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 |
|---|---|---|---|---|---|---|---|---|---|---|
find_all (h: t 'a) (k: key) : list 'a
ensures { result = h[k] } | val | find_all | stdlib | stdlib/hashtbl.mlw | [
"list.List",
"map.Map"
] | [
"key",
"list"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
NotFound | exception | NotFound | stdlib | stdlib/hashtbl.mlw | [
"list.List",
"map.Map"
] | [] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
defensive_find (h: t 'a) (k: key) : 'a
ensures { match h[k] with Nil -> false | Cons v _ -> result = v end }
raises { NotFound -> h[k] = Nil } | val | defensive_find | stdlib | stdlib/hashtbl.mlw | [
"list.List",
"map.Map"
] | [
"NotFound",
"key"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
copy (h: t 'a) : t 'a
ensures { forall k: key. result[k] = h[k] } | val | copy | stdlib | stdlib/hashtbl.mlw | [
"list.List",
"map.Map"
] | [
"key"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
remove (h: t 'a) (k: key) : unit writes {h}
ensures { h[k] = match (old h)[k] with Nil -> Nil | Cons _ l -> l end }
ensures { forall k': key. k' <> k -> h[k'] = (old h)[k'] } | val | remove | stdlib | stdlib/hashtbl.mlw | [
"list.List",
"map.Map"
] | [
"key",
"unit"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
replace (h: t 'a) (k: key) (v: 'a) : unit writes {h}
ensures {
h[k] = Cons v (match (old h)[k] with Nil -> Nil | Cons _ l -> l end) }
ensures { forall k': key. k' <> k -> h[k'] = (old h)[k'] } | val | replace | stdlib | stdlib/hashtbl.mlw | [
"list.List",
"map.Map"
] | [
"key",
"unit"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
mode | = RNE | RNA | RTP | RTN | RTZ | type | mode | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
to_nearest (m:mode) | = m = RNE \/ m = RNA | predicate | to_nearest | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"mode"
] | {h <ul> <li>RNE : Round Nearest ties to Even <li>RNA : Round Nearest ties to Away <li>RTP : Round Towards Positive <li>RTN : Round Towards Negative <li>RTZ : Round Towards Zero </ul>} | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 |
eb : int | constant | eb | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"int"
] | {2 Part I - Public Interface} | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
sb : int | constant | sb | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"int"
] | the number of bits in the exponent. | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
eb_gt_1: 1 < eb | axiom | eb_gt_1 | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"eb"
] | the number of bits in the significand, including the hidden bit. | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
sb_gt_1: 1 < sb | axiom | sb_gt_1 | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"sb"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
zeroF : t | val constant | zeroF | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [] | {3 Constructors and Constants} | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
add mode t t : t | val function | add | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"mode"
] | {3 Operators} | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
sub mode t t : t | val function | sub | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"mode"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
mul mode t t : t | val function | mul | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"mode"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
div mode t t : t | val function | div | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"mode"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
abs t : t | val function | abs | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [] | The four basic operations, rounded in the given mode | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
neg t : t | val function | neg | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [] | Absolute value | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
fma mode t t t : t | val function | fma | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"mode"
] | Opposite | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
sqrt mode t : t | val function | sqrt | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"mode"
] | Fused multiply-add: x * y + z | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
(.-_) (x:t) : t | = neg x | let function | (.-_) | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"neg"
] | Square root | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 |
(.+) (x y:t) : t | = add RNE x y | let function | (.+) | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"add"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
(.-) (x y:t) : t | = sub RNE x y | let function | (.-) | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"sub"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
(.*) (x y:t) : t | = mul RNE x y | let function | (.*) | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"mul"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
(./) (x y:t) : t | = div RNE x y | let function | (./) | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"div"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
roundToIntegral mode t : t | val function | roundToIntegral | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"mode"
] | Notations for operations in the default mode RNE | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
min t t : t | function | min | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [] | Rounding to an integer | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
max t t : t | function | max | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
le t t | val predicate | le | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [] | {3 Comparisons} | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
lt t t | val predicate | lt | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
eq t t | val predicate | eq | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
(.<=) (x:t) (y:t) | = le x y | let predicate | (.<=) | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"le"
] | equality on floats, different from = since not (eq NaN NaN) | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 |
(.<) (x:t) (y:t) | = lt x y | let predicate | (.<) | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"lt"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
(.>=) (x:t) (y:t) | = ge x y | let predicate | (.>=) | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"ge"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
(.>) (x:t) (y:t) | = gt x y | let predicate | (.>) | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"gt"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
(.=) (x:t) (y:t) | = eq x y | let predicate | (.=) | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"eq"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
is_normal t | predicate | is_normal | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [] | {3 Classification of numbers} | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
is_subnormal t | predicate | is_subnormal | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
is_zero t | val predicate | is_zero | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
is_infinite t | val predicate | is_infinite | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
is_nan t | val predicate | is_nan | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
is_positive t | val predicate | is_positive | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
is_negative t | val predicate | is_negative | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
is_finite t | predicate | is_finite | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [] | helper predicate for zeros, normals and subnormals. not defined so that the axiomatisation below can use it without talking about subnormals | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
is_plus_infinity (x:t) | = is_infinite x /\ is_positive x | predicate | is_plus_infinity | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"is_infinite",
"is_positive"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
is_minus_infinity (x:t) | = is_infinite x /\ is_negative x | predicate | is_minus_infinity | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"is_infinite",
"is_negative"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
is_plus_zero (x:t) | = is_zero x /\ is_positive x | predicate | is_plus_zero | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"is_positive",
"is_zero"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
is_minus_zero (x:t) | = is_zero x /\ is_negative x | predicate | is_minus_zero | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"is_negative",
"is_zero"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
is_not_nan (x:t) | = is_finite x \/ is_infinite x | predicate | is_not_nan | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"is_finite",
"is_infinite"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
is_not_nan: forall x:t. is_not_nan x <-> not (is_nan x) | axiom | is_not_nan | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"is_nan"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
is_not_finite: forall x:t.
