fact
stringlengths
5
124
type
stringclasses
3 values
library
stringclasses
5 values
imports
listlengths
0
177
filename
stringclasses
414 values
symbolic_name
stringlengths
1
57
docstring
stringclasses
1 value
IEa : forall x y.
lemma
examples
[ "bv.BV32", "int.Int", "int.NumOf", "bv.BV32", "Utils", "int.Int", "int.NumOf", "bool.Bool", "bv.BV32", "Utils" ]
examples/hackers-delight.mlw
IEa
IEb : forall x y.
lemma
examples
[ "bv.BV32", "int.Int", "int.NumOf", "bv.BV32", "Utils", "int.Int", "int.NumOf", "bool.Bool", "bv.BV32", "Utils" ]
examples/hackers-delight.mlw
IEb
IE3 : forall x y.
lemma
examples
[ "bv.BV32", "int.Int", "int.NumOf", "bv.BV32", "Utils", "int.Int", "int.NumOf", "bool.Bool", "bv.BV32", "Utils" ]
examples/hackers-delight.mlw
IE3
IE4 : forall x y.
lemma
examples
[ "bv.BV32", "int.Int", "int.NumOf", "bv.BV32", "Utils", "int.Int", "int.NumOf", "bool.Bool", "bv.BV32", "Utils" ]
examples/hackers-delight.mlw
IE4
SR1 : forall x n. ult n size_bv ->
lemma
examples
[ "bv.BV32", "int.Int", "int.NumOf", "bv.BV32", "Utils", "int.Int", "int.NumOf", "bool.Bool", "bv.BV32", "Utils" ]
examples/hackers-delight.mlw
SR1
RS_left : forall x.
lemma
examples
[ "bv.BV32", "int.Int", "int.NumOf", "bv.BV32", "Utils", "int.Int", "int.NumOf", "bool.Bool", "bv.BV32", "Utils" ]
examples/hackers-delight.mlw
RS_left
RS_right : forall x.
lemma
examples
[ "bv.BV32", "int.Int", "int.NumOf", "bv.BV32", "Utils", "int.Int", "int.NumOf", "bool.Bool", "bv.BV32", "Utils" ]
examples/hackers-delight.mlw
RS_right
BP : forall a b c d x y.
lemma
examples
[ "bv.BV32", "int.Int", "int.NumOf", "bv.BV32", "Utils", "int.Int", "int.NumOf", "bool.Bool", "bv.BV32", "Utils" ]
examples/hackers-delight.mlw
BP
max(x y : t) : t
function
examples
[ "bv.BV32", "int.Int", "int.NumOf", "bv.BV32", "Utils", "int.Int", "int.NumOf", "bool.Bool", "bv.BV32", "Utils" ]
examples/hackers-delight.mlw
max
min(x y : t) : t
function
examples
[ "bv.BV32", "int.Int", "int.NumOf", "bv.BV32", "Utils", "int.Int", "int.NumOf", "bool.Bool", "bv.BV32", "Utils" ]
examples/hackers-delight.mlw
min
count(bv : t) : t
function
examples
[ "bv.BV32", "int.Int", "int.NumOf", "bv.BV32", "Utils", "int.Int", "int.NumOf", "bool.Bool", "bv.BV32", "Utils" ]
examples/hackers-delight.mlw
count
hammingD(a b : t) : t
function
examples
[ "bv.BV32", "int.Int", "int.NumOf", "bv.BV32", "Utils", "int.Int", "int.NumOf", "bool.Bool", "bv.BV32", "Utils" ]
examples/hackers-delight.mlw
hammingD
fun_or(f g : 'a -> bool) : 'a -> bool
function
examples
[ "bv.BV32", "int.Int", "int.NumOf", "bv.BV32", "Utils", "int.Int", "int.NumOf", "bool.Bool", "bv.BV32", "Utils" ]
examples/hackers-delight.mlw
fun_or
toGray(bv : t) : t
function
examples
[ "bv.BV32", "int.Int", "int.NumOf", "bv.BV32", "Utils", "int.Int", "int.NumOf", "bool.Bool", "bv.BV32", "Utils" ]
examples/hackers-delight.mlw
toGray
fromGray(gr : t) : t
function
examples
