fact stringlengths 7 4.84k | type stringclasses 18 values | library stringclasses 14 values | imports listlengths 0 27 | filename stringclasses 205 values | symbolic_name stringlengths 1 49 | docstring stringlengths 6 2.5k ⌀ |
|---|---|---|---|---|---|---|
eval_operation_inject:
forall op vl1 vl2 v1 m1 m2,
Val.inject_list f vl1 vl2 ->
Mem.inject f m1 m2 ->
eval_operation genv (Vptr sp1 Ptrofs.zero) op vl1 m1 = Some v1 ->
exists v2,
eval_operation genv (Vptr sp2 Ptrofs.zero) (shift_stack_operation delta op) vl2 m2 = Some v2
/\ Val.inject f v1 v2. | Lemma | aarch64 | [
"Axioms",
"Coqlib",
"BoolEqual",
"AST",
"Integers",
"Floats",
"Values",
"Memory",
"Globalenvs",
"Events"
] | aarch64/Op.v | eval_operation_inject | null |
builtin_arg_ok_1
(A: Type) (ba: builtin_arg A) (c: builtin_arg_constraint) :=
match c, ba with
| OK_all, _ => true
| OK_const, (BA_int _ | BA_long _ | BA_float _ | BA_single _) => true
| OK_addrstack, BA_addrstack _ => true
| OK_addressing, BA_addrstack _ => true
| OK_addressing, BA_addptr (BA _) (BA_int _) => true
| OK_addressing, BA_addptr (BA _) (BA_long _) => true
| _, _ => false
end. | Definition | aarch64 | [
"Axioms",
"Coqlib",
"BoolEqual",
"AST",
"Integers",
"Floats",
"Values",
"Memory",
"Globalenvs",
"Events"
] | aarch64/Op.v | builtin_arg_ok_1 | * Handling of builtin arguments |
builtin_arg_ok
(A: Type) (ba: builtin_arg A) (c: builtin_arg_constraint) :=
match ba with
| (BA _ | BA_splitlong (BA _) (BA _)) => true
| _ => builtin_arg_ok_1 ba c
end. | Definition | aarch64 | [
"Axioms",
"Coqlib",
"BoolEqual",
"AST",
"Integers",
"Floats",
"Values",
"Memory",
"Globalenvs",
"Events"
] | aarch64/Op.v | builtin_arg_ok | null |
unary_constructor_sound (cstr: expr -> expr) (sem: val -> val) : Prop :=
forall le a x,
eval_expr ge sp e m le a x ->
exists v, eval_expr ge sp e m le (cstr a) v /\ Val.lessdef (sem x) v. | Definition | aarch64 | [
"Coqlib",
"Zbits",
"AST",
"Integers",
"Floats",
"Values",
"Memory",
"Globalenvs",
"Cminor",
"Op",
"CminorSel",
"SelectOp",
"SelectLong",
"SelectOpproof"
] | aarch64/SelectLongproof.v | unary_constructor_sound | null |
binary_constructor_sound (cstr: expr -> expr -> expr) (sem: val -> val -> val) : Prop :=
forall le a x b y,
eval_expr ge sp e m le a x ->
eval_expr ge sp e m le b y ->
exists v, eval_expr ge sp e m le (cstr a b) v /\ Val.lessdef (sem x y) v. | Definition | aarch64 | [
"Coqlib",
"Zbits",
"AST",
"Integers",
"Floats",
"Values",
"Memory",
"Globalenvs",
"Cminor",
"Op",
"CminorSel",
"SelectOp",
"SelectLong",
"SelectOpproof"
] | aarch64/SelectLongproof.v | binary_constructor_sound | null |
partial_unary_constructor_sound (cstr: expr -> expr) (sem: val -> option val) : Prop :=
forall le a x y,
eval_expr ge sp e m le a x ->
sem x = Some y ->
exists v, eval_expr ge sp e m le (cstr a) v /\ Val.lessdef y v. | Definition | aarch64 | [
"Coqlib",
"Zbits",
"AST",
"Integers",
"Floats",
"Values",
"Memory",
"Globalenvs",
"Cminor",
"Op",
"CminorSel",
"SelectOp",
"SelectLong",
"SelectOpproof"
] | aarch64/SelectLongproof.v | partial_unary_constructor_sound | null |
partial_binary_constructor_sound (cstr: expr -> expr -> expr) (sem: val -> val -> option val) : Prop :=
forall le a x b y z,
eval_expr ge sp e m le a x ->
eval_expr ge sp e m le b y ->
sem x y = Some z ->
exists v, eval_expr ge sp e m le (cstr a b) v /\ Val.lessdef z v. | Definition | aarch64 | [
"Coqlib",
"Zbits",
"AST",
"Integers",
"Floats",
"Values",
"Memory",
"Globalenvs",
"Cminor",
"Op",
"CminorSel",
"SelectOp",
"SelectLong",
"SelectOpproof"
] | aarch64/SelectLongproof.v | partial_binary_constructor_sound | null |
eval_longconst:
forall le n, eval_expr ge sp e m le (longconst n) (Vlong n). | Theorem | aarch64 | [
"Coqlib",
"Zbits",
"AST",
"Integers",
"Floats",
"Values",
"Memory",
"Globalenvs",
"Cminor",
"Op",
"CminorSel",
"SelectOp",
"SelectLong",
"SelectOpproof"
] | aarch64/SelectLongproof.v | eval_longconst | ** Constants |
eval_intoflong: unary_constructor_sound intoflong Val.loword. | Theorem | aarch64 | [
"Coqlib",
"Zbits",
"AST",
"Integers",
"Floats",
"Values",
"Memory",
"Globalenvs",
"Cminor",
"Op",
"CminorSel",
"SelectOp",
"SelectLong",
"SelectOpproof"
] | aarch64/SelectLongproof.v | eval_intoflong | ** Conversions |
eval_longofintu: unary_constructor_sound longofintu Val.longofintu. | Theorem | aarch64 | [
"Coqlib",
"Zbits",
"AST",
"Integers",
"Floats",
"Values",
"Memory",
"Globalenvs",
"Cminor",
"Op",
"CminorSel",
