phanerozoic/Why3 · Datasets at Hugging Face

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
add_int(e: list or_integer_float) : int	function	examples	[ "export", "export", "export", "SumList", "SumList", "ref.Ref" ]	examples/add_list.mlw	add_int
add_real(e: list or_integer_float) : real	function	examples	[ "export", "export", "export", "SumList", "SumList", "ref.Ref" ]	examples/add_list.mlw	add_real
add_int(e: list or_integer_float) : int	function	examples	[ "export", "export", "export", "SumList", "SumList", "ref.Ref" ]	examples/add_list_vc_sp.mlw	add_int
add_real(e: list or_integer_float) : real	function	examples	[ "export", "export", "export", "SumList", "SumList", "ref.Ref" ]	examples/add_list_vc_sp.mlw	add_real
f(p: position) : int	function	examples	[ "int.Int", "int.MinMax" ]	examples/alpha_beta.mlw	f
eval(g: game_tree) : int	function	examples	[ "int.Int", "int.MinMax" ]	examples/alpha_beta.mlw	eval
evals(s: game_trees) : int	function	examples	[ "int.Int", "int.MinMax" ]	examples/alpha_beta.mlw	evals
lt_trans : forall s1 s2 s3. perm4 s1 -> perm4 s2 -> perm4 s3 ->	lemma	examples	[ "int.Int", "seq.Seq", "seq.Mem", "seq.Distinct" ]	examples/anagrammi.mlw	lt_trans
pr1(i1: int) : line->bool	function	examples	[ "int.Int", "seq.Seq", "seq.Mem", "seq.Distinct" ]	examples/anagrammi.mlw	pr1
pr2(i1 i2: int) : line->bool	function	examples	[ "int.Int", "seq.Seq", "seq.Mem", "seq.Distinct" ]	examples/anagrammi.mlw	pr2
pr3(i1 i2 i3: int) : line->bool	function	examples	[ "int.Int", "seq.Seq", "seq.Mem", "seq.Distinct" ]	examples/anagrammi.mlw	pr3
perm4(s: line) = length s = 4 && (forall i. 0 <= i < 4 -> 1 <= s[i] <= 4) &&	predicate	examples	[ "int.Int", "seq.Seq", "seq.Mem", "seq.Distinct" ]	examples/anagrammi.mlw	perm4
lt(s1 s2: line) = exists i. 0 <= i < 4 && s1[i] < s2[i] &&	predicate	examples	[ "int.Int", "seq.Seq", "seq.Mem", "seq.Distinct" ]	examples/anagrammi.mlw	lt
sorted(o: seq line) = (* only permutations *)	predicate	examples	[ "int.Int", "seq.Seq", "seq.Mem", "seq.Distinct" ]	examples/anagrammi.mlw	sorted
a : int	function	examples	[ "int.Int", "ref.Refint", "array.Array", "export", "export", "export", "ARM" ]	examples/arm.mlw	a
inv(a : array int) = a[0] = 0 /\ length a = 11 /\ forall k:int. 1 <= k <= 10 -> 0 < a[k]	predicate	examples	[ "int.Int", "ref.Refint", "array.Array", "export", "export", "export", "ARM" ]	examples/arm.mlw	inv
separation(fp : int) = a+10 < fp-24	predicate	examples	[ "int.Int", "ref.Refint", "array.Array", "export", "export", "export", "ARM" ]	examples/arm.mlw	separation
inv(mem: map int int) = mem[a] = 0 /\ forall k:int. 1 <= k <= 10 -> 0 < mem[a + k]	predicate	examples	[ "int.Int", "ref.Refint", "array.Array", "export", "export", "export", "ARM" ]	examples/arm.mlw	inv
vertices_cardinal_pos : cardinal vertices > 0	lemma	examples	[ "export", "export", "export", "export", "export", "map.Map", "map.Const", "Graph", "int.IntInf", "ref.Ref" ]	examples/bellman_ford.mlw	vertices_cardinal_pos
path_in_vertices : forall v1 v2: vertex, l: list vertex.	lemma	examples	[ "export", "export", "export", "export", "export", "map.Map", "map.Const", "Graph", "int.IntInf", "ref.Ref" ]	examples/bellman_ford.mlw	path_in_vertices
long_path_decomposition : forall l v. path s l v /\ length l >= cardinal vertices ->	lemma	examples	[ "export", "export", "export", "export", "export", "map.Map", "map.Const", "Graph", "int.IntInf", "ref.Ref" ]	examples/bellman_ford.mlw	long_path_decomposition
long_path_reduction : forall l v. path s l v /\ length l >= cardinal vertices ->	lemma	examples	[ "export", "export", "export", "export", "export", "map.Map", "map.Const", "Graph", "int.IntInf", "ref.Ref" ]	examples/bellman_ford.mlw	long_path_reduction
key_lemma_2 : forall m: distmap. inv1 m (cardinal vertices) empty -> inv2 m edges ->	lemma	examples	[ "export", "export", "export", "export", "export", "map.Map", "map.Const", "Graph", "int.IntInf", "ref.Ref" ]	examples/bellman_ford.mlw	key_lemma_2
create(x: 'a) : t 'a	function	examples	[ "export", "export", "export", "export", "export", "map.Map", "map.Const", "Graph", "int.IntInf", "ref.Ref" ]	examples/bellman_ford.mlw	create
edge(x y: vertex) = mem (x,y) edges	predicate	examples	[ "export", "export", "export", "export", "export", "map.Map", "map.Const", "Graph", "int.IntInf", "ref.Ref" ]	examples/bellman_ford.mlw	edge
edge = edge	predicate	examples	[ "export", "export", "export", "export", "export", "map.Map", "map.Const", "Graph", "int.IntInf", "ref.Ref" ]	examples/bellman_ford.mlw	edge
negative_cycle(v: vertex) = mem v vertices /\	predicate	examples	[ "export", "export", "export", "export", "export", "map.Map", "map.Const", "Graph", "int.IntInf", "ref.Ref" ]	examples/bellman_ford.mlw	negative_cycle
