUTABELLE_HOME/mutabelle.ML\"
+ \"$MUTABELLE_HOME/mutabelle_extra.ML\"
+begin
+
+ML {*
+val mtds = [
+ MutabelleExtra.quickcheck_mtd (Config.put Quickcheck.tester \"random\") \"random\",
+ MutabelleExtra.quickcheck_mtd (Config.put Quickcheck.tester \"exhaustive\") \"exhaustive\"
+]
+*}
+
+ML {*
+fun mutation_testing_of thy =
+ (MutabelleExtra.random_seed := 1.0;
+ MutabelleExtra.thms_of false thy
+ |> (fn thms => MutabelleExtra.mutate_theorems_and_write_report
+ @{theory} mtds thms (\"$MUTABELLE_OUTPUT_PATH/log\")))
+*}
+
+ML {*
+ mutation_testing_of @{theory $MUTABELLE_TEST_THEORY}
+*}
+
+end" > $MUTABELLE_OUTPUT_PATH/Mutabelle_Test.thy
+
+# execution
+
+$ISABELLE_PROCESS -e 'use_thy "$MUTABELLE_OUTPUT_PATH/Mutabelle_Test"' -q $MUTABELLE_LOGIC > /dev/null 2>&1
+
+# make statistics
+
+GenuineCex_random=$(cat $MUTABELLE_OUTPUT_PATH/log | grep "quickcheck_random: GenuineCex" | wc -l)
+NoCex_random=$(cat $MUTABELLE_OUTPUT_PATH/log | grep "quickcheck_random: NoCex" | wc -l)
+Timeout_random=$(cat /$MUTABELLE_OUTPUT_PATH/log | grep "quickcheck_random: Timeout" | wc -l)
+Errors_random=$(cat $MUTABELLE_OUTPUT_PATH/log | grep "quickcheck_random: Error" | wc -l)
+
+GenuineCex_exh=$(cat $MUTABELLE_OUTPUT_PATH/log | grep "quickcheck_exhaustive: GenuineCex" | wc -l)
+NoCex_exh=$(cat $MUTABELLE_OUTPUT_PATH/log | grep "quickcheck_exhaustive: NoCex" | wc -l)
+Timeout_exh=$(cat $MUTABELLE_OUTPUT_PATH/log | grep "quickcheck_exhaustive: Timeout" | wc -l)
+Errors_exh=$(cat $MUTABELLE_OUTPUT_PATH/log | grep "quickcheck_exhaustive: Error" | wc -l)
+
+
+echo "random :" C: $GenuineCex_random N: $NoCex_random T: $Timeout_random E: $Errors_random
+echo "exhaustive :" C: $GenuineCex_exh N: $NoCex_exh T: $Timeout_exh E: $Errors_exh
+
--- a/src/HOL/Mutabelle/mutabelle_extra.ML Mon Dec 06 11:41:24 2010 +0100
+++ b/src/HOL/Mutabelle/mutabelle_extra.ML Mon Dec 06 13:17:26 2010 +0100
@@ -25,6 +25,9 @@
val solve_direct_mtd : mtd
val try_mtd : mtd
(*
+val sledgehammer_mtd : mtd
+*)
+(*
val refute_mtd : mtd
val nitpick_mtd : mtd
*)
@@ -143,15 +146,26 @@
fun invoke_try thy t =
let
- val state = Proof.theorem NONE (K I) (map (single o rpair []) [t]) (ProofContext.init_global thy)
+ val state = Proof.theorem NONE (K I) (map (single o rpair []) [t]) (ProofContext.init_global thy)
in
- case Try.invoke_try NONE state of
+ case Try.invoke_try (SOME (seconds 5.0)) state of
true => (Solved, ([], NONE))
| false => (Unsolved, ([], NONE))
end
val try_mtd = ("try", invoke_try)
+(** sledgehammer **)
+(*
+fun invoke_sledgehammer thy t =
+ if can (Goal.prove_global thy (Term.add_free_names t []) [] t)
+ (fn {context, ...} => Sledgehammer_Tactics.sledgehammer_with_metis_tac context 1) then
+ (Solved, ([], NONE))
+ else
+ (Unsolved, ([], NONE))
+
+val sledgehammer_mtd = ("sledgehammer", invoke_sledgehammer)