"SelectOp",
"SelectLong",
"SelectOpproof"
] | aarch64/SelectLongproof.v | eval_longofintu | null |
eval_longofint: unary_constructor_sound longofint Val.longofint. | Theorem | aarch64 | [
"Coqlib",
"Zbits",
"AST",
"Integers",
"Floats",
"Values",
"Memory",
"Globalenvs",
"Cminor",
"Op",
"CminorSel",
"SelectOp",
"SelectLong",
"SelectOpproof"
] | aarch64/SelectLongproof.v | eval_longofint | null |
eval_addlimm:
forall n, unary_constructor_sound (addlimm n) (fun x => Val.addl x (Vlong n)). | Theorem | aarch64 | [
"Coqlib",
"Zbits",
"AST",
"Integers",
"Floats",
"Values",
"Memory",
"Globalenvs",
"Cminor",
"Op",
"CminorSel",
"SelectOp",
"SelectLong",
"SelectOpproof"
] | aarch64/SelectLongproof.v | eval_addlimm | ** Addition, opposite, subtraction |
eval_addl: binary_constructor_sound addl Val.addl. | Theorem | aarch64 | [
"Coqlib",
"Zbits",
"AST",
"Integers",
"Floats",
"Values",
"Memory",
"Globalenvs",
"Cminor",
"Op",
"CminorSel",
"SelectOp",
"SelectLong",
"SelectOpproof"
] | aarch64/SelectLongproof.v | eval_addl | null |
eval_negl: unary_constructor_sound negl (fun v => Val.subl (Vlong Int64.zero) v). | Theorem | aarch64 | [
"Coqlib",
"Zbits",
"AST",
"Integers",
"Floats",
"Values",
"Memory",
"Globalenvs",
"Cminor",
"Op",
"CminorSel",
"SelectOp",
"SelectLong",
"SelectOpproof"
] | aarch64/SelectLongproof.v | eval_negl | null |
eval_subl: binary_constructor_sound subl Val.subl. | Theorem | aarch64 | [
"Coqlib",
"Zbits",
"AST",
"Integers",
"Floats",
"Values",
"Memory",
"Globalenvs",
"Cminor",
"Op",
"CminorSel",
"SelectOp",
"SelectLong",
"SelectOpproof"
] | aarch64/SelectLongproof.v | eval_subl | null |
eval_shllimm_base: forall le a n x,
eval_expr ge sp e m le a x ->
Int.ltu n Int64.iwordsize' = true ->
eval_expr ge sp e m le (shllimm_base a n) (Val.shll x (Vint n)). | Remark | aarch64 | [
"Coqlib",
"Zbits",
"AST",
"Integers",
"Floats",
"Values",
"Memory",
"Globalenvs",
"Cminor",
"Op",
"CminorSel",
"SelectOp",
"SelectLong",
"SelectOpproof"
] | aarch64/SelectLongproof.v | eval_shllimm_base | ** Immediate shifts |
eval_shllimm:
forall n, unary_constructor_sound (fun a => shllimm a n)
(fun x => Val.shll x (Vint n)). | Theorem | aarch64 | [
"Coqlib",
"Zbits",
"AST",
"Integers",
"Floats",
"Values",
"Memory",
"Globalenvs",
"Cminor",
"Op",
"CminorSel",
"SelectOp",
"SelectLong",
"SelectOpproof"
] | aarch64/SelectLongproof.v | eval_shllimm | null |
eval_shrluimm_base: forall le a n x,
eval_expr ge sp e m le a x ->
Int.ltu n Int64.iwordsize' = true ->
eval_expr ge sp e m le (shrluimm_base a n) (Val.shrlu x (Vint n)). | Remark | aarch64 | [
"Coqlib",
"Zbits",
"AST",
"Integers",
"Floats",
"Values",
"Memory",
"Globalenvs",
"Cminor",
"Op",
"CminorSel",
"SelectOp",
"SelectLong",
"SelectOpproof"
] | aarch64/SelectLongproof.v | eval_shrluimm_base | null |
sub_shift_amount:
forall y z,
Int.ltu y Int64.iwordsize' = true -> Int.ltu z Int64.iwordsize' = true -> Int.unsigned y <= Int.unsigned z ->
Int.ltu (Int.sub z y) Int64.iwordsize' = true. | Remark | aarch64 | [
"Coqlib",
"Zbits",
"AST",
"Integers",
"Floats",
"Values",
"Memory",
"Globalenvs",
"Cminor",
"Op",
"CminorSel",
"SelectOp",
"SelectLong",
"SelectOpproof"
] | aarch64/SelectLongproof.v | sub_shift_amount | null |
eval_shrluimm:
forall n, unary_constructor_sound (fun a => shrluimm a n)
(fun x => Val.shrlu x (Vint n)). | Theorem | aarch64 | [
"Coqlib",
"Zbits",
"AST",
"Integers",
"Floats",
"Values",
"Memory",
"Globalenvs",
"Cminor",
"Op",
"CminorSel",
"SelectOp",
"SelectLong",
"SelectOpproof"
] | aarch64/SelectLongproof.v | eval_shrluimm | null |
eval_shrlimm_base: forall le a n x,
eval_expr ge sp e m le a x ->
Int.ltu n Int64.iwordsize' = true ->
eval_expr ge sp e m le (shrlimm_base a n) (Val.shrl x (Vint n)). | Remark | aarch64 | [
"Coqlib",
"Zbits",
"AST",
"Integers",
"Floats",
"Values",
"Memory",
"Globalenvs",
"Cminor",
"Op",
"CminorSel",
"SelectOp",
"SelectLong",
"SelectOpproof"
] | aarch64/SelectLongproof.v | eval_shrlimm_base | null |
eval_shrlimm:
forall n, unary_constructor_sound (fun a => shrlimm a n)
(fun x => Val.shrl x (Vint n)). | Theorem | aarch64 | [
"Coqlib",
"Zbits",
"AST",
"Integers",
"Floats",
"Values",
"Memory",
"Globalenvs",
"Cminor",
"Op",
"CminorSel",
"SelectOp",
"SelectLong",
"SelectOpproof"
] | aarch64/SelectLongproof.v | eval_shrlimm | null |
eval_mullimm_base:
forall n, unary_constructor_sound (mullimm_base n) (fun x => Val.mull x (Vlong n)). | Lemma | aarch64 | [
"Coqlib",
"Zbits",
