diff options
Diffstat (limited to 'backends')
| -rw-r--r-- | backends/hol4/Primitives.sml | 385 | ||||
| -rw-r--r-- | backends/hol4/Test.sml | 7 |
2 files changed, 387 insertions, 5 deletions
diff --git a/backends/hol4/Primitives.sml b/backends/hol4/Primitives.sml new file mode 100644 index 00000000..4d77b84a --- /dev/null +++ b/backends/hol4/Primitives.sml @@ -0,0 +1,385 @@ +open HolKernel boolLib bossLib Parse +open boolTheory arithmeticTheory integerTheory intLib listTheory stringTheory + +val primitives_theory_name = "Primitives" +val _ = new_theory primitives_theory_name + +(* TODO: val _ = export_theory(); *) + +(*** Result *) +Datatype: + error = Failure +End + +Datatype: + result = Return 'a | Fail error | Loop +End + +Type M = ``: 'a result`` + +val bind_def = Define ` + (bind : 'a M -> ('a -> 'b M) -> 'b M) x f = + case x of + Return y => f y + | Fail e => Fail e + | Loop => Loop`; + +val bind_name = fst (dest_const “bind”) + +val return_def = Define ` + (return : 'a -> 'a M) x = + Return x`; + +val massert_def = Define ‘massert b = if b then Return () else Fail Failure’ + +Overload monad_bind = ``bind`` +Overload monad_unitbind = ``\x y. bind x (\z. y)`` +Overload monad_ignore_bind = ``\x y. bind x (\z. y)`` + +(* Allow the use of monadic syntax *) +val _ = monadsyntax.enable_monadsyntax () + +(*** Misc *) +Type char = “:char” +Type string = “:string” + +val mem_replace_fwd_def = Define ‘mem_replace_fwd (x : 'a) (y :'a) : 'a = x’ +val mem_replace_back_def = Define ‘mem_replace_back (x : 'a) (y :'a) : 'a = y’ + +(*** Scalars *) +(* Remark: most of the following code was partially generated *) + +(* The bounds for the isize/usize types are opaque, because they vary with + the architecture *) +val _ = new_constant ("isize_min", “:int”) +val _ = new_constant ("isize_max", “:int”) +val _ = new_constant ("usize_max", “:int”) + +val _ = new_type ("usize", 0) +val _ = new_type ("u8", 0) +val _ = new_type ("u16", 0) +val _ = new_type ("u32", 0) +val _ = new_type ("u64", 0) +val _ = new_type ("u128", 0) +val _ = new_type ("isize", 0) +val _ = new_type ("i8", 0) +val _ = new_type ("i16", 0) +val _ = new_type ("i32", 0) +val _ = new_type ("i64", 0) +val _ = new_type ("i128", 0) + +val _ = new_constant ("isize_to_int", “:isize -> int”) +val _ = new_constant ("i8_to_int", “:i8 -> int”) +val _ = new_constant ("i16_to_int", “:i16 -> int”) +val _ = new_constant ("i32_to_int", “:i32 -> int”) +val _ = new_constant ("i64_to_int", “:i64 -> int”) +val _ = new_constant ("i128_to_int", “:i128 -> int”) +val _ = new_constant ("usize_to_int", “:usize -> int”) +val _ = new_constant ("u8_to_int", “:u8 -> int”) +val _ = new_constant ("u16_to_int", “:u16 -> int”) +val _ = new_constant ("u32_to_int", “:u32 -> int”) +val _ = new_constant ("u64_to_int", “:u64 -> int”) +val _ = new_constant ("u128_to_int", “:u128 -> int”) + +val _ = new_constant ("int_to_isize", “:int -> isize”) +val _ = new_constant ("int_to_i8", “:int -> i8”) +val _ = new_constant ("int_to_i16", “:int -> i16”) +val _ = new_constant ("int_to_i32", “:int -> i32”) +val _ = new_constant ("int_to_i64", “:int -> i64”) +val _ = new_constant ("int_to_i128", “:int -> i128”) +val _ = new_constant ("int_to_usize", “:int -> usize”) +val _ = new_constant ("int_to_u8", “:int -> u8”) +val _ = new_constant ("int_to_u16", “:int -> u16”) +val _ = new_constant ("int_to_u32", “:int -> u32”) +val _ = new_constant ("int_to_u64", “:int -> u64”) +val _ = new_constant ("int_to_u128", “:int -> u128”) + +(* The bounds *) +val i8_min_def = Define ‘i8_min = (-128:int)’ +val i8_max_def = Define ‘i8_max = (127:int)’ +val i16_min_def = Define ‘i16_min = (-32768:int)’ +val i16_max_def = Define ‘i16_max = (32767:int)’ +val i32_min_def = Define ‘i32_min = (-2147483648:int)’ +val i32_max_def = Define ‘i32_max = (2147483647:int)’ +val i64_min_def = Define ‘i64_min = (-9223372036854775808:int)’ +val i64_max_def = Define ‘i64_max = (9223372036854775807:int)’ +val i128_min_def = Define ‘i128_min = (-170141183460469231731687303715884105728:int)’ +val i128_max_def = Define ‘i128_max = (170141183460469231731687303715884105727:int)’ +val u8_max_def = Define ‘u8_max = (255:int)’ +val u16_max_def = Define ‘u16_max = (65535:int)’ +val u32_max_def = Define ‘u32_max = (4294967295:int)’ +val u64_max_def = Define ‘u64_max = (18446744073709551615:int)’ +val u128_max_def = Define ‘u128_max = (340282366920938463463374607431768211455:int)’ + +val all_bound_defs = [ + i8_min_def, i8_max_def, + i16_min_def, i16_max_def, + i32_min_def, i32_max_def, + i64_min_def, i64_max_def, + i128_min_def, i128_max_def, + u8_max_def, + u16_max_def, + u32_max_def, + u64_max_def, + u128_max_def +] + +(* The following bounds are valid for all architectures *) +val isize_bounds = new_axiom ("isize_bounds", “isize_min <= i16_min /\ isize_max >= i16_max”) +val usize_bounds = new_axiom ("usize_bounds", “usize_max >= u16_max”) + +(* Conversion bounds *) +val isize_to_int_bounds = new_axiom ("isize_to_int_bounds", + “!n. isize_min <= isize_to_int n /\ isize_to_int n <= isize_max”) + +val i8_to_int_bounds = new_axiom ("i8_to_int_bounds", + “!n. i8_min <= i8_to_int n /\ i8_to_int n <= i8_max”) + +val i16_to_int_bounds = new_axiom ("i16_to_int_bounds", + “!n. i16_min <= i16_to_int n /\ i16_to_int n <= i16_max”) + +val i32_to_int_bounds = new_axiom ("i32_to_int_bounds", + “!n. i32_min <= i32_to_int n /\ i32_to_int n <= i32_max”) + +val i64_to_int_bounds = new_axiom ("i64_to_int_bounds", + “!n. i64_min <= i64_to_int n /\ i64_to_int n <= i64_max”) + +val i128_to_int_bounds = new_axiom ("i128_to_int_bounds", + “!n. i128_min <= i128_to_int n /\ i128_to_int n <= i128_max”) + +val usize_to_int_bounds = new_axiom ("usize_to_int_bounds", + “!n. 0 <= usize_to_int n /\ usize_to_int n <= usize_max”) + +val u8_to_int_bounds = new_axiom ("u8_to_int_bounds", + “!n. 0 <= u8_to_int n /\ u8_to_int n <= u8_max”) + +val u16_to_int_bounds = new_axiom ("u16_to_int_bounds", + “!n. 0 <= u16_to_int n /\ u16_to_int n <= u16_max”) + +val u32_to_int_bounds = new_axiom ("u32_to_int_bounds", + “!n. 0 <= u32_to_int n /\ u32_to_int n <= u32_max”) + +val u64_to_int_bounds = new_axiom ("u64_to_int_bounds", + “!n. 0 <= u64_to_int n /\ u64_to_int n <= u64_max”) + +val u128_to_int_bounds = new_axiom ("u128_to_int_bounds", + “!n. 0 <= u128_to_int n /\ u128_to_int n <= u128_max”) + +(* Conversion to and from int. + + Note that for isize and usize, we write the lemmas in such a way that the + proofs are easily automatable for constants. + *) +val int_to_isize_id = + new_axiom ("int_to_isize_id", + “!n. (i16_min <= n \/ isize_min <= n) /\ (n <= i16_max \/ n <= isize_max) ==> + isize_to_int (int_to_isize n) = n”) + +val int_to_usize_id = + new_axiom ("int_to_usize_id", + “!n. 0 <= n /\ (n <= u16_max \/ n <= usize_max) ==> usize_to_int (int_to_usize n) = n”) + +val int_to_i8_id = + new_axiom ("int_to_i8_id", + “!n. i8_min <= n /\ n <= i8_max ==> i8_to_int (int_to_i8 n) = n”) + +val int_to_i16_id = + new_axiom ("int_to_i16_id", + “!n. i16_min <= n /\ n <= i16_max ==> i16_to_int (int_to_i16 n) = n”) + +val int_to_i32_id = + new_axiom ("int_to_i32_id", + “!n. i32_min <= n /\ n <= i32_max ==> i32_to_int (int_to_i32 n) = n”) + +val int_to_i64_id = + new_axiom ("int_to_i64_id", + “!n. i64_min <= n /\ n <= i64_max ==> i64_to_int (int_to_i64 n) = n”) + +val int_to_i128_id = + new_axiom ("int_to_i128_id", + “!n. i128_min <= n /\ n <= i128_max ==> i128_to_int (int_to_i128 n) = n”) + +val int_to_u8_id = + new_axiom ("int_to_u8_id", + “!n. 0 <= n /\ n <= u8_max ==> u8_to_int (int_to_u8 n) = n”) + +val int_to_u16_id = + new_axiom ("int_to_u16_id", + “!n. 0 <= n /\ n <= u16_max ==> u16_to_int (int_to_u16 n) = n”) + +val int_to_u32_id = + new_axiom ("int_to_u32_id", + “!n. 0 <= n /\ n <= u32_max ==> u32_to_int (int_to_u32 n) = n”) + +val int_to_u64_id = + new_axiom ("int_to_u64_id", + “!n. 0 <= n /\ n <= u64_max ==> u64_to_int (int_to_u64 n) = n”) + +val int_to_u128_id = + new_axiom ("int_to_u128_id", + “!n. 0 <= n /\ n <= u128_max ==> u128_to_int (int_to_u128 n) = n”) + +val all_conversion_id_lemmas = [ + int_to_isize_id, + int_to_i8_id, + int_to_i16_id, + int_to_i32_id, + int_to_i64_id, + int_to_i128_id, + int_to_usize_id, + int_to_u8_id, + int_to_u16_id, + int_to_u32_id, + int_to_u64_id, + int_to_u128_id +] + +(** Utilities to define the arithmetic operations *) +val mk_isize_def = Define + ‘mk_isize n = + if isize_min <= n /\ n <= isize_max then Return (int_to_isize n) + else Fail Failure’ + +val mk_i8_def = Define + ‘mk_i8 n = + if i8_min <= n /\ n <= i8_max then Return (int_to_i8 n) + else Fail Failure’ + +val mk_i16_def = Define + ‘mk_i16 n = + if i16_min <= n /\ n <= i16_max then Return (int_to_i16 n) + else Fail Failure’ + +val mk_i32_def = Define + ‘mk_i32 n = + if i32_min <= n /\ n <= i32_max then Return (int_to_i32 n) + else Fail Failure’ + +val mk_i64_def = Define + ‘mk_i64 n = + if i64_min <= n /\ n <= i64_max then Return (int_to_i64 n) + else Fail Failure’ + +val mk_i128_def = Define + ‘mk_i128 n = + if i128_min <= n /\ n <= i128_max then Return (int_to_i128 n) + else Fail Failure’ + +val mk_usize_def = Define + ‘mk_usize n = + if 0 <= n /\ n <= usize_max then Return (int_to_usize n) + else Fail Failure’ + +val mk_u8_def = Define + ‘mk_u8 n = + if 0 <= n /\ n <= u8_max then Return (int_to_u8 n) + else Fail Failure’ + +val mk_u16_def = Define + ‘mk_u16 n = + if 0 <= n /\ n <= u16_max then Return (int_to_u16 n) + else Fail Failure’ + +val mk_u32_def = Define + ‘mk_u32 n = + if 0 <= n /\ n <= u32_max then Return (int_to_u32 n) + else Fail Failure’ + +val mk_u64_def = Define + ‘mk_u64 n = + if 0 <= n /\ n <= u64_max then Return (int_to_u64 n) + else Fail Failure’ + +val mk_u128_def = Define + ‘mk_u128 n = + if 0 <= n /\ n <= u128_max then Return (int_to_u128 n) + else Fail Failure’ + +val isize_add_def = Define ‘isize_add x y = mk_isize ((isize_to_int x) + (isize_to_int y))’ +val i8_add_def = Define ‘i8_add x y = mk_i8 ((i8_to_int x) + (i8_to_int y))’ +val i16_add_def = Define ‘i16_add x y = mk_i16 ((i16_to_int x) + (i16_to_int y))’ +val i32_add_def = Define ‘i32_add x y = mk_i32 ((i32_to_int x) + (i32_to_int y))’ +val i64_add_def = Define ‘i64_add x y = mk_i64 ((i64_to_int x) + (i64_to_int y))’ +val i128_add_def = Define ‘i128_add x y = mk_i128 ((i128_to_int x) + (i128_to_int y))’ +val usize_add_def = Define ‘usize_add x y = mk_usize ((usize_to_int x) + (usize_to_int y))’ +val u8_add_def = Define ‘u8_add x y = mk_u8 ((u8_to_int x) + (u8_to_int y))’ +val u16_add_def = Define ‘u16_add x y = mk_u16 ((u16_to_int x) + (u16_to_int y))’ +val u32_add_def = Define ‘u32_add x y = mk_u32 ((u32_to_int x) + (u32_to_int y))’ +val u64_add_def = Define ‘u64_add x y = mk_u64 ((u64_to_int x) + (u64_to_int y))’ +val u128_add_def = Define ‘u128_add x y = mk_u128 ((u128_to_int x) + (u128_to_int y))’ + +val isize_sub_def = Define ‘isize_sub x y = mk_isize ((isize_to_int x) - (isize_to_int y))’ +val i8_sub_def = Define ‘i8_sub x y = mk_i8 ((i8_to_int x) - (i8_to_int y))’ +val i16_sub_def = Define ‘i16_sub x y = mk_i16 ((i16_to_int x) - (i16_to_int y))’ +val i32_sub_def = Define ‘i32_sub x y = mk_i32 ((i32_to_int x) - (i32_to_int y))’ +val i64_sub_def = Define ‘i64_sub x y = mk_i64 ((i64_to_int x) - (i64_to_int y))’ +val i128_sub_def = Define ‘i128_sub x y = mk_i128 ((i128_to_int x) - (i128_to_int y))’ +val usize_sub_def = Define ‘usize_sub x y = mk_usize ((usize_to_int x) - (usize_to_int y))’ +val u8_sub_def = Define ‘u8_sub x y = mk_u8 ((u8_to_int x) - (u8_to_int y))’ +val u16_sub_def = Define ‘u16_sub x y = mk_u16 ((u16_to_int x) - (u16_to_int y))’ +val u32_sub_def = Define ‘u32_sub x y = mk_u32 ((u32_to_int x) - (u32_to_int y))’ +val u64_sub_def = Define ‘u64_sub x y = mk_u64 ((u64_to_int x) - (u64_to_int y))’ +val u128_sub_def = Define ‘u128_sub x y = mk_u128 ((u128_to_int x) - (u128_to_int y))’ + +val isize_mul_def = Define ‘isize_mul x y = mk_isize ((isize_to_int x) * (isize_to_int y))’ +val i8_mul_def = Define ‘i8_mul x y = mk_i8 ((i8_to_int x) * (i8_to_int y))’ +val i16_mul_def = Define ‘i16_mul x y = mk_i16 ((i16_to_int x) * (i16_to_int y))’ +val i32_mul_def = Define ‘i32_mul x y = mk_i32 ((i32_to_int x) * (i32_to_int y))’ +val i64_mul_def = Define ‘i64_mul x y = mk_i64 ((i64_to_int x) * (i64_to_int y))’ +val i128_mul_def = Define ‘i128_mul x y = mk_i128 ((i128_to_int x) * (i128_to_int y))’ +val usize_mul_def = Define ‘usize_mul x y = mk_usize ((usize_to_int x) * (usize_to_int y))’ +val u8_mul_def = Define ‘u8_mul x y = mk_u8 ((u8_to_int x) * (u8_to_int y))’ +val u16_mul_def = Define ‘u16_mul x y = mk_u16 ((u16_to_int x) * (u16_to_int y))’ +val u32_mul_def = Define ‘u32_mul x y = mk_u32 ((u32_to_int x) * (u32_to_int y))’ +val u64_mul_def = Define ‘u64_mul x y = mk_u64 ((u64_to_int x) * (u64_to_int y))’ +val u128_mul_def = Define ‘u128_mul x y = mk_u128 ((u128_to_int x) * (u128_to_int y))’ + +val isize_div_def = Define ‘isize_div x y = + if isize_to_int y = 0 then Fail Failure else mk_isize ((isize_to_int x) / (isize_to_int y))’ +val i8_div_def = Define ‘i8_div x y = + if i8_to_int y = 0 then Fail Failure else mk_i8 ((i8_to_int x) / (i8_to_int y))’ +val i16_div_def = Define ‘i16_div x y = + if i16_to_int y = 0 then Fail Failure else mk_i16 ((i16_to_int