--- a/src/HOL/Library/Predicate_Compile_Alternative_Defs.thy Wed Mar 31 16:44:41 2010 +0200
+++ b/src/HOL/Library/Predicate_Compile_Alternative_Defs.thy Wed Mar 31 16:44:41 2010 +0200
@@ -1,5 +1,5 @@
theory Predicate_Compile_Alternative_Defs
-imports "../Predicate_Compile"
+imports Main
begin
section {* Common constants *}
@@ -46,15 +46,95 @@
setup {* Predicate_Compile_Data.ignore_consts [@{const_name div}, @{const_name mod}, @{const_name times}] *}
-subsection {* Inductive definitions for arithmetic on natural numbers *}
+section {* Arithmetic operations *}
+
+subsection {* Arithmetic on naturals and integers *}
+
+definition plus_eq_nat :: "nat => nat => nat => bool"
+where
+ "plus_eq_nat x y z = (x + y = z)"
-inductive plusP
+definition minus_eq_nat :: "nat => nat => nat => bool"
+where
+ "minus_eq_nat x y z = (x - y = z)"
+
+definition plus_eq_int :: "int => int => int => bool"
+where
+ "plus_eq_int x y z = (x + y = z)"
+
+definition minus_eq_int :: "int => int => int => bool"
+where
+ "minus_eq_int x y z = (x - y = z)"
+
+definition subtract
where
- "plusP x 0 x"
-| "plusP x y z ==> plusP x (Suc y) (Suc z)"
+ [code_inline]: "subtract x y = y - x"
-setup {* Predicate_Compile_Fun.add_function_predicate_translation
- (@{term "op + :: nat => nat => nat"}, @{term "plusP"}) *}
+setup {*
+let
+ val Fun = Predicate_Compile_Aux.Fun
+ val Input = Predicate_Compile_Aux.Input
+ val Output = Predicate_Compile_Aux.Output
+ val Bool = Predicate_Compile_Aux.Bool
+ val iio = Fun (Input, Fun (Input, Fun (Output, Bool)))
+ val ioi = Fun (Input, Fun (Output, Fun (Input, Bool)))
+ val oii = Fun (Output, Fun (Input, Fun (Input, Bool)))
+ val ooi = Fun (Output, Fun (Output, Fun (Input, Bool)))
+ val plus_nat = Predicate_Compile_Core.functional_compilation @{const_name plus} iio
+ val minus_nat = Predicate_Compile_Core.functional_compilation @{const_name "minus"} iio
+ fun subtract_nat compfuns (_ : typ) =
+ let
+ val T = Predicate_Compile_Aux.mk_predT compfuns @{typ nat}
+ in
+ absdummy (@{typ nat}, absdummy (@{typ nat},
+ Const (@{const_name "If"}, @{typ bool} --> T --> T --> T) $
+ (@{term "op > :: nat => nat => bool"} $ Bound 1 $ Bound 0) $
+ Predicate_Compile_Aux.mk_bot compfuns @{typ nat} $
+ Predicate_Compile_Aux.mk_single compfuns
+ (@{term "op - :: nat => nat => nat"} $ Bound 0 $ Bound 1)))
+ end
+ fun enumerate_addups_nat compfuns (_ : typ) =
+ absdummy (@{typ nat}, Predicate_Compile_Aux.mk_iterate_upto compfuns @{typ "nat * nat"}
+ (absdummy (@{typ code_numeral}, @{term "Pair :: nat => nat => nat * nat"} $
+ (@{term "Code_Numeral.nat_of"} $ Bound 0) $
+ (@{term "op - :: nat => nat => nat"} $ Bound 1 $ (@{term "Code_Numeral.nat_of"} $ Bound 0))),
+ @{term "0 :: code_numeral"}, @{term "Code_Numeral.of_nat"} $ Bound 0))
+ fun enumerate_nats compfuns (_ : typ) =
+ let
+ val (single_const, _) = strip_comb (Predicate_Compile_Aux.mk_single compfuns @{term "0 :: nat"})
+ val T = Predicate_Compile_Aux.mk_predT compfuns @{typ nat}
+ in
+ absdummy(@{typ nat}, absdummy (@{typ nat},
+ Const (@{const_name If}, @{typ bool} --> T --> T --> T) $
+ (@{term "op = :: nat => nat => bool"} $ Bound 0 $ @{term "0::nat"}) $
+ (Predicate_Compile_Aux.mk_iterate_upto compfuns @{typ nat} (@{term "Code_Numeral.nat_of"},
+ @{term "0::code_numeral"}, @{term "Code_Numeral.of_nat"} $ Bound 1)) $
+ (single_const $ (@{term "op + :: nat => nat => nat"} $ Bound 1 $ Bound 0))))
+ end
+in
+ Predicate_Compile_Core.force_modes_and_compilations @{const_name plus_eq_nat}
+ [(iio, (plus_nat, false)), (oii, (subtract_nat, false)), (ioi, (subtract_nat, false)),
+ (ooi, (enumerate_addups_nat, false))]
+ #> Predicate_Compile_Fun.add_function_predicate_translation
+ (@{term "plus :: nat => nat => nat"}, @{term "plus_eq_nat"})
+ #> Predicate_Compile_Core.force_modes_and_compilations @{const_name minus_eq_nat}
+ [(iio, (minus_nat, false)), (oii, (enumerate_nats, false))]
+ #> Predicate_Compile_Fun.add_function_predicate_translation
+ (@{term "minus :: nat => nat => nat"}, @{term "minus_eq_nat"})
+ #> Predicate_Compile_Core.force_modes_and_functions @{const_name plus_eq_int}
+ [(iio, (@{const_name plus}, false)), (ioi, (@{const_name subtract}, false)),
+ (oii, (@{const_name subtract}, false))]
+ #> Predicate_Compile_Fun.add_function_predicate_translation
+ (@{term "plus :: int => int => int"}, @{term "plus_eq_int"})
+ #> Predicate_Compile_Core.force_modes_and_functions @{const_name minus_eq_int}
+ [(iio, (@{const_name minus}, false)), (oii, (@{const_name plus}, false)),
+ (ioi, (@{const_name minus}, false))]
+ #> Predicate_Compile_Fun.add_function_predicate_translation
+ (@{term "minus :: int => int => int"}, @{term "minus_eq_int"})
+end
+*}
+
+subsection {* Inductive definitions for ordering on naturals *}
inductive less_nat
where
@@ -88,12 +168,18 @@
section {* Alternative list definitions *}
-text {* size simps are not yet added to the Spec_Rules interface. So they are just added manually here! *}
-
-lemma [code_pred_def]:
- "length [] = 0"
- "length (x # xs) = Suc (length xs)"
-by auto
+subsection {* Alternative rules for length *}
+
+definition size_list :: "'a list => nat"
+where "size_list = size"
+
+lemma size_list_simps:
+ "size_list [] = 0"
+ "size_list (x # xs) = Suc (size_list xs)"
+by (auto simp add: size_list_def)
+
+declare size_list_simps[code_pred_def]
+declare size_list_def[symmetric, code_pred_inline]
subsection {* Alternative rules for set *}