+*)
(*
fun invoke_refute thy t =
let
@@ -287,7 +301,14 @@
@{const_name "Pure.term"},
@{const_name "top_class.top"},
(*@{const_name "HOL.equal"},*)
- @{const_name "Quotient.Quot_True"}
+ @{const_name "Quotient.Quot_True"},
+ @{const_name "equal_fun_inst.equal_fun"},
+ @{const_name "equal_bool_inst.equal_bool"},
+ @{const_name "ord_fun_inst.less_eq_fun"},
+ @{const_name "ord_fun_inst.less_fun"},
+ @{const_name Metis.fequal},
+ @{const_name Meson.skolem},
+ @{const_name transfer_morphism}
(*@{const_name "==>"}, @{const_name "=="}*)]
val forbidden_mutant_consts =
@@ -426,11 +447,12 @@
else
mutants
val mutants = mutants
- |> take_random max_mutants
|> map Mutabelle.freeze |> map freezeT
(* |> filter (not o is_forbidden_mutant) *)
|> List.mapPartial (try (Sign.cert_term thy))
- |> List.filter (is_some o try (cterm_of thy))
+ |> List.filter (is_some o try (Thm.cterm_of thy))
+ |> List.filter (is_some o try (Syntax.check_term (ProofContext.init_global thy)))
+ |> take_random max_mutants
val _ = map (fn t => Output.urgent_message ("MUTANT: " ^ Syntax.string_of_term_global thy t)) mutants
in
create_entry thy thm exec mutants mtds
--- a/src/HOL/Option.thy Mon Dec 06 11:41:24 2010 +0100
+++ b/src/HOL/Option.thy Mon Dec 06 13:17:26 2010 +0100
@@ -81,7 +81,7 @@
"map f o sum_case g h = sum_case (map f o g) (map f o h)"
by (rule ext) (simp split: sum.split)
-type_mapper Option.map proof -
+type_lifting Option.map proof -
fix f g x
show "Option.map f (Option.map g x) = Option.map (\<lambda>x. f (g x)) x"
by (cases x) simp_all
--- a/src/HOL/Product_Type.thy Mon Dec 06 11:41:24 2010 +0100
+++ b/src/HOL/Product_Type.thy Mon Dec 06 13:17:26 2010 +0100
@@ -835,7 +835,7 @@
"map_pair f g (a, b) = (f a, g b)"
by (simp add: map_pair_def)
-type_mapper map_pair
+type_lifting map_pair
by (simp_all add: split_paired_all)
lemma fst_map_pair [simp]:
--- a/src/HOL/Quickcheck.thy Mon Dec 06 11:41:24 2010 +0100
+++ b/src/HOL/Quickcheck.thy Mon Dec 06 13:17:26 2010 +0100
@@ -129,7 +129,6 @@
use "Tools/quickcheck_generators.ML"
setup Quickcheck_Generators.setup
-declare [[quickcheck_tester = random]]
subsection {* Code setup *}
--- a/src/HOL/Sum_Type.thy Mon Dec 06 11:41:24 2010 +0100
+++ b/src/HOL/Sum_Type.thy Mon Dec 06 13:17:26 2010 +0100
@@ -95,7 +95,7 @@
"sum_map f1 f2 (Inl a) = Inl (f1 a)"
| "sum_map f1 f2 (Inr a) = Inr (f2 a)"
-type_mapper sum_map proof -
+type_lifting sum_map proof -
fix f g h i s
show "sum_map f g (sum_map h i s) = sum_map (\<lambda>x. f (h x)) (\<lambda>x. g (i x)) s"
by (cases s) simp_all
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Tools/type_lifting.ML Mon Dec 06 13:17:26 2010 +0100
@@ -0,0 +1,217 @@
+(* Title: HOL/Tools/type_lifting.ML
+ Author: Florian Haftmann, TU Muenchen
+
+Functorial structure of types.
