statement stringlengths 1 15.9k | proof stringlengths 0 44.6k | type stringclasses 18
values | symbolic_name stringlengths 1 61 | library stringclasses 21
values | filename stringclasses 502
values | imports listlengths 0 38 | deps listlengths 0 64 | docstring stringlengths 0 500 | source_url stringclasses 1
value | commit stringclasses 1
value |
|---|---|---|---|---|---|---|---|---|---|---|
opp_involutive:
forall m. opp (opp m) = m | lemma | opp_involutive | examples/verifythis_2016_matrix_multiplication | examples/verifythis_2016_matrix_multiplication/matrices.mlw | [
"Matrix",
"MatrixArithmetic",
"MatrixGen",
"int.Int",
"int.Sum",
"sum_extended.Sum_extended"
] | [
"opp"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
opposite_add: forall m1 m2.
m1 === m2 -> opp (add m1 m2) = add (opp m1) (opp m2) | lemma | opposite_add | examples/verifythis_2016_matrix_multiplication | examples/verifythis_2016_matrix_multiplication/matrices.mlw | [
"Matrix",
"MatrixArithmetic",
"MatrixGen",
"int.Int",
"int.Sum",
"sum_extended.Sum_extended"
] | [
"add",
"opp"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
ft1 (a b c: mat int) (i j: int) : int -> int -> int | =
fun k -> smulf (mul_atom a b i k) (get c k j) | function | ft1 | examples/verifythis_2016_matrix_multiplication | examples/verifythis_2016_matrix_multiplication/matrices.mlw | [
"Matrix",
"MatrixArithmetic",
"MatrixGen",
"int.Int",
"int.Sum",
"sum_extended.Sum_extended"
] | [
"get",
"int",
"mat",
"mul_atom",
"smulf"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
ft2 (a b c: mat int) (i j: int) : int -> int -> int | =
fun k -> smulf (mul_atom b c k j) (get a i k) | function | ft2 | examples/verifythis_2016_matrix_multiplication | examples/verifythis_2016_matrix_multiplication/matrices.mlw | [
"Matrix",
"MatrixArithmetic",
"MatrixGen",
"int.Int",
"int.Sum",
"sum_extended.Sum_extended"
] | [
"get",
"int",
"mat",
"mul_atom",
"smulf"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
mul_assoc_get (a b c: mat int) (i j: int)
requires { cols a = rows b }
requires { cols b = rows c }
requires { 0 <= i < (rows a) /\ 0 <= j < (cols c) }
ensures { get (mul (mul a b) c) i j = get (mul a (mul b c)) i j } | = let ft1 = ft1 a b c i j in
let ft2 = ft2 a b c i j in
fubini ft1 ft2 0 (cols b) 0 (cols a);
sum_ext (mul_atom (mul a b) c i j) (sumf ft1 0 (cols a)) 0 (cols b);
assert { get (mul (mul a b) c) i j = sum (sumf ft1 0 (cols a)) 0 (cols b) };
sum_ext (mul_atom a (mul b c) i j) (sumf ft2 0 (cols b)) 0 (... | let lemma | mul_assoc_get | examples/verifythis_2016_matrix_multiplication | examples/verifythis_2016_matrix_multiplication/matrices.mlw | [
"Matrix",
"MatrixArithmetic",
"MatrixGen",
"int.Int",
"int.Sum",
"sum_extended.Sum_extended"
] | [
"cols",
"ft1",
"ft2",
"fubini",
"get",
"int",
"mat",
"mul",
"mul_atom",
"rows",
"sum",
"sum_ext",
"sumf"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
mul_assoc:
forall a b c. cols a = rows b -> cols b = rows c ->
let ab = mul a b in
let bc = mul b c in
let a_bc = mul a bc in
let ab_c = mul ab c in
a_bc = ab_c
by a_bc == ab_c | lemma | mul_assoc | examples/verifythis_2016_matrix_multiplication | examples/verifythis_2016_matrix_multiplication/matrices.mlw | [
"Matrix",
"MatrixArithmetic",
"MatrixGen",
"int.Int",
"int.Sum",
"sum_extended.Sum_extended"
] | [
"ab",
"bc",
"cols",
"mul",
"rows"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
mul_distr_right_get (a b c: mat int) (i j: int)
requires { 0 <= i < rows a /\ 0 <= j < cols c }
requires { cols b = rows c}
requires { a === b }
ensures { get (mul (add a b) c) i j = get (add (mul a c) (mul b c)) i j } | = let mac = mul_atom a c i j in
let mbc = mul_atom b c i j in
assert { get (add (mul a c) (mul b c)) i j =
get (mul a c) i j + get (mul b c) i j =
sum (addf mac mbc) 0 (cols b) };
sum_ext (addf mac mbc) (mul_atom (add a b) c i j) 0 (cols b) | let lemma | mul_distr_right_get | examples/verifythis_2016_matrix_multiplication | examples/verifythis_2016_matrix_multiplication/matrices.mlw | [
"Matrix",
"MatrixArithmetic",
"MatrixGen",
"int.Int",
"int.Sum",
"sum_extended.Sum_extended"
] | [
"add",
"addf",
"cols",
"get",
"int",
"mat",
"mul",
"mul_atom",
"rows",
"sum",
"sum_ext"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
mul_distr_right:
forall a b c. a === b -> cols b = rows c ->
mul (add a b) c = add (mul a c) (mul b c)
by mul (add a b) c == add (mul a c) (mul b c) | lemma | mul_distr_right | examples/verifythis_2016_matrix_multiplication | examples/verifythis_2016_matrix_multiplication/matrices.mlw | [
"Matrix",
"MatrixArithmetic",
"MatrixGen",
"int.Int",
"int.Sum",
"sum_extended.Sum_extended"
] | [
"add",
"cols",
"mul",
"rows"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
mul_distr_left_get (a b c: mat int) (i j : int)
requires { 0 <= i < rows a /\ 0 <= j < cols c }
requires { cols a = rows b }
requires { b === c }
ensures { get (mul a (add b c)) i j = get (add (mul a b) (mul a c)) i j } | = let mab = mul_atom a b i j in
let mac = mul_atom a c i j in
assert { get (add (mul a b) (mul a c)) i j =
get (mul a b) i j + get (mul a c) i j =
sum (addf mab mac) 0 (cols a) };
sum_ext (addf mab mac) (mul_atom a (add b c) i j) 0 (cols a) | let lemma | mul_distr_left_get | examples/verifythis_2016_matrix_multiplication | examples/verifythis_2016_matrix_multiplication/matrices.mlw | [
"Matrix",
"MatrixArithmetic",
"MatrixGen",
"int.Int",
"int.Sum",
"sum_extended.Sum_extended"
] | [
"add",
"addf",
"cols",
"get",
"int",
"mat",
"mul",
"mul_atom",
"rows",
"sum",
"sum_ext"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
mul_distr_left:
forall a b c. b === c -> cols a = rows b ->
mul a (add b c) = add (mul a b) (mul a c)
by mul a (add b c) == add (mul a b) (mul a c) | lemma | mul_distr_left | examples/verifythis_2016_matrix_multiplication | examples/verifythis_2016_matrix_multiplication/matrices.mlw | [
"Matrix",
"MatrixArithmetic",
"MatrixGen",
"int.Int",
"int.Sum",
"sum_extended.Sum_extended"
] | [
"add",
"cols",
"mul",
"rows"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
mul_zero_right:
forall a c. 0 <= c -> mul a (zero a.cols c) = zero a.rows c | lemma | mul_zero_right | examples/verifythis_2016_matrix_multiplication | examples/verifythis_2016_matrix_multiplication/matrices.mlw | [
"Matrix",
"MatrixArithmetic",
"MatrixGen",
"int.Int",
"int.Sum",
"sum_extended.Sum_extended"
] | [
"cols",
"mul",
"rows",
"zero"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
mul_zero_left:
forall a r. 0 <= r -> mul (zero r a.rows) a = zero r a.cols | lemma | mul_zero_left | examples/verifythis_2016_matrix_multiplication | examples/verifythis_2016_matrix_multiplication/matrices.mlw | [
"Matrix",
"MatrixArithmetic",
"MatrixGen",
"int.Int",
"int.Sum",
"sum_extended.Sum_extended"
] | [
"cols",
"mul",
"rows",
"zero"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
mul_opp:
forall a b. a.cols = b.rows ->
let oa = opp a in
let ob = opp b in
let ab = mul a b in
let oab = opp ab in
mul oa b = oab = mul a ob
by add (mul oa b) (add ab oab) = oab = add (mul a ob) (add ab oab) | lemma | mul_opp | examples/verifythis_2016_matrix_multiplication | examples/verifythis_2016_matrix_multiplication/matrices.mlw | [
