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author | Son Ho | 2023-10-26 15:55:12 +0200 |
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committer | Son Ho | 2023-10-26 15:55:12 +0200 |
commit | c8c9be9b7d9866f9761a21adbadd923d4a79bb09 (patch) | |
tree | 5fdff294f03a42ffa6e0987ff851873e9121c3f2 /tests/fstar/demo | |
parent | 7ffcb8e9c5c03f198362fd27bd42f30064541509 (diff) |
Update Primitives.fst
Diffstat (limited to '')
-rw-r--r-- | tests/fstar/demo/Primitives.fst | 405 |
1 files changed, 405 insertions, 0 deletions
diff --git a/tests/fstar/demo/Primitives.fst b/tests/fstar/demo/Primitives.fst new file mode 100644 index 00000000..e9391834 --- /dev/null +++ b/tests/fstar/demo/Primitives.fst @@ -0,0 +1,405 @@ +/// This file lists primitive and assumed functions and types +module Primitives +open FStar.Mul +open FStar.List.Tot + +#set-options "--z3rlimit 15 --fuel 0 --ifuel 1" + +(*** Utilities *) +val list_update (#a : Type0) (ls : list a) (i : nat{i < length ls}) (x : a) : + ls':list a{ + length ls' = length ls /\ + index ls' i == x + } +#push-options "--fuel 1" +let rec list_update #a ls i x = + match ls with + | x' :: ls -> if i = 0 then x :: ls else x' :: list_update ls (i-1) x +#pop-options + +(*** Result *) +type error : Type0 = +| Failure +| OutOfFuel + +type result (a : Type0) : Type0 = +| Return : v:a -> result a +| Fail : e:error -> result a + +// Monadic return operator +unfold let return (#a : Type0) (x : a) : result a = Return x + +// Monadic bind operator. +// Allows to use the notation: +// ``` +// let* x = y in +// ... +// ``` +unfold let (let*) (#a #b : Type0) (m: result a) + (f: (x:a) -> Pure (result b) (requires (m == Return x)) (ensures fun _ -> True)) : + result b = + match m with + | Return x -> f x + | Fail e -> Fail e + +// Monadic assert(...) +let massert (b:bool) : result unit = if b then Return () else Fail Failure + +// Normalize and unwrap a successful result (used for globals). +let eval_global (#a : Type0) (x : result a{Return? (normalize_term x)}) : a = Return?.v x + +(*** Misc *) +type char = FStar.Char.char +type string = string + +let is_zero (n: nat) : bool = n = 0 +let decrease (n: nat{n > 0}) : nat = n - 1 + +let mem_replace_fwd (a : Type0) (x : a) (y : a) : a = x +let mem_replace_back (a : Type0) (x : a) (y : a) : a = y + +(*** Scalars *) +/// Rem.: most of the following code was partially generated + +let isize_min : int = -9223372036854775808 // TODO: should be opaque +let isize_max : int = 9223372036854775807 // TODO: should be opaque +let i8_min : int = -128 +let i8_max : int = 127 +let i16_min : int = -32768 +let i16_max : int = 32767 +let i32_min : int = -2147483648 +let i32_max : int = 2147483647 +let i64_min : int = -9223372036854775808 +let i64_max : int = 9223372036854775807 +let i128_min : int = -170141183460469231731687303715884105728 +let i128_max : int = 170141183460469231731687303715884105727 +let usize_min : int = 0 +let usize_max : int = 4294967295 // TODO: should be opaque +let u8_min : int = 0 +let u8_max : int = 255 +let u16_min : int = 0 +let u16_max : int = 65535 +let u32_min : int = 0 +let u32_max : int = 4294967295 +let u64_min : int = 0 +let u64_max : int = 18446744073709551615 +let u128_min : int = 0 +let u128_max : int = 340282366920938463463374607431768211455 + +type scalar_ty = +| Isize +| I8 +| I16 +| I32 +| I64 +| I128 +| Usize +| U8 +| U16 +| U32 +| U64 +| U128 + +let scalar_min (ty : scalar_ty) : int = + match ty with + | Isize -> isize_min + | I8 -> i8_min + | I16 -> i16_min + | I32 -> i32_min + | I64 -> i64_min + | I128 -> i128_min + | Usize -> usize_min + | U8 -> u8_min + | U16 -> u16_min + | U32 -> u32_min + | U64 -> u64_min + | U128 -> u128_min + +let scalar_max (ty : scalar_ty) : int = + match ty with + | Isize -> isize_max + | I8 -> i8_max + | I16 -> i16_max + | I32 -> i32_max + | I64 -> i64_max + | I128 -> i128_max + | Usize -> usize_max + | U8 -> u8_max + | U16 -> u16_max + | U32 -> u32_max + | U64 -> u64_max + | U128 -> u128_max + +type scalar (ty : scalar_ty) : eqtype = x:int{scalar_min ty <= x && x <= scalar_max ty} + +let mk_scalar (ty : scalar_ty) (x : int) : result (scalar ty) = + if scalar_min ty <= x && scalar_max ty >= x then Return x else Fail Failure + +let scalar_neg (#ty : scalar_ty) (x : scalar ty) : result (scalar ty) = mk_scalar ty (-x) + +let scalar_div (#ty : scalar_ty) (x : scalar ty) (y : scalar ty) : result (scalar ty) = + if y <> 0 then mk_scalar ty (x / y) else Fail Failure + +/// The remainder operation +let int_rem (x : int) (y : int{y <> 0}) : int = + if x >= 0 then (x % y) else -(x % y) + +(* Checking consistency with Rust *) +let _ = assert_norm(int_rem 1 2 = 1) +let _ = assert_norm(int_rem (-1) 2 = -1) +let _ = assert_norm(int_rem 1 (-2) = 1) +let _ = assert_norm(int_rem (-1) (-2) = -1) + +let scalar_rem (#ty : scalar_ty) (x : scalar ty) (y : scalar ty) : result (scalar ty) = + if y <> 0 then mk_scalar ty (int_rem x y) else Fail Failure + +let scalar_add (#ty : scalar_ty) (x : scalar ty) (y : scalar ty) : result (scalar ty) = + mk_scalar ty (x + y) + +let scalar_sub (#ty : scalar_ty) (x : scalar ty) (y : scalar ty) : result (scalar ty) = + mk_scalar ty (x - y) + +let scalar_mul (#ty : scalar_ty) (x : scalar ty) (y : scalar ty) : result (scalar ty) = + mk_scalar ty (x * y) + +(** Cast an integer from a [src_ty] to a [tgt_ty] *) +// TODO: check the semantics of casts in Rust +let scalar_cast (src_ty : scalar_ty) (tgt_ty : scalar_ty) (x : scalar src_ty) : result (scalar tgt_ty) = + mk_scalar tgt_ty x + +/// The scalar types +type isize : eqtype = scalar Isize +type i8 : eqtype = scalar I8 +type i16 : eqtype = scalar I16 +type i32 : eqtype = scalar I32 +type i64 : eqtype = scalar I64 +type i128 : eqtype = scalar I128 +type usize : eqtype = scalar Usize +type u8 : eqtype = scalar U8 +type u16 : eqtype = scalar U16 +type u32 : eqtype = scalar U32 +type u64 : eqtype = scalar U64 +type u128 : eqtype = scalar U128 + + +let core_isize_min : isize = isize_min +let core_isize_max : isize = isize_max +let core_i8_min : i8 = i8_min +let core_i8_max : i8 = i8_max +let core_i16_min : i16 = i16_min +let core_i16_max : i16 = i16_max +let core_i32_min : i32 = i32_min +let core_i32_max : i32 = i32_max +let core_i64_min : i64 = i64_min +let core_i64_max : i64 = i64_max +let core_i128_min : i128 = i128_min +let core_i128_max : i128 = i128_max + +let core_usize_min : usize = usize_min +let core_usize_max : usize = usize_max +let core_u8_min : u8 = u8_min +let core_u8_max : u8 = u8_max +let core_u16_min : u16 = u16_min +let core_u16_max : u16 = u16_max +let core_u32_min : u32 = u32_min +let core_u32_max : u32 = u32_max +let core_u64_min : u64 = u64_min +let core_u64_max : u64 = u64_max +let core_u128_min : u128 = u128_min +let core_u128_max : u128 = u128_max + +/// Negation +let isize_neg = scalar_neg #Isize +let i8_neg = scalar_neg #I8 +let i16_neg = scalar_neg #I16 +let i32_neg = scalar_neg #I32 +let i64_neg = scalar_neg #I64 +let i128_neg = scalar_neg #I128 + +/// Division +let isize_div = scalar_div #Isize +let i8_div = scalar_div #I8 +let i16_div = scalar_div #I16 +let i32_div = scalar_div #I32 +let i64_div = scalar_div #I64 +let i128_div = scalar_div #I128 +let usize_div = scalar_div #Usize +let u8_div = scalar_div #U8 +let u16_div = scalar_div #U16 +let u32_div = scalar_div #U32 +let u64_div = scalar_div #U64 +let u128_div = scalar_div #U128 + +/// Remainder +let isize_rem = scalar_rem #Isize +let i8_rem = scalar_rem #I8 +let i16_rem = scalar_rem #I16 +let i32_rem = scalar_rem #I32 +let i64_rem = scalar_rem #I64 +let i128_rem = scalar_rem #I128 +let usize_rem = scalar_rem #Usize +let u8_rem = scalar_rem #U8 +let u16_rem = scalar_rem #U16 +let u32_rem = scalar_rem #U32 +let u64_rem = scalar_rem #U64 +let u128_rem = scalar_rem #U128 + +/// Addition +let isize_add = scalar_add #Isize +let i8_add = scalar_add #I8 +let i16_add = scalar_add #I16 +let i32_add = scalar_add #I32 +let i64_add = scalar_add #I64 +let i128_add = scalar_add #I128 +let usize_add = scalar_add #Usize +let u8_add = scalar_add #U8 +let u16_add = scalar_add #U16 +let u32_add = scalar_add #U32 +let u64_add = scalar_add #U64 +let u128_add = scalar_add #U128 + +/// Substraction +let isize_sub = scalar_sub #Isize +let i8_sub = scalar_sub #I8 +let i16_sub = scalar_sub #I16 +let i32_sub = scalar_sub #I32 +let i64_sub = scalar_sub #I64 +let i128_sub = scalar_sub #I128 +let usize_sub = scalar_sub #Usize +let u8_sub = scalar_sub #U8 +let u16_sub = scalar_sub #U16 +let u32_sub = scalar_sub #U32 +let u64_sub = scalar_sub #U64 +let u128_sub = scalar_sub #U128 + +/// Multiplication +let isize_mul = scalar_mul #Isize +let i8_mul = scalar_mul #I8 +let i16_mul = scalar_mul #I16 +let i32_mul = scalar_mul #I32 +let i64_mul = scalar_mul #I64 +let i128_mul = scalar_mul #I128 +let usize_mul = scalar_mul #Usize +let u8_mul = scalar_mul #U8 +let u16_mul = scalar_mul #U16 +let u32_mul = scalar_mul #U32 +let u64_mul = scalar_mul #U64 +let u128_mul = scalar_mul #U128 + +(*** Range *) +type range (a : Type0) = { + start : a; + end_ : a; +} + +(*** Array *) +type array (a : Type0) (n : usize) = s:list a{length s = n} + +// We tried putting the normalize_term condition as a refinement on the list +// but it didn't work. It works with the requires clause. +let mk_array (a : Type0) (n : usize) + (l : list a) : + Pure (array a n) + (requires (normalize_term(FStar.List.Tot.length l) = n)) + (ensures (fun _ -> True)) = + normalize_term_spec (FStar.List.Tot.length l); + l + +let array_index_shared (a : Type0) (n : usize) (x : array a n) (i : usize) : result a = + if i < length x then Return (index x i) + else Fail Failure + +let array_index_mut_fwd (a : Type0) (n : usize) (x : array a n) (i : usize) : result a = + if i < length x then Return (index x i) + else Fail Failure + +let array_index_mut_back (a : Type0) (n : usize) (x : array a n) (i : usize) (nx : a) : result (array a n) = + if i < length x then Return (list_update x i nx) + else Fail Failure + +(*** Slice *) +type slice (a : Type0) = s:list a{length s <= usize_max} + +let slice_len (a : Type0) (s : slice a) : usize = length