value(n: num) : int	function	examples	[ "int.Int", "list.List" ]	examples/bignum.mlw	value
valid(n: num) = match n with	predicate	examples	[ "int.Int", "list.List" ]	examples/bignum.mlw	valid
upper_bound : forall n. n >= 2 -> f n <= 2 * log2 n	lemma	examples	[ "int.Int", "int.ComputerDivision", "ref.Ref", "array.Array", "int.Int", "ref.Ref", "array.Array", "int.Int", "int.ComputerDivision", "ref.Ref", "array.Array", "int.Int", "mach.int.Int32", "ref.Ref", "mach.array.Array32", "int.Int", "int.ComputerDivision", "ref.Ref", "array.Array", "int.Int", "int.ComputerDivision", "ref.Ref", "array.Array", "int.Int", "matrix.Matrix" ]	examples/binary_search.mlw	upper_bound
log2(n: int) : int	function	examples	[ "int.Int", "int.ComputerDivision", "ref.Ref", "array.Array", "int.Int", "ref.Ref", "array.Array", "int.Int", "int.ComputerDivision", "ref.Ref", "array.Array", "int.Int", "mach.int.Int32", "ref.Ref", "mach.array.Array32", "int.Int", "int.ComputerDivision", "ref.Ref", "array.Array", "int.Int", "int.ComputerDivision", "ref.Ref", "array.Array", "int.Int", "matrix.Matrix" ]	examples/binary_search.mlw	log2
f(n: int) : int	function	examples	[ "int.Int", "int.ComputerDivision", "ref.Ref", "array.Array", "int.Int", "ref.Ref", "array.Array", "int.Int", "int.ComputerDivision", "ref.Ref", "array.Array", "int.Int", "mach.int.Int32", "ref.Ref", "mach.array.Array32", "int.Int", "int.ComputerDivision", "ref.Ref", "array.Array", "int.Int", "int.ComputerDivision", "ref.Ref", "array.Array", "int.Int", "matrix.Matrix" ]	examples/binary_search.mlw	f
comb(n k: int) : int	function	examples	[ "int.Int", "int.EuclideanDivision", "int.MinMax" ]	examples/binomial.mlw	comb
le_roots_trans : forall x y l. le x y -> le_roots y l -> le_roots x l	lemma	examples	[ "int.Int", "list.List", "list.Length", "list.Reverse", "list.Append", "int.Power" ]	examples/binomial_heap.mlw	le_roots_trans
heaps_append : forall h1 [@induction] h2. heaps h1 -> heaps h2 -> heaps (h1 ++ h2)	lemma	examples	[ "int.Int", "list.List", "list.Length", "list.Reverse", "list.Append", "int.Power" ]	examples/binomial_heap.mlw	heaps_append
heaps_reverse : forall h. heaps h -> heaps (reverse h)	lemma	examples	[ "int.Int", "list.List", "list.Length", "list.Reverse", "list.Append", "int.Power" ]	examples/binomial_heap.mlw	heaps_reverse
occ_append : forall l1 [@induction] l2 x. occ x (l1 ++ l2) = occ x l1 + occ x l2	lemma	examples	[ "int.Int", "list.List", "list.Length", "list.Reverse", "list.Append", "int.Power" ]	examples/binomial_heap.mlw	occ_append
occ_reverse : forall x l. occ x l = occ x (reverse l)	lemma	examples	[ "int.Int", "list.List", "list.Length", "list.Reverse", "list.Append", "int.Power" ]	examples/binomial_heap.mlw	occ_reverse
has_order_length : forall l k. has_order k l -> length l = k	lemma	examples	[ "int.Int", "list.List", "list.Length", "list.Reverse", "list.Append", "int.Power" ]	examples/binomial_heap.mlw	has_order_length
inv_trans : forall m1 m2 h. m1 <= m2 -> inv m2 h -> inv m1 h	lemma	examples	[ "int.Int", "list.List", "list.Length", "list.Reverse", "list.Append", "int.Power" ]	examples/binomial_heap.mlw	inv_trans
binomial_tree_size : forall t. binomial_tree t -> size t.children = power 2 t.rank - 1	lemma	examples	[ "int.Int", "list.List", "list.Length", "list.Reverse", "list.Append", "int.Power" ]	examples/binomial_heap.mlw	binomial_tree_size
heap_size : forall h. inv 0 h -> size h >= power 2 (length h) - 1	lemma	examples	[ "int.Int", "list.List", "list.Length", "list.Reverse", "list.Append", "int.Power" ]	examples/binomial_heap.mlw	heap_size
size(l: list tree) : int	function	examples	[ "int.Int", "list.List", "list.Length", "list.Reverse", "list.Append", "int.Power" ]	examples/binomial_heap.mlw	size
link(t1 t2: tree) : tree	function	examples	[ "int.Int", "list.List", "list.Length", "list.Reverse", "list.Append", "int.Power" ]	examples/binomial_heap.mlw	link
rel = le, axiom .	predicate	examples	[ "int.Int", "list.List", "list.Length", "list.Reverse", "list.Append", "int.Power" ]	examples/binomial_heap.mlw	rel
heaps(l: list tree) = match l with	predicate	examples	[ "int.Int", "list.List", "list.Length", "list.Reverse", "list.Append", "int.Power" ]	examples/binomial_heap.mlw	heaps
binomial_tree(t: tree) = t.rank = length t.children &&	predicate	examples	[ "int.Int", "list.List", "list.Length", "list.Reverse", "list.Append", "int.Power" ]	examples/binomial_heap.mlw	binomial_tree