not (is_finite x) <-> (is_infinite x \/ is_nan x) | axiom | is_not_finite | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"is_finite",
"is_infinite",
"is_nan"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
plus_infinity : t | constant | plus_infinity | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [] | some constants for special values it is not specified that these are unique, i.e. it is not true that forall x. is_nan x -> x = not_a_number | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
plus_infinity_spec: is_plus_infinity plus_infinity | axiom | plus_infinity_spec | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"is_plus_infinity",
"plus_infinity"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
minus_infinity : t | constant | minus_infinity | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
minus_infinity_spec: is_minus_infinity minus_infinity | axiom | minus_infinity_spec | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"is_minus_infinity",
"minus_infinity"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
not_a_number : t | constant | not_a_number | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
not_a_number_spec: is_nan not_a_number | axiom | not_a_number_spec | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"is_nan",
"not_a_number"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
to_real t : real | function | to_real | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [] | to real | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
zeroF_is_positive : is_positive zeroF | axiom | zeroF_is_positive | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"is_positive",
"zeroF"
] | {3 Constructors and Constants} | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
zeroF_is_zero : is_zero zeroF | axiom | zeroF_is_zero | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"is_zero",
"zeroF"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
zero_to_real : forall x [is_zero x].
is_zero x <-> is_finite x /\ to_real x = 0.0 | axiom | zero_to_real | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"is_finite",
"is_zero",
"to_real"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
of_int (m:mode) (x:int) : t | function | of_int | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"int",
"mode"
] | also note that this function never yields a subnormal, or a NaN, or -0 | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
to_int (m:mode) (x:t) : int | function | to_int | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"int",
"mode"
] | to_int +INF > 0 // nope | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
zero_of_int : forall m. zeroF = of_int m 0 | axiom | zero_of_int | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"of_int",
"zeroF"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
max_real : real | constant | max_real | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
max_int : int | constant | max_int | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"int"
] | defined when cloning | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
emax : int | = pow2 (eb - 1) | constant | emax | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"eb",
"int",
"pow2"
] | defined when cloning | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 |
max_int_spec : max_int = pow2 emax - pow2 (emax - sb) | axiom | max_int_spec | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"emax",
"max_int",
"pow2",
"sb"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
max_real_int: max_real = FromInt.from_int max_int | axiom | max_real_int | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"from_int",
"max_int",
"max_real"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
in_range (x:real) | = -. max_real <=. x <=. max_real | predicate | in_range | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"max_real"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
in_int_range (i:int) | = - max_int <= i <= max_int | predicate | in_int_range | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"int",
"max_int"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
is_finite: forall x:t. is_finite x -> in_range (to_real x) | axiom | is_finite | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"in_range",
"to_real"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
no_overflow (m:mode) (x:real) | = in_range (round m x) | predicate | no_overflow | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"in_range",
"mode",
"round"
] | used as a condition to propagate is_finite | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 |
Bounded_real_no_overflow [@W:non_conservative_extension:N] :
forall m:mode, x:real. in_range x -> no_overflow m x | axiom | Bounded_real_no_overflow | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"in_range",
"mode",
"no_overflow"
] | Axioms on round | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
Round_monotonic :
forall m:mode, x y:real. x <=. y -> round m x <=. round m y | axiom | Round_monotonic | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"mode",
"round"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
Round_to_real :
forall m:mode, x:t. is_finite x -> round m (to_real x) = to_real x | axiom | Round_to_real | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"is_finite",
"mode",
"round",
"to_real"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
Round_down_le:
forall x:real. round RTN x <=. x | axiom | Round_down_le | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"round"
] | rounding up and down | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
Round_up_ge:
forall x:real. round RTP x >=. x | axiom | Round_up_ge | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"round"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
Round_down_neg:
forall x:real. round RTN (-.x) = -. round RTP x | axiom | Round_down_neg | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"round"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
Round_up_neg:
forall x:real. round RTP (-.x) = -. round RTN x | axiom | Round_up_neg | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"round"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
pow2sb : int | constant | pow2sb | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"int"
] | The biggest representable integer whose predecessor (i.e. -1) is representable | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
pow2sb: pow2sb = pow2 sb | axiom | pow2sb | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"pow2",
"sb"
] | defined when cloning | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
in_safe_int_range (i: int) | = - pow2sb <= i <= pow2sb | predicate | in_safe_int_range | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"int",
"pow2sb"
] | range in which every integer is representable | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 |
Exact_rounding_for_integers:
forall m:mode, i:int.
