Proof Assistant Projects
Collection
Digesting proof assistant libraries for AI ingestion. • 103 items • Updated • 3
statement stringlengths 8 1.65k | proof stringlengths 0 4.38k | type stringclasses 4
values | symbolic_name stringlengths 1 29 | library stringclasses 35
values | filename stringclasses 126
values | imports listlengths 0 20 | deps listlengths 0 29 | docstring stringclasses 1
value | source_url stringclasses 1
value | commit stringclasses 1
value |
|---|---|---|---|---|---|---|---|---|---|---|
LessFloat (x y : Float) : Set where
less-float : primFloatLess x y ≡ true → LessFloat x y | data | LessFloat | Builtin | src/Builtin/Float.agda | [
"Prelude",
"Prelude.Equality.Unsafe",
"Agda.Builtin.Float"
] | [
"true"
] | https://github.com/UlfNorell/agda-prelude | 4230566d3ae229b6a00258587651ac7bfd38d088 | ||
natToFloat : Nat → Float | natToFloat = primNatToFloat | function | natToFloat | Builtin | src/Builtin/Float.agda | [
"Prelude",
"Prelude.Equality.Unsafe",
"Agda.Builtin.Float"
] | [] | https://github.com/UlfNorell/agda-prelude | 4230566d3ae229b6a00258587651ac7bfd38d088 | |
intToFloat : Int → Float | intToFloat (pos x) = natToFloat x
intToFloat (negsuc x) = primFloatMinus -1.0 (natToFloat x) | function | intToFloat | Builtin | src/Builtin/Float.agda | [
"Prelude",
"Prelude.Equality.Unsafe",
"Agda.Builtin.Float"
] | [
"natToFloat",
"negsuc",
"pos"
] | https://github.com/UlfNorell/agda-prelude | 4230566d3ae229b6a00258587651ac7bfd38d088 | |
EqFloat : Eq Float | function | EqFloat | Builtin | src/Builtin/Float.agda | [
"Prelude",
"Prelude.Equality.Unsafe",
"Agda.Builtin.Float"
] | [
"Eq"
] | https://github.com/UlfNorell/agda-prelude | 4230566d3ae229b6a00258587651ac7bfd38d088 | ||
OrdFloat : Ord Float | OrdFloat = defaultOrd cmpFloat
where
cmpFloat : ∀ x y → Comparison LessFloat x y
cmpFloat x y with inspect (primFloatLess x y)
... | true with≡ eq = less (less-float eq)
... | false with≡ _ with inspect (primFloatLess y x)
... | true with≡ eq = greater (less-float eq)
... |... | function | OrdFloat | Builtin | src/Builtin/Float.agda | [
"Prelude",
"Prelude.Equality.Unsafe",
"Agda.Builtin.Float"
] | [
"...",
"Comparison",
"LessFloat",
"Ord",
"defaultOrd",
"eq",
"false",
"true",
"unsafeEqual"
] | https://github.com/UlfNorell/agda-prelude | 4230566d3ae229b6a00258587651ac7bfd38d088 | |
OrdLawsFloat : Ord/Laws Float | function | OrdLawsFloat | Builtin | src/Builtin/Float.agda | [
"Prelude",
"Prelude.Equality.Unsafe",
"Agda.Builtin.Float"
] | [
"Ord/Laws"
] | https://github.com/UlfNorell/agda-prelude | 4230566d3ae229b6a00258587651ac7bfd38d088 | ||
ShowFloat : Show Float | ShowFloat = simpleShowInstance primShowFloat | function | ShowFloat | Builtin | src/Builtin/Float.agda | [
"Prelude",
"Prelude.Equality.Unsafe",
"Agda.Builtin.Float"
] | [
"Show",
"simpleShowInstance"
] | https://github.com/UlfNorell/agda-prelude | 4230566d3ae229b6a00258587651ac7bfd38d088 | |
NumFloat : Number Float | function | NumFloat | Builtin | src/Builtin/Float.agda | [
"Prelude",
"Prelude.Equality.Unsafe",
"Agda.Builtin.Float"
] | [] | https://github.com/UlfNorell/agda-prelude | 4230566d3ae229b6a00258587651ac7bfd38d088 | ||
SemiringFloat : Semiring Float | function | SemiringFloat | Builtin | src/Builtin/Float.agda | [
"Prelude",
"Prelude.Equality.Unsafe",
"Agda.Builtin.Float"
] | [
"Semiring"
] | https://github.com/UlfNorell/agda-prelude | 4230566d3ae229b6a00258587651ac7bfd38d088 | ||
SubFloat : Subtractive Float | function | SubFloat | Builtin | src/Builtin/Float.agda | [