nth_as_bv_is_int : forall a i.	lemma	examples	[ "int.Int", "int.NumOf", "bv.BV8", "ref.Ref", "int.EuclideanDivision", "int.Int", "int.NumOf", "bv.BV32", "ref.Ref", "int.Int", "int.NumOf", "mach.bv.BVCheck32", "BitCounting32", "int.Int", "int.NumOf", "number.Parity", "bool.Bool", "mach.bv.BVCheck32", "BitCounting32", "Numofbit", "Hamming", "int.Int", "int.NumOf", "number.Parity", "bool.Bool", "mach.bv.BVCheck32", "BitCounting32", "Hamming" ]	examples/bitcount.mlw	nth_as_bv_is_int
symmetric : forall a b. hammingD_logic a b = hammingD_logic b a	lemma	examples	[ "int.Int", "int.NumOf", "bv.BV8", "ref.Ref", "int.EuclideanDivision", "int.Int", "int.NumOf", "bv.BV32", "ref.Ref", "int.Int", "int.NumOf", "mach.bv.BVCheck32", "BitCounting32", "int.Int", "int.NumOf", "number.Parity", "bool.Bool", "mach.bv.BVCheck32", "BitCounting32", "Numofbit", "Hamming", "int.Int", "int.NumOf", "number.Parity", "bool.Bool", "mach.bv.BVCheck32", "BitCounting32", "Hamming" ]	examples/bitcount.mlw	symmetric
numof_ytpmE : forall p : int -> bool, a b : int.	lemma	examples	[ "int.Int", "int.NumOf", "bv.BV8", "ref.Ref", "int.EuclideanDivision", "int.Int", "int.NumOf", "bv.BV32", "ref.Ref", "int.Int", "int.NumOf", "mach.bv.BVCheck32", "BitCounting32", "int.Int", "int.NumOf", "number.Parity", "bool.Bool", "mach.bv.BVCheck32", "BitCounting32", "Numofbit", "Hamming", "int.Int", "int.NumOf", "number.Parity", "bool.Bool", "mach.bv.BVCheck32", "BitCounting32", "Hamming" ]	examples/bitcount.mlw	numof_ytpmE
triangleInequality : forall a b c.	lemma	examples	[ "int.Int", "int.NumOf", "bv.BV8", "ref.Ref", "int.EuclideanDivision", "int.Int", "int.NumOf", "bv.BV32", "ref.Ref", "int.Int", "int.NumOf", "mach.bv.BVCheck32", "BitCounting32", "int.Int", "int.NumOf", "number.Parity", "bool.Bool", "mach.bv.BVCheck32", "BitCounting32", "Numofbit", "Hamming", "int.Int", "int.NumOf", "number.Parity", "bool.Bool", "mach.bv.BVCheck32", "BitCounting32", "Hamming" ]	examples/bitcount.mlw	triangleInequality
bv_odd : forall b : t. odd (t'int b) <-> nth b 0	lemma	examples	[ "int.Int", "int.NumOf", "bv.BV8", "ref.Ref", "int.EuclideanDivision", "int.Int", "int.NumOf", "bv.BV32", "ref.Ref", "int.Int", "int.NumOf", "mach.bv.BVCheck32", "BitCounting32", "int.Int", "int.NumOf", "number.Parity", "bool.Bool", "mach.bv.BVCheck32", "BitCounting32", "Numofbit", "Hamming", "int.Int", "int.NumOf", "number.Parity", "bool.Bool", "mach.bv.BVCheck32", "BitCounting32", "Hamming" ]	examples/bitcount.mlw	bv_odd
asciiProp : forall a b.	lemma	examples	[ "int.Int", "int.NumOf", "bv.BV8", "ref.Ref", "int.EuclideanDivision", "int.Int", "int.NumOf", "bv.BV32", "ref.Ref", "int.Int", "int.NumOf", "mach.bv.BVCheck32", "BitCounting32", "int.Int", "int.NumOf", "number.Parity", "bool.Bool", "mach.bv.BVCheck32", "BitCounting32", "Numofbit", "Hamming", "int.Int", "int.NumOf", "number.Parity", "bool.Bool", "mach.bv.BVCheck32", "BitCounting32", "Hamming" ]	examples/bitcount.mlw	asciiProp
iso : forall b.	lemma	examples	[ "int.Int", "int.NumOf", "bv.BV8", "ref.Ref", "int.EuclideanDivision", "int.Int", "int.NumOf", "bv.BV32", "ref.Ref", "int.Int", "int.NumOf", "mach.bv.BVCheck32", "BitCounting32", "int.Int", "int.NumOf", "number.Parity", "bool.Bool", "mach.bv.BVCheck32", "BitCounting32", "Numofbit", "Hamming", "int.Int", "int.NumOf", "number.Parity", "bool.Bool", "mach.bv.BVCheck32", "BitCounting32", "Hamming" ]	examples/bitcount.mlw	iso
nthGray : forall b i.	lemma	examples	[ "int.Int", "int.NumOf", "bv.BV8", "ref.Ref", "int.EuclideanDivision", "int.Int", "int.NumOf", "bv.BV32", "ref.Ref", "int.Int", "int.NumOf", "mach.bv.BVCheck32", "BitCounting32", "int.Int", "int.NumOf", "number.Parity", "bool.Bool", "mach.bv.BVCheck32", "BitCounting32", "Numofbit", "Hamming", "int.Int", "int.NumOf", "number.Parity", "bool.Bool", "mach.bv.BVCheck32", "BitCounting32", "Hamming" ]	examples/bitcount.mlw	nthGray
lastNthGray : forall b.	lemma	examples	[ "int.Int", "int.NumOf", "bv.BV8", "ref.Ref", "int.EuclideanDivision", "int.Int", "int.NumOf", "bv.BV32", "ref.Ref", "int.Int", "int.NumOf", "mach.bv.BVCheck32", "BitCounting32", "int.Int", "int.NumOf", "number.Parity", "bool.Bool", "mach.bv.BVCheck32", "BitCounting32", "Numofbit", "Hamming", "int.Int", "int.NumOf", "number.Parity", "bool.Bool", "mach.bv.BVCheck32", "BitCounting32", "Hamming" ]	examples/bitcount.mlw	lastNthGray
nthBinary : forall b i.	lemma	examples	[ "int.Int", "int.NumOf", "bv.BV8", "ref.Ref", "int.EuclideanDivision", "int.Int", "int.NumOf", "bv.BV32", "ref.Ref", "int.Int", "int.NumOf", "mach.bv.BVCheck32", "BitCounting32", "int.Int", "int.NumOf", "number.Parity", "bool.Bool", "mach.bv.BVCheck32", "BitCounting32", "Numofbit", "Hamming", "int.Int", "int.NumOf", "number.Parity", "bool.Bool", "mach.bv.BVCheck32", "BitCounting32", "Hamming" ]	examples/bitcount.mlw	nthBinary