[ "bv.BV32", "int.Int", "int.NumOf", "bv.BV32", "Utils", "int.Int", "int.NumOf", "bool.Bool", "bv.BV32", "Utils" ]
examples/hackers-delight.mlw
fromGray
validAscii(b : t) = (nth_bv (count b) zeros) = False
predicate
examples
[ "bv.BV32", "int.Int", "int.NumOf", "bv.BV32", "Utils", "int.Int", "int.NumOf", "bool.Bool", "bv.BV32", "Utils" ]
examples/hackers-delight.mlw
validAscii
addDontOverflow(a b : t) = ule b (add b a) /\ ule a (add b a)
predicate
examples
[ "bv.BV32", "int.Int", "int.NumOf", "bv.BV32", "Utils", "int.Int", "int.NumOf", "bool.Bool", "bv.BV32", "Utils" ]
examples/hackers-delight.mlw
addDontOverflow
bucket_bounds : forall n: int. 0 < n ->
lemma
examples
[ "int.Int", "int.ComputerDivision", "option.Option", "list.List", "list.Mem", "map.Map", "map.Const", "array.Array" ]
examples/hashtbl_impl.mlw
bucket_bounds
biginv(_b: big) = 89>55 (* used to enforce the type invariant *)
predicate
examples
[ "int.Int", "int.MinMax", "array.Array", "int.Int", "ref.Refint", "fmap.MapImpInt", "array.Array", "int.Int", "int.Abs", "ref.Refint", "array.Array", "array.ArraySum", "int.Int", "int.Sum", "int.Abs", "ref.Ref", "mach.int.Int32", "mach.array.Array32" ]
examples/hillel_challenge.mlw
biginv
add_last : forall s: seq int, x.
lemma
examples
[ "int.Int", "seq.Seq", "seq.SortedInt", "seq.SumInt" ]
examples/huffman_with_two_queues.mlw
add_last
sorted_tail : forall s. sorted s -> length s >= 1 -> sorted s[1 .. ]
lemma
examples
[ "int.Int", "seq.Seq", "seq.SortedInt", "seq.SumInt" ]
examples/huffman_with_two_queues.mlw
sorted_tail
sorted_tail_tail : forall s. sorted s -> length s >= 2 -> sorted s[2 .. ]
lemma
examples
[ "int.Int", "seq.Seq", "seq.SortedInt", "seq.SumInt" ]
examples/huffman_with_two_queues.mlw
sorted_tail_tail
last(s: seq int) : int
function
examples
[ "int.Int", "seq.Seq", "seq.SortedInt", "seq.SumInt" ]
examples/huffman_with_two_queues.mlw
last
pr(k: int) = p k && p (k+1)
predicate
examples
[ "export", "Hyps", "Hyps", "Hyps", "Hyps", "ref.Ref", "Hyps", "ref.Ref" ]
examples/induction.mlw
pr
p = pr, lemma base, lemma induction_step
predicate
examples
[ "export", "Hyps", "Hyps", "Hyps", "Hyps", "ref.Ref", "Hyps", "ref.Ref" ]
examples/induction.mlw
p
p = p, constant bound = zero
predicate
examples
[ "export", "Hyps", "Hyps", "Hyps", "Hyps", "ref.Ref", "Hyps", "ref.Ref" ]
examples/induction.mlw
p
le = le
predicate
examples
[ "of", "int.Int", "array.Array", "array.IntArraySorted", "array.ArrayPermut", "array.ArrayEq", "int.Int", "array.Array", "array.ArrayPermut", "array.ArrayEq", "int.Int", "array.Array", "array.ArraySwap", "array.ArrayPermut" ]
examples/insertion_sort.mlw
le
sorted(a : array elt) = M.sorted_sub a.elts 0 a.length
predicate
examples
[ "of", "int.Int", "array.Array", "array.IntArraySorted", "array.ArrayPermut", "array.ArrayEq", "int.Int", "array.Array", "array.ArrayPermut", "array.ArrayEq", "int.Int", "array.Array", "array.ArraySwap", "array.ArrayPermut" ]
examples/insertion_sort.mlw
sorted
rel = le, axiom .