"Prelude",
"Prelude.Equality.Unsafe",
"Agda.Builtin.Float"
] | [
"Subtractive"
] | https://github.com/UlfNorell/agda-prelude | 4230566d3ae229b6a00258587651ac7bfd38d088 | ||
NegFloat : Negative Float | function | NegFloat | Builtin | src/Builtin/Float.agda | [
"Prelude",
"Prelude.Equality.Unsafe",
"Agda.Builtin.Float"
] | [] | https://github.com/UlfNorell/agda-prelude | 4230566d3ae229b6a00258587651ac7bfd38d088 | ||
FracFloat : Fractional Float | function | FracFloat | Builtin | src/Builtin/Float.agda | [
"Prelude",
"Prelude.Equality.Unsafe",
"Agda.Builtin.Float"
] | [
"Fractional"
] | https://github.com/UlfNorell/agda-prelude | 4230566d3ae229b6a00258587651ac7bfd38d088 | ||
isFinite : Float → Bool | isFinite x = not (isNaN x || isInfinite x)
-- Non-maybe rounding, that returns 0 for ±Inf and NaN | function | isFinite | Builtin | src/Builtin/Float.agda | [
"Prelude",
"Prelude.Equality.Unsafe",
"Agda.Builtin.Float"
] | [
"isInfinite",
"isNaN",
"not"
] | https://github.com/UlfNorell/agda-prelude | 4230566d3ae229b6a00258587651ac7bfd38d088 | |
round! : Float → Int | round! = fromMaybe 0 ∘ round | function | round! | Builtin | src/Builtin/Float.agda | [
"Prelude",
"Prelude.Equality.Unsafe",
"Agda.Builtin.Float"
] | [
"fromMaybe",
"round"
] | https://github.com/UlfNorell/agda-prelude | 4230566d3ae229b6a00258587651ac7bfd38d088 | |
floor! : Float → Int | floor! = fromMaybe 0 ∘ floor | function | floor! | Builtin | src/Builtin/Float.agda | [
"Prelude",
"Prelude.Equality.Unsafe",
"Agda.Builtin.Float"
] | [
"floor",
"fromMaybe"
] | https://github.com/UlfNorell/agda-prelude | 4230566d3ae229b6a00258587651ac7bfd38d088 | |
ceiling! : Float → Int | ceiling! = fromMaybe 0 ∘ ceiling | function | ceiling! | Builtin | src/Builtin/Float.agda | [
"Prelude",
"Prelude.Equality.Unsafe",
"Agda.Builtin.Float"
] | [
"ceiling",
"fromMaybe"
] | https://github.com/UlfNorell/agda-prelude | 4230566d3ae229b6a00258587651ac7bfd38d088 | |
π : Float | π = 3.141592653589793 | function | π | Builtin | src/Builtin/Float.agda | [
"Prelude",
"Prelude.Equality.Unsafe",
"Agda.Builtin.Float"
] | [] | https://github.com/UlfNorell/agda-prelude | 4230566d3ae229b6a00258587651ac7bfd38d088 | |
cos : Float → Float | cos x = sin (π / 2.0 - x) | function | cos | Builtin | src/Builtin/Float.agda | [
"Prelude",
"Prelude.Equality.Unsafe",
"Agda.Builtin.Float"
] | [
"sin"
] | https://github.com/UlfNorell/agda-prelude | 4230566d3ae229b6a00258587651ac7bfd38d088 | |
tan : Float → Float | tan x = sin x / cos x | function | tan | Builtin | src/Builtin/Float.agda | [
"Prelude",
"Prelude.Equality.Unsafe",
"Agda.Builtin.Float"
] | [
"cos",
"sin"
] | https://github.com/UlfNorell/agda-prelude | 4230566d3ae229b6a00258587651ac7bfd38d088 | |
log : Float → Float → Float | log base x = ln x / ln base | function | log | Builtin | src/Builtin/Float.agda | [
"Prelude",
"Prelude.Equality.Unsafe",
"Agda.Builtin.Float"
] | [
"ln"
] | https://github.com/UlfNorell/agda-prelude | 4230566d3ae229b6a00258587651ac7bfd38d088 | |
_**_ : Float → Float → Float | function | _**_ | Builtin | src/Builtin/Float.agda | [
"Prelude",
"Prelude.Equality.Unsafe",
"Agda.Builtin.Float"
] | [] | https://github.com/UlfNorell/agda-prelude | 4230566d3ae229b6a00258587651ac7bfd38d088 | ||
NaN : Float | NaN = 0.0 / 0.0 | function | NaN | Builtin | src/Builtin/Float.agda | [
"Prelude",
"Prelude.Equality.Unsafe",
"Agda.Builtin.Float"
] | [] | https://github.com/UlfNorell/agda-prelude | 4230566d3ae229b6a00258587651ac7bfd38d088 | |