evenOdd : forall b.	lemma	examples	[ "int.Int", "int.NumOf", "bv.BV8", "ref.Ref", "int.EuclideanDivision", "int.Int", "int.NumOf", "bv.BV32", "ref.Ref", "int.Int", "int.NumOf", "mach.bv.BVCheck32", "BitCounting32", "int.Int", "int.NumOf", "number.Parity", "bool.Bool", "mach.bv.BVCheck32", "BitCounting32", "Numofbit", "Hamming", "int.Int", "int.NumOf", "number.Parity", "bool.Bool", "mach.bv.BVCheck32", "BitCounting32", "Hamming" ]	examples/bitcount.mlw	evenOdd
nth_as_bv(a i : t) : t	function	examples	[ "int.Int", "int.NumOf", "bv.BV8", "ref.Ref", "int.EuclideanDivision", "int.Int", "int.NumOf", "bv.BV32", "ref.Ref", "int.Int", "int.NumOf", "mach.bv.BVCheck32", "BitCounting32", "int.Int", "int.NumOf", "number.Parity", "bool.Bool", "mach.bv.BVCheck32", "BitCounting32", "Numofbit", "Hamming", "int.Int", "int.NumOf", "number.Parity", "bool.Bool", "mach.bv.BVCheck32", "BitCounting32", "Hamming" ]	examples/bitcount.mlw	nth_as_bv
count_logic(n:t) : int	function	examples	[ "int.Int", "int.NumOf", "bv.BV8", "ref.Ref", "int.EuclideanDivision", "int.Int", "int.NumOf", "bv.BV32", "ref.Ref", "int.Int", "int.NumOf", "mach.bv.BVCheck32", "BitCounting32", "int.Int", "int.NumOf", "number.Parity", "bool.Bool", "mach.bv.BVCheck32", "BitCounting32", "Numofbit", "Hamming", "int.Int", "int.NumOf", "number.Parity", "bool.Bool", "mach.bv.BVCheck32", "BitCounting32", "Hamming" ]	examples/bitcount.mlw	count_logic
hammingD_logic(a b : t) : int	function	examples	[ "int.Int", "int.NumOf", "bv.BV8", "ref.Ref", "int.EuclideanDivision", "int.Int", "int.NumOf", "bv.BV32", "ref.Ref", "int.Int", "int.NumOf", "mach.bv.BVCheck32", "BitCounting32", "int.Int", "int.NumOf", "number.Parity", "bool.Bool", "mach.bv.BVCheck32", "BitCounting32", "Numofbit", "Hamming", "int.Int", "int.NumOf", "number.Parity", "bool.Bool", "mach.bv.BVCheck32", "BitCounting32", "Hamming" ]	examples/bitcount.mlw	hammingD_logic
fun_or(f g : 'a -> bool) : 'a -> bool	function	examples	[ "int.Int", "int.NumOf", "bv.BV8", "ref.Ref", "int.EuclideanDivision", "int.Int", "int.NumOf", "bv.BV32", "ref.Ref", "int.Int", "int.NumOf", "mach.bv.BVCheck32", "BitCounting32", "int.Int", "int.NumOf", "number.Parity", "bool.Bool", "mach.bv.BVCheck32", "BitCounting32", "Numofbit", "Hamming", "int.Int", "int.NumOf", "number.Parity", "bool.Bool", "mach.bv.BVCheck32", "BitCounting32", "Hamming" ]	examples/bitcount.mlw	fun_or
fun_or(f g : 'a -> bool) : 'a -> bool	function	examples	[ "int.Int", "int.NumOf", "bv.BV8", "ref.Ref", "int.EuclideanDivision", "int.Int", "int.NumOf", "bv.BV32", "ref.Ref", "int.Int", "int.NumOf", "mach.bv.BVCheck32", "BitCounting32", "int.Int", "int.NumOf", "number.Parity", "bool.Bool", "mach.bv.BVCheck32", "BitCounting32", "Numofbit", "Hamming", "int.Int", "int.NumOf", "number.Parity", "bool.Bool", "mach.bv.BVCheck32", "BitCounting32", "Hamming" ]	examples/bitcount.mlw	fun_or
toGray(bv : t) : t	function	examples	[ "int.Int", "int.NumOf", "bv.BV8", "ref.Ref", "int.EuclideanDivision", "int.Int", "int.NumOf", "bv.BV32", "ref.Ref", "int.Int", "int.NumOf", "mach.bv.BVCheck32", "BitCounting32", "int.Int", "int.NumOf", "number.Parity", "bool.Bool", "mach.bv.BVCheck32", "BitCounting32", "Numofbit", "Hamming", "int.Int", "int.NumOf", "number.Parity", "bool.Bool", "mach.bv.BVCheck32", "BitCounting32", "Hamming" ]	examples/bitcount.mlw	toGray
fromGray(gr : t) : t	function	examples	[ "int.Int", "int.NumOf", "bv.BV8", "ref.Ref", "int.EuclideanDivision", "int.Int", "int.NumOf", "bv.BV32", "ref.Ref", "int.Int", "int.NumOf", "mach.bv.BVCheck32", "BitCounting32", "int.Int", "int.NumOf", "number.Parity", "bool.Bool", "mach.bv.BVCheck32", "BitCounting32", "Numofbit", "Hamming", "int.Int", "int.NumOf", "number.Parity", "bool.Bool", "mach.bv.BVCheck32", "BitCounting32", "Hamming" ]	examples/bitcount.mlw	fromGray
step0(n x1 : t) = x1 = sub n (bw_and (lsr_bv n (1 : t)) (0x55555555 : t))	predicate	examples	[ "int.Int", "int.NumOf", "bv.BV8", "ref.Ref", "int.EuclideanDivision", "int.Int", "int.NumOf", "bv.BV32", "ref.Ref", "int.Int", "int.NumOf", "mach.bv.BVCheck32", "BitCounting32", "int.Int", "int.NumOf", "number.Parity", "bool.Bool", "mach.bv.BVCheck32", "BitCounting32", "Numofbit", "Hamming", "int.Int", "int.NumOf", "number.Parity", "bool.Bool", "mach.bv.BVCheck32", "BitCounting32", "Hamming" ]	examples/bitcount.mlw	step0
step1(x1 x2 : t) = x2 = add (bw_and x1 (0x33333333 : t))	predicate	examples	[ "int.Int", "int.NumOf", "bv.BV8", "ref.Ref", "int.EuclideanDivision", "int.Int", "int.NumOf", "bv.BV32", "ref.Ref", "int.Int", "int.NumOf", "mach.bv.BVCheck32", "BitCounting32", "int.Int", "int.NumOf", "number.Parity", "bool.Bool", "mach.bv.BVCheck32", "BitCounting32", "Numofbit", "Hamming", "int.Int", "int.NumOf", "number.Parity", "bool.Bool", "mach.bv.BVCheck32", "BitCounting32", "Hamming" ]	examples/bitcount.mlw	step1