"Matrix",
"MatrixArithmetic",
"MatrixGen",
"int.Int",
"int.Sum",
"sum_extended.Sum_extended"
] | [
"ab",
"add",
"cols",
"mul",
"opp",
"rows"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
ofs2 (a: mat int) (ai aj: int) : int -> int -> int | = fun i j -> get a (ai + i) (aj + j) | function | ofs2 | examples/verifythis_2016_matrix_multiplication | examples/verifythis_2016_matrix_multiplication/matrices.mlw | [
"Matrix",
"MatrixArithmetic",
"MatrixGen",
"int.Int",
"int.Sum",
"sum_extended.Sum_extended"
] | [
"get",
"int",
"mat"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
block (a: mat int) (r dr c dc: int) : mat int | =
create dr dc (ofs2 a r c) | function | block | examples/verifythis_2016_matrix_multiplication | examples/verifythis_2016_matrix_multiplication/matrices.mlw | [
"Matrix",
"MatrixArithmetic",
"MatrixGen",
"int.Int",
"int.Sum",
"sum_extended.Sum_extended"
] | [
"create",
"int",
"mat",
"ofs2"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
c_blocks (a a1 a2: mat int) | =
0 <= a1.cols <= a.cols /\ a1 = block a 0 a.rows 0 a1.cols /\
a2 = block a 0 a.rows a1.cols (a.cols - a1.cols) | predicate | c_blocks | examples/verifythis_2016_matrix_multiplication | examples/verifythis_2016_matrix_multiplication/matrices.mlw | [
"Matrix",
"MatrixArithmetic",
"MatrixGen",
"int.Int",
"int.Sum",
"sum_extended.Sum_extended"
] | [
"a1",
"a2",
"block",
"cols",
"int",
"mat",
"rows"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
r_blocks (a a1 a2: mat int) | =
0 <= a1.rows <= a.rows /\ a1 = block a 0 a1.rows 0 a.cols /\
a2 = block a a1.rows (a.rows - a1.rows) 0 a.cols | predicate | r_blocks | examples/verifythis_2016_matrix_multiplication | examples/verifythis_2016_matrix_multiplication/matrices.mlw | [
"Matrix",
"MatrixArithmetic",
"MatrixGen",
"int.Int",
"int.Sum",
"sum_extended.Sum_extended"
] | [
"a1",
"a2",
"block",
"cols",
"int",
"mat",
"rows"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
block_mul_ij (a a1 a2 b b1 b2: mat int) (k: int) : unit
requires { a.cols = b.rows /\ a1.cols = b1.rows}
requires { 0 <= k <= a.cols }
requires { c_blocks a a1 a2 /\ r_blocks b b1 b2 }
ensures { forall i j. 0 <= i < a.rows -> 0 <= j < b.cols ->
0 <= k <= a1.cols ->
s... | = if 0 < k then begin
let k = k - 1 in
assert { forall i j. 0 <= i < a.rows -> 0 <= j < b.cols ->
mul_atom a b i j k = if k < a1.cols then mul_atom a1 b1 i j k
else mul_atom a2 b2 i j (k - a1.cols) };
block_mul_ij a a1 a2 b b1 b2 k
end | let | block_mul_ij | examples/verifythis_2016_matrix_multiplication | examples/verifythis_2016_matrix_multiplication/matrices.mlw | [
"Matrix",
"MatrixArithmetic",
"MatrixGen",
"int.Int",
"int.Sum",
"sum_extended.Sum_extended"
] | [
"a1",
"a2",
"b1",
"b2",
"c_blocks",
"cols",
"int",
"mat",
"mul_atom",
"r_blocks",
"rows",
"sum",
"unit"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
mul_split (a a1 a2 b b1 b2: mat int) : unit
requires { a.cols = b.rows /\ a1.cols = b1.rows}
requires { c_blocks a a1 a2 /\ r_blocks b b1 b2 }
ensures {add (mul a1 b1) (mul a2 b2) = mul a b } | = block_mul_ij a a1 a2 b b1 b2 a.cols;
assert { add (mul a1 b1) (mul a2 b2) == mul a b } | let lemma | mul_split | examples/verifythis_2016_matrix_multiplication | examples/verifythis_2016_matrix_multiplication/matrices.mlw | [
"Matrix",
"MatrixArithmetic",
"MatrixGen",
"int.Int",
"int.Sum",
"sum_extended.Sum_extended"
] | [
"a1",
"a2",
"add",
"b1",
"b2",
"block_mul_ij",
"c_blocks",
"cols",
"int",
"mat",
"mul",
"r_blocks",
"rows",
"unit"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
mul_block_cell (a b: mat int) (r dr c dc i j: int) : unit
requires { a.cols = b.rows }
requires { 0 <= r /\ r + dr <= a.rows }
requires { 0 <= c /\ c + dc <= b.cols }
requires { 0 <= i < dr /\ 0 <= j < dc }
ensures { ofs2 (mul a b) r c i j =
get (mul (block a r dr 0 a.cols) (block b ... | = let a' = block a r dr 0 a.cols in
let b' = block b 0 b.rows c dc in
sum_ext (mul_atom a b (i + r) (j + c)) (mul_atom a' b' i j) 0 a.cols | let lemma | mul_block_cell | examples/verifythis_2016_matrix_multiplication | examples/verifythis_2016_matrix_multiplication/matrices.mlw | [
"Matrix",
"MatrixArithmetic",
"MatrixGen",
"int.Int",
"int.Sum",
"sum_extended.Sum_extended"
] | [
"block",
"cols",
"get",
"int",
"mat",
"mul",
"mul_atom",
"ofs2",
"rows",
"sum_ext",
"unit"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
mul_block:
forall a b: mat int, r dr c dc: int.
a.cols = b.rows -> 0 <= r <= r + dr <= a.rows ->
0 <= c <= c + dc <= b.cols ->
let a' = block a r dr 0 a.cols in
let b' = block b 0 b.rows c dc in
let m' = block (mul a b) r dr c dc in
m' = mul a' b'
by m' == mul a' b' | lemma | mul_block | examples/verifythis_2016_matrix_multiplication | examples/verifythis_2016_matrix_multiplication/matrices.mlw | [
"Matrix",
"MatrixArithmetic",
"MatrixGen",
"int.Int",
"int.Sum",
"sum_extended.Sum_extended"
] | [
"block",
"cols",
"int",
"mat",
"mul",
"rows"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
mono | = {
m_prod : list int;
m_pos : bool;
} | type | mono | examples/verifythis_2016_matrix_multiplication | examples/verifythis_2016_matrix_multiplication/matrices_ring_simp.mlw | [
"int.Int",
"list.List",
"matrices.Matrix",
"matrices.MatrixArithmetic"
] | [
"int",
"list"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
l_mdl (f:int -> mat int) (l:list int) : mat int | =
match l with
| Nil -> zero (-1) (-1)
| Cons x Nil -> f x
| Cons x q -> mul (f x) (l_mdl f q)
end | function | l_mdl | examples/verifythis_2016_matrix_multiplication | examples/verifythis_2016_matrix_multiplication/matrices_ring_simp.mlw | [
"int.Int",
"list.List",
"matrices.Matrix",
"matrices.MatrixArithmetic"
] | [
"int",
"list",
"mat",
"mul",
"zero"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
l_vld (f:int -> mat int) (r c:int) (l:list int) | =
match l with
| Nil -> false
| Cons x Nil -> rows (f x) = r && cols (f x) = c
| Cons x q -> rows (f x) = r && l_vld f (cols (f x)) c q
end | predicate | l_vld | examples/verifythis_2016_matrix_multiplication | examples/verifythis_2016_matrix_multiplication/matrices_ring_simp.mlw | [
"int.Int",
"list.List",
"matrices.Matrix",
"matrices.MatrixArithmetic"
] | [
"cols",
"int",
"list",
"mat",
"rows"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
l_mdl_ok (f:int -> mat int) (r c:int) (l:list int) : unit
requires { l_vld f r c l }
ensures { let rs = l_mdl f l in rows rs = r /\ cols rs = c }
variant { l } | = match l with
| Nil -> absurd
| Cons _ Nil -> ()
| Cons x q -> l_mdl_ok f (cols (f x)) c q
end | let lemma | l_mdl_ok | examples/verifythis_2016_matrix_multiplication | examples/verifythis_2016_matrix_multiplication/matrices_ring_simp.mlw | [
"int.Int",
"list.List",
"matrices.Matrix",
"matrices.MatrixArithmetic"
] | [
"cols",
"int",
"l_mdl",
"l_vld",
"list",
"mat",
"rows",
"unit"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
m_mdl (f:int -> mat int) (m:mono) : mat int | =
let m0 = l_mdl f m.m_prod in
if m.m_pos then m0 else opp m0 | function | m_mdl | examples/verifythis_2016_matrix_multiplication | examples/verifythis_2016_matrix_multiplication/matrices_ring_simp.mlw | [