+*)
+
+signature TYPE_LIFTING =
+sig
+ val find_atomic: theory -> typ -> (typ * (bool * bool)) list
+ val construct_mapper: theory -> (string * bool -> term)
+ -> bool -> typ -> typ -> term
+ val type_lifting: string option -> term -> theory -> Proof.state
+ type entry
+ val entries: theory -> entry Symtab.table
+end;
+
+structure Type_Lifting : TYPE_LIFTING =
+struct
+
+val compositionalityN = "compositionality";
+val identityN = "identity";
+
+(** functorial mappers and their properties **)
+
+(* bookkeeping *)
+
+type entry = { mapper: string, variances: (sort * (bool * bool)) list,
+ compositionality: thm, identity: thm };
+
+structure Data = Theory_Data(
+ type T = entry Symtab.table
+ val empty = Symtab.empty
+ fun merge (xy : T * T) = Symtab.merge (K true) xy
+ val extend = I
+);
+
+val entries = Data.get;
+
+
+(* type analysis *)
+
+fun find_atomic thy T =
+ let
+ val variances_of = Option.map #variances o Symtab.lookup (Data.get thy);
+ fun add_variance is_contra T =
+ AList.map_default (op =) (T, (false, false))
+ ((if is_contra then apsnd else apfst) (K true));
+ fun analyze' is_contra (_, (co, contra)) T =
+ (if co then analyze is_contra T else I)
+ #> (if contra then analyze (not is_contra) T else I)
+ and analyze is_contra (T as Type (tyco, Ts)) = (case variances_of tyco
+ of NONE => add_variance is_contra T
+ | SOME variances => fold2 (analyze' is_contra) variances Ts)
+ | analyze is_contra T = add_variance is_contra T;
+ in analyze false T [] end;
+
+fun construct_mapper thy atomic =
+ let
+ val lookup = the o Symtab.lookup (Data.get thy);
+ fun constructs is_contra (_, (co, contra)) T T' =
+ (if co then [construct is_contra T T'] else [])
+ @ (if contra then [construct (not is_contra) T T'] else [])
+ and construct is_contra (T as Type (tyco, Ts)) (T' as Type (_, Ts')) =
+ let
+ val { mapper, variances, ... } = lookup tyco;
+ val args = maps (fn (arg_pattern, (T, T')) =>
+ constructs is_contra arg_pattern T T')
+ (variances ~~ (Ts ~~ Ts'));
+ val (U, U') = if is_contra then (T', T) else (T, T');
+ in list_comb (Const (mapper, map fastype_of args ---> U --> U'), args) end
+ | construct is_contra (TFree (v, _)) (TFree _) = atomic (v, is_contra);
+ in construct end;
+
+
+(* mapper properties *)
+
+fun make_compositionality_prop variances (tyco, mapper) =
+ let
+ fun invents n k nctxt =
+ let
+ val names = Name.invents nctxt n k;
+ in (names, fold Name.declare names nctxt) end;
+ val (((vs1, vs2), vs3), _) = Name.context
+ |> invents Name.aT (length variances)
+ ||>> invents Name.aT (length variances)
+ ||>> invents Name.aT (length variances);
+ fun mk_Ts vs = map2 (fn v => fn (sort, _) => TFree (v, sort))
+ vs variances;
+ val (Ts1, Ts2, Ts3) = (mk_Ts vs1, mk_Ts vs2, mk_Ts vs3);
+ fun mk_argT ((T, T'), (_, (co, contra))) =
+ (if co then [(T --> T')] else [])
+ @ (if contra then [(T' --> T)] else []);
+ val contras = maps (fn (_, (co, contra)) =>
+ (if co then [false] else []) @ (if contra then [true] else [])) variances;
+ val Ts21 = maps mk_argT ((Ts2 ~~ Ts1) ~~ variances);
+ val Ts32 = maps mk_argT ((Ts3 ~~ Ts2) ~~ variances);
+ val ((names21, names32), nctxt) = Name.context
+ |> invents "f" (length Ts21)
+ ||>> invents "f" (length Ts32);
+ val T1 = Type (tyco, Ts1);
+ val T2 = Type (tyco, Ts2);
