From 78734dc530ee209b5a0946e82bf98b97e374bed0 Mon Sep 17 00:00:00 2001
From: Son Ho
Date: Fri, 8 Mar 2024 16:08:39 +0100
Subject: Update the Makefile and remove the split files for F*

---
 backends/fstar/split/Primitives.fst | 884 ------------------------------------
 1 file changed, 884 deletions(-)
 delete mode 100644 backends/fstar/split/Primitives.fst

(limited to 'backends/fstar/split/Primitives.fst')

diff --git a/backends/fstar/split/Primitives.fst b/backends/fstar/split/Primitives.fst
deleted file mode 100644
index a3ffbde4..00000000
--- a/backends/fstar/split/Primitives.fst
+++ /dev/null
@@ -1,884 +0,0 @@
-/// 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 core_mem_replace (a : Type0) (x : a) (y : a) : a = x
-let core_mem_replace_back (a : Type0) (x : a) (y : a) : a = y
-
-// We don't really use raw pointers for now
-type mut_raw_ptr (t : Type0) = { v : t }
-type const_raw_ptr (t : Type0) = { v : t }
-
-(*** Scalars *)
-/// Rem.: most of the following code was partially generated
-
-assume val size_numbits : pos
-
-// TODO: we could use FStar.Int.int_t and FStar.UInt.int_t
-
-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 is_unsigned = function
-  | Isize | I8 | I16 | I32 | I64 | I128 -> false
-  | Usize | U8 | U16 | U32 | U64 | U128 -> true
-
-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)
-
-let scalar_xor (#ty : scalar_ty)
-    (x : scalar ty) (y : scalar ty) : scalar ty =
-  match ty with
-  | U8 -> FStar.UInt.logxor #8 x y
-  | U16 -> FStar.UInt.logxor #16 x y
-  | U32 -> FStar.UInt.logxor #32 x y
-  | U64 -> FStar.UInt.logxor #64 x y
-  | U128 -> FStar.UInt.logxor #128 x y
-  | Usize -> admit() // TODO
-  | I8 ->
-    // Encoding issues...
-    normalize_spec (FStar.Int.int_t 8);
-    normalize_spec (scalar I8);
-    FStar.Int.logxor #8 x y
-  | I16 ->
-    // Encoding issues...
-    normalize_spec (FStar.Int.int_t 16);
-    normalize_spec (scalar I16);
-    FStar.Int.logxor #16 x y
-  | I32 -> FStar.Int.logxor #32 x y
-  | I64 -> FStar.Int.logxor #64 x y
-  | I128 ->
-    // Encoding issues...
-    normalize_spec (FStar.Int.int_t 128);
-    normalize_spec (scalar I128);
-    FStar.Int.logxor #128 x y
-  | Isize -> admit() // TODO
-
-let scalar_or (#ty : scalar_ty)
-    (x : scalar ty) (y : scalar ty) : scalar ty =
-  match ty with
-  | U8 -> FStar.UInt.logor #8 x y
-  | U16 -> FStar.UInt.logor #16 x y
-  | U32 -> FStar.UInt.logor #32 x y
-  | U64 -> FStar.UInt.logor #64 x y
-  | U128 -> FStar.UInt.logor #128 x y
-  | Usize -> admit() // TODO
-  | I8 ->
-    // Encoding issues...
-    normalize_spec (FStar.Int.int_t 8);
-    normalize_spec (scalar I8);
-    FStar.Int.logor #8 x y
-  | I16 ->
-    // Encoding issues...
-    normalize_spec (FStar.Int.int_t 16);
-    normalize_spec (scalar I16);
-    FStar.Int.logor #16 x y
-  | I32 -> FStar.Int.logor #32 x y
-  | I64 -> FStar.Int.logor #64 x y
-  | I128 ->
-    // Encoding issues...