Inf : Float | Inf = 1.0 / 0.0 | function | Inf | Builtin | src/Builtin/Float.agda | [
"Prelude",
"Prelude.Equality.Unsafe",
"Agda.Builtin.Float"
] | [] | https://github.com/UlfNorell/agda-prelude | 4230566d3ae229b6a00258587651ac7bfd38d088 | |
-Inf : Float | -Inf = -1.0 / 0.0 | function | -Inf | Builtin | src/Builtin/Float.agda | [
"Prelude",
"Prelude.Equality.Unsafe",
"Agda.Builtin.Float"
] | [] | https://github.com/UlfNorell/agda-prelude | 4230566d3ae229b6a00258587651ac7bfd38d088 | |
... | true = yes unsafeEqual | ... | false = no unsafeNotEqual | function | ... | Builtin | src/Builtin/Float.agda | [
"Prelude",
"Prelude.Equality.Unsafe",
"Agda.Builtin.Float"
] | [
"false",
"true",
"unsafeEqual",
"unsafeNotEqual"
] | https://github.com/UlfNorell/agda-prelude | 4230566d3ae229b6a00258587651ac7bfd38d088 | |
Ord/Laws.super OrdLawsFloat = it | function | Ord/Laws.super | Builtin | src/Builtin/Float.agda | [
"Prelude",
"Prelude.Equality.Unsafe",
"Agda.Builtin.Float"
] | [
"OrdLawsFloat",
"it"
] | https://github.com/UlfNorell/agda-prelude | 4230566d3ae229b6a00258587651ac7bfd38d088 | ||
less-antirefl {{OrdLawsFloat}} (less-float eq) = unsafeNotEqual eq | function | less-antirefl | Builtin | src/Builtin/Float.agda | [
"Prelude",
"Prelude.Equality.Unsafe",
"Agda.Builtin.Float"
] | [
"OrdLawsFloat",
"eq",
"unsafeNotEqual"
] | https://github.com/UlfNorell/agda-prelude | 4230566d3ae229b6a00258587651ac7bfd38d088 | ||
less-trans {{OrdLawsFloat}} (less-float _) (less-float _) = less-float unsafeEqual | function | less-trans | Builtin | src/Builtin/Float.agda | [
"Prelude",
"Prelude.Equality.Unsafe",
"Agda.Builtin.Float"
] | [
"OrdLawsFloat",
"unsafeEqual"
] | https://github.com/UlfNorell/agda-prelude | 4230566d3ae229b6a00258587651ac7bfd38d088 | ||
Number.Constraint NumFloat _ = ⊤ | function | Number.Constraint | Builtin | src/Builtin/Float.agda | [
"Prelude",
"Prelude.Equality.Unsafe",
"Agda.Builtin.Float"
] | [
"NumFloat"
] | https://github.com/UlfNorell/agda-prelude | 4230566d3ae229b6a00258587651ac7bfd38d088 | ||
Number.fromNat NumFloat x = primNatToFloat x | function | Number.fromNat | Builtin | src/Builtin/Float.agda | [
"Prelude",
"Prelude.Equality.Unsafe",
"Agda.Builtin.Float"
] | [
"NumFloat"
] | https://github.com/UlfNorell/agda-prelude | 4230566d3ae229b6a00258587651ac7bfd38d088 | ||
Semiring.zro SemiringFloat = 0.0 | function | Semiring.zro | Builtin | src/Builtin/Float.agda | [
"Prelude",
"Prelude.Equality.Unsafe",
"Agda.Builtin.Float"
] | [
"SemiringFloat"
] | https://github.com/UlfNorell/agda-prelude | 4230566d3ae229b6a00258587651ac7bfd38d088 | ||
Semiring.one SemiringFloat = 1.0 | function | Semiring.one | Builtin | src/Builtin/Float.agda | [
"Prelude",
"Prelude.Equality.Unsafe",
"Agda.Builtin.Float"
] | [
"SemiringFloat"
] | https://github.com/UlfNorell/agda-prelude | 4230566d3ae229b6a00258587651ac7bfd38d088 | ||
Semiring._+_ SemiringFloat = primFloatPlus | function | Semiring._+_ | Builtin | src/Builtin/Float.agda | [
"Prelude",
"Prelude.Equality.Unsafe",
"Agda.Builtin.Float"
] | [
"SemiringFloat"
] | https://github.com/UlfNorell/agda-prelude | 4230566d3ae229b6a00258587651ac7bfd38d088 | ||
Semiring._*_ SemiringFloat = primFloatTimes | function | Semiring._*_ | Builtin | src/Builtin/Float.agda | [
"Prelude",
"Prelude.Equality.Unsafe",
"Agda.Builtin.Float"
] | [
"SemiringFloat"
] | https://github.com/UlfNorell/agda-prelude | 4230566d3ae229b6a00258587651ac7bfd38d088 | ||