"AST",
"Integers",
"Floats",
"Values",
"Memory",
"Globalenvs",
"Cminor",
"Op",
"CminorSel",
"SelectOp",
"SelectLong",
"SelectOpproof"
] | aarch64/SelectLongproof.v | eval_mullimm_base | ** Multiplication |
eval_mullimm:
forall n, unary_constructor_sound (mullimm n) (fun x => Val.mull x (Vlong n)). | Theorem | aarch64 | [
"Coqlib",
"Zbits",
"AST",
"Integers",
"Floats",
"Values",
"Memory",
"Globalenvs",
"Cminor",
"Op",
"CminorSel",
"SelectOp",
"SelectLong",
"SelectOpproof"
] | aarch64/SelectLongproof.v | eval_mullimm | null |
eval_mull: binary_constructor_sound mull Val.mull. | Theorem | aarch64 | [
"Coqlib",
"Zbits",
"AST",
"Integers",
"Floats",
"Values",
"Memory",
"Globalenvs",
"Cminor",
"Op",
"CminorSel",
"SelectOp",
"SelectLong",
"SelectOpproof"
] | aarch64/SelectLongproof.v | eval_mull | null |
eval_mullhu:
forall n, unary_constructor_sound (fun a => mullhu a n) (fun v => Val.mullhu v (Vlong n)). | Theorem | aarch64 | [
"Coqlib",
"Zbits",
"AST",
"Integers",
"Floats",
"Values",
"Memory",
"Globalenvs",
"Cminor",
"Op",
"CminorSel",
"SelectOp",
"SelectLong",
"SelectOpproof"
] | aarch64/SelectLongproof.v | eval_mullhu | null |
eval_mullhs:
forall n, unary_constructor_sound (fun a => mullhs a n) (fun v => Val.mullhs v (Vlong n)). | Theorem | aarch64 | [
"Coqlib",
"Zbits",
"AST",
"Integers",
"Floats",
"Values",
"Memory",
"Globalenvs",
"Cminor",
"Op",
"CminorSel",
"SelectOp",
"SelectLong",
"SelectOpproof"
] | aarch64/SelectLongproof.v | eval_mullhs | null |
eval_zero_ext_l:
forall sz, 0 <= sz -> unary_constructor_sound (zero_ext_l sz) (Val.zero_ext_l sz). | Theorem | aarch64 | [
"Coqlib",
"Zbits",
"AST",
"Integers",
"Floats",
"Values",
"Memory",
"Globalenvs",
"Cminor",
"Op",
"CminorSel",
"SelectOp",
"SelectLong",
"SelectOpproof"
] | aarch64/SelectLongproof.v | eval_zero_ext_l | Integer conversions |
eval_notl: unary_constructor_sound notl Val.notl. | Theorem | aarch64 | [
"Coqlib",
"Zbits",
"AST",
"Integers",
"Floats",
"Values",
"Memory",
"Globalenvs",
"Cminor",
"Op",
"CminorSel",
"SelectOp",
"SelectLong",
"SelectOpproof"
] | aarch64/SelectLongproof.v | eval_notl | Bitwise not, and, or, xor |
eval_andlimm_base:
forall n, unary_constructor_sound (andlimm_base n) (fun x => Val.andl x (Vlong n)). | Lemma | aarch64 | [
"Coqlib",
"Zbits",
"AST",
"Integers",
"Floats",
"Values",
"Memory",
"Globalenvs",
"Cminor",
"Op",
"CminorSel",
"SelectOp",
"SelectLong",
"SelectOpproof"
] | aarch64/SelectLongproof.v | eval_andlimm_base | null |
eval_andlimm:
forall n, unary_constructor_sound (andlimm n) (fun x => Val.andl x (Vlong n)). | Theorem | aarch64 | [
"Coqlib",
"Zbits",
"AST",
"Integers",
"Floats",
"Values",
"Memory",
"Globalenvs",
"Cminor",
"Op",
"CminorSel",
"SelectOp",
"SelectLong",
"SelectOpproof"
] | aarch64/SelectLongproof.v | eval_andlimm | null |
eval_andl: binary_constructor_sound andl Val.andl. | Theorem | aarch64 | [
"Coqlib",
"Zbits",
"AST",
"Integers",
"Floats",
"Values",
"Memory",
"Globalenvs",
"Cminor",
"Op",
"CminorSel",
"SelectOp",
"SelectLong",
"SelectOpproof"
] | aarch64/SelectLongproof.v | eval_andl | null |
eval_orlimm:
forall n, unary_constructor_sound (orlimm n) (fun x => Val.orl x (Vlong n)). | Theorem | aarch64 | [
"Coqlib",
"Zbits",
"AST",
"Integers",
"Floats",
"Values",
"Memory",
"Globalenvs",
"Cminor",
"Op",
"CminorSel",
"SelectOp",
"SelectLong",
"SelectOpproof"
] | aarch64/SelectLongproof.v | eval_orlimm | null |
eval_orl: binary_constructor_sound orl Val.orl. | Theorem | aarch64 | [
"Coqlib",
"Zbits",
"AST",
"Integers",
"Floats",
"Values",
"Memory",
"Globalenvs",
"Cminor",
"Op",
"CminorSel",
"SelectOp",
"SelectLong",
"SelectOpproof"
] | aarch64/SelectLongproof.v | eval_orl | null |
eval_xorlimm_base:
forall n, unary_constructor_sound (xorlimm_base n) (fun x => Val.xorl x (Vlong n)). | Lemma | aarch64 | [
"Coqlib",
"Zbits",
"AST",
"Integers",
"Floats",
"Values",
"Memory",
"Globalenvs",
"Cminor",
"Op",
"CminorSel",
"SelectOp",
"SelectLong",
"SelectOpproof"
] | aarch64/SelectLongproof.v | eval_xorlimm_base | null |
eval_xorlimm:
forall n, unary_constructor_sound (xorlimm n) (fun x => Val.xorl x (Vlong n)). | Theorem | aarch64 | [
"Coqlib",
"Zbits",
"AST",
"Integers",
"Floats",
"Values",
"Memory",
"Globalenvs",
"Cminor",
"Op",
"CminorSel",
"SelectOp",
"SelectLong",
"SelectOpproof"
] | aarch64/SelectLongproof.v | eval_xorlimm | null |
eval_xorl: binary_constructor_sound xorl Val.xorl. | Theorem | aarch64 | [
"Coqlib",
"Zbits",