-    normalize_spec (FStar.Int.int_t 128);
-    normalize_spec (scalar I128);
-    FStar.Int.logor #128 x y
-  | Isize -> admit() // TODO
-
-let scalar_and (#ty : scalar_ty)
-    (x : scalar ty) (y : scalar ty) : scalar ty =
-  match ty with
-  | U8 -> FStar.UInt.logand #8 x y
-  | U16 -> FStar.UInt.logand #16 x y
-  | U32 -> FStar.UInt.logand #32 x y
-  | U64 -> FStar.UInt.logand #64 x y
-  | U128 -> FStar.UInt.logand #128 x y
-  | Usize -> admit() // TODO
-  | I8 ->
-    // Encoding issues...
-    normalize_spec (FStar.Int.int_t 8);
-    normalize_spec (scalar I8);
-    FStar.Int.logand #8 x y
-  | I16 ->
-    // Encoding issues...
-    normalize_spec (FStar.Int.int_t 16);
-    normalize_spec (scalar I16);
-    FStar.Int.logand #16 x y
-  | I32 -> FStar.Int.logand #32 x y
-  | I64 -> FStar.Int.logand #64 x y
-  | I128 ->
-    // Encoding issues...
-    normalize_spec (FStar.Int.int_t 128);
-    normalize_spec (scalar I128);
-    FStar.Int.logand #128 x y
-  | Isize -> admit() // TODO
-
-// Shift left
-let scalar_shl (#ty0 #ty1 : scalar_ty)
-    (x : scalar ty0) (y : scalar ty1) : result (scalar ty0) =
-  admit()
-
-// Shift right
-let scalar_shr (#ty0 #ty1 : scalar_ty)
-    (x : scalar ty0) (y : scalar ty1) : result (scalar ty0) =
-  admit()
-
-(** 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
-
-// This can't fail, but for now we make all casts faillible (easier for the translation)
-let scalar_cast_bool (tgt_ty : scalar_ty) (x : bool) : result (scalar tgt_ty) =
-  mk_scalar tgt_ty (if x then 1 else 0)
-
-/// 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
-
-/// Subtraction
-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
-
-/// Xor
-let u8_xor = scalar_xor #U8
-let u16_xor = scalar_xor #U16
-let u32_xor = scalar_xor #U32
-let u64_xor = scalar_xor #U64
-let u128_xor = scalar_xor #U128
-let usize_xor = scalar_xor #Usize
-let i8_xor = scalar_xor #I8
-let i16_xor = scalar_xor #I16
-let i32_xor = scalar_xor #I32
-let i64_xor = scalar_xor #I64
-let i128_xor = scalar_xor #I128
-let isize_xor = scalar_xor #Isize
-
-/// Or
-let u8_or = scalar_or #U8
-let u16_or = scalar_or #U16
-let u32_or = scalar_or #U32
-let u64_or = scalar_or #U64
-let u128_or = scalar_or #U128
-let usize_or = scalar_or #Usize
-let i8_or = scalar_or #I8
-let i16_or = scalar_or #I16
-let i32_or = scalar_or #I32
-let i64_or = scalar_or #I64
-let i128_or = scalar_or #I128
-let isize_or = scalar_or #Isize
-
-/// And
-let u8_and = scalar_and #U8
-let u16_and = scalar_and #U16
-let u32_and = scalar_and #U32
-let u64_and = scalar_and #U64
-let u128_and = scalar_and #U128
-let usize_and = scalar_and #Usize
-let i8_and = scalar_and #I8
-let i16_and = scalar_and #I16
-let i32_and = scalar_and #I32
-let i64_and = scalar_and #I64
-let i128_and = scalar_and #I128
-let isize_and = scalar_and #Isize
-
-/// Shift left
-let u8_shl #ty = scalar_shl #U8 #ty
-let u16_shl #ty = scalar_shl #U16 #ty
-let u32_shl #ty = scalar_shl #U32 #ty
-let u64_shl #ty = scalar_shl #U64 #ty
-let u128_shl #ty = scalar_shl #U128 #ty
-let usize_shl #ty = scalar_shl #Usize #ty
-let i8_shl #ty = scalar_shl #I8 #ty
-let i16_shl #ty = scalar_shl #I16 #ty
-let i32_shl #ty = scalar_shl #I32 #ty