validAscii(b : t) = even (count_logic b)	predicate	examples	[ "int.Int", "int.NumOf", "bv.BV8", "ref.Ref", "int.EuclideanDivision", "int.Int", "int.NumOf", "bv.BV32", "ref.Ref", "int.Int", "int.NumOf", "mach.bv.BVCheck32", "BitCounting32", "int.Int", "int.NumOf", "number.Parity", "bool.Bool", "mach.bv.BVCheck32", "BitCounting32", "Numofbit", "Hamming", "int.Int", "int.NumOf", "number.Parity", "bool.Bool", "mach.bv.BVCheck32", "BitCounting32", "Hamming" ]	examples/bitcount.mlw	validAscii
ttt : forall x y. (add_over x y) -> (forall i. ult i x -> add_over i y)	lemma	examples	[ "use", "int.Power", "int.EuclideanDivision", "bv.BV32", "bv.BV8", "bv.BV64", "bv.BVConverter_32_64", "bv.BVConverter_8_32", "ref.Ref", "int.Int", "bv.BV32", "int.Int", "bv.BV32", "int.Int", "int.EuclideanDivision", "bv.BV32", "array.Array", "int.Int", "bv.BV32" ]	examples/bitvector_examples.mlw	ttt
bv32_bounds_bv : forall b. ule zeros b /\ ule b ones	lemma	examples	[ "use", "int.Power", "int.EuclideanDivision", "bv.BV32", "bv.BV8", "bv.BV64", "bv.BVConverter_32_64", "bv.BVConverter_8_32", "ref.Ref", "int.Int", "bv.BV32", "int.Int", "bv.BV32", "int.Int", "int.EuclideanDivision", "bv.BV32", "array.Array", "int.Int", "bv.BV32" ]	examples/bitvector_examples.mlw	bv32_bounds_bv
to_int_ule : forall b c. ule b c -> t'int b <= t'int c	lemma	examples	[ "use", "int.Power", "int.EuclideanDivision", "bv.BV32", "bv.BV8", "bv.BV64", "bv.BVConverter_32_64", "bv.BVConverter_8_32", "ref.Ref", "int.Int", "bv.BV32", "int.Int", "bv.BV32", "int.Int", "int.EuclideanDivision", "bv.BV32", "array.Array", "int.Int", "bv.BV32" ]	examples/bitvector_examples.mlw	to_int_ule
to_int_ult : forall b c. ult b c -> t'int b < t'int c	lemma	examples	[ "use", "int.Power", "int.EuclideanDivision", "bv.BV32", "bv.BV8", "bv.BV64", "bv.BVConverter_32_64", "bv.BVConverter_8_32", "ref.Ref", "int.Int", "bv.BV32", "int.Int", "bv.BV32", "int.Int", "int.EuclideanDivision", "bv.BV32", "array.Array", "int.Int", "bv.BV32" ]	examples/bitvector_examples.mlw	to_int_ult
bv32_bounds_0 : forall b. 0 <= t'int b	lemma	examples	[ "use", "int.Power", "int.EuclideanDivision", "bv.BV32", "bv.BV8", "bv.BV64", "bv.BVConverter_32_64", "bv.BVConverter_8_32", "ref.Ref", "int.Int", "bv.BV32", "int.Int", "bv.BV32", "int.Int", "int.EuclideanDivision", "bv.BV32", "array.Array", "int.Int", "bv.BV32" ]	examples/bitvector_examples.mlw	bv32_bounds_0
bv32_bounds : forall b. 0 <= t'int b < 0x1_0000_0000	lemma	examples	[ "use", "int.Power", "int.EuclideanDivision", "bv.BV32", "bv.BV8", "bv.BV64", "bv.BVConverter_32_64", "bv.BVConverter_8_32", "ref.Ref", "int.Int", "bv.BV32", "int.Int", "bv.BV32", "int.Int", "int.EuclideanDivision", "bv.BV32", "array.Array", "int.Int", "bv.BV32" ]	examples/bitvector_examples.mlw	bv32_bounds
in_range(n : t) = (ule (0:t) n) /\ (ule n (0x0000_00FF:t))	predicate	examples	[ "use", "int.Power", "int.EuclideanDivision", "bv.BV32", "bv.BV8", "bv.BV64", "bv.BVConverter_32_64", "bv.BVConverter_8_32", "ref.Ref", "int.Int", "bv.BV32", "int.Int", "bv.BV32", "int.Int", "int.EuclideanDivision", "bv.BV32", "array.Array", "int.Int", "bv.BV32" ]	examples/bitvector_examples.mlw	in_range
add_over(x y : t) = (uge (add x y) x) /\ (uge (add x y) y)	predicate	examples	[ "use", "int.Power", "int.EuclideanDivision", "bv.BV32", "bv.BV8", "bv.BV64", "bv.BVConverter_32_64", "bv.BVConverter_8_32", "ref.Ref", "int.Int", "bv.BV32", "int.Int", "bv.BV32", "int.Int", "int.EuclideanDivision", "bv.BV32", "array.Array", "int.Int", "bv.BV32" ]	examples/bitvector_examples.mlw	add_over
nth64 : forall value:BV64.t, i:int. 0 <= i < 64 ->	lemma	examples	[ "int.Int", "int.EuclideanDivision", "array.Array", "ref.Ref", "bv.BV32", "bv.BV8", "bv.BV64", "mach.bv.BVCheck8", "mach.bv.BVCheck32", "mach.bv.BVCheck64", "bv.BVConverter_32_64", "bv.BVConverter_8_32", "mach.bv.BV" ]	examples/bitwalker.mlw	nth64
nth8 : forall value:BV8.t, i:int. 0 <= i < 8 ->	lemma	examples	[ "int.Int", "int.EuclideanDivision", "array.Array", "ref.Ref", "bv.BV32", "bv.BV8", "bv.BV64", "mach.bv.BVCheck8", "mach.bv.BVCheck32", "mach.bv.BVCheck64", "bv.BVConverter_32_64", "bv.BVConverter_8_32", "mach.bv.BV" ]	examples/bitwalker.mlw	nth8
maxvalue(len : BV32.t) : BV64.t	function	examples	[ "int.Int", "int.EuclideanDivision", "array.Array", "ref.Ref", "bv.BV32", "bv.BV8", "bv.BV64", "mach.bv.BVCheck8", "mach.bv.BVCheck32", "mach.bv.BVCheck64", "bv.BVConverter_32_64", "bv.BVConverter_8_32", "mach.bv.BV" ]	examples/bitwalker.mlw	maxvalue