"int.Int",
"list.List",
"matrices.Matrix",
"matrices.MatrixArithmetic"
] | [
"int",
"l_mdl",
"mat",
"mono",
"opp"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
m_mdl_ok (f:int -> mat int) (r c:int) (m:mono) : unit
requires { l_vld f r c m.m_prod }
ensures { let rs = m_mdl f m in rows rs = r /\ cols rs = c } | = l_mdl_ok f r c m.m_prod | let lemma | m_mdl_ok | examples/verifythis_2016_matrix_multiplication | examples/verifythis_2016_matrix_multiplication/matrices_ring_simp.mlw | [
"int.Int",
"list.List",
"matrices.Matrix",
"matrices.MatrixArithmetic"
] | [
"cols",
"int",
"l_mdl_ok",
"l_vld",
"m_mdl",
"mat",
"mono",
"rows",
"unit"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
lm_mdl (f:int -> mat int) (r c:int) (l:list mono) : mat int | =
match l with
| Nil -> zero r c
| Cons x q -> add (lm_mdl f r c q) (m_mdl f x)
end | function | lm_mdl | examples/verifythis_2016_matrix_multiplication | examples/verifythis_2016_matrix_multiplication/matrices_ring_simp.mlw | [
"int.Int",
"list.List",
"matrices.Matrix",
"matrices.MatrixArithmetic"
] | [
"add",
"int",
"list",
"m_mdl",
"mat",
"mono",
"zero"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
lm_mdl_simp (f:int -> mat int) (r c:int) (l:list mono) : mat int | =
match l with
| Nil -> zero r c
| Cons x Nil -> m_mdl f x
| Cons x q -> add (lm_mdl_simp f r c q) (m_mdl f x)
end | function | lm_mdl_simp | examples/verifythis_2016_matrix_multiplication | examples/verifythis_2016_matrix_multiplication/matrices_ring_simp.mlw | [
"int.Int",
"list.List",
"matrices.Matrix",
"matrices.MatrixArithmetic"
] | [
"add",
"int",
"list",
"m_mdl",
"mat",
"mono",
"zero"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
lm_vld (f:int -> mat int) (r c:int) (l:list mono) | =
match l with
| Nil -> true
| Cons x q -> l_vld f r c x.m_prod && lm_vld f r c q
end | predicate | lm_vld | examples/verifythis_2016_matrix_multiplication | examples/verifythis_2016_matrix_multiplication/matrices_ring_simp.mlw | [
"int.Int",
"list.List",
"matrices.Matrix",
"matrices.MatrixArithmetic"
] | [
"int",
"l_vld",
"list",
"mat",
"mono"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
lm_mdl_ok (f:int -> mat int) (r c:int) (l:list mono) : unit
requires { lm_vld f r c l /\ r >= 0 /\ c >= 0 }
ensures { let rs = lm_mdl f r c l in rows rs = r /\ cols rs = c }
variant { l } | = match l with
| Nil -> ()
| Cons _ q -> lm_mdl_ok f r c q
end | let lemma | lm_mdl_ok | examples/verifythis_2016_matrix_multiplication | examples/verifythis_2016_matrix_multiplication/matrices_ring_simp.mlw | [
"int.Int",
"list.List",
"matrices.Matrix",
"matrices.MatrixArithmetic"
] | [
"cols",
"int",
"list",
"lm_mdl",
"lm_vld",
"mat",
"mono",
"rows",
"unit"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
lm_mdl_same (f:int -> mat int) (r c:int) (l:list mono) : unit
requires { lm_vld f r c l }
ensures { lm_mdl_simp f r c l = lm_mdl f r c l }
variant { l } | = match l with
| Nil -> ()
| Cons _ Nil -> ()
| Cons _ q -> lm_mdl_same f r c q
end | let | lm_mdl_same | examples/verifythis_2016_matrix_multiplication | examples/verifythis_2016_matrix_multiplication/matrices_ring_simp.mlw | [
"int.Int",
"list.List",
"matrices.Matrix",
"matrices.MatrixArithmetic"
] | [
"int",
"list",
"lm_mdl",
"lm_mdl_simp",
"lm_vld",
"mat",
"mono",
"unit"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
l_compare (l1 l2:list int) : int | = match l1, l2 with
| Nil, Nil -> 0
| Nil, _ -> (-1)
| _, Nil -> 1
| Cons x q, Cons y r ->
if x < y then (-1) else if x > y then 1 else l_compare q r
end | function | l_compare | examples/verifythis_2016_matrix_multiplication | examples/verifythis_2016_matrix_multiplication/matrices_ring_simp.mlw | [
"int.Int",
"list.List",
"matrices.Matrix",
"matrices.MatrixArithmetic"
] | [
"int",
"list"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
l_compare_zero (l1 l2:list int) : unit
requires { l_compare l1 l2 = 0 }
ensures { l1 = l2 }
variant { l1 } | = match l1, l2 with
| Nil, Nil -> ()
| Cons _ q, Cons _ r -> l_compare_zero q r
| _ -> absurd
end | let | l_compare_zero | examples/verifythis_2016_matrix_multiplication | examples/verifythis_2016_matrix_multiplication/matrices_ring_simp.mlw | [
"int.Int",
"list.List",
"matrices.Matrix",
"matrices.MatrixArithmetic"
] | [
"int",
"l_compare",
"list",
"unit"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
m_lower (m1 m2:mono) | =
let cmp = l_compare m1.m_prod m2.m_prod in
cmp < 0 || (cmp = 0 && (m1.m_pos -> m2.m_pos)) | predicate | m_lower | examples/verifythis_2016_matrix_multiplication | examples/verifythis_2016_matrix_multiplication/matrices_ring_simp.mlw | [
"int.Int",
"list.List",
"matrices.Matrix",
"matrices.MatrixArithmetic"
] | [
"cmp",
"l_compare",
"mono"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
m_collapse (l:list mono) (m:mono) : list mono | = match l with
| Nil -> Cons m Nil
| Cons x q ->
if not x.m_pos && m.m_pos && l_compare m.m_prod x.m_prod = 0
then q
else Cons m l
end | function | m_collapse | examples/verifythis_2016_matrix_multiplication | examples/verifythis_2016_matrix_multiplication/matrices_ring_simp.mlw | [
"int.Int",
"list.List",
"matrices.Matrix",
"matrices.MatrixArithmetic"
] | [
"l_compare",
"list",
"mono"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
m_collapse_ok (f:int -> mat int) (r c:int)
(l:list mono) (m:mono) : list mono
requires { lm_vld f r c l /\ l_vld f r c m.m_prod }
requires { r >= 0 /\ c >= 0 }
ensures { result = m_collapse l m /\ lm_vld f r c result }
ensures { lm_mdl f r c result = add (lm_mdl f r c... | = let res = m_collapse l m in
match l with
| Nil -> ()
| Cons x q ->
if not x.m_pos && m.m_pos && l_compare m.m_prod x.m_prod = 0
then begin
l_compare_zero m.m_prod x.m_prod;
assert { lm_mdl f r c q =
add (m_mdl f m) (add (lm_mdl f r c q) (m_mdl f x)) }
... | let | m_collapse_ok | examples/verifythis_2016_matrix_multiplication | examples/verifythis_2016_matrix_multiplication/matrices_ring_simp.mlw | [
"int.Int",
"list.List",
"matrices.Matrix",
"matrices.MatrixArithmetic"
] | [
"add",
"int",
"l_compare",
"l_compare_zero",
"l_vld",
"list",
"lm_mdl",
"lm_vld",
"m_collapse",
"m_mdl",
"mat",
"mono"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
lm_collapse (acc l:list mono) : list mono | = match l with
| Nil -> acc
| Cons x q -> lm_collapse (m_collapse acc x) q
end | function | lm_collapse | examples/verifythis_2016_matrix_multiplication | examples/verifythis_2016_matrix_multiplication/matrices_ring_simp.mlw | [
"int.Int",
"list.List",
"matrices.Matrix",
"matrices.MatrixArithmetic"
] | [
"acc",
"list",
"m_collapse",
"mono"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
lm_collapse_ok (f:int -> mat int) (r c:int)
(acc l:list mono) : list mono
requires { lm_vld f r c acc /\ lm_vld f r c l }
requires { r >= 0 /\ c >= 0 }
ensures { result = lm_collapse acc l /\ lm_vld f r c result }
ensures { lm_mdl f r c result = add (lm_mdl f r c... | = match l with
| Nil -> acc
| Cons x q -> lm_collapse_ok f r c (m_collapse_ok f r c acc x) q
end | let | lm_collapse_ok | examples/verifythis_2016_matrix_multiplication | examples/verifythis_2016_matrix_multiplication/matrices_ring_simp.mlw | [
"int.Int",
"list.List",