-let i64_shl #ty = scalar_shl #I64 #ty
-let i128_shl #ty = scalar_shl #I128 #ty
-let isize_shl #ty = scalar_shl #Isize #ty
-
-/// Shift right
-let u8_shr #ty = scalar_shr #U8 #ty
-let u16_shr #ty = scalar_shr #U16 #ty
-let u32_shr #ty = scalar_shr #U32 #ty
-let u64_shr #ty = scalar_shr #U64 #ty
-let u128_shr #ty = scalar_shr #U128 #ty
-let usize_shr #ty = scalar_shr #Usize #ty
-let i8_shr #ty = scalar_shr #I8 #ty
-let i16_shr #ty = scalar_shr #I16 #ty
-let i32_shr #ty = scalar_shr #I32 #ty
-let i64_shr #ty = scalar_shr #I64 #ty
-let i128_shr #ty = scalar_shr #I128 #ty
-let isize_shr #ty = scalar_shr #Isize #ty
-
-(*** core::ops *)
-
-// Trait declaration: [core::ops::index::Index]
-noeq type core_ops_index_Index (self idx : Type0) = {
-  output : Type0;
-  index : self → idx → result output
-}
-
-// Trait declaration: [core::ops::index::IndexMut]
-noeq type core_ops_index_IndexMut (self idx : Type0) = {
-  indexInst : core_ops_index_Index self idx;
-  index_mut : self → idx → result indexInst.output;
-  index_mut_back : self → idx → indexInst.output → result self;
-}
-
-// Trait declaration [core::ops::deref::Deref]
-noeq type core_ops_deref_Deref (self : Type0) = {
-  target : Type0;
-  deref : self → result target;
-}
-
-// Trait declaration [core::ops::deref::DerefMut]
-noeq type core_ops_deref_DerefMut (self : Type0) = {
-  derefInst : core_ops_deref_Deref self;
-  deref_mut : self → result derefInst.target;
-  deref_mut_back : self → derefInst.target → result self;
-}
-
-type core_ops_range_Range (a : Type0) = {
-  start : a;
-  end_ : a;
-}
-
-(*** [alloc] *)
-
-let alloc_boxed_Box_deref (t : Type0) (x : t) : result t = Return x
-let alloc_boxed_Box_deref_mut (t : Type0) (x : t) : result t = Return x
-let alloc_boxed_Box_deref_mut_back (t : Type) (_ : t) (x : t) : result t = Return x
-
-// Trait instance
-let alloc_boxed_Box_coreopsDerefInst (self : Type0) : core_ops_deref_Deref self = {
-  target = self;
-  deref = alloc_boxed_Box_deref self;
-}
-
-// Trait instance
-let alloc_boxed_Box_coreopsDerefMutInst (self : Type0) : core_ops_deref_DerefMut self = {
-  derefInst = alloc_boxed_Box_coreopsDerefInst self;
-  deref_mut = alloc_boxed_Box_deref_mut self;
-  deref_mut_back = alloc_boxed_Box_deref_mut_back self;
-}
-
-(*** 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_usize (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_update_usize (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_usize (a : Type0) (x : slice a) (i : usize) : result a =
-  if i < length x then Return (index x i)
-  else Fail Failure
-
-let slice_update_usize (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 (a : Type0) (n : usize) (x : array a n) : result (slice a) = Return x
-let array_from_slice (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 (a : Type0) (n : usize) (x : array a n) (r : core_ops_range_Range usize) : result (slice a) =
-  admit()
-
-let array_update_subslice (a : Type0) (n : usize) (x : array a n) (r : core_ops_range_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 (a : Type0) (x : slice a) (r : core_ops_range_Range usize) : result (slice a) =
-  admit()
-