minimum(tree elt) : elt	function	examples	[ "int.Int", "bintree.Tree", "export", "export", "int.ComputerDivision", "bintree.Height", "int.Power" ]	examples/braun_trees.mlw	minimum
rel = le, axiom .	predicate	examples	[ "int.Int", "bintree.Tree", "export", "export", "int.ComputerDivision", "bintree.Height", "int.Power" ]	examples/braun_trees.mlw	rel
heap(t: tree elt) = match t with	predicate	examples	[ "int.Int", "bintree.Tree", "export", "export", "int.ComputerDivision", "bintree.Height", "int.Power" ]	examples/braun_trees.mlw	heap
inv(t: tree elt) = match t with	predicate	examples	[ "int.Int", "bintree.Tree", "export", "export", "int.ComputerDivision", "bintree.Height", "int.Power" ]	examples/braun_trees.mlw	inv
closest : forall a b c: int.	lemma	examples	[ "int.Int", "ref.Ref", "int.Abs" ]	examples/bresenham.mlw	closest
best(x2 y2 x y: int) = forall y': int. abs (x2 * y - x * y2) <= abs (x2 * y' - x * y2)	predicate	examples	[ "int.Int", "ref.Ref", "int.Abs" ]	examples/bresenham.mlw	best
drop_left : forall a: array 'a, n: int. 0 <= n < length a ->	lemma	examples	[ "int.Int", "array.Array", "ref.Refint", "set.FsetInt", "int.Int", "array.Array", "ref.Refint", "bag.Bag" ]	examples/coincidence_count.mlw	drop_left
not_mem_inter_r : forall a: array int, i: int, s: fset int. 0 <= i < length a ->	lemma	examples	[ "int.Int", "array.Array", "ref.Refint", "set.FsetInt", "int.Int", "array.Array", "ref.Refint", "bag.Bag" ]	examples/coincidence_count.mlw	not_mem_inter_r
not_mem_inter_l : forall a: array int, i: int, s: fset int. 0 <= i < length a ->	lemma	examples	[ "int.Int", "array.Array", "ref.Refint", "set.FsetInt", "int.Int", "array.Array", "ref.Refint", "bag.Bag" ]	examples/coincidence_count.mlw	not_mem_inter_l
not_mem_inter_r : forall a: array int, i: int, s: bag int. 0 <= i < length a ->	lemma	examples	[ "int.Int", "array.Array", "ref.Refint", "set.FsetInt", "int.Int", "array.Array", "ref.Refint", "bag.Bag" ]	examples/coincidence_count.mlw	not_mem_inter_r
not_mem_inter_l : forall a: array int, i: int, s: bag int. 0 <= i < length a ->	lemma	examples	[ "int.Int", "array.Array", "ref.Refint", "set.FsetInt", "int.Int", "array.Array", "ref.Refint", "bag.Bag" ]	examples/coincidence_count.mlw	not_mem_inter_l
setof(a: array 'a) : fset 'a	function	examples	[ "int.Int", "array.Array", "ref.Refint", "set.FsetInt", "int.Int", "array.Array", "ref.Refint", "bag.Bag" ]	examples/coincidence_count.mlw	setof
cc(a b: array int) : int	function	examples	[ "int.Int", "array.Array", "ref.Refint", "set.FsetInt", "int.Int", "array.Array", "ref.Refint", "bag.Bag" ]	examples/coincidence_count.mlw	cc
bagof(a: array 'a) : bag 'a	function	examples	[ "int.Int", "array.Array", "ref.Refint", "set.FsetInt", "int.Int", "array.Array", "ref.Refint", "bag.Bag" ]	examples/coincidence_count.mlw	bagof
increasing(a: array int) = forall i j. 0 <= i < j < length a -> a[i] < a[j]	predicate	examples	[ "int.Int", "array.Array", "ref.Refint", "set.FsetInt", "int.Int", "array.Array", "ref.Refint", "bag.Bag" ]	examples/coincidence_count.mlw	increasing
increasing(a: array int) = forall i j. 0 <= i < j < length a -> a[i] <= a[j]	predicate	examples	[ "int.Int", "array.Array", "ref.Refint", "set.FsetInt", "int.Int", "array.Array", "ref.Refint", "bag.Bag" ]	examples/coincidence_count.mlw	increasing
le = (<), goal Transitive.Trans	predicate	examples	[ "list.List", "set.SetAppInt", "list.Elements", "list.Mem", "int.Int", "list.List", "list.Elements", "list.Mem", "int.Int", "list.List", "list.Mem", "int.Int" ]	examples/coincidence_count_list.mlw	le
le = rel, goal Transitive.Trans	predicate	examples	[ "list.List", "set.SetAppInt", "list.Elements", "list.Mem", "int.Int", "list.List", "list.Elements", "list.Mem", "int.Int", "list.List", "list.Mem", "int.Int" ]	examples/coincidence_count_list.mlw	le
le = (<), goal Transitive.Trans	predicate	examples	[ "list.List", "set.SetAppInt", "list.Elements", "list.Mem", "int.Int", "list.List", "list.Elements", "list.Mem", "int.Int", "list.List", "list.Mem", "int.Int" ]	examples/coincidence_count_list.mlw	le
is_partition(a: array int) = (* at least one element *)	predicate	examples	[ "int.Int", "ref.Refint", "array.Array", "int.Int", "ref.Ref", "mach.int.Int32", "mach.array.Array32", "int.Int", "array.Array", "Conjugate" ]	examples/conjugate.mlw	is_partition
is_conjugate(a b: array int) = b.length > a[0] &&	predicate	examples	[ "int.Int", "ref.Refint", "array.Array", "int.Int", "ref.Ref", "mach.int.Int32", "mach.array.Array32", "int.Int", "array.Array", "Conjugate" ]	examples/conjugate.mlw	is_conjugate