"AST",
"Integers",
"Floats",
"Values",
"Memory",
"Globalenvs",
"Cminor",
"Op",
"CminorSel",
"SelectOp",
"SelectLong",
"SelectOpproof"
] | aarch64/SelectLongproof.v | eval_xorl | null |
eval_divls_base: partial_binary_constructor_sound divls_base Val.divls. | Theorem | aarch64 | [
"Coqlib",
"Zbits",
"AST",
"Integers",
"Floats",
"Values",
"Memory",
"Globalenvs",
"Cminor",
"Op",
"CminorSel",
"SelectOp",
"SelectLong",
"SelectOpproof"
] | aarch64/SelectLongproof.v | eval_divls_base | ** Integer division and modulus |
eval_modls_base: partial_binary_constructor_sound modls_base Val.modls. | Theorem | aarch64 | [
"Coqlib",
"Zbits",
"AST",
"Integers",
"Floats",
"Values",
"Memory",
"Globalenvs",
"Cminor",
"Op",
"CminorSel",
"SelectOp",
"SelectLong",
"SelectOpproof"
] | aarch64/SelectLongproof.v | eval_modls_base | null |
eval_divlu_base: partial_binary_constructor_sound divlu_base Val.divlu. | Theorem | aarch64 | [
"Coqlib",
"Zbits",
"AST",
"Integers",
"Floats",
"Values",
"Memory",
"Globalenvs",
"Cminor",
"Op",
"CminorSel",
"SelectOp",
"SelectLong",
"SelectOpproof"
] | aarch64/SelectLongproof.v | eval_divlu_base | null |
eval_modlu_base: partial_binary_constructor_sound modlu_base Val.modlu. | Theorem | aarch64 | [
"Coqlib",
"Zbits",
"AST",
"Integers",
"Floats",
"Values",
"Memory",
"Globalenvs",
"Cminor",
"Op",
"CminorSel",
"SelectOp",
"SelectLong",
"SelectOpproof"
] | aarch64/SelectLongproof.v | eval_modlu_base | null |
eval_shrxlimm:
forall le a n x z,
eval_expr ge sp e m le a x ->
Val.shrxl x (Vint n) = Some z ->
exists v, eval_expr ge sp e m le (shrxlimm a n) v /\ Val.lessdef z v. | Theorem | aarch64 | [
"Coqlib",
"Zbits",
"AST",
"Integers",
"Floats",
"Values",
"Memory",
"Globalenvs",
"Cminor",
"Op",
"CminorSel",
"SelectOp",
"SelectLong",
"SelectOpproof"
] | aarch64/SelectLongproof.v | eval_shrxlimm | null |
eval_shll: binary_constructor_sound shll Val.shll. | Theorem | aarch64 | [
"Coqlib",
"Zbits",
"AST",
"Integers",
"Floats",
"Values",
"Memory",
"Globalenvs",
"Cminor",
"Op",
"CminorSel",
"SelectOp",
"SelectLong",
"SelectOpproof"
] | aarch64/SelectLongproof.v | eval_shll | General shifts |
eval_shrl: binary_constructor_sound shrl Val.shrl. | Theorem | aarch64 | [
"Coqlib",
"Zbits",
"AST",
"Integers",
"Floats",
"Values",
"Memory",
"Globalenvs",
"Cminor",
"Op",
"CminorSel",
"SelectOp",
"SelectLong",
"SelectOpproof"
] | aarch64/SelectLongproof.v | eval_shrl | null |
eval_shrlu: binary_constructor_sound shrlu Val.shrlu. | Theorem | aarch64 | [
"Coqlib",
"Zbits",
"AST",
"Integers",
"Floats",
"Values",
"Memory",
"Globalenvs",
"Cminor",
"Op",
"CminorSel",
"SelectOp",
"SelectLong",
"SelectOpproof"
] | aarch64/SelectLongproof.v | eval_shrlu | null |
option_map_of_bool_inv: forall ov w,
option_map Val.of_bool ov = Some w -> Val.of_optbool ov = w. | Remark | aarch64 | [
"Coqlib",
"Zbits",
"AST",
"Integers",
"Floats",
"Values",
"Memory",
"Globalenvs",
"Cminor",
"Op",
"CminorSel",
"SelectOp",
"SelectLong",
"SelectOpproof"
] | aarch64/SelectLongproof.v | option_map_of_bool_inv | Comparisons |
eval_complimm_default: forall le a x c n2 v,
sem c x (Vlong n2) = Some v ->
eval_expr ge sp e m le a x ->
eval_expr ge sp e m le (Eop (Ocmp (default c n2)) (a:::Enil)) v. | Lemma | aarch64 | [
"Coqlib",
"Zbits",
"AST",
"Integers",
"Floats",
"Values",
"Memory",
"Globalenvs",
"Cminor",
"Op",
"CminorSel",
"SelectOp",
"SelectLong",
"SelectOpproof"
] | aarch64/SelectLongproof.v | eval_complimm_default | null |
eval_complimm:
forall le c a n2 x v,
eval_expr ge sp e m le a x ->
sem c x (Vlong n2) = Some v ->
eval_expr ge sp e m le (complimm default intsem c a n2) v. | Lemma | aarch64 | [
"Coqlib",
"Zbits",
"AST",
"Integers",
"Floats",
"Values",
"Memory",
"Globalenvs",
"Cminor",
"Op",
"CminorSel",
"SelectOp",
"SelectLong",
"SelectOpproof"
] | aarch64/SelectLongproof.v | eval_complimm | null |
eval_complimm_swap:
forall le c a n2 x v,
eval_expr ge sp e m le a x ->
sem c (Vlong n2) x = Some v ->
eval_expr ge sp e m le (complimm default intsem (swap_comparison c) a n2) v. | Lemma | aarch64 | [
"Coqlib",
"Zbits",
"AST",
"Integers",
"Floats",
"Values",
"Memory",
"Globalenvs",
"Cminor",
"Op",
"CminorSel",
"SelectOp",
"SelectLong",
"SelectOpproof"
] | aarch64/SelectLongproof.v | eval_complimm_swap | null |
eval_cmpl:
forall c le a x b y v,
eval_expr ge sp e m le a x ->
eval_expr ge sp e m le b y ->
Val.cmpl c x y = Some v ->
eval_expr ge sp e m le (cmpl c a b) v. | Theorem | aarch64 | [