-let slice_update_subslice (a : Type0) (x : slice a) (r : core_ops_range_Range usize) (ns : slice a) : result (slice a) =
-  admit()
-
-(*** Vector *)
-type alloc_vec_Vec (a : Type0) = v:list a{length v <= usize_max}
-
-let alloc_vec_Vec_new (a  : Type0) : alloc_vec_Vec a = assert_norm(length #a [] == 0); []
-let alloc_vec_Vec_len (a : Type0) (v : alloc_vec_Vec a) : usize = length v
-
-// Helper
-let alloc_vec_Vec_index_usize (#a : Type0) (v : alloc_vec_Vec a) (i : usize) : result a =
-  if i < length v then Return (index v i) else Fail Failure
-// Helper
-let alloc_vec_Vec_update_usize (#a : Type0) (v : alloc_vec_Vec a) (i : usize) (x : a) : result (alloc_vec_Vec a) =
-  if i < length v then Return (list_update v i x) else Fail Failure
-
-// The **forward** function shouldn't be used
-let alloc_vec_Vec_push_fwd (a  : Type0) (v : alloc_vec_Vec a) (x : a) : unit = ()
-let alloc_vec_Vec_push (a  : Type0) (v : alloc_vec_Vec a) (x : a) :
-  Pure (result (alloc_vec_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 alloc_vec_Vec_insert_fwd (a : Type0) (v : alloc_vec_Vec a) (i : usize) (x : a) : result unit =
-  if i < length v then Return () else Fail Failure
-let alloc_vec_Vec_insert (a : Type0) (v : alloc_vec_Vec a) (i : usize) (x : a) : result (alloc_vec_Vec a) =
-  if i < length v then Return (list_update v i x) else Fail Failure
-
-// Trait declaration: [core::slice::index::private_slice_index::Sealed]
-type core_slice_index_private_slice_index_Sealed (self : Type0) = unit
-
-// Trait declaration: [core::slice::index::SliceIndex]
-noeq type core_slice_index_SliceIndex (self t : Type0) = {
-  sealedInst : core_slice_index_private_slice_index_Sealed self;
-  output : Type0;
-  get : self → t → result (option output);
-  get_mut : self → t → result (option output);
-  get_mut_back : self → t → option output → result t;
-  get_unchecked : self → const_raw_ptr t → result (const_raw_ptr output);
-  get_unchecked_mut : self → mut_raw_ptr t → result (mut_raw_ptr output);
-  index : self → t → result output;
-  index_mut : self → t → result output;
-  index_mut_back : self → t → output → result t;
-}
-
-// [core::slice::index::[T]::index]: forward function
-let core_slice_index_Slice_index
-  (t idx : Type0) (inst : core_slice_index_SliceIndex idx (slice t))
-  (s : slice t) (i : idx) : result inst.output =
-  let* x = inst.get i s in
-  match x with
-  | None -> Fail Failure
-  | Some x -> Return x
-
-// [core::slice::index::Range:::get]: forward function
-let core_slice_index_RangeUsize_get (t : Type0) (i : core_ops_range_Range usize) (s : slice t) :
-  result (option (slice t)) =
-  admit () // TODO
-
-// [core::slice::index::Range::get_mut]: forward function
-let core_slice_index_RangeUsize_get_mut
-  (t : Type0) : core_ops_range_Range usize → slice t → result (option (slice t)) =
-  admit () // TODO
-
-// [core::slice::index::Range::get_mut]: backward function 0
-let core_slice_index_RangeUsize_get_mut_back
-  (t : Type0) :
-  core_ops_range_Range usize → slice t → option (slice t) → result (slice t) =
-  admit () // TODO
-
-// [core::slice::index::Range::get_unchecked]: forward function
-let core_slice_index_RangeUsize_get_unchecked
-  (t : Type0) :