+ val T3 = Type (tyco, Ts3);
+ val x = Free (the_single (Name.invents nctxt (Long_Name.base_name tyco) 1), T3);
+ val (args21, args32) = (names21 ~~ Ts21, names32 ~~ Ts32);
+ val args31 = map2 (fn is_contra => fn ((f21, T21), (f32, T32)) =>
+ if not is_contra then
+ Abs ("x", domain_type T32, Free (f21, T21) $ (Free (f32, T32) $ Bound 0))
+ else
+ Abs ("x", domain_type T21, Free (f32, T32) $ (Free (f21, T21) $ Bound 0))
+ ) contras (args21 ~~ args32)
+ fun mk_mapper T T' args = list_comb (Const (mapper,
+ map fastype_of args ---> T --> T'), args);
+ val lhs = mk_mapper T2 T1 (map Free args21) $
+ (mk_mapper T3 T2 (map Free args32) $ x);
+ val rhs = mk_mapper T3 T1 args31 $ x;
+ in (map Free (args21 @ args32) @ [x], (HOLogic.mk_Trueprop o HOLogic.mk_eq) (lhs, rhs)) end;
+
+fun make_identity_prop variances (tyco, mapper) =
+ let
+ val vs = Name.invents Name.context Name.aT (length variances);
+ val Ts = map2 (fn v => fn (sort, _) => TFree (v, sort)) vs variances;
+ fun bool_num b = if b then 1 else 0;
+ fun mk_argT (T, (_, (co, contra))) =
+ replicate (bool_num co + bool_num contra) (T --> T)
+ val Ts' = maps mk_argT (Ts ~~ variances)
+ val T = Type (tyco, Ts);
+ val x = Free (Long_Name.base_name tyco, T);
+ val lhs = list_comb (Const (mapper, Ts' ---> T --> T),
+ map (fn T => Abs ("x", domain_type T, Bound 0)) Ts') $ x;
+ in (x, (HOLogic.mk_Trueprop o HOLogic.mk_eq) (lhs, x)) end;
+
+
+(* analyzing and registering mappers *)
+
+fun consume eq x [] = (false, [])
+ | consume eq x (ys as z :: zs) = if eq (x, z) then (true, zs) else (false, ys);
+
+fun split_mapper_typ "fun" T =
+ let
+ val (Ts', T') = strip_type T;
+ val (Ts'', T'') = split_last Ts';
+ val (Ts''', T''') = split_last Ts'';
+ in (Ts''', T''', T'' --> T') end
+ | split_mapper_typ tyco T =
+ let
+ val (Ts', T') = strip_type T;
+ val (Ts'', T'') = split_last Ts';
+ in (Ts'', T'', T') end;
+
+fun analyze_variances thy tyco T =
+ let
+ fun bad_typ () = error ("Bad mapper type: " ^ Syntax.string_of_typ_global thy T);
+ val (Ts, T1, T2) = split_mapper_typ tyco T
+ handle List.Empty => bad_typ ();
+ val _ = pairself
+ ((fn tyco' => if tyco' = tyco then () else bad_typ ()) o fst o dest_Type) (T1, T2)
+ val (vs1, vs2) = pairself (map dest_TFree o snd o dest_Type) (T1, T2)
+ handle TYPE _ => bad_typ ();
+ val _ = if has_duplicates (eq_fst (op =)) (vs1 @ vs2)
+ then bad_typ () else ();
+ fun check_variance_pair (var1 as (v1, sort1), var2 as (v2, sort2)) =
+ let
+ val coT = TFree var1 --> TFree var2;
+ val contraT = TFree var2 --> TFree var1;
+ val sort = Sign.inter_sort thy (sort1, sort2);
+ in
+ consume (op =) coT
+ ##>> consume (op =) contraT
+ #>> pair sort
+ end;
+ val (variances, left_variances) = fold_map check_variance_pair (vs1 ~~ vs2) Ts;
+ val _ = if null left_variances then () else bad_typ ();
+ in variances end;
+
+fun gen_type_lifting prep_term some_prfx raw_t thy =
+ let
+ val (mapper, T) = case prep_term thy raw_t
+ of Const cT => cT
+ | t => error ("No constant: " ^ Syntax.string_of_term_global thy t);
+ val prfx = the_default (Long_Name.base_name mapper) some_prfx;
+ val _ = Type.no_tvars T;
+ fun add_tycos (Type (tyco, Ts)) = insert (op =) tyco #> fold add_tycos Ts
+ | add_tycos _ = I;
+ val tycos = add_tycos T [];