"Coqlib",
"Zbits",
"AST",
"Integers",
"Floats",
"Values",
"Memory",
"Globalenvs",
"Cminor",
"Op",
"CminorSel",
"SelectOp",
"SelectLong",
"SelectOpproof"
] | aarch64/SelectLongproof.v | eval_cmpl | null |
eval_cmplu:
forall c le a x b y v,
eval_expr ge sp e m le a x ->
eval_expr ge sp e m le b y ->
Val.cmplu (Mem.valid_pointer m) c x y = Some v ->
eval_expr ge sp e m le (cmplu c a b) v. | Theorem | aarch64 | [
"Coqlib",
"Zbits",
"AST",
"Integers",
"Floats",
"Values",
"Memory",
"Globalenvs",
"Cminor",
"Op",
"CminorSel",
"SelectOp",
"SelectLong",
"SelectOpproof"
] | aarch64/SelectLongproof.v | eval_cmplu | null |
eval_longoffloat: partial_unary_constructor_sound longoffloat Val.longoffloat. | Theorem | aarch64 | [
"Coqlib",
"Zbits",
"AST",
"Integers",
"Floats",
"Values",
"Memory",
"Globalenvs",
"Cminor",
"Op",
"CminorSel",
"SelectOp",
"SelectLong",
"SelectOpproof"
] | aarch64/SelectLongproof.v | eval_longoffloat | Floating-point conversions |
eval_longuoffloat: partial_unary_constructor_sound longuoffloat Val.longuoffloat. | Theorem | aarch64 | [
"Coqlib",
"Zbits",
"AST",
"Integers",
"Floats",
"Values",
"Memory",
"Globalenvs",
"Cminor",
"Op",
"CminorSel",
"SelectOp",
"SelectLong",
"SelectOpproof"
] | aarch64/SelectLongproof.v | eval_longuoffloat | null |
eval_floatoflong: partial_unary_constructor_sound floatoflong Val.floatoflong. | Theorem | aarch64 | [
"Coqlib",
"Zbits",
"AST",
"Integers",
"Floats",
"Values",
"Memory",
"Globalenvs",
"Cminor",
"Op",
"CminorSel",
"SelectOp",
"SelectLong",
"SelectOpproof"
] | aarch64/SelectLongproof.v | eval_floatoflong | null |
eval_floatoflongu: partial_unary_constructor_sound floatoflongu Val.floatoflongu. | Theorem | aarch64 | [
"Coqlib",
"Zbits",
"AST",
"Integers",
"Floats",
"Values",
"Memory",
"Globalenvs",
"Cminor",
"Op",
"CminorSel",
"SelectOp",
"SelectLong",
"SelectOpproof"
] | aarch64/SelectLongproof.v | eval_floatoflongu | null |
eval_longofsingle: partial_unary_constructor_sound longofsingle Val.longofsingle. | Theorem | aarch64 | [
"Coqlib",
"Zbits",
"AST",
"Integers",
"Floats",
"Values",
"Memory",
"Globalenvs",
"Cminor",
"Op",
"CminorSel",
"SelectOp",
"SelectLong",
"SelectOpproof"
] | aarch64/SelectLongproof.v | eval_longofsingle | null |
eval_longuofsingle: partial_unary_constructor_sound longuofsingle Val.longuofsingle. | Theorem | aarch64 | [
"Coqlib",
"Zbits",
"AST",
"Integers",
"Floats",
"Values",
"Memory",
"Globalenvs",
"Cminor",
"Op",
"CminorSel",
"SelectOp",
"SelectLong",
"SelectOpproof"
] | aarch64/SelectLongproof.v | eval_longuofsingle | null |
eval_singleoflong: partial_unary_constructor_sound singleoflong Val.singleoflong. | Theorem | aarch64 | [
"Coqlib",
"Zbits",
"AST",
"Integers",
"Floats",
"Values",
"Memory",
"Globalenvs",
"Cminor",
"Op",
"CminorSel",
"SelectOp",
"SelectLong",
"SelectOpproof"
] | aarch64/SelectLongproof.v | eval_singleoflong | null |
eval_singleoflongu: partial_unary_constructor_sound singleoflongu Val.singleoflongu. | Theorem | aarch64 | [
"Coqlib",
"Zbits",
"AST",
"Integers",
"Floats",
"Values",
"Memory",
"Globalenvs",
"Cminor",
"Op",
"CminorSel",
"SelectOp",
"SelectLong",
"SelectOpproof"
] | aarch64/SelectLongproof.v | eval_singleoflongu | null |
unary_constructor_sound (cstr: expr -> expr) (sem: val -> val) : Prop :=
forall le a x,
eval_expr ge sp e m le a x ->
exists v, eval_expr ge sp e m le (cstr a) v /\ Val.lessdef (sem x) v. | Definition | aarch64 | [
"Coqlib",
"Zbits",
"AST",
"Integers",
"Floats",
"Values",
"Memory",
"Builtins",
"Globalenvs",
"Cminor",
"Op",
"CminorSel",
"SelectOp"
] | aarch64/SelectOpproof.v | unary_constructor_sound | We now show that the code generated by "smart constructor" functions
such as [Selection.notint] behaves as expected. Continuing the
[notint] example, we show that if the expression [e]
evaluates to some integer value [Vint n], then [Selection.notint e]
evaluates to a value [Vint (Int.not n)] which is indeed the integer
negation of the value of [e].
All proofs follow a common pattern:
- Reasoning by case over the result of the classification functions
(such as [add_match] for integer addition), gathering additional
information on the shape of the argument expressions in the non-default
cases.
- Inversion of the evaluations of the arguments, exploiting the additional
information thus gathered.
- Equational reasoning over the arithmetic operations performed,
using the lemmas from the [Int] and [Float] modules.