-  core_ops_range_Range usize → const_raw_ptr (slice t) → result (const_raw_ptr (slice t)) =
-  // Don't know what the model should be - for now we always fail to make
-  // sure code which uses it fails
-  fun _ _ -> Fail Failure
-
-// [core::slice::index::Range::get_unchecked_mut]: forward function
-let core_slice_index_RangeUsize_get_unchecked_mut
-  (t : Type0) :
-  core_ops_range_Range usize → mut_raw_ptr (slice t) → result (mut_raw_ptr (slice t)) =
-  // Don't know what the model should be - for now we always fail to make
-  // sure code which uses it fails
-  fun _ _ -> Fail Failure
-
-// [core::slice::index::Range::index]: forward function
-let core_slice_index_RangeUsize_index
-  (t : Type0) : core_ops_range_Range usize → slice t → result (slice t) =
-  admit () // TODO
-
-// [core::slice::index::Range::index_mut]: forward function
-let core_slice_index_RangeUsize_index_mut
-  (t : Type0) : core_ops_range_Range usize → slice t → result (slice t) =
-  admit () // TODO
-
-// [core::slice::index::Range::index_mut]: backward function 0
-let core_slice_index_RangeUsize_index_mut_back
-  (t : Type0) : core_ops_range_Range usize → slice t → slice t → result (slice t) =
-  admit () // TODO
-
-// [core::slice::index::[T]::index_mut]: forward function
-let core_slice_index_Slice_index_mut
-  (t idx : Type0) (inst : core_slice_index_SliceIndex idx (slice t)) :
-  slice t → idx → result inst.output =
-  admit () // 
-
-// [core::slice::index::[T]::index_mut]: backward function 0
-let core_slice_index_Slice_index_mut_back
-  (t idx : Type0) (inst : core_slice_index_SliceIndex idx (slice t)) :
-  slice t → idx → inst.output → result (slice t) =
-  admit () // TODO
-
-// [core::array::[T; N]::index]: forward function
-let core_array_Array_index
-  (t idx : Type0) (n : usize) (inst : core_ops_index_Index (slice t) idx)
-  (a : array t n) (i : idx) : result inst.output =
-  admit () // TODO
-
-// [core::array::[T; N]::index_mut]: forward function
-let core_array_Array_index_mut
-  (t idx : Type0) (n : usize) (inst : core_ops_index_IndexMut (slice t) idx)
-  (a : array t n) (i : idx) : result inst.indexInst.output =
-  admit () // TODO
-
-// [core::array::[T; N]::index_mut]: backward function 0
-let core_array_Array_index_mut_back
-  (t idx : Type0) (n : usize) (inst : core_ops_index_IndexMut (slice t) idx)
-  (a : array t n) (i : idx) (x : inst.indexInst.output) : result (array t n) =
-  admit () // TODO
-
-// Trait implementation: [core::slice::index::private_slice_index::Range]
-let core_slice_index_private_slice_index_SealedRangeUsizeInst
-  : core_slice_index_private_slice_index_Sealed (core_ops_range_Range usize) = ()
-
-// Trait implementation: [core::slice::index::Range]
-let core_slice_index_SliceIndexRangeUsizeSliceTInst (t : Type0) :
-  core_slice_index_SliceIndex (core_ops_range_Range usize) (slice t) = {
-  sealedInst = core_slice_index_private_slice_index_SealedRangeUsizeInst;
-  output = slice t;
-  get = core_slice_index_RangeUsize_get t;
-  get_mut = core_slice_index_RangeUsize_get_mut t;
-  get_mut_back = core_slice_index_RangeUsize_get_mut_back t;
-  get_unchecked = core_slice_index_RangeUsize_get_unchecked t;
-  get_unchecked_mut = core_slice_index_RangeUsize_get_unchecked_mut t;