"matrices.Matrix",
"matrices.MatrixArithmetic"
] | [
"acc",
"add",
"int",
"list",
"lm_collapse",
"lm_mdl",
"lm_vld",
"m_collapse_ok",
"mat",
"mono"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
cat_rev (acc l:list 'a) : list 'a | = match l with
| Nil -> acc
| Cons x q -> cat_rev (Cons x acc) q
end | function | cat_rev | examples/verifythis_2016_matrix_multiplication | examples/verifythis_2016_matrix_multiplication/matrices_ring_simp.mlw | [
"int.Int",
"list.List",
"matrices.Matrix",
"matrices.MatrixArithmetic"
] | [
"acc",
"list"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
cat_rev_ok (f:int -> mat int) (r c:int)
(acc l:list mono) : list mono
requires { lm_vld f r c acc /\ lm_vld f r c l }
requires { r >= 0 /\ c >= 0 }
ensures { result = cat_rev acc l /\ lm_vld f r c result }
ensures { lm_mdl f r c result = add (lm_mdl f r c acc) (lm_mdl f r c l) }
vari... | = match l with
| Nil -> acc
| Cons x q -> cat_rev_ok f r c (Cons x acc) q
end | let | cat_rev_ok | examples/verifythis_2016_matrix_multiplication | examples/verifythis_2016_matrix_multiplication/matrices_ring_simp.mlw | [
"int.Int",
"list.List",
"matrices.Matrix",
"matrices.MatrixArithmetic"
] | [
"acc",
"add",
"cat_rev",
"int",
"list",
"lm_mdl",
"lm_vld",
"mat",
"mono"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
lm_dump (x:mono) (acc l:list mono) : (list mono,list mono) | =
match l with
| Nil -> (acc, Nil)
| Cons y q ->
if m_lower x y then (acc, l) else lm_dump x (m_collapse acc y) q
end | function | lm_dump | examples/verifythis_2016_matrix_multiplication | examples/verifythis_2016_matrix_multiplication/matrices_ring_simp.mlw | [
"int.Int",
"list.List",
"matrices.Matrix",
"matrices.MatrixArithmetic"
] | [
"acc",
"list",
"m_collapse",
"m_lower",
"mono"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
lm_dump_ok (f:int -> mat int) (r c:int)
(x:mono) (acc l:list mono) : (list mono,list mono)
requires { r >= 0 /\ c >= 0 }
requires { lm_vld f r c acc /\ lm_vld f r c l }
ensures { result = lm_dump x acc l }
ensures { let (acc2,l2) = result in
lm_vld f r c acc2 /\ lm_vld f r c l2 /\
... | = match l with
| Nil -> (acc, Nil)
| Cons y q ->
if m_lower x y then (acc, l)
else lm_dump_ok f r c x (m_collapse_ok f r c acc y) q
end | let | lm_dump_ok | examples/verifythis_2016_matrix_multiplication | examples/verifythis_2016_matrix_multiplication/matrices_ring_simp.mlw | [
"int.Int",
"list.List",
"matrices.Matrix",
"matrices.MatrixArithmetic"
] | [
"acc",
"add",
"int",
"list",
"lm_dump",
"lm_mdl",
"lm_vld",
"m_collapse_ok",
"m_lower",
"mat",
"mono"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
lm_merge (acc l1 l2:list mono) : list mono | = match l1 with
| Nil -> cat_rev Nil (lm_collapse acc l2)
| Cons x q ->
let (acc,l2) = lm_dump x acc l2 in
lm_merge (m_collapse acc x) q l2
end | function | lm_merge | examples/verifythis_2016_matrix_multiplication | examples/verifythis_2016_matrix_multiplication/matrices_ring_simp.mlw | [
"int.Int",
"list.List",
"matrices.Matrix",
"matrices.MatrixArithmetic"
] | [
"acc",
"cat_rev",
"list",
"lm_collapse",
"lm_dump",
"m_collapse",
"mono"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
lm_merge_ok (f:int -> mat int) (r c:int)
(acc l1 l2:list mono) : list mono
requires { r >= 0 /\ c >= 0 /\ lm_vld f r c acc }
requires { lm_vld f r c l1 /\ lm_vld f r c l2 }
ensures { result = lm_merge acc l1 l2 /\ lm_vld f r c result }
ensures { lm_mdl f r c result =
add (lm_mdl f ... | = match l1 with
| Nil -> cat_rev_ok f r c Nil (lm_collapse_ok f r c acc l2)
| Cons x q -> let (acc,l2) = lm_dump_ok f r c x acc l2 in
lm_merge_ok f r c (m_collapse_ok f r c acc x) q l2
end | let | lm_merge_ok | examples/verifythis_2016_matrix_multiplication | examples/verifythis_2016_matrix_multiplication/matrices_ring_simp.mlw | [
"int.Int",
"list.List",
"matrices.Matrix",
"matrices.MatrixArithmetic"
] | [
"acc",
"add",
"cat_rev_ok",
"int",
"list",
"lm_collapse_ok",
"lm_dump_ok",
"lm_mdl",
"lm_merge",
"lm_vld",
"m_collapse_ok",
"mat",
"mono"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
cat (l1 l2:list 'a) : list 'a | = match l1 with
| Nil -> l2
| Cons x q -> Cons x (cat q l2)
end | function | cat | examples/verifythis_2016_matrix_multiplication | examples/verifythis_2016_matrix_multiplication/matrices_ring_simp.mlw | [
"int.Int",
"list.List",
"matrices.Matrix",
"matrices.MatrixArithmetic"
] | [
"list"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
cat_ok (f:int -> mat int) (r k c:int)
(l1 l2:list int) : list int
requires { r >= 0 /\ k >= 0 /\ c >= 0 }
requires { l_vld f r k l1 /\ l_vld f k c l2 }
ensures { result = cat l1 l2 /\ l_vld f r c result }
ensures { l_mdl f result = mul (l_mdl f l1) (l_mdl f l2) }
v... | = match l1, l2 with
| Nil, _ | _, Nil -> absurd
| Cons x Nil, _ -> Cons x l2
| Cons x q, _ -> Cons x (cat_ok f (cols (f x)) k c q l2)
end | let | cat_ok | examples/verifythis_2016_matrix_multiplication | examples/verifythis_2016_matrix_multiplication/matrices_ring_simp.mlw | [
"int.Int",
"list.List",
"matrices.Matrix",
"matrices.MatrixArithmetic"
] | [
"cat",
"cols",
"int",
"l_mdl",
"l_vld",
"list",
"mat",
"mul"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
m_mul (m1 m2:mono) : mono | =
{ m_pos = (m1.m_pos <-> m2.m_pos); m_prod = cat m1.m_prod m2.m_prod } | function | m_mul | examples/verifythis_2016_matrix_multiplication | examples/verifythis_2016_matrix_multiplication/matrices_ring_simp.mlw | [
"int.Int",
"list.List",
"matrices.Matrix",
"matrices.MatrixArithmetic"
] | [
"cat",
"mono"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
m_mul_ok (f:int -> mat int) (r k c:int) (m1 m2:mono) : mono
requires { r >= 0 /\ k >= 0 /\ c >= 0 }
requires { l_vld f r k m1.m_prod /\ l_vld f k c m2.m_prod }
ensures { result = m_mul m1 m2 /\ l_vld f r c result.m_prod }
ensures { m_mdl f result = mul (m_mdl f m1) (m_mdl f m2) } | = { m_pos = (if m1.m_pos then m2.m_pos else not m2.m_pos);
m_prod = cat_ok f r k c m1.m_prod m2.m_prod } | let | m_mul_ok | examples/verifythis_2016_matrix_multiplication | examples/verifythis_2016_matrix_multiplication/matrices_ring_simp.mlw | [
"int.Int",
"list.List",
"matrices.Matrix",
"matrices.MatrixArithmetic"
] | [
"cat_ok",
"int",
"l_vld",
"m_mdl",
"m_mul",
"mat",
"mono",
"mul"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
m_distribute (m:mono) (l:list mono) : list mono | = match l with
| Nil -> Nil
| Cons x q -> Cons (m_mul m x) (m_distribute m q)
end | function | m_distribute | examples/verifythis_2016_matrix_multiplication | examples/verifythis_2016_matrix_multiplication/matrices_ring_simp.mlw | [
"int.Int",
"list.List",
"matrices.Matrix",
"matrices.MatrixArithmetic"
] | [
"list",
"m_mul",
"mono"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
m_distribute_ok (f:int -> mat int) (r k c:int)
(m:mono) (l:list mono) : list mono
requires { r >= 0 /\ k >= 0 /\ c >= 0 }
requires { l_vld f r k m.m_prod /\ lm_vld f k c l }
ensures { result = m_distribute m l /\ lm_vld f r c result }
ensures { lm_mdl f r c resu... | = match l with
| Nil -> Nil
| Cons x q -> Cons (m_mul_ok f r k c m x) (m_distribute_ok f r k c m q)