x) / (i16_to_int y))’ +val i32_div_def = Define ‘i32_div x y = + if i32_to_int y = 0 then Fail Failure else mk_i32 ((i32_to_int x) / (i32_to_int y))’ +val i64_div_def = Define ‘i64_div x y = + if i64_to_int y = 0 then Fail Failure else mk_i64 ((i64_to_int x) / (i64_to_int y))’ +val i128_div_def = Define ‘i128_div x y = + if i128_to_int y = 0 then Fail Failure else mk_i128 ((i128_to_int x) / (i128_to_int y))’ +val usize_div_def = Define ‘usize_div x y = + if usize_to_int y = 0 then Fail Failure else mk_usize ((usize_to_int x) / (usize_to_int y))’ +val u8_div_def = Define ‘u8_div x y = + if u8_to_int y = 0 then Fail Failure else mk_u8 ((u8_to_int x) / (u8_to_int y))’ +val u16_div_def = Define ‘u16_div x y = + if u16_to_int y = 0 then Fail Failure else mk_u16 ((u16_to_int x) / (u16_to_int y))’ +val u32_div_def = Define ‘u32_div x y = + if u32_to_int y = 0 then Fail Failure else mk_u32 ((u32_to_int x) / (u32_to_int y))’ +val u64_div_def = Define ‘u64_div x y = + if u64_to_int y = 0 then Fail Failure else mk_u64 ((u64_to_int x) / (u64_to_int y))’ +val u128_div_def = Define ‘u128_div x y = + if u128_to_int y = 0 then Fail Failure else mk_u128 ((u128_to_int x) / (u128_to_int y))’ + +val isize_mod_def = Define ‘isize_mod x y = + if isize_to_int y = 0 then Fail Failure else mk_isize ((isize_to_int x) % (isize_to_int y))’ +val i8_mod_def = Define ‘i8_mod x y = + if i8_to_int y = 0 then Fail Failure else mk_i8 ((i8_to_int x) % (i8_to_int y))’ +val i16_mod_def = Define ‘i16_mod x y = + if i16_to_int y = 0 then Fail Failure else mk_i16 ((i16_to_int x) % (i16_to_int y))’ +val i32_mod_def = Define ‘i32_mod x y = + if i32_to_int y = 0 then Fail Failure else mk_i32 ((i32_to_int x) % (i32_to_int y))’ +val i64_mod_def = Define ‘i64_mod x y = + if i64_to_int y = 0 then Fail Failure else mk_i64 ((i64_to_int x) % (i64_to_int y))’ +val i128_mod_def = Define ‘i128_mod x y = + if i128_to_int y = 0 then Fail Failure else mk_i128 ((i128_to_int x) % (i128_to_int y))’ +val usize_mod_def = Define ‘usize_mod x y = + if usize_to_int y = 0 then Fail Failure else mk_usize ((usize_to_int x) % (usize_to_int y))’ +val u8_mod_def = Define ‘u8_mod x y = + if u8_to_int y = 0 then Fail Failure else mk_u8 ((u8_to_int x) % (u8_to_int y))’ +val u16_mod_def = Define ‘u16_mod x y = + if u16_to_int y = 0 then Fail Failure else mk_u16 ((u16_to_int x) % (u16_to_int y))’ +val u32_mod_def = Define ‘u32_mod x y = + if u32_to_int y = 0 then Fail Failure else mk_u32 ((u32_to_int x) % (u32_to_int y))’ +val u64_mod_def = Define ‘u64_mod x y = + if u64_to_int y = 0 then Fail Failure else mk_u64 ((u64_to_int x) % (u64_to_int y))’ +val u128_mod_def = Define ‘u128_mod x y = + if u128_to_int y = 0 then Fail Failure else mk_u128 ((u128_to_int x) % (u128_to_int y))’ diff --git a/backends/hol4/Test.sml b/backends/hol4/Test.sml index b16b67fb..61d0706d 100644 --- a/backends/hol4/Test.sml +++ b/backends/hol4/Test.sml @@ -168,11 +168,8 @@ val i32_to_int_bounds = "i32_to_int_bounds", “!n. i32_min <= i32_to_int n /\ i32_to_int n <= i32_max”) -val int_to_u32_id = - new_axiom ( - "int_to_u32_id", - “!n. 0 <= n /\ n <= u32_max ==> - u32_to_int (int_to_u32 n) = n”) +val int_to_u32_id = new_axiom ("int_to_u32_id", + “!n. 0 <= n /\ n <= u32_max ==> u32_to_int (int_to_u32 n) = n”) val int_to_i32_id = new_axiom ( |