+ val tyco = if tycos = ["fun"] then "fun"
+ else case remove (op =) "fun" tycos
+ of [tyco] => tyco
+ | _ => error ("Bad number of type constructors: " ^ Syntax.string_of_typ_global thy T);
+ val variances = analyze_variances thy tyco T;
+ val compositionality_prop = uncurry (fold_rev Logic.all)
+ (make_compositionality_prop variances (tyco, mapper));
+ val identity_prop = uncurry Logic.all
+ (make_identity_prop variances (tyco, mapper));
+ val qualify = Binding.qualify true prfx o Binding.name;
+ fun after_qed [single_compositionality, single_identity] lthy =
+ lthy
+ |> Local_Theory.note ((qualify compositionalityN, []), single_compositionality)
+ ||>> Local_Theory.note ((qualify identityN, []), single_identity)
+ |-> (fn ((_, [compositionality]), (_, [identity])) =>
+ (Local_Theory.background_theory o Data.map)
+ (Symtab.update (tyco, { mapper = mapper, variances = variances,
+ compositionality = compositionality, identity = identity })));
+ in
+ thy
+ |> Named_Target.theory_init
+ |> Proof.theorem NONE after_qed (map (fn t => [(t, [])]) [compositionality_prop, identity_prop])
+ end
+
+val type_lifting = gen_type_lifting Sign.cert_term;
+val type_lifting_cmd = gen_type_lifting Syntax.read_term_global;
+
+val _ =
+ Outer_Syntax.command "type_lifting" "register operations managing the functorial structure of a type" Keyword.thy_goal
+ (Scan.option (Parse.name --| Parse.$$$ ":") -- Parse.term
+ >> (fn (prfx, t) => Toplevel.print o (Toplevel.theory_to_proof (type_lifting_cmd prfx t))));
+
+end;
--- a/src/HOL/Tools/type_mapper.ML Mon Dec 06 11:41:24 2010 +0100
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,217 +0,0 @@
-(* Title: HOL/Tools/type_mapper.ML
- Author: Florian Haftmann, TU Muenchen
-
-Functorial mappers on types.
-*)
-
-signature TYPE_MAPPER =
-sig
- val find_atomic: theory -> typ -> (typ * (bool * bool)) list
- val construct_mapper: theory -> (string * bool -> term)
- -> bool -> typ -> typ -> term
- val type_mapper: string option -> term -> theory -> Proof.state
- type entry
- val entries: theory -> entry Symtab.table
-end;
-
-structure Type_Mapper : TYPE_MAPPER =
-struct
-
-val compositionalityN = "compositionality";
-val identityN = "identity";
-
-(** functorial mappers and their properties **)
-
-(* bookkeeping *)
-
-type entry = { mapper: string, variances: (sort * (bool * bool)) list,
- compositionality: thm, identity: thm };
-
-structure Data = Theory_Data(
- type T = entry Symtab.table
- val empty = Symtab.empty
- fun merge (xy : T * T) = Symtab.merge (K true) xy
- val extend = I
-);
-
-val entries = Data.get;
-
-
-(* type analysis *)
-
-fun find_atomic thy T =
- let
- val variances_of = Option.map #variances o Symtab.lookup (Data.get thy);
- fun add_variance is_contra T =
- AList.map_default (op =) (T, (false, false))
- ((if is_contra then apsnd else apfst) (K true));
- fun analyze' is_contra (_, (co, contra)) T =
- (if co then analyze is_contra T else I)
- #> (if contra then analyze (not is_contra) T else I)
- and analyze is_contra (T as Type (tyco, Ts)) = (case variances_of tyco
- of NONE => add_variance is_contra T
- | SOME variances => fold2 (analyze' is_contra) variances Ts)
- | analyze is_contra T = add_variance is_contra T;
- in analyze false T [] end;
-