-  index = core_slice_index_RangeUsize_index t;
-  index_mut = core_slice_index_RangeUsize_index_mut t;
-  index_mut_back = core_slice_index_RangeUsize_index_mut_back t;
-}
-
-// Trait implementation: [core::slice::index::[T]]
-let core_ops_index_IndexSliceTIInst (t idx : Type0)
-  (inst : core_slice_index_SliceIndex idx (slice t)) :
-  core_ops_index_Index (slice t) idx = {
-  output = inst.output;
-  index = core_slice_index_Slice_index t idx inst;
-}
-
-// Trait implementation: [core::slice::index::[T]]
-let core_ops_index_IndexMutSliceTIInst (t idx : Type0)
-  (inst : core_slice_index_SliceIndex idx (slice t)) :
-  core_ops_index_IndexMut (slice t) idx = {
-  indexInst = core_ops_index_IndexSliceTIInst t idx inst;
-  index_mut = core_slice_index_Slice_index_mut t idx inst;
-  index_mut_back = core_slice_index_Slice_index_mut_back t idx inst;
-}
-
-// Trait implementation: [core::array::[T; N]]
-let core_ops_index_IndexArrayInst (t idx : Type0) (n : usize)
-  (inst : core_ops_index_Index (slice t) idx) :
-  core_ops_index_Index (array t n) idx = {
-  output = inst.output;
-  index = core_array_Array_index t idx n inst;
-}
-
-// Trait implementation: [core::array::[T; N]]
-let core_ops_index_IndexMutArrayIInst (t idx : Type0) (n : usize)
-  (inst : core_ops_index_IndexMut (slice t) idx) :
-  core_ops_index_IndexMut (array t n) idx = {
-  indexInst = core_ops_index_IndexArrayInst t idx n inst.indexInst;
-  index_mut = core_array_Array_index_mut t idx n inst;
-  index_mut_back = core_array_Array_index_mut_back t idx n inst;
-}
-
-// [core::slice::index::usize::get]: forward function
-let core_slice_index_usize_get
-  (t : Type0) : usize → slice t → result (option t) =
-  admit () // TODO
-
-// [core::slice::index::usize::get_mut]: forward function
-let core_slice_index_usize_get_mut
-  (t : Type0) : usize → slice t → result (option t) =
-  admit () // TODO
-
-// [core::slice::index::usize::get_mut]: backward function 0
-let core_slice_index_usize_get_mut_back
-  (t : Type0) : usize → slice t → option t → result (slice t) =
-  admit () // TODO
-
-// [core::slice::index::usize::get_unchecked]: forward function
-let core_slice_index_usize_get_unchecked
-  (t : Type0) : usize → const_raw_ptr (slice t) → result (const_raw_ptr t) =
-  admit () // TODO
-
-// [core::slice::index::usize::get_unchecked_mut]: forward function
-let core_slice_index_usize_get_unchecked_mut
-  (t : Type0) : usize → mut_raw_ptr (slice t) → result (mut_raw_ptr t) =
-  admit () // TODO
-
-// [core::slice::index::usize::index]: forward function
-let core_slice_index_usize_index (t : Type0) : usize → slice t → result t =
-  admit () // TODO
-
-// [core::slice::index::usize::index_mut]: forward function
-let core_slice_index_usize_index_mut (t : Type0) : usize → slice t → result t =
-  admit () // TODO
-
-// [core::slice::index::usize::index_mut]: backward function 0
-let core_slice_index_usize_index_mut_back
-  (t : Type0) : usize → slice t → t → result (slice t) =
-  admit () // TODO
-
-// Trait implementation: [core::slice::index::private_slice_index::usize]
-let core_slice_index_private_slice_index_SealedUsizeInst
-  : core_slice_index_private_slice_index_Sealed usize = ()