end | let | m_distribute_ok | examples/verifythis_2016_matrix_multiplication | examples/verifythis_2016_matrix_multiplication/matrices_ring_simp.mlw | [
"int.Int",
"list.List",
"matrices.Matrix",
"matrices.MatrixArithmetic"
] | [
"int",
"l_vld",
"list",
"lm_mdl",
"lm_vld",
"m_distribute",
"m_mdl",
"m_mul_ok",
"mat",
"mono",
"mul"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
lm_distribute (l1 l2:list mono) : list mono | = match l1 with
| Nil -> Nil
| Cons x q -> lm_merge Nil (m_distribute x l2) (lm_distribute q l2)
end | function | lm_distribute | examples/verifythis_2016_matrix_multiplication | examples/verifythis_2016_matrix_multiplication/matrices_ring_simp.mlw | [
"int.Int",
"list.List",
"matrices.Matrix",
"matrices.MatrixArithmetic"
] | [
"list",
"lm_merge",
"m_distribute",
"mono"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
lm_distribute_ok (f:int -> mat int) (r k c:int)
(l1 l2:list mono) : list mono
requires { r >= 0 /\ k >= 0 /\ c >= 0 }
requires { lm_vld f r k l1 /\ lm_vld f k c l2 }
ensures { result = lm_distribute l1 l2 /\ lm_vld f r c result }
ensures { lm_mdl f r c result =... | = match l1 with
| Nil -> Nil
| Cons x q ->
lm_merge_ok f r c Nil (m_distribute_ok f r k c x l2)
(lm_distribute_ok f r k c q l2)
end | let | lm_distribute_ok | examples/verifythis_2016_matrix_multiplication | examples/verifythis_2016_matrix_multiplication/matrices_ring_simp.mlw | [
"int.Int",
"list.List",
"matrices.Matrix",
"matrices.MatrixArithmetic"
] | [
"int",
"list",
"lm_distribute",
"lm_mdl",
"lm_merge_ok",
"lm_vld",
"m_distribute_ok",
"mat",
"mono",
"mul"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
lm_opp (l:list mono) : list mono | = match l with
| Nil -> Nil
| Cons x q ->
lm_merge Nil (Cons { x with m_pos = not x.m_pos } Nil)
(lm_opp q)
end | function | lm_opp | examples/verifythis_2016_matrix_multiplication | examples/verifythis_2016_matrix_multiplication/matrices_ring_simp.mlw | [
"int.Int",
"list.List",
"matrices.Matrix",
"matrices.MatrixArithmetic"
] | [
"list",
"lm_merge",
"mono"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
lm_opp_ok (f:int -> mat int) (r c:int)
(l:list mono) : list mono
requires { r >= 0 /\ c >= 0 /\ lm_vld f r c l }
ensures { result = lm_opp l /\ lm_vld f r c result }
ensures { lm_mdl f r c result = opp (lm_mdl f r c l) }
variant { l } | = match l with
| Nil -> Nil
| Cons x q -> let m2 = { x with m_pos = not x.m_pos } in
lm_merge_ok f r c Nil (Cons m2 Nil) (lm_opp_ok f r c q);
end | let | lm_opp_ok | examples/verifythis_2016_matrix_multiplication | examples/verifythis_2016_matrix_multiplication/matrices_ring_simp.mlw | [
"int.Int",
"list.List",
"matrices.Matrix",
"matrices.MatrixArithmetic"
] | [
"int",
"list",
"lm_mdl",
"lm_merge_ok",
"lm_opp",
"lm_vld",
"mat",
"mono",
"opp"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
empty : int -> mat int | = zero 0 | constant | empty | examples/verifythis_2016_matrix_multiplication | examples/verifythis_2016_matrix_multiplication/matrices_ring_simp.mlw | [
"int.Int",
"list.List",
"matrices.Matrix",
"matrices.MatrixArithmetic"
] | [
"int",
"mat",
"zero"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
env | = {
mutable ev_f : int -> mat int;
mutable ev_c : int;
} | type | env | examples/verifythis_2016_matrix_multiplication | examples/verifythis_2016_matrix_multiplication/matrices_ring_simp.mlw | [
"int.Int",
"list.List",
"matrices.Matrix",
"matrices.MatrixArithmetic"
] | [
"int",
"mat"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
expr | = {
e_body : list LOCAL.mono;
e_rows : int;
e_cols : int;
} | type | expr | examples/verifythis_2016_matrix_multiplication | examples/verifythis_2016_matrix_multiplication/matrices_ring_simp.mlw | [
"int.Int",
"list.List",
"matrices.Matrix",
"matrices.MatrixArithmetic"
] | [
"int",
"list",
"mono"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
e_vld (env:env) (e:expr) | =
e.e_rows >= 0 /\ e.e_cols >= 0 /\
LOCAL.lm_vld env.ev_f e.e_rows e.e_cols e.e_body | predicate | e_vld | examples/verifythis_2016_matrix_multiplication | examples/verifythis_2016_matrix_multiplication/matrices_ring_simp.mlw | [
"int.Int",
"list.List",
"matrices.Matrix",
"matrices.MatrixArithmetic"
] | [
"env",
"expr",
"lm_vld"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
e_mdl (env:env) (e:expr) : mat int | =
LOCAL.lm_mdl_simp env.ev_f e.e_rows e.e_cols e.e_body | function | e_mdl | examples/verifythis_2016_matrix_multiplication | examples/verifythis_2016_matrix_multiplication/matrices_ring_simp.mlw | [
"int.Int",
"list.List",
"matrices.Matrix",
"matrices.MatrixArithmetic"
] | [
"env",
"expr",
"int",
"lm_mdl_simp",
"mat"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
extends (f:int -> mat int) (c:int) (v:mat int) : int -> mat int | =
fun n -> if n <> c then f n else v | function | extends | examples/verifythis_2016_matrix_multiplication | examples/verifythis_2016_matrix_multiplication/matrices_ring_simp.mlw | [
"int.Int",
"list.List",
"matrices.Matrix",
"matrices.MatrixArithmetic"
] | [
"int",
"mat"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
extends_rw : forall f c v n.
extends f c v n = if n <> c then f n else v | lemma | extends_rw | examples/verifythis_2016_matrix_multiplication | examples/verifythis_2016_matrix_multiplication/matrices_ring_simp.mlw | [
"int.Int",
"list.List",
"matrices.Matrix",
"matrices.MatrixArithmetic"
] | [
"extends"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
symb_env () : env
ensures { result.ev_c --> 0 } | = { ev_f = LOCAL.empty; ev_c = 0 } | let | symb_env | examples/verifythis_2016_matrix_multiplication | examples/verifythis_2016_matrix_multiplication/matrices_ring_simp.mlw | [
"int.Int",
"list.List",
"matrices.Matrix",
"matrices.MatrixArithmetic"
] | [
"empty",
"env"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
symb_mat (m:mat int) (n:int) : expr | =
{ e_rows = m.rows; e_cols = m.cols;
e_body = Cons { LOCAL.m_pos = true; LOCAL.m_prod = Cons n Nil } Nil } | function | symb_mat | examples/verifythis_2016_matrix_multiplication | examples/verifythis_2016_matrix_multiplication/matrices_ring_simp.mlw | [
"int.Int",
"list.List",
"matrices.Matrix",
"matrices.MatrixArithmetic"
] | [
"cols",
"expr",
"int",
"mat",
"rows"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
symb_reg (ghost env:env) (m:mat int) : expr
writes { env }
ensures { env.ev_c --> old env.ev_c + 1 }
ensures { env.ev_f --> extends (old env.ev_f) (old env.ev_c) m }
ensures { result --> symb_mat m (old env.ev_c) }
ensures { e_vld env result } | = let id = env.ev_c in
env.ev_f <- extends env.ev_f id m; env.ev_c <- id + 1;
symb_mat m id | let | symb_reg | examples/verifythis_2016_matrix_multiplication | examples/verifythis_2016_matrix_multiplication/matrices_ring_simp.mlw | [
"int.Int",
"list.List",
"matrices.Matrix",
"matrices.MatrixArithmetic"
] | [
"e_vld",
"env",
"expr",
"extends",
"id",
"int",
"mat",
"symb_mat"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
symb_opp (e:expr) : expr | =
{ e_rows = e.e_rows; e_cols = e.e_cols; e_body = LOCAL.lm_opp e.e_body } | function | symb_opp | examples/verifythis_2016_matrix_multiplication | examples/verifythis_2016_matrix_multiplication/matrices_ring_simp.mlw | [