predicate
examples
[ "list.List", "list.Permut", "a", "int.Int", "list.List", "list.NumOcc", "list.Permut", "int.Int", "list.List", "list.NumOcc", "list.Permut" ]
examples/insertion_sort_list.mlw
rel
le = le, goal Transitive.Trans
predicate
examples
[ "list.List", "list.Permut", "a", "int.Int", "list.List", "list.NumOcc", "list.Permut", "int.Int", "list.List", "list.NumOcc", "list.Permut" ]
examples/insertion_sort_list.mlw
le
rel = le, axiom .
predicate
examples
[ "list.List", "list.Permut", "a", "int.Int", "list.List", "list.NumOcc", "list.Permut", "int.Int", "list.List", "list.NumOcc", "list.Permut" ]
examples/insertion_sort_list.mlw
rel
le = le, goal Transitive.Trans
predicate
examples
[ "list.List", "list.Permut", "a", "int.Int", "list.List", "list.NumOcc", "list.Permut", "int.Int", "list.List", "list.NumOcc", "list.Permut" ]
examples/insertion_sort_list.mlw
le
ge(x y: elt) = le y x
predicate
examples
[ "list.List", "list.Permut", "a", "int.Int", "list.List", "list.NumOcc", "list.Permut", "int.Int", "list.List", "list.NumOcc", "list.Permut" ]
examples/insertion_sort_list.mlw
ge
le = ge, goal Transitive.Trans
predicate
examples
[ "list.List", "list.Permut", "a", "int.Int", "list.List", "list.NumOcc", "list.Permut", "int.Int", "list.List", "list.NumOcc", "list.Permut" ]
examples/insertion_sort_list.mlw
le
gt(x y: elt) = ge x y && not (eq x y)
predicate
examples
[ "list.List", "list.Permut", "a", "int.Int", "list.List", "list.NumOcc", "list.Permut", "int.Int", "list.List", "list.NumOcc", "list.Permut" ]
examples/insertion_sort_list.mlw
gt
rel = le, axiom .
predicate
examples
[ "list.List", "list.Permut", "a", "int.Int", "list.List", "list.NumOcc", "list.Permut", "int.Int", "list.List", "list.NumOcc", "list.Permut" ]
examples/insertion_sort_list.mlw
rel
le = le, goal Transitive.Trans
predicate
examples
[ "list.List", "list.Permut", "a", "int.Int", "list.List", "list.NumOcc", "list.Permut", "int.Int", "list.List", "list.NumOcc", "list.Permut" ]
examples/insertion_sort_list.mlw
le
ge(x y: elt) = le y x
predicate
examples
[ "list.List", "list.Permut", "a", "int.Int", "list.List", "list.NumOcc", "list.Permut", "int.Int", "list.List", "list.NumOcc", "list.Permut" ]
examples/insertion_sort_list.mlw
ge
le = ge, goal Transitive.Trans
predicate
examples
[ "list.List", "list.Permut", "a", "int.Int", "list.List", "list.NumOcc", "list.Permut", "int.Int", "list.List", "list.NumOcc", "list.Permut" ]
examples/insertion_sort_list.mlw
le
list_le(ul vl: list elt) = match ul, vl with
predicate
examples
[ "list.List", "list.Permut", "a", "int.Int", "list.List", "list.NumOcc", "list.Permut", "int.Int", "list.List", "list.NumOcc", "list.Permut" ]
examples/insertion_sort_list.mlw
list_le
le = le
predicate
examples
[ "int.Int", "ref.Ref", "ref.Refint", "array.Array", "array.IntArraySorted", "array.ArrayPermut", "int.Int", "ref.Ref", "ref.Refint", "array.Array", "array.ArrayPermut", "int.Int", "ref.Ref", "ref.Refint", "map.Map", "array.Array", "array.ArrayPermut", "predicate", "int.Int", "ref.Ref", "ref.Refint", "map.Map", "array.Array", "array.ArrayPermut" ]