s + +let slice_index_shared (a : Type0) (x : slice a) (i : usize) : result a = + if i < length x then Return (index x i) + else Fail Failure + +let slice_index_mut_fwd (a : Type0) (x : slice a) (i : usize) : result a = + if i < length x then Return (index x i) + else Fail Failure + +let slice_index_mut_back (a : Type0) (x : slice a) (i : usize) (nx : a) : result (slice a) = + if i < length x then Return (list_update x i nx) + else Fail Failure + +(*** Subslices *) + +let array_to_slice_shared (a : Type0) (n : usize) (x : array a n) : result (slice a) = Return x +let array_to_slice_mut_fwd (a : Type0) (n : usize) (x : array a n) : result (slice a) = Return x +let array_to_slice_mut_back (a : Type0) (n : usize) (x : array a n) (s : slice a) : result (array a n) = + if length s = n then Return s + else Fail Failure + +// TODO: finish the definitions below (there lacks [List.drop] and [List.take] in the standard library *) +let array_subslice_shared (a : Type0) (n : usize) (x : array a n) (r : range usize) : result (slice a) = + admit() + +let array_subslice_mut_fwd (a : Type0) (n : usize) (x : array a n) (r : range usize) : result (slice a) = + admit() + +let array_subslice_mut_back (a : Type0) (n : usize) (x : array a n) (r : range usize) (ns : slice a) : result (array a n) = + admit() + +let array_repeat (a : Type0) (n : usize) (x : a) : array a n = + admit() + +let slice_subslice_shared (a : Type0) (x : slice a) (r : range usize) : result (slice a) = + admit() + +let slice_subslice_mut_fwd (a : Type0) (x : slice a) (r : range usize) : result (slice a) = + admit() + +let slice_subslice_mut_back (a : Type0) (x : slice a) (r : range usize) (ns : slice a) : result (slice a) = + admit() + +(*** Vector *) +type vec (a : Type0) = v:list a{length v <= usize_max} + +let vec_new (a : Type0) : vec a = assert_norm(length #a [] == 0); [] +let vec_len (a : Type0) (v : vec a) : usize = length v + +// The **forward** function shouldn't be used +let vec_push_fwd (a : Type0) (v : vec a) (x : a) : unit = () +let vec_push_back (a : Type0) (v : vec a) (x : a) : + Pure (result (vec a)) + (requires True) + (ensures (fun res -> + match res with + | Fail e -> e == Failure + | Return v' -> length v' = length v + 1)) = + if length v < usize_max then begin + (**) assert_norm(length [x] == 1); + (**) append_length v [x]; + (**) assert(length (append v [x]) = length v + 1); + Return (append v [x]) + end + else Fail Failure + +// The **forward** function shouldn't be used +let vec_insert_fwd (a : Type0) (v : vec a) (i : usize) (x : a) : result unit = + if i < length v then Return () else Fail Failure +let vec_insert_back (a : Type0) (v : vec a) (i : usize) (x : a) : result (vec a) = + if i < length v then Return (list_update v i x) else Fail Failure + +// The **backward** function shouldn't be used +let vec_index_fwd (a : Type0) (v : vec a) (i : usize) : result a = + if i < length v then Return (index v i) else Fail Failure +let vec_index_back (a : Type0) (v : vec a) (i : usize) (x : a) : result unit = + if i < length v then Return () else Fail Failure + +let vec_index_mut_fwd (a : Type0) (v : vec a) (i : usize) : result a = + if i < length v then Return (index v i) else Fail Failure +let vec_index_mut_back (a : Type0) (v : vec a) (i : usize) (nx : a) : result (vec a) = + if i < length v then Return (list_update v i nx) else Fail Failure |