"int.Int",
"list.List",
"matrices.Matrix",
"matrices.MatrixArithmetic"
] | [
"expr",
"lm_opp"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
symb_opp (env:env) (e:expr) : expr
requires { e_vld env e }
ensures { e_vld env result }
ensures { result --> symb_opp e }
ensures { e_mdl env result = opp (e_mdl env e) } | = let (r,c) = (e.e_rows,e.e_cols) in
LOCAL.lm_mdl_same env.ev_f r c e.e_body;
let res = { e_rows = r; e_cols = c;
e_body = LOCAL.lm_opp_ok env.ev_f r c e.e_body } in
LOCAL.lm_mdl_same env.ev_f r c res.e_body;
res | let | symb_opp | examples/verifythis_2016_matrix_multiplication | examples/verifythis_2016_matrix_multiplication/matrices_ring_simp.mlw | [
"int.Int",
"list.List",
"matrices.Matrix",
"matrices.MatrixArithmetic"
] | [
"e_mdl",
"e_vld",
"env",
"expr",
"lm_mdl_same",
"lm_opp_ok",
"opp"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
symb_add (e1 e2:expr) : expr | =
{ e_rows = e1.e_rows; e_cols = e1.e_cols;
e_body = LOCAL.lm_merge Nil e1.e_body e2.e_body } | function | symb_add | examples/verifythis_2016_matrix_multiplication | examples/verifythis_2016_matrix_multiplication/matrices_ring_simp.mlw | [
"int.Int",
"list.List",
"matrices.Matrix",
"matrices.MatrixArithmetic"
] | [
"expr",
"lm_merge"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
symb_add (env:env) (e1 e2:expr) : expr
requires { e_vld env e1 /\ e_vld env e2 }
requires { e1.e_rows = e2.e_rows /\ e1.e_cols = e2.e_cols }
ensures { e_vld env result }
ensures { result --> symb_add e1 e2 }
ensures { e_mdl env result = add (e_mdl env e1) (e_mdl env e2) } | = let (r,c) = (e1.e_rows, e1.e_cols) in
LOCAL.lm_mdl_same env.ev_f r c e1.e_body;
LOCAL.lm_mdl_same env.ev_f r c e2.e_body;
let res = { e_rows = r; e_cols = c;
e_body = LOCAL.lm_merge_ok env.ev_f r c Nil e1.e_body e2.e_body } in
LOCAL.lm_mdl_same env.ev_f r c res.e_body;
res | let | symb_add | examples/verifythis_2016_matrix_multiplication | examples/verifythis_2016_matrix_multiplication/matrices_ring_simp.mlw | [
"int.Int",
"list.List",
"matrices.Matrix",
"matrices.MatrixArithmetic"
] | [
"add",
"e_mdl",
"e_vld",
"env",
"expr",
"lm_mdl_same",
"lm_merge_ok"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
symb_sub (e1 e2:expr) : expr | =
symb_add e1 (symb_opp e2) | function | symb_sub | examples/verifythis_2016_matrix_multiplication | examples/verifythis_2016_matrix_multiplication/matrices_ring_simp.mlw | [
"int.Int",
"list.List",
"matrices.Matrix",
"matrices.MatrixArithmetic"
] | [
"expr",
"symb_add",
"symb_opp"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
symb_sub (env:env) (e1 e2:expr) : expr
requires { e_vld env e1 /\ e_vld env e2 }
requires { e1.e_rows = e2.e_rows /\ e1.e_cols = e2.e_cols }
ensures { e_vld env result }
ensures { result --> symb_sub e1 e2 }
ensures { e_mdl env result = sub (e_mdl env e1) (e_mdl env e2) } | = symb_add env e1 (symb_opp env e2) | let | symb_sub | examples/verifythis_2016_matrix_multiplication | examples/verifythis_2016_matrix_multiplication/matrices_ring_simp.mlw | [
"int.Int",
"list.List",
"matrices.Matrix",
"matrices.MatrixArithmetic"
] | [
"e_mdl",
"e_vld",
"env",
"expr",
"sub",
"symb_add",
"symb_opp"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
symb_mul (e1 e2:expr) : expr | =
{ e_rows = e1.e_rows; e_cols = e2.e_cols;
e_body = LOCAL.lm_distribute e1.e_body e2.e_body } | function | symb_mul | examples/verifythis_2016_matrix_multiplication | examples/verifythis_2016_matrix_multiplication/matrices_ring_simp.mlw | [
"int.Int",
"list.List",
"matrices.Matrix",
"matrices.MatrixArithmetic"
] | [
"expr",
"lm_distribute"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
symb_mul (env:env) (e1 e2:expr) : expr
requires { e_vld env e1 /\ e_vld env e2 }
requires { e1.e_cols = e2.e_rows }
ensures { e_vld env result }
ensures { result --> symb_mul e1 e2 }
ensures { e_mdl env result = mul (e_mdl env e1) (e_mdl env e2) } | = let (r,k,c) = (e1.e_rows,e1.e_cols,e2.e_cols) in
LOCAL.lm_mdl_same env.ev_f r k e1.e_body;
LOCAL.lm_mdl_same env.ev_f k c e2.e_body;
let res = { e_rows = r; e_cols = c;
e_body = LOCAL.lm_distribute_ok env.ev_f r k c e1.e_body e2.e_body } in
LOCAL.lm_mdl_same env.ev_f r c res.e_body;
res | let | symb_mul | examples/verifythis_2016_matrix_multiplication | examples/verifythis_2016_matrix_multiplication/matrices_ring_simp.mlw | [
"int.Int",
"list.List",
"matrices.Matrix",
"matrices.MatrixArithmetic"
] | [
"e_mdl",
"e_vld",
"env",
"expr",
"lm_distribute_ok",
"lm_mdl_same",
"mul"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
harness (a11 a12 a22 b11 b21 b22:mat int) : unit
requires { a11 === a12 === a22 === b11 === b21 === b22 }
requires { a11.rows = a11.cols } | = let env = symb_env () in
let e_a11 = symb_reg env a11 in
let e_a12 = symb_reg env a12 in
let e_a22 = symb_reg env a22 in
let e_b11 = symb_reg env b11 in
let e_b21 = symb_reg env b21 in
let e_b22 = symb_reg env b22 in
let x1 = symb_mul env (symb_add env e_a11 e_a22)
... | let | harness | examples/verifythis_2016_matrix_multiplication | examples/verifythis_2016_matrix_multiplication/matrices_ring_simp.mlw | [
"int.Int",
"list.List",
"matrices.Matrix",
"matrices.MatrixArithmetic"
] | [
"cols",
"e_mdl",
"env",
"int",
"mat",
"rows",
"symb_add",
"symb_env",
"symb_mul",
"symb_reg",
"symb_sub",
"unit",
"x1"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
mul_atom (a b: matrix int) (i j: int) : int -> int | =
fun k -> a.elts[i][k] * b.elts[k][j] | function | mul_atom | examples/verifythis_2016_matrix_multiplication | examples/verifythis_2016_matrix_multiplication/naive.mlw | [
"int.Int",
"int.Sum",
"map.Map",
"matrix.Matrix"
] | [
"int",
"matrix"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
matrix_product (m a b: matrix int) | =
forall i j. 0 <= i < m.rows -> 0 <= j < m.columns ->
m.elts[i][j] = sum (mul_atom a b i j) 0 a.columns
let mult_naive (a b: matrix int) : matrix int
requires { a.columns = b.rows }
ensures { result.rows = a.rows /\ result.columns = b.columns }
ensures { matrix_product result a b }
= let rs ... | predicate | matrix_product | examples/verifythis_2016_matrix_multiplication | examples/verifythis_2016_matrix_multiplication/naive.mlw | [
"int.Int",
"int.Sum",
"map.Map",
"matrix.Matrix"
] | [
"get",
"int",
"make",
"matrix",
"mul_atom",
"rows",
"set",
"sum"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
mdl (m: matrix 'a) : mat {'a} | =
create m.rows m.columns m.elts | let function | mdl | examples/verifythis_2016_matrix_multiplication | examples/verifythis_2016_matrix_multiplication/strassen.mlw | [
"int.EuclideanDivision",
"int.Int",
"int.Sum",
"map.Map",
"matrices.BlockMul",
"matrices.Matrix",
"matrices.MatrixArithmetic",
"matrices_ring_simp.Symb",
"matrix.Matrix",
"number.Parity",
"ref.Ref"
] | [
"create",
"mat",
"matrix",
"rows"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
with_symb | = {
phy : matrix int;
ghost sym : expr;
} | type | with_symb | examples/verifythis_2016_matrix_multiplication | examples/verifythis_2016_matrix_multiplication/strassen.mlw | [
"int.EuclideanDivision",
"int.Int",
"int.Sum",
"map.Map",
"matrices.BlockMul",
"matrices.Matrix",
"matrices.MatrixArithmetic",
"matrices_ring_simp.Symb",