in_safe_int_range i ->
round m (FromInt.from_int i) = FromInt.from_int i | axiom | Exact_rounding_for_integers | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"from_int",
"in_safe_int_range",
"int",
"mode",
"round"
] | {4 round and integers} | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
from_real mode real : t | function | from_real | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"mode"
] | {4 conversion from real to float} | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
from_real_in_range :
forall m:mode, r : real. in_range (round m r) ->
let f = from_real m r in is_finite f /\ to_real f = round m r | axiom | from_real_in_range | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"from_real",
"in_range",
"is_finite",
"mode",
"round",
"to_real"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
from_real_large_neg :
forall m:mode, r : real. round m r <. -. max_real ->
let f = from_real m r in is_infinite f /\ is_negative f | axiom | from_real_large_neg | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"from_real",
"is_infinite",
"is_negative",
"max_real",
"mode",
"round"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
from_real_large_pos :
forall m:mode, r : real. round m r >. max_real ->
let f = from_real m r in is_infinite f /\ is_positive f | axiom | from_real_large_pos | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"from_real",
"is_infinite",
"is_positive",
"max_real",
"mode",
"round"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
same_sign (x y : t) | =
(is_positive x /\ is_positive y) \/ (is_negative x /\ is_negative y) | predicate | same_sign | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"is_negative",
"is_positive"
] | Comparison predicates | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 |
diff_sign (x y : t) | =
(is_positive x /\ is_negative y) \/ (is_negative x /\ is_positive y) | predicate | diff_sign | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"is_negative",
"is_positive"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | |
feq_eq: forall x y.
is_finite x -> is_finite y -> not (is_zero x) -> x .= y -> x = y | axiom | feq_eq | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"is_finite",
"is_zero"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
eq_feq: forall x y.
is_finite x -> is_finite y -> x = y -> x .= y | axiom | eq_feq | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"is_finite"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
eq_refl: forall x. is_finite x -> x .= x | axiom | eq_refl | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"is_finite"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
eq_sym :
forall x y. x .= y -> y .= x | axiom | eq_sym | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
eq_trans :
forall x y z. x .= y -> y .= z -> x .= z | axiom | eq_trans | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
eq_zero: zeroF .= (.- zeroF) | axiom | eq_zero | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"zeroF"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
eq_to_real_finite: forall x y.
is_finite x /\ is_finite y -> (x .= y <-> to_real x = to_real y) | axiom | eq_to_real_finite | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"is_finite",
"to_real"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
eq_special: forall x y. x .= y ->
(is_not_nan x /\ is_not_nan y
/\ ((is_finite x /\ is_finite y)
\/ (is_infinite x /\ is_infinite y /\ same_sign x y))) | axiom | eq_special | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"is_finite",
"is_infinite",
"is_not_nan",
"same_sign"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 | ||
lt_finite: forall x y [lt x y].
is_finite x /\ is_finite y -> (lt x y <-> to_real x <. to_real y) | axiom | lt_finite | stdlib | stdlib/ieee_float.mlw | [
"Float32",
"Float64",
"Float_BV_Converter",
"GenericFloat",
"RoundingMode",
"bv.BV16",
"bv.BV32",
"bv.BV64",
"bv.BV8",
"bv.Pow2int",
"int.Int",
"real.Abs",
"real.FromInt",
"real.Real",
"real.RealInfix",
"real.Square",
"real.Truncate"
] | [
"is_finite",
"lt",
"to_real"
] | https://gitlab.inria.fr/why3/why3 | 7c59064b4eed9a4059292599f3a657716aa34784 |
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