- Construction of an evaluation derivation for the expression returned
by the smart constructor. |
binary_constructor_sound (cstr: expr -> expr -> expr) (sem: val -> val -> val) : Prop :=
forall le a x b y,
eval_expr ge sp e m le a x ->
eval_expr ge sp e m le b y ->
exists v, eval_expr ge sp e m le (cstr a b) v /\ Val.lessdef (sem x y) v. | Definition | aarch64 | [
"Coqlib",
"Zbits",
"AST",
"Integers",
"Floats",
"Values",
"Memory",
"Builtins",
"Globalenvs",
"Cminor",
"Op",
"CminorSel",
"SelectOp"
] | aarch64/SelectOpproof.v | binary_constructor_sound | null |
eval_addrsymbol:
forall le id ofs,
exists v, eval_expr ge sp e m le (addrsymbol id ofs) v /\ Val.lessdef (Genv.symbol_address ge id ofs) v. | Theorem | aarch64 | [
"Coqlib",
"Zbits",
"AST",
"Integers",
"Floats",
"Values",
"Memory",
"Builtins",
"Globalenvs",
"Cminor",
"Op",
"CminorSel",
"SelectOp"
] | aarch64/SelectOpproof.v | eval_addrsymbol | ** Constants |
eval_addrstack:
forall le ofs,
exists v, eval_expr ge sp e m le (addrstack ofs) v /\ Val.lessdef (Val.offset_ptr sp ofs) v. | Theorem | aarch64 | [
"Coqlib",
"Zbits",
"AST",
"Integers",
"Floats",
"Values",
"Memory",
"Builtins",
"Globalenvs",
"Cminor",
"Op",
"CminorSel",
"SelectOp"
] | aarch64/SelectOpproof.v | eval_addrstack | null |
eval_addimm:
forall n, unary_constructor_sound (addimm n) (fun x => Val.add x (Vint n)). | Theorem | aarch64 | [
"Coqlib",
"Zbits",
"AST",
"Integers",
"Floats",
"Values",
"Memory",
"Builtins",
"Globalenvs",
"Cminor",
"Op",
"CminorSel",
"SelectOp"
] | aarch64/SelectOpproof.v | eval_addimm | ** Addition, opposite, subtraction |
eval_add: binary_constructor_sound add Val.add. | Theorem | aarch64 | [
"Coqlib",
"Zbits",
"AST",
"Integers",
"Floats",
"Values",
"Memory",
"Builtins",
"Globalenvs",
"Cminor",
"Op",
"CminorSel",
"SelectOp"
] | aarch64/SelectOpproof.v | eval_add | null |
eval_negint: unary_constructor_sound negint (fun v => Val.sub Vzero v). | Theorem | aarch64 | [
"Coqlib",
"Zbits",
"AST",
"Integers",
"Floats",
"Values",
"Memory",
"Builtins",
"Globalenvs",
"Cminor",
"Op",
"CminorSel",
"SelectOp"
] | aarch64/SelectOpproof.v | eval_negint | null |
eval_sub: binary_constructor_sound sub Val.sub. | Theorem | aarch64 | [
"Coqlib",
"Zbits",
"AST",
"Integers",
"Floats",
"Values",
"Memory",
"Builtins",
"Globalenvs",
"Cminor",
"Op",
"CminorSel",
"SelectOp"
] | aarch64/SelectOpproof.v | eval_sub | null |
eval_shlimm_base: forall le a n x,
eval_expr ge sp e m le a x ->
Int.ltu n Int.iwordsize = true ->
eval_expr ge sp e m le (shlimm_base a n) (Val.shl x (Vint n)). | Remark | aarch64 | [
"Coqlib",
"Zbits",
"AST",
"Integers",
"Floats",
"Values",
"Memory",
"Builtins",
"Globalenvs",
"Cminor",
"Op",
"CminorSel",
"SelectOp"
] | aarch64/SelectOpproof.v | eval_shlimm_base | ** Immediate shifts |
eval_shlimm:
forall n, unary_constructor_sound (fun a => shlimm a n)
(fun x => Val.shl x (Vint n)). | Theorem | aarch64 | [
"Coqlib",
"Zbits",
"AST",
"Integers",
"Floats",
"Values",
"Memory",
"Builtins",
"Globalenvs",
"Cminor",
"Op",
"CminorSel",
"SelectOp"
] | aarch64/SelectOpproof.v | eval_shlimm | null |
eval_shruimm_base: forall le a n x,
eval_expr ge sp e m le a x ->
Int.ltu n Int.iwordsize = true ->
eval_expr ge sp e m le (shruimm_base a n) (Val.shru x (Vint n)). | Remark | aarch64 | [
"Coqlib",
"Zbits",
"AST",
"Integers",
"Floats",
"Values",
"Memory",
"Builtins",
"Globalenvs",
"Cminor",
"Op",
"CminorSel",
"SelectOp"
] | aarch64/SelectOpproof.v | eval_shruimm_base | null |
sub_shift_amount:
forall y z,
Int.ltu y Int.iwordsize = true -> Int.ltu z Int.iwordsize = true -> Int.unsigned y <= Int.unsigned z ->
Int.ltu (Int.sub z y) Int.iwordsize = true. | Remark | aarch64 | [
"Coqlib",
"Zbits",
"AST",
"Integers",
"Floats",
"Values",
"Memory",
"Builtins",
"Globalenvs",
"Cminor",
"Op",
"CminorSel",
"SelectOp"
] | aarch64/SelectOpproof.v | sub_shift_amount | null |
eval_shruimm:
forall n, unary_constructor_sound (fun a => shruimm a n)
(fun x => Val.shru x (Vint n)). | Theorem | aarch64 | [
"Coqlib",
"Zbits",
"AST",
"Integers",
"Floats",
"Values",
"Memory",
"Builtins",
"Globalenvs",
"Cminor",
"Op",
"CminorSel",
"SelectOp"
] | aarch64/SelectOpproof.v | eval_shruimm | null |
eval_shrimm_base: forall le a n x,
eval_expr ge sp e m le a x ->
Int.ltu n Int.iwordsize = true ->
eval_expr ge sp e m le (shrimm_base a n) (Val.shr x (Vint n)). | Remark | aarch64 | [