"matrix.Matrix",
"number.Parity",
"ref.Ref"
] | [
"expr",
"int",
"matrix",
"sym"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
with_symb_vld (env:env) (ws:with_symb) | =
e_mdl env ws.sym = ws.phy.mdl /\ e_vld env ws.sym /\
ws.sym.e_rows = ws.phy.mdl.F.rows /\
ws.sym.e_cols = ws.phy.mdl.F.cols | predicate | with_symb_vld | examples/verifythis_2016_matrix_multiplication | examples/verifythis_2016_matrix_multiplication/strassen.mlw | [
"int.EuclideanDivision",
"int.Int",
"int.Sum",
"map.Map",
"matrices.BlockMul",
"matrices.Matrix",
"matrices.MatrixArithmetic",
"matrices_ring_simp.Symb",
"matrix.Matrix",
"number.Parity",
"ref.Ref"
] | [
"cols",
"e_mdl",
"e_vld",
"env",
"mdl",
"rows",
"sym",
"with_symb"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
block (a: matrix int) (r dr c dc: int) : matrix int
requires { 0 <= r <= r + dr <= a.mdl.F.rows }
requires { 0 <= c <= c + dc <= a.mdl.F.cols }
ensures { result.mdl = block a.mdl r dr c dc }
ensures { result.mdl.F.rows = dr /\ result.mdl.F.cols = dc } | = let res = make dr dc 0 in
blit a res r 0 dr c 0 dc;
assert { res.mdl == block a.mdl r dr c dc };
res | let | block | examples/verifythis_2016_matrix_multiplication | examples/verifythis_2016_matrix_multiplication/strassen.mlw | [
"int.EuclideanDivision",
"int.Int",
"int.Sum",
"map.Map",
"matrices.BlockMul",
"matrices.Matrix",
"matrices.MatrixArithmetic",
"matrices_ring_simp.Symb",
"matrix.Matrix",
"number.Parity",
"ref.Ref"
] | [
"blit",
"cols",
"int",
"make",
"matrix",
"mdl",
"rows"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
block_ws (ghost env:env) (a:matrix int) (r dr c dc: int) : with_symb
requires { 0 <= r <= r + dr <= a.mdl.F.rows }
requires { 0 <= c <= c + dc <= a.mdl.F.cols }
ensures { let rm = result.phy.mdl in
rm = block a.mdl r dr c dc /\ rm.F.rows = dr /\ rm.F.cols = dc }
ensures { result.sym --> symb_mat r... | = let m = block a r dr c dc in
{ phy = m;
sym = ghost symb_reg env m.mdl }
let add (a b: matrix int) : matrix int
requires { a.mdl === b.mdl }
ensures { result.mdl = add a.mdl b.mdl }
ensures { result.mdl === a.mdl }
= let res = make a.rows a.columns 0 in
for i = 0 to a.rows - 1 do
... | let | block_ws | examples/verifythis_2016_matrix_multiplication | examples/verifythis_2016_matrix_multiplication/strassen.mlw | [
"int.EuclideanDivision",
"int.Int",
"int.Sum",
"map.Map",
"matrices.BlockMul",
"matrices.Matrix",
"matrices.MatrixArithmetic",
"matrices_ring_simp.Symb",
"matrix.Matrix",
"number.Parity",
"ref.Ref"
] | [
"add",
"block",
"cols",
"env",
"extends",
"get",
"int",
"j'",
"make",
"matrix",
"mdl",
"rows",
"set",
"sym",
"symb_mat",
"symb_reg",
"with_symb",
"with_symb_vld"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
add_ws (ghost env:env) (a b:with_symb) : with_symb
requires { a.phy.mdl === b.phy.mdl }
requires { with_symb_vld env a /\ with_symb_vld env b }
ensures { result.phy.mdl = add a.phy.mdl b.phy.mdl }
ensures { result.sym --> symb_add a.sym b.sym }
ensures { with_symb_vld env result } | = { phy = add a.phy b.phy;
sym = ghost symb_add env a.sym b.sym }
let sub (a b: matrix int): matrix int
requires { a.mdl === b.mdl }
ensures { result.mdl = sub a.mdl b.mdl }
ensures { result.mdl === a.mdl}
= let res = make a.rows a.columns 0 in
for i = 0 to a.rows - 1 do
invariant { ... | let | add_ws | examples/verifythis_2016_matrix_multiplication | examples/verifythis_2016_matrix_multiplication/strassen.mlw | [
"int.EuclideanDivision",
"int.Int",
"int.Sum",
"map.Map",
"matrices.BlockMul",
"matrices.Matrix",
"matrices.MatrixArithmetic",
"matrices_ring_simp.Symb",
"matrix.Matrix",
"number.Parity",
"ref.Ref"
] | [
"add",
"env",
"get",
"int",
"j'",
"make",
"matrix",
"mdl",
"rows",
"set",
"sub",
"sym",
"symb_add",
"with_symb",
"with_symb_vld"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
sub_ws (ghost env:env) (a b:with_symb) : with_symb
requires { a.phy.mdl === b.phy.mdl }
requires { with_symb_vld env a /\ with_symb_vld env b }
ensures { result.phy.mdl = sub a.phy.mdl b.phy.mdl }
ensures { result.sym --> symb_sub a.sym b.sym }
ensures { with_symb_vld env result } | = { phy = sub a.phy b.phy;
sym = ghost symb_sub env a.sym b.sym }
let mult_ijk (a b:matrix int) : matrix int
requires { a.mdl.F.cols = b.mdl.F.rows }
ensures { result.mdl.F.rows = a.mdl.F.rows }
ensures { result.mdl.F.cols = b.mdl.F.cols }
ensures { result.mdl = mul a.mdl b.mdl }
= let r = ro... | let | sub_ws | examples/verifythis_2016_matrix_multiplication | examples/verifythis_2016_matrix_multiplication/strassen.mlw | [
"int.EuclideanDivision",
"int.Int",
"int.Sum",
"map.Map",
"matrices.BlockMul",
"matrices.Matrix",
"matrices.MatrixArithmetic",
"matrices_ring_simp.Symb",
"matrix.Matrix",
"number.Parity",
"ref.Ref"
] | [
"cols",
"env",
"get",
"int",
"make",
"matrix",
"mdl",
"mul",
"mul_atom",
"mul_cell",
"rows",
"set",
"sub",
"sum",
"sym",
"symb_sub",
"with_symb",
"with_symb_vld"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
assoc_proof (a b c:matrix int) : unit
requires { a.mdl.F.cols = b.mdl.F.rows /\ b.mdl.F.cols = c.mdl.F.rows } | = let ab = mult_ikj a b in
let bc = mult_ikj b c in
let ab_c = mult_ikj ab c in
let a_bc = mult_ikj a bc in
assert { ab_c.mdl = a_bc.mdl };
assert { ab_c.rows = a_bc.rows && ab_c.columns = a_bc.columns &&
forall i j. 0 <= i < ab_c.rows /\ 0 <= j < ab_c.columns ->
ab_c.elts[i][j] = F.ge... | let | assoc_proof | examples/verifythis_2016_matrix_multiplication | examples/verifythis_2016_matrix_multiplication/strassen.mlw | [
"int.EuclideanDivision",
"int.Int",
"int.Sum",
"map.Map",
"matrices.BlockMul",
"matrices.Matrix",
"matrices.MatrixArithmetic",
"matrices_ring_simp.Symb",
"matrix.Matrix",
"number.Parity",
"ref.Ref"
] | [
"ab",
"bc",
"cols",
"get",
"int",
"matrix",
"mdl",
"rows",
"unit"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
mul_naive (a b: matrix int)
requires { a.mdl.F.cols = b.mdl.F.rows }
ensures { result.mdl.F.rows = a.mdl.F.rows }
ensures { result.mdl.F.cols = b.mdl.F.cols }
ensures { result.mdl = mul a.mdl b.mdl } | = mult_ijk a b | let | mul_naive | examples/verifythis_2016_matrix_multiplication | examples/verifythis_2016_matrix_multiplication/strassen.mlw | [
"int.EuclideanDivision",
"int.Int",
"int.Sum",
"map.Map",
"matrices.BlockMul",
"matrices.Matrix",
"matrices.MatrixArithmetic",
"matrices_ring_simp.Symb",
"matrix.Matrix",
"number.Parity",
"ref.Ref"
] | [
"cols",
"int",
"matrix",
"mdl",
"mul",
"rows"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
double_block (a:matrix int) (r1 dr1 c1 dc1 r2 dr2 c2 dc2:int) : unit
requires { 0 <= r1 <= r1 + dr1 <= a.mdl.F.rows }
requires { 0 <= c1 <= c1 + dc1 <= a.mdl.F.cols }
requires { 0 <= r2 <= r2 + dr2 <= dr1 }
requires { 0 <= c2 <= c2 + dc2 <= dc1 }
ensures { block (block a.mdl r1 dr1 c1 dc1) r2 dr2 c2... | = assert { block (block a.mdl r1 dr1 c1 dc1) r2 dr2 c2 dc2 ==
block a.mdl (r1+r2) dr2 (c1+c2) dc2 } | let | double_block | examples/verifythis_2016_matrix_multiplication | examples/verifythis_2016_matrix_multiplication/strassen.mlw | [
"int.EuclideanDivision",
"int.Int",
"int.Sum",
"map.Map",
"matrices.BlockMul",
"matrices.Matrix",
"matrices.MatrixArithmetic",
"matrices_ring_simp.Symb",