-fun construct_mapper thy atomic =
- let
- val lookup = the o Symtab.lookup (Data.get thy);
- fun constructs is_contra (_, (co, contra)) T T' =
- (if co then [construct is_contra T T'] else [])
- @ (if contra then [construct (not is_contra) T T'] else [])
- and construct is_contra (T as Type (tyco, Ts)) (T' as Type (_, Ts')) =
- let
- val { mapper, variances, ... } = lookup tyco;
- val args = maps (fn (arg_pattern, (T, T')) =>
- constructs is_contra arg_pattern T T')
- (variances ~~ (Ts ~~ Ts'));
- val (U, U') = if is_contra then (T', T) else (T, T');
- in list_comb (Const (mapper, map fastype_of args ---> U --> U'), args) end
- | construct is_contra (TFree (v, _)) (TFree _) = atomic (v, is_contra);
- in construct end;
-
-
-(* mapper properties *)
-
-fun make_compositionality_prop variances (tyco, mapper) =
- let
- fun invents n k nctxt =
- let
- val names = Name.invents nctxt n k;
- in (names, fold Name.declare names nctxt) end;
- val (((vs1, vs2), vs3), _) = Name.context
- |> invents Name.aT (length variances)
- ||>> invents Name.aT (length variances)
- ||>> invents Name.aT (length variances);
- fun mk_Ts vs = map2 (fn v => fn (sort, _) => TFree (v, sort))
- vs variances;
- val (Ts1, Ts2, Ts3) = (mk_Ts vs1, mk_Ts vs2, mk_Ts vs3);
- fun mk_argT ((T, T'), (_, (co, contra))) =
- (if co then [(T --> T')] else [])
- @ (if contra then [(T' --> T)] else []);
- val contras = maps (fn (_, (co, contra)) =>
- (if co then [false] else []) @ (if contra then [true] else [])) variances;
- val Ts21 = maps mk_argT ((Ts2 ~~ Ts1) ~~ variances);
- val Ts32 = maps mk_argT ((Ts3 ~~ Ts2) ~~ variances);
- val ((names21, names32), nctxt) = Name.context
- |> invents "f" (length Ts21)
- ||>> invents "f" (length Ts32);
- val T1 = Type (tyco, Ts1);
- val T2 = Type (tyco, Ts2);
- val T3 = Type (tyco, Ts3);
- val x = Free (the_single (Name.invents nctxt (Long_Name.base_name tyco) 1), T3);
- val (args21, args32) = (names21 ~~ Ts21, names32 ~~ Ts32);
- val args31 = map2 (fn is_contra => fn ((f21, T21), (f32, T32)) =>
- if not is_contra then
- Abs ("x", domain_type T32, Free (f21, T21) $ (Free (f32, T32) $ Bound 0))
- else
- Abs ("x", domain_type T21, Free (f32, T32) $ (Free (f21, T21) $ Bound 0))
- ) contras (args21 ~~ args32)
- fun mk_mapper T T' args = list_comb (Const (mapper,
- map fastype_of args ---> T --> T'), args);
- val lhs = mk_mapper T2 T1 (map Free args21) $
- (mk_mapper T3 T2 (map Free args32) $ x);
- val rhs = mk_mapper T3 T1 args31 $ x;
- in (map Free (args21 @ args32) @ [x], (HOLogic.mk_Trueprop o HOLogic.mk_eq) (lhs, rhs)) end;
-
-fun make_identity_prop variances (tyco, mapper) =
- let
- val vs = Name.invents Name.context Name.aT (length variances);
- val Ts = map2 (fn v => fn (sort, _) => TFree (v, sort)) vs variances;
- fun bool_num b = if b then 1 else 0;
- fun mk_argT (T, (_, (co, contra))) =
- replicate (bool_num co + bool_num contra) (T --> T)
- val Ts' = maps mk_argT (Ts ~~ variances)
- val T = Type (tyco, Ts);
- val x = Free (Long_Name.base_name tyco, T);
- val lhs = list_comb (Const (mapper, Ts' ---> T --> T),
- map (fn T => Abs ("x", domain_type T, Bound 0)) Ts') $ x;
- in (x, (HOLogic.mk_Trueprop o HOLogic.mk_eq) (lhs, x)) end;
-
-
-(* analyzing and registering mappers *)
-
-fun consume eq x [] = (false, [])