"Coqlib",
"Zbits",
"AST",
"Integers",
"Floats",
"Values",
"Memory",
"Builtins",
"Globalenvs",
"Cminor",
"Op",
"CminorSel",
"SelectOp"
] | aarch64/SelectOpproof.v | eval_shrimm_base | null |
eval_shrimm:
forall n, unary_constructor_sound (fun a => shrimm a n)
(fun x => Val.shr x (Vint n)). | Theorem | aarch64 | [
"Coqlib",
"Zbits",
"AST",
"Integers",
"Floats",
"Values",
"Memory",
"Builtins",
"Globalenvs",
"Cminor",
"Op",
"CminorSel",
"SelectOp"
] | aarch64/SelectOpproof.v | eval_shrimm | null |
eval_mulimm_base:
forall n, unary_constructor_sound (mulimm_base n) (fun x => Val.mul x (Vint n)). | Lemma | aarch64 | [
"Coqlib",
"Zbits",
"AST",
"Integers",
"Floats",
"Values",
"Memory",
"Builtins",
"Globalenvs",
"Cminor",
"Op",
"CminorSel",
"SelectOp"
] | aarch64/SelectOpproof.v | eval_mulimm_base | ** Multiplication |
eval_mulimm:
forall n, unary_constructor_sound (mulimm n) (fun x => Val.mul x (Vint n)). | Theorem | aarch64 | [
"Coqlib",
"Zbits",
"AST",
"Integers",
"Floats",
"Values",
"Memory",
"Builtins",
"Globalenvs",
"Cminor",
"Op",
"CminorSel",
"SelectOp"
] | aarch64/SelectOpproof.v | eval_mulimm | null |
eval_mul: binary_constructor_sound mul Val.mul. | Theorem | aarch64 | [
"Coqlib",
"Zbits",
"AST",
"Integers",
"Floats",
"Values",
"Memory",
"Builtins",
"Globalenvs",
"Cminor",
"Op",
"CminorSel",
"SelectOp"
] | aarch64/SelectOpproof.v | eval_mul | null |
eval_mulhs: binary_constructor_sound mulhs Val.mulhs. | Theorem | aarch64 | [
"Coqlib",
"Zbits",
"AST",
"Integers",
"Floats",
"Values",
"Memory",
"Builtins",
"Globalenvs",
"Cminor",
"Op",
"CminorSel",
"SelectOp"
] | aarch64/SelectOpproof.v | eval_mulhs | null |
eval_mulhu: binary_constructor_sound mulhu Val.mulhu. | Theorem | aarch64 | [
"Coqlib",
"Zbits",
"AST",
"Integers",
"Floats",
"Values",
"Memory",
"Builtins",
"Globalenvs",
"Cminor",
"Op",
"CminorSel",
"SelectOp"
] | aarch64/SelectOpproof.v | eval_mulhu | null |
eval_zero_ext:
forall sz, 0 <= sz -> unary_constructor_sound (zero_ext sz) (Val.zero_ext sz). | Theorem | aarch64 | [
"Coqlib",
"Zbits",
"AST",
"Integers",
"Floats",
"Values",
"Memory",
"Builtins",
"Globalenvs",
"Cminor",
"Op",
"CminorSel",
"SelectOp"
] | aarch64/SelectOpproof.v | eval_zero_ext | Integer conversions |
eval_sign_ext:
forall sz, 0 < sz -> unary_constructor_sound (sign_ext sz) (Val.sign_ext sz). | Theorem | aarch64 | [
"Coqlib",
"Zbits",
"AST",
"Integers",
"Floats",
"Values",
"Memory",
"Builtins",
"Globalenvs",
"Cminor",
"Op",
"CminorSel",
"SelectOp"
] | aarch64/SelectOpproof.v | eval_sign_ext | null |
eval_cast8signed: unary_constructor_sound cast8signed (Val.sign_ext 8). | Theorem | aarch64 | [
"Coqlib",
"Zbits",
"AST",
"Integers",
"Floats",
"Values",
"Memory",
"Builtins",
"Globalenvs",
"Cminor",
"Op",
"CminorSel",
"SelectOp"
] | aarch64/SelectOpproof.v | eval_cast8signed | null |
eval_cast8unsigned: unary_constructor_sound cast8unsigned (Val.zero_ext 8). | Theorem | aarch64 | [
"Coqlib",
"Zbits",
"AST",
"Integers",
"Floats",
"Values",
"Memory",
"Builtins",
"Globalenvs",
"Cminor",
"Op",
"CminorSel",
"SelectOp"
] | aarch64/SelectOpproof.v | eval_cast8unsigned | null |
eval_cast16signed: unary_constructor_sound cast16signed (Val.sign_ext 16). | Theorem | aarch64 | [
"Coqlib",
"Zbits",
"AST",
"Integers",
"Floats",
"Values",
"Memory",
"Builtins",
"Globalenvs",
"Cminor",
"Op",
"CminorSel",
"SelectOp"
] | aarch64/SelectOpproof.v | eval_cast16signed | null |
eval_cast16unsigned: unary_constructor_sound cast16unsigned (Val.zero_ext 16). | Theorem | aarch64 | [
"Coqlib",
"Zbits",
"AST",
"Integers",
"Floats",
"Values",
"Memory",
"Builtins",
"Globalenvs",
"Cminor",
"Op",
"CminorSel",
"SelectOp"
] | aarch64/SelectOpproof.v | eval_cast16unsigned | null |
eval_notint: unary_constructor_sound notint Val.notint. | Theorem | aarch64 | [
"Coqlib",
"Zbits",
"AST",
"Integers",
"Floats",
"Values",
"Memory",
"Builtins",
"Globalenvs",
"Cminor",
"Op",
"CminorSel",
"SelectOp"
] | aarch64/SelectOpproof.v | eval_notint | Bitwise not, and, or, xor |
eval_andimm_base:
forall n, unary_constructor_sound (andimm_base n) (fun x => Val.and x (Vint n)). | Lemma | aarch64 | [
"Coqlib",
"Zbits",
"AST",
"Integers",
"Floats",
"Values",
"Memory",
"Builtins",
"Globalenvs",
"Cminor",
"Op",
"CminorSel",
"SelectOp"
] | aarch64/SelectOpproof.v | eval_andimm_base | null |
eval_andimm:
forall n, unary_constructor_sound (andimm n) (fun x => Val.and x (Vint n)). | Theorem | aarch64 | [
"Coqlib",
"Zbits",
"AST",
"Integers",
"Floats",
"Values",
"Memory",
"Builtins",
"Globalenvs",
"Cminor",
"Op",
"CminorSel",
"SelectOp"
] | aarch64/SelectOpproof.v | eval_andimm | null |
eval_and: binary_constructor_sound and Val.and. | Theorem | aarch64 | [
"Coqlib",
"Zbits",
"AST",
"Integers",
"Floats",
"Values",
"Memory",
"Builtins",
"Globalenvs",
"Cminor",
"Op",
"CminorSel",
"SelectOp"
] | aarch64/SelectOpproof.v | eval_and | null |
eval_orimm:
forall n, unary_constructor_sound (orimm n) (fun x => Val.or x (Vint n)). | Theorem | aarch64 | [
"Coqlib",
"Zbits",
"AST",
"Integers",
"Floats",
"Values",
"Memory",
"Builtins",
"Globalenvs",
"Cminor",
"Op",
"CminorSel",
"SelectOp"
] | aarch64/SelectOpproof.v | eval_orimm | null |
eval_same_expr:
forall a1 a2 le v1 v2,
same_expr_pure a1 a2 = true ->
eval_expr ge sp e m le a1 v1 ->
eval_expr ge sp e m le a2 v2 ->
a1 = a2 /\ v1 = v2. | Remark | aarch64 | [
"Coqlib",
"Zbits",
"AST",
"Integers",
"Floats",
"Values",
"Memory",
"Builtins",
"Globalenvs",
"Cminor",
"Op",
"CminorSel",
"SelectOp"
] | aarch64/SelectOpproof.v | eval_same_expr | null |
eval_or: binary_constructor_sound or Val.or. | Theorem | aarch64 | [
"Coqlib",
"Zbits",
"AST",
"Integers",
"Floats",
"Values",
"Memory",
"Builtins",
"Globalenvs",
"Cminor",
"Op",
"CminorSel",
"SelectOp"
] | aarch64/SelectOpproof.v | eval_or | null |
eval_xorimm_base:
forall n, unary_constructor_sound (xorimm_base n) (fun x => Val.xor x (Vint n)). | Lemma | aarch64 | [
"Coqlib",
"Zbits",
"AST",
"Integers",
"Floats",
"Values",
"Memory",
"Builtins",
"Globalenvs",
"Cminor",
"Op",
"CminorSel",
"SelectOp"
] | aarch64/SelectOpproof.v | eval_xorimm_base | null |
eval_xorimm:
forall n, unary_constructor_sound (xorimm n) (fun x => Val.xor x (Vint n)). | Theorem | aarch64 | [
"Coqlib",
"Zbits",
"AST",
"Integers",
"Floats",
"Values",
"Memory",
"Builtins",
"Globalenvs",
"Cminor",
"Op",
"CminorSel",
"SelectOp"
] | aarch64/SelectOpproof.v | eval_xorimm | null |
eval_xor: binary_constructor_sound xor Val.xor. | Theorem | aarch64 | [
"Coqlib",
"Zbits",
"AST",
"Integers",
"Floats",
"Values",
"Memory",
"Builtins",
"Globalenvs",
"Cminor",
"Op",
"CminorSel",
"SelectOp"
] | aarch64/SelectOpproof.v | eval_xor | null |
eval_divs_base:
forall le a b x y z,
eval_expr ge sp e m le a x ->
eval_expr ge sp e m le b y ->
Val.divs x y = Some z ->
exists v, eval_expr ge sp e m le (divs_base a b) v /\ Val.lessdef z v. | Theorem | aarch64 | [
"Coqlib",
"Zbits",
"AST",
"Integers",
"Floats",
"Values",
"Memory",
"Builtins",
"Globalenvs",
"Cminor",
"Op",
"CminorSel",
"SelectOp"
] | aarch64/SelectOpproof.v | eval_divs_base | ** Integer division and modulus |
eval_mods_base:
forall le a b x y z,
eval_expr ge sp e m le a x ->
eval_expr ge sp e m le b y ->
Val.mods x y = Some z ->
exists v, eval_expr ge sp e m le (mods_base a b) v /\ Val.lessdef z v. | Theorem | aarch64 | [
"Coqlib",
"Zbits",
"AST",
"Integers",
"Floats",
"Values",
"Memory",
"Builtins",
"Globalenvs",
"Cminor",
"Op",
"CminorSel",
"SelectOp"
] | aarch64/SelectOpproof.v | eval_mods_base | null |
eval_divu_base:
forall le a x b y z,
eval_expr ge sp e m le a x ->
eval_expr ge sp e m le b y ->
Val.divu x y = Some z ->
exists v, eval_expr ge sp e m le (divu_base a b) v /\ Val.lessdef z v. | Theorem | aarch64 | [
"Coqlib",
"Zbits",
"AST",
"Integers",
"Floats",
"Values",
"Memory",
"Builtins",
"Globalenvs",
"Cminor",
"Op",
"CminorSel",
"SelectOp"
] | aarch64/SelectOpproof.v | eval_divu_base | null |
eval_modu_base:
forall le a x b y z,
eval_expr ge sp e m le a x ->
eval_expr ge sp e m le b y ->
Val.modu x y = Some z ->
exists v, eval_expr ge sp e m le (modu_base a b) v /\ Val.lessdef z v. | Theorem | aarch64 | [
"Coqlib",
"Zbits",
"AST",
"Integers",
"Floats",
"Values",
"Memory",
"Builtins",
"Globalenvs",
"Cminor",
"Op",
"CminorSel",
"SelectOp"
] | aarch64/SelectOpproof.v | eval_modu_base | null |
eval_shrximm:
forall le a n x z,
eval_expr ge sp e m le a x ->
Val.shrx x (Vint n) = Some z ->
exists v, eval_expr ge sp e m le (shrximm a n) v /\ Val.lessdef z v. | Theorem | aarch64 | [
"Coqlib",
"Zbits",
"AST",
"Integers",
"Floats",
"Values",
"Memory",
"Builtins",
"Globalenvs",
"Cminor",
"Op",
"CminorSel",
"SelectOp"
] | aarch64/SelectOpproof.v | eval_shrximm | null |
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