"matrix.Matrix",
"number.Parity",
"ref.Ref"
] | [
"block",
"c1",
"c2",
"cols",
"int",
"matrix",
"mdl",
"r1",
"r2",
"rows",
"unit"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
padding (a: matrix int) (r c: int) : matrix int
requires { a.mdl.F.rows <= r }
requires { a.mdl.F.cols <= c }
ensures { result.mdl.F.rows = r }
ensures { result.mdl.F.cols = c }
ensures { a.mdl = block result.mdl 0 a.mdl.F.rows 0 a.mdl.F.cols }
ensures { let dr = (r - a.mdl.F.rows) in
... | = let res = make r c 0 in
let nr = a.rows in
let nc = a.columns in
blit a res 0 0 nr 0 0 nc;
assert { let dc = c - nc in zero nr dc == block res.mdl 0 nr nc dc };
assert { let dr = r - nr in zero dr nc == block res.mdl nr dr 0 nc };
assert { a.mdl == block res.mdl 0 nr 0... | let | padding | examples/verifythis_2016_matrix_multiplication | examples/verifythis_2016_matrix_multiplication/strassen.mlw | [
"int.EuclideanDivision",
"int.Int",
"int.Sum",
"map.Map",
"matrices.BlockMul",
"matrices.Matrix",
"matrices.MatrixArithmetic",
"matrices_ring_simp.Symb",
"matrix.Matrix",
"number.Parity",
"ref.Ref"
] | [
"blit",
"block",
"cols",
"int",
"make",
"matrix",
"mdl",
"rows",
"zero"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
strassen (a b: matrix int) (ghost flag:int) : matrix int
requires { a.mdl.F.cols = b.mdl.F.rows }
requires { flag >= 0 }
requires { flag = 0 ->
a.mdl.F.rows = 1 \/ a.mdl.F.cols = 1 \/ b.mdl.F.cols = 1 \/
(even a.mdl.F.rows /\ even a.mdl.F.cols /\ even b.mdl.F.cols) }
ensures { result.mdl = m... | = let cut_off = begin ensures { result >= 1 } 42 end in
let (rw, md, cl)= (a.rows, a.columns, b.columns) in
assert { rw = a.mdl.F.rows /\ md = a.mdl.F.cols /\ cl = b.mdl.F.cols };
if rw <= cut_off || md <= cut_off || cl <= cut_off
then mul_naive a b else
let div2 (n: int) : (int,int)
requires ... | let | strassen | examples/verifythis_2016_matrix_multiplication | examples/verifythis_2016_matrix_multiplication/strassen.mlw | [
"int.EuclideanDivision",
"int.Int",
"int.Sum",
"map.Map",
"matrices.BlockMul",
"matrices.Matrix",
"matrices.MatrixArithmetic",
"matrices_ring_simp.Symb",
"matrix.Matrix",
"number.Parity",
"ref.Ref"
] | [
"add_ws",
"blit",
"block",
"block_ws",
"c_blocks",
"cols",
"div",
"div2",
"double_block",
"e_mdl",
"even",
"get",
"int",
"make",
"matrix",
"md",
"mdl",
"mod",
"mul",
"mul_naive",
"padding",
"r_blocks",
"rows",
"sub_ws",
"sym",
"symb_env",
"symb_mul",
"with_symb"... | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
sum_ext (f g: int -> int) (a b: int) : unit
requires {forall i. a <= i < b -> f i = g i }
ensures { sum f a b = sum g a b } | = () | let | sum_ext | examples/verifythis_2016_matrix_multiplication | examples/verifythis_2016_matrix_multiplication/sum_extended.mlw | [
"int.Int",
"int.Sum"
] | [
"int",
"sum",
"unit"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
datatype | = TYunit | TYint | TYbool | type | datatype | examples/WP_revisited | examples/WP_revisited/blocking_semantics5.mlw | [
"FreshVariables",
"SemOp",
"Syntax",
"Typing",
"TypingAndSemantics",
"bool.Bool",
"int.Int",
"list.Append",
"list.List",
"map.Const",
"map.Map"
] | [] | types and values | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 |
value | = Vvoid | Vint int | Vbool bool | type | value | examples/WP_revisited | examples/WP_revisited/blocking_semantics5.mlw | [
"FreshVariables",
"SemOp",
"Syntax",
"Typing",
"TypingAndSemantics",
"bool.Bool",
"int.Int",
"list.Append",
"list.List",
"map.Const",
"map.Map"
] | [
"int"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
operator | = Oplus | Ominus | Omult | Ole | type | operator | examples/WP_revisited | examples/WP_revisited/blocking_semantics5.mlw | [
"FreshVariables",
"SemOp",
"Syntax",
"Typing",
"TypingAndSemantics",
"bool.Bool",
"int.Int",
"list.Append",
"list.List",
"map.Const",
"map.Map"
] | [] | terms and formulas | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 |
mident | type | mident | examples/WP_revisited | examples/WP_revisited/blocking_semantics5.mlw | [
"FreshVariables",
"SemOp",
"Syntax",
"Typing",
"TypingAndSemantics",
"bool.Bool",
"int.Int",
"list.Append",
"list.List",
"map.Const",
"map.Map"
] | [] | ident for mutable variables | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
mident_decide :
forall m1 m2: mident. m1 = m2 \/ m1 <> m2 | lemma | mident_decide | examples/WP_revisited | examples/WP_revisited/blocking_semantics5.mlw | [
"FreshVariables",
"SemOp",
"Syntax",
"Typing",
"TypingAndSemantics",
"bool.Bool",
"int.Int",
"list.Append",
"list.List",
"map.Const",
"map.Map"
] | [
"mident"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
ident | type | ident | examples/WP_revisited | examples/WP_revisited/blocking_semantics5.mlw | [
"FreshVariables",
"SemOp",
"Syntax",
"Typing",
"TypingAndSemantics",
"bool.Bool",
"int.Int",
"list.Append",
"list.List",
"map.Const",
"map.Map"
] | [] | ident for immutable variables | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
ident_decide :
forall m1 m2: ident. m1 = m2 \/ m1 <> m2 | lemma | ident_decide | examples/WP_revisited | examples/WP_revisited/blocking_semantics5.mlw | [
"FreshVariables",
"SemOp",
"Syntax",
"Typing",
"TypingAndSemantics",
"bool.Bool",
"int.Int",
"list.Append",
"list.List",
"map.Const",
"map.Map"
] | [
"ident"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
term | =
| Tvalue value
| Tvar ident
| Tderef mident
| Tbin term operator term | type | term | examples/WP_revisited | examples/WP_revisited/blocking_semantics5.mlw | [
"FreshVariables",
"SemOp",
"Syntax",
"Typing",
"TypingAndSemantics",
"bool.Bool",
"int.Int",
"list.Append",
"list.List",
"map.Const",
"map.Map"
] | [
"ident",
"mident",
"operator",
"value"
] | Terms | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 |
fmla | =
| Fterm term
| Fand fmla fmla
| Fnot fmla
| Fimplies fmla fmla
| Flet ident term fmla (* let id = term in fmla *)
| Fforall ident datatype fmla | type | fmla | examples/WP_revisited | examples/WP_revisited/blocking_semantics5.mlw | [
"FreshVariables",
"SemOp",
"Syntax",
"Typing",
"TypingAndSemantics",
"bool.Bool",
"int.Int",
"list.Append",
"list.List",
"map.Const",
"map.Map"
] | [
"datatype",
"ident",
"term"
] | Formulas | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 |
stmt | =
| Sskip
| Sassign mident term
| Sseq stmt stmt
| Sif term stmt stmt
| Sassert fmla
| Swhile term fmla stmt | type | stmt | examples/WP_revisited | examples/WP_revisited/blocking_semantics5.mlw | [
"FreshVariables",
"SemOp",
"Syntax",
"Typing",
"TypingAndSemantics",
"bool.Bool",
"int.Int",
"list.Append",
"list.List",
"map.Const",
"map.Map"
] | [
"fmla",
"mident",
"term"
] | Statements | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 |
decide_is_skip:
forall s:stmt. s = Sskip \/ s <> Sskip | lemma | decide_is_skip | examples/WP_revisited | examples/WP_revisited/blocking_semantics5.mlw | [
"FreshVariables",
"SemOp",
"Syntax",
"Typing",
"TypingAndSemantics",
"bool.Bool",
"int.Int",
"list.Append",
"list.List",
"map.Const",
"map.Map"
] | [
"stmt"
] | while cond invariant inv body | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 |
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