- | consume eq x (ys as z :: zs) = if eq (x, z) then (true, zs) else (false, ys);
-
-fun split_mapper_typ "fun" T =
- let
- val (Ts', T') = strip_type T;
- val (Ts'', T'') = split_last Ts';
- val (Ts''', T''') = split_last Ts'';
- in (Ts''', T''', T'' --> T') end
- | split_mapper_typ tyco T =
- let
- val (Ts', T') = strip_type T;
- val (Ts'', T'') = split_last Ts';
- in (Ts'', T'', T') end;
-
-fun analyze_variances thy tyco T =
- let
- fun bad_typ () = error ("Bad mapper type: " ^ Syntax.string_of_typ_global thy T);
- val (Ts, T1, T2) = split_mapper_typ tyco T
- handle List.Empty => bad_typ ();
- val _ = pairself
- ((fn tyco' => if tyco' = tyco then () else bad_typ ()) o fst o dest_Type) (T1, T2)
- val (vs1, vs2) = pairself (map dest_TFree o snd o dest_Type) (T1, T2)
- handle TYPE _ => bad_typ ();
- val _ = if has_duplicates (eq_fst (op =)) (vs1 @ vs2)
- then bad_typ () else ();
- fun check_variance_pair (var1 as (v1, sort1), var2 as (v2, sort2)) =
- let
- val coT = TFree var1 --> TFree var2;
- val contraT = TFree var2 --> TFree var1;
- val sort = Sign.inter_sort thy (sort1, sort2);
- in
- consume (op =) coT
- ##>> consume (op =) contraT
- #>> pair sort
- end;
- val (variances, left_variances) = fold_map check_variance_pair (vs1 ~~ vs2) Ts;
- val _ = if null left_variances then () else bad_typ ();
- in variances end;
-
-fun gen_type_mapper prep_term some_prfx raw_t thy =
- let
- val (mapper, T) = case prep_term thy raw_t
- of Const cT => cT
- | t => error ("No constant: " ^ Syntax.string_of_term_global thy t);
- val prfx = the_default (Long_Name.base_name mapper) some_prfx;
- val _ = Type.no_tvars T;
- fun add_tycos (Type (tyco, Ts)) = insert (op =) tyco #> fold add_tycos Ts
- | add_tycos _ = I;
- val tycos = add_tycos T [];
- val tyco = if tycos = ["fun"] then "fun"
- else case remove (op =) "fun" tycos
- of [tyco] => tyco
- | _ => error ("Bad number of type constructors: " ^ Syntax.string_of_typ_global thy T);
- val variances = analyze_variances thy tyco T;
- val compositionality_prop = uncurry (fold_rev Logic.all)
- (make_compositionality_prop variances (tyco, mapper));
- val identity_prop = uncurry Logic.all
- (make_identity_prop variances (tyco, mapper));
- val qualify = Binding.qualify true prfx o Binding.name;
- fun after_qed [single_compositionality, single_identity] lthy =
- lthy
- |> Local_Theory.note ((qualify compositionalityN, []), single_compositionality)
- ||>> Local_Theory.note ((qualify identityN, []), single_identity)
- |-> (fn ((_, [compositionality]), (_, [identity])) =>
- (Local_Theory.background_theory o Data.map)
- (Symtab.update (tyco, { mapper = mapper, variances = variances,
- compositionality = compositionality, identity = identity })));
- in
- thy
- |> Named_Target.theory_init
- |> Proof.theorem NONE after_qed (map (fn t => [(t, [])]) [compositionality_prop, identity_prop])
- end
-
-val type_mapper = gen_type_mapper Sign.cert_term;
-val type_mapper_cmd = gen_type_mapper Syntax.read_term_global;
-
-val _ =
- Outer_Syntax.command "type_mapper" "register functorial mapper for type with its properties" Keyword.thy_goal
- (Scan.option (Parse.name --| Parse.$$$ ":") -- Parse.term
- >> (fn (prfx, t) => Toplevel.print o (Toplevel.theory_to_proof (type_mapper_cmd prfx t))));
-
-end;