add_int(e: list or_integer_float) : int

function

examples

[ "export", "export", "export", "SumList", "SumList", "ref.Ref" ]

examples/add_list.mlw

add_int

add_real(e: list or_integer_float) : real

function

examples

[ "export", "export", "export", "SumList", "SumList", "ref.Ref" ]

examples/add_list.mlw

add_real

add_int(e: list or_integer_float) : int

function

examples

[ "export", "export", "export", "SumList", "SumList", "ref.Ref" ]

examples/add_list_vc_sp.mlw

add_int

add_real(e: list or_integer_float) : real

function

examples

[ "export", "export", "export", "SumList", "SumList", "ref.Ref" ]

examples/add_list_vc_sp.mlw

add_real

f(p: position) : int

function

examples

[ "int.Int", "int.MinMax" ]

examples/alpha_beta.mlw

f

eval(g: game_tree) : int

function

examples

[ "int.Int", "int.MinMax" ]

examples/alpha_beta.mlw

eval

evals(s: game_trees) : int

function

examples

[ "int.Int", "int.MinMax" ]

examples/alpha_beta.mlw

evals

lt_trans : forall s1 s2 s3. perm4 s1 -> perm4 s2 -> perm4 s3 ->

lemma

examples

[ "int.Int", "seq.Seq", "seq.Mem", "seq.Distinct" ]

examples/anagrammi.mlw

lt_trans

pr1(i1: int) : line->bool

function

examples

[ "int.Int", "seq.Seq", "seq.Mem", "seq.Distinct" ]

examples/anagrammi.mlw

pr1

pr2(i1 i2: int) : line->bool

function

examples

[ "int.Int", "seq.Seq", "seq.Mem", "seq.Distinct" ]

examples/anagrammi.mlw

pr2

pr3(i1 i2 i3: int) : line->bool

function

examples

[ "int.Int", "seq.Seq", "seq.Mem", "seq.Distinct" ]

examples/anagrammi.mlw

pr3

perm4(s: line) = length s = 4 && (forall i. 0 <= i < 4 -> 1 <= s[i] <= 4) &&

predicate

examples

[ "int.Int", "seq.Seq", "seq.Mem", "seq.Distinct" ]

examples/anagrammi.mlw

perm4

lt(s1 s2: line) = exists i. 0 <= i < 4 && s1[i] < s2[i] &&

predicate

examples

[ "int.Int", "seq.Seq", "seq.Mem", "seq.Distinct" ]