-
-// Trait implementation: [core::slice::index::usize]
-let core_slice_index_SliceIndexUsizeSliceTInst (t : Type0) :
-  core_slice_index_SliceIndex usize (slice t) = {
-  sealedInst = core_slice_index_private_slice_index_SealedUsizeInst;
-  output = t;
-  get = core_slice_index_usize_get t;
-  get_mut = core_slice_index_usize_get_mut t;
-  get_mut_back = core_slice_index_usize_get_mut_back t;
-  get_unchecked = core_slice_index_usize_get_unchecked t;
-  get_unchecked_mut = core_slice_index_usize_get_unchecked_mut t;
-  index = core_slice_index_usize_index t;
-  index_mut = core_slice_index_usize_index_mut t;
-  index_mut_back = core_slice_index_usize_index_mut_back t;
-}
-
-// [alloc::vec::Vec::index]: forward function
-let alloc_vec_Vec_index (t idx : Type0) (inst : core_slice_index_SliceIndex idx (slice t))
-  (self : alloc_vec_Vec t) (i : idx) : result inst.output =
-  admit () // TODO
-
-// [alloc::vec::Vec::index_mut]: forward function
-let alloc_vec_Vec_index_mut (t idx : Type0) (inst : core_slice_index_SliceIndex idx (slice t))
-  (self : alloc_vec_Vec t) (i : idx) : result inst.output =
-  admit () // TODO
-
-// [alloc::vec::Vec::index_mut]: backward function 0
-let alloc_vec_Vec_index_mut_back
-  (t idx : Type0) (inst : core_slice_index_SliceIndex idx (slice t))
-  (self : alloc_vec_Vec t) (i : idx) (x : inst.output) : result (alloc_vec_Vec t) =
-  admit () // TODO
-
-// Trait implementation: [alloc::vec::Vec]
-let alloc_vec_Vec_coreopsindexIndexInst (t idx : Type0)
-  (inst : core_slice_index_SliceIndex idx (slice t)) :
-  core_ops_index_Index (alloc_vec_Vec t) idx = {
-  output = inst.output;
-  index = alloc_vec_Vec_index t idx inst;
-}
-
-// Trait implementation: [alloc::vec::Vec]
-let alloc_vec_Vec_coreopsindexIndexMutInst (t idx : Type0)
-  (inst : core_slice_index_SliceIndex idx (slice t)) :
-  core_ops_index_IndexMut (alloc_vec_Vec t) idx = {
-  indexInst = alloc_vec_Vec_coreopsindexIndexInst t idx inst;
-  index_mut = alloc_vec_Vec_index_mut t idx inst;
-  index_mut_back = alloc_vec_Vec_index_mut_back t idx inst;
-}
-
-(*** Theorems *)
-
-let alloc_vec_Vec_index_eq (#a : Type0) (v : alloc_vec_Vec a) (i : usize) :
-  Lemma (
-    alloc_vec_Vec_index a usize (core_slice_index_SliceIndexUsizeSliceTInst a) v i ==
-      alloc_vec_Vec_index_usize v i)
-  [SMTPat (alloc_vec_Vec_index a usize (core_slice_index_SliceIndexUsizeSliceTInst a) v i)]
-  =
-  admit()
-
-let alloc_vec_Vec_index_mut_eq (#a : Type0) (v : alloc_vec_Vec a) (i : usize) :
-  Lemma (
-    alloc_vec_Vec_index_mut a usize (core_slice_index_SliceIndexUsizeSliceTInst a) v i ==
-      alloc_vec_Vec_index_usize v i)
-  [SMTPat (alloc_vec_Vec_index_mut a usize (core_slice_index_SliceIndexUsizeSliceTInst a) v i)]
-  =
-  admit()
-
-let alloc_vec_Vec_index_mut_back_eq (#a : Type0) (v : alloc_vec_Vec a) (i : usize) (x : a) :
-  Lemma (
-    alloc_vec_Vec_index_mut_back a usize (core_slice_index_SliceIndexUsizeSliceTInst a) v i x ==
-      alloc_vec_Vec_update_usize v i x)
-  [SMTPat (alloc_vec_Vec_index_mut_back a usize (core_slice_index_SliceIndexUsizeSliceTInst a) v i x)]
-  =
-  admit()
-- 
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