examples/insertion_sort_naive.mlw
le
sorted(a : array elt) = M.sorted_sub a.elts 0 a.length
predicate
examples
[ "int.Int", "ref.Ref", "ref.Refint", "array.Array", "array.IntArraySorted", "array.ArrayPermut", "int.Int", "ref.Ref", "ref.Refint", "array.Array", "array.ArrayPermut", "int.Int", "ref.Ref", "ref.Refint", "map.Map", "array.Array", "array.ArrayPermut", "predicate", "int.Int", "ref.Ref", "ref.Refint", "map.Map", "array.Array", "array.ArrayPermut" ]
examples/insertion_sort_naive.mlw
sorted
is_permutation_inverse : forall a b: array int. length a = length b ->
lemma
examples
[ "int.Int", "int.NumOf", "ref.Ref", "array.Array", "array.Array", "InverseInPlace" ]
examples/inverse_in_place.mlw
is_permutation_inverse
is_permutation(a: array int) = forall i. 0 <= i < length a ->
predicate
examples
[ "int.Int", "int.NumOf", "ref.Ref", "array.Array", "array.Array", "InverseInPlace" ]
examples/inverse_in_place.mlw
is_permutation
sqr_non_neg : forall x:int. sqr x >= 0
lemma
examples
[ "int.Int", "int.Int", "ref.Refint", "Square", "int.Int", "mach.int.Int", "ref.Ref", "Square" ]
examples/isqrt.mlw
sqr_non_neg
sqr_increasing : forall x y:int. 0 <= x <= y -> sqr x <= sqr y
lemma
examples
[ "int.Int", "int.Int", "ref.Refint", "Square", "int.Int", "mach.int.Int", "ref.Ref", "Square" ]
examples/isqrt.mlw
sqr_increasing
sqr_sum : forall x y : int. sqr(x+y) = sqr x + 2*x*y + sqr y
lemma
examples
[ "int.Int", "int.Int", "ref.Refint", "Square", "int.Int", "mach.int.Int", "ref.Ref", "Square" ]
examples/isqrt.mlw
sqr_sum
sqr(x:int) : int
function
examples
[ "int.Int", "int.Int", "ref.Refint", "Square", "int.Int", "mach.int.Int", "ref.Ref", "Square" ]
examples/isqrt.mlw
sqr
isqrt_spec(x res:int) = res >= 0 /\ sqr res <= x < sqr (res + 1)
predicate
examples
[ "int.Int", "int.Int", "ref.Refint", "Square", "int.Int", "mach.int.Int", "ref.Ref", "Square" ]
examples/isqrt.mlw
isqrt_spec
sqr_add2 : forall x y.
lemma
examples
[ "of", "ref.Ref", "bv.BV16", "ref.Ref", "bv.BV32", "ref.Ref", "bv.BV64" ]
examples/isqrt_von_neumann.mlw
sqr_add2
sqr_add2 : forall x y.
lemma
examples
[ "of", "ref.Ref", "bv.BV16", "ref.Ref", "bv.BV32", "ref.Ref", "bv.BV64" ]
examples/isqrt_von_neumann.mlw
sqr_add2
sqr_add2 : forall x y.
lemma
examples
[ "of", "ref.Ref", "bv.BV16", "ref.Ref", "bv.BV32", "ref.Ref", "bv.BV64" ]
examples/isqrt_von_neumann.mlw
sqr_add2
sqr(x:t) : t
function
examples
[ "of", "ref.Ref", "bv.BV16", "ref.Ref", "bv.BV32", "ref.Ref", "bv.BV64" ]
examples/isqrt_von_neumann.mlw
sqr
succ(x:t) : t
function
examples
[ "of", "ref.Ref", "bv.BV16", "ref.Ref", "bv.BV32", "ref.Ref", "bv.BV64" ]
examples/isqrt_von_neumann.mlw
succ
pred(x:t) : t
function
examples
[ "of", "ref.Ref", "bv.BV16", "ref.Ref", "bv.BV32", "ref.Ref", "bv.BV64" ]
examples/isqrt_von_neumann.mlw
pred
pow2(n:t) : t
function
examples
[ "of", "ref.Ref", "bv.BV16", "ref.Ref", "bv.BV32", "ref.Ref", "bv.BV64" ]
examples/isqrt_von_neumann.mlw
pow2
sqr(x:t) : t
function
examples