examples/anagrammi.mlw

lt

sorted(o: seq line) = (* only permutations *)

predicate

examples

[ "int.Int", "seq.Seq", "seq.Mem", "seq.Distinct" ]

examples/anagrammi.mlw

sorted

a : int

function

examples

[ "int.Int", "ref.Refint", "array.Array", "export", "export", "export", "ARM" ]

examples/arm.mlw

a

inv(a : array int) = a[0] = 0 /\ length a = 11 /\ forall k:int. 1 <= k <= 10 -> 0 < a[k]

predicate

examples

[ "int.Int", "ref.Refint", "array.Array", "export", "export", "export", "ARM" ]

examples/arm.mlw

inv

separation(fp : int) = a+10 < fp-24

predicate

examples

[ "int.Int", "ref.Refint", "array.Array", "export", "export", "export", "ARM" ]

examples/arm.mlw

separation

inv(mem: map int int) = mem[a] = 0 /\ forall k:int. 1 <= k <= 10 -> 0 < mem[a + k]

predicate

examples

[ "int.Int", "ref.Refint", "array.Array", "export", "export", "export", "ARM" ]

examples/arm.mlw

inv

vertices_cardinal_pos : cardinal vertices > 0

lemma

examples

[ "export", "export", "export", "export", "export", "map.Map", "map.Const", "Graph", "int.IntInf", "ref.Ref" ]

examples/bellman_ford.mlw

vertices_cardinal_pos

path_in_vertices : forall v1 v2: vertex, l: list vertex.

lemma

examples

[ "export", "export", "export", "export", "export", "map.Map", "map.Const", "Graph", "int.IntInf", "ref.Ref" ]

examples/bellman_ford.mlw

path_in_vertices

long_path_decomposition : forall l v. path s l v /\ length l >= cardinal vertices ->

lemma

examples

[ "export", "export", "export", "export", "export", "map.Map", "map.Const", "Graph", "int.IntInf", "ref.Ref" ]

examples/bellman_ford.mlw

long_path_decomposition

long_path_reduction : forall l v. path s l v /\ length l >= cardinal vertices ->

lemma

examples

[ "export", "export", "export", "export", "export", "map.Map", "map.Const", "Graph", "int.IntInf", "ref.Ref" ]

examples/bellman_ford.mlw

long_path_reduction

key_lemma_2 : forall m: distmap. inv1 m (cardinal vertices) empty -> inv2 m edges ->

lemma

examples

[ "export", "export", "export", "export", "export", "map.Map", "map.Const", "Graph", "int.IntInf", "ref.Ref" ]

examples/bellman_ford.mlw

key_lemma_2

create(x: 'a) : t 'a

function

examples

[ "export", "export", "export", "export", "export", "map.Map", "map.Const", "Graph", "int.IntInf", "ref.Ref" ]

examples/bellman_ford.mlw

create

edge(x y: vertex) = mem (x,y) edges

predicate

examples

[ "export", "export", "export", "export", "export", "map.Map", "map.Const", "Graph", "int.IntInf", "ref.Ref" ]

examples/bellman_ford.mlw

edge

edge = edge

predicate

examples

[ "export", "export", "export", "export", "export", "map.Map", "map.Const", "Graph", "int.IntInf", "ref.Ref" ]

examples/bellman_ford.mlw

edge

negative_cycle(v: vertex) = mem v vertices /\

predicate

examples

[ "export", "export", "export", "export", "export", "map.Map", "map.Const", "Graph", "int.IntInf", "ref.Ref" ]

examples/bellman_ford.mlw

negative_cycle

value(n: num) : int

function

examples

[ "int.Int", "list.List" ]

examples/bignum.mlw

value

valid(n: num) = match n with

predicate

examples

[ "int.Int", "list.List" ]

examples/bignum.mlw

valid

upper_bound : forall n. n >= 2 -> f n <= 2 * log2 n

lemma

examples

[ "int.Int", "int.ComputerDivision", "ref.Ref", "array.Array", "int.Int", "ref.Ref", "array.Array", "int.Int", "int.ComputerDivision", "ref.Ref", "array.Array", "int.Int", "mach.int.Int32", "ref.Ref", "mach.array.Array32", "int.Int", "int.ComputerDivision", "ref.Ref", "array.Array", "int.Int", "int.ComputerDivision", "ref.Ref", "array.Array", "int.Int", "matrix.Matrix" ]

examples/binary_search.mlw

upper_bound

log2(n: int) : int

function

examples

[ "int.Int", "int.ComputerDivision", "ref.Ref", "array.Array", "int.Int", "ref.Ref", "array.Array", "int.Int", "int.ComputerDivision", "ref.Ref", "array.Array", "int.Int", "mach.int.Int32", "ref.Ref", "mach.array.Array32", "int.Int", "int.ComputerDivision", "ref.Ref", "array.Array", "int.Int", "int.ComputerDivision", "ref.Ref", "array.Array", "int.Int", "matrix.Matrix" ]

examples/binary_search.mlw

log2

f(n: int) : int

function

examples

[ "int.Int", "int.ComputerDivision", "ref.Ref", "array.Array", "int.Int", "ref.Ref", "array.Array", "int.Int", "int.ComputerDivision", "ref.Ref", "array.Array", "int.Int", "mach.int.Int32", "ref.Ref", "mach.array.Array32", "int.Int", "int.ComputerDivision", "ref.Ref", "array.Array", "int.Int", "int.ComputerDivision", "ref.Ref", "array.Array", "int.Int", "matrix.Matrix" ]

examples/binary_search.mlw

f

comb(n k: int) : int

function

examples

[ "int.Int", "int.EuclideanDivision", "int.MinMax" ]

examples/binomial.mlw

comb

le_roots_trans : forall x y l. le x y -> le_roots y l -> le_roots x l

lemma

examples