[ "of", "ref.Ref", "bv.BV16", "ref.Ref", "bv.BV32", "ref.Ref", "bv.BV64" ]
examples/isqrt_von_neumann.mlw
sqr
succ(x:t) : t
function
examples
[ "of", "ref.Ref", "bv.BV16", "ref.Ref", "bv.BV32", "ref.Ref", "bv.BV64" ]
examples/isqrt_von_neumann.mlw
succ
pred(x:t) : t
function
examples
[ "of", "ref.Ref", "bv.BV16", "ref.Ref", "bv.BV32", "ref.Ref", "bv.BV64" ]
examples/isqrt_von_neumann.mlw
pred
pow2(n:t) : t
function
examples
[ "of", "ref.Ref", "bv.BV16", "ref.Ref", "bv.BV32", "ref.Ref", "bv.BV64" ]
examples/isqrt_von_neumann.mlw
pow2
sqr(x:t) : t
function
examples
[ "of", "ref.Ref", "bv.BV16", "ref.Ref", "bv.BV32", "ref.Ref", "bv.BV64" ]
examples/isqrt_von_neumann.mlw
sqr
succ(x:t) : t
function
examples
[ "of", "ref.Ref", "bv.BV16", "ref.Ref", "bv.BV32", "ref.Ref", "bv.BV64" ]
examples/isqrt_von_neumann.mlw
succ
pred(x:t) : t
function
examples
[ "of", "ref.Ref", "bv.BV16", "ref.Ref", "bv.BV32", "ref.Ref", "bv.BV64" ]
examples/isqrt_von_neumann.mlw
pred
pow2(n:t) : t
function
examples
[ "of", "ref.Ref", "bv.BV16", "ref.Ref", "bv.BV32", "ref.Ref", "bv.BV64" ]
examples/isqrt_von_neumann.mlw
pow2
rel = le, axiom .
predicate
examples
[ "int.Int", "array.Array", "array.ArraySwap", "array.ArrayPermut" ]
examples/i_cant_believe_it_can_sort.mlw
rel
le = le, axiom .
predicate
examples
[ "int.Int", "array.Array", "array.ArraySwap", "array.ArrayPermut" ]
examples/i_cant_believe_it_can_sort.mlw
le
ht(t: tree) : int
function
examples
[ "int.Int", "int.MinMax" ]
examples/just_join.mlw
ht
height(t: tree) : int
function
examples
[ "int.Int", "int.MinMax" ]
examples/just_join.mlw
height
rel = lt, axiom .
predicate
examples
[ "int.Int", "int.MinMax" ]
examples/just_join.mlw
rel
wf(t: tree) = match t with
predicate
examples
[ "int.Int", "int.MinMax" ]
examples/just_join.mlw
wf
bst(t: tree) = match t with
predicate
examples
[ "int.Int", "int.MinMax" ]
examples/just_join.mlw
bst
avl(t: tree) = match t with
predicate
examples
[ "int.Int", "int.MinMax" ]
examples/just_join.mlw
avl
le_refl : forall x. x <= x
lemma
examples
[ "int.Int", "int.Int", "int.Int", "set.Set" ]
examples/kleene_algebra.mlw
le_refl
le_antisym : forall x y. x <= y -> y <= x -> x = y
lemma
examples
[ "int.Int", "int.Int", "int.Int", "set.Set" ]
examples/kleene_algebra.mlw
le_antisym
le_trans : forall x y z. x <= y -> y <= z -> x <= z
lemma
examples
[ "int.Int", "int.Int", "int.Int", "set.Set" ]
examples/kleene_algebra.mlw
le_trans
zero_le : forall x. zero <= x
lemma
examples
[ "int.Int", "int.Int", "int.Int", "set.Set" ]
examples/kleene_algebra.mlw
zero_le
le_compat_add : forall x y z. x <= y -> x + z <= y + z
lemma
examples
[ "int.Int", "int.Int", "int.Int", "set.Set" ]
examples/kleene_algebra.mlw
le_compat_add
le_add : forall x y. x <= x + y
lemma
examples
[ "int.Int", "int.Int", "int.Int", "set.Set" ]
examples/kleene_algebra.mlw
le_add
le_add_le : forall x y z. x <= z -> y <= z -> x + y <= z
lemma
examples
[ "int.Int", "int.Int", "int.Int", "set.Set" ]
examples/kleene_algebra.mlw
le_add_le
add_le : forall x y z. x + y <= z -> x <= z
lemma
examples
[ "int.Int", "int.Int", "int.Int", "set.Set" ]
examples/kleene_algebra.mlw
add_le
le_compat_add_left : forall x y z. x <= y -> z * x <= z * y
lemma
examples
[ "int.Int", "int.Int", "int.Int", "set.Set" ]
examples/kleene_algebra.mlw
le_compat_add_left
le_compat_add_right : forall x y z. x <= y -> x * z <= y * z
lemma
examples
[ "int.Int", "int.Int", "int.Int", "set.Set" ]
examples/kleene_algebra.mlw
le_compat_add_right
one_le_star : forall x. one <= !x
lemma
examples
[ "int.Int", "int.Int", "int.Int", "set.Set" ]
examples/kleene_algebra.mlw
one_le_star
mul_var_le_star : forall x. x * !x <= !x
lemma
examples
[ "int.Int", "int.Int", "int.Int", "set.Set" ]
examples/kleene_algebra.mlw
mul_var_le_star
var_mul_le_star : forall x. !x * x <= !x
lemma
examples
[ "int.Int", "int.Int", "int.Int", "set.Set" ]
examples/kleene_algebra.mlw
var_mul_le_star
power_le_star : forall i x. i >= 0 -> x ^ i <= !x
lemma
examples
[ "int.Int", "int.Int", "int.Int", "set.Set" ]
examples/kleene_algebra.mlw
power_le_star
star_mul_star : forall x. !x * !x = !x
lemma
examples
[ "int.Int", "int.Int", "int.Int", "set.Set" ]
examples/kleene_algebra.mlw
star_mul_star
star_star : forall x. !(!x) = !x
lemma
examples
[ "int.Int", "int.Int", "int.Int", "set.Set" ]
examples/kleene_algebra.mlw
star_star
star_unfold_left : forall x. one + x * !x = !x
lemma
examples
[ "int.Int", "int.Int", "int.Int", "set.Set" ]
examples/kleene_algebra.mlw
star_unfold_left
star_unfold_right : forall x. one + !x * x = !x
lemma
examples
[ "int.Int", "int.Int", "int.Int", "set.Set" ]
examples/kleene_algebra.mlw
star_unfold_right
star_le : forall x y. x <= y -> !x <= !y
lemma
examples
[ "int.Int", "int.Int", "int.Int", "set.Set" ]
examples/kleene_algebra.mlw
star_le
le_star_left_right : forall x y z. z * x <= y * z -> z * !x <= !y * z
lemma
examples
[ "int.Int", "int.Int", "int.Int", "set.Set" ]
examples/kleene_algebra.mlw
le_star_left_right
le_star_right_left : forall x y z. x * z <= z * y -> !x * z <= z * !y
lemma
examples
[ "int.Int", "int.Int", "int.Int", "set.Set" ]
examples/kleene_algebra.mlw
le_star_right_left
slide_left : forall x y. !(x + y) = !x * !(y * !x)
lemma
examples
[ "int.Int", "int.Int", "int.Int", "set.Set" ]
examples/kleene_algebra.mlw
slide_left
slide_right : forall x y. !(x + y) = !(!x * y) * !x
lemma
examples
[ "int.Int", "int.Int", "int.Int", "set.Set" ]
examples/kleene_algebra.mlw
slide_right
sum_pow_left : forall x a b.
lemma
examples
[ "int.Int", "int.Int", "int.Int", "set.Set" ]
examples/kleene_algebra.mlw
sum_pow_left
mul_sum_pow : forall x a b.
lemma
examples
[ "int.Int", "int.Int", "int.Int", "set.Set" ]
examples/kleene_algebra.mlw
mul_sum_pow
sum_pow_le_star : forall x a b.
lemma
examples
[ "int.Int", "int.Int", "int.Int", "set.Set" ]
examples/kleene_algebra.mlw
sum_pow_le_star
Conway_equality : forall x n.
lemma
examples
[ "int.Int", "int.Int", "int.Int", "set.Set" ]
examples/kleene_algebra.mlw
Conway_equality
zero_def : forall x. not mem x zero
lemma
examples
[ "int.Int", "int.Int", "int.Int", "set.Set" ]
examples/kleene_algebra.mlw
zero_def