Subtractive._-_ SubFloat = primFloatMinus | function | Subtractive._-_ | Builtin | src/Builtin/Float.agda | [
"Prelude",
"Prelude.Equality.Unsafe",
"Agda.Builtin.Float"
] | [
"SubFloat"
] | https://github.com/UlfNorell/agda-prelude | 4230566d3ae229b6a00258587651ac7bfd38d088 | ||
Subtractive.negate SubFloat = primFloatNegate | function | Subtractive.negate | Builtin | src/Builtin/Float.agda | [
"Prelude",
"Prelude.Equality.Unsafe",
"Agda.Builtin.Float"
] | [
"SubFloat"
] | https://github.com/UlfNorell/agda-prelude | 4230566d3ae229b6a00258587651ac7bfd38d088 | ||
Negative.Constraint NegFloat _ = ⊤ | function | Negative.Constraint | Builtin | src/Builtin/Float.agda | [
"Prelude",
"Prelude.Equality.Unsafe",
"Agda.Builtin.Float"
] | [
"NegFloat"
] | https://github.com/UlfNorell/agda-prelude | 4230566d3ae229b6a00258587651ac7bfd38d088 | ||
Negative.fromNeg NegFloat x = negate (primNatToFloat x) | function | Negative.fromNeg | Builtin | src/Builtin/Float.agda | [
"Prelude",
"Prelude.Equality.Unsafe",
"Agda.Builtin.Float"
] | [
"NegFloat",
"negate"
] | https://github.com/UlfNorell/agda-prelude | 4230566d3ae229b6a00258587651ac7bfd38d088 | ||
Fractional.Constraint FracFloat _ _ = ⊤ | function | Fractional.Constraint | Builtin | src/Builtin/Float.agda | [
"Prelude",
"Prelude.Equality.Unsafe",
"Agda.Builtin.Float"
] | [
"FracFloat"
] | https://github.com/UlfNorell/agda-prelude | 4230566d3ae229b6a00258587651ac7bfd38d088 | ||
Fractional._/_ FracFloat x y = primFloatDiv x y | function | Fractional._/_ | Builtin | src/Builtin/Float.agda | [
"Prelude",
"Prelude.Equality.Unsafe",
"Agda.Builtin.Float"
] | [
"FracFloat"
] | https://github.com/UlfNorell/agda-prelude | 4230566d3ae229b6a00258587651ac7bfd38d088 | ||
floor = primFloatFloor | function | floor | Builtin | src/Builtin/Float.agda | [
"Prelude",
"Prelude.Equality.Unsafe",
"Agda.Builtin.Float"
] | [] | https://github.com/UlfNorell/agda-prelude | 4230566d3ae229b6a00258587651ac7bfd38d088 | ||
round = primFloatRound | function | round | Builtin | src/Builtin/Float.agda | [
"Prelude",
"Prelude.Equality.Unsafe",
"Agda.Builtin.Float"
] | [] | https://github.com/UlfNorell/agda-prelude | 4230566d3ae229b6a00258587651ac7bfd38d088 | ||
ceiling = primFloatCeiling | function | ceiling | Builtin | src/Builtin/Float.agda | [
"Prelude",
"Prelude.Equality.Unsafe",
"Agda.Builtin.Float"
] | [] | https://github.com/UlfNorell/agda-prelude | 4230566d3ae229b6a00258587651ac7bfd38d088 | ||
exp = primFloatExp | function | exp | Builtin | src/Builtin/Float.agda | [
"Prelude",
"Prelude.Equality.Unsafe",
"Agda.Builtin.Float"
] | [] | https://github.com/UlfNorell/agda-prelude | 4230566d3ae229b6a00258587651ac7bfd38d088 | ||
ln = primFloatLog | function | ln | Builtin | src/Builtin/Float.agda | [
"Prelude",
"Prelude.Equality.Unsafe",
"Agda.Builtin.Float"
] | [] | https://github.com/UlfNorell/agda-prelude | 4230566d3ae229b6a00258587651ac7bfd38d088 | ||
sin = primFloatSin | function | sin | Builtin | src/Builtin/Float.agda | [
"Prelude",
"Prelude.Equality.Unsafe",
"Agda.Builtin.Float"
] | [] | https://github.com/UlfNorell/agda-prelude | 4230566d3ae229b6a00258587651ac7bfd38d088 | ||
sqrt = primFloatSqrt | function | sqrt | Builtin | src/Builtin/Float.agda | [
"Prelude",
"Prelude.Equality.Unsafe",
"Agda.Builtin.Float"
] | [] | https://github.com/UlfNorell/agda-prelude | 4230566d3ae229b6a00258587651ac7bfd38d088 | ||
isNaN = primFloatIsNaN | function | isNaN | Builtin | src/Builtin/Float.agda | [
"Prelude",
"Prelude.Equality.Unsafe",
"Agda.Builtin.Float"
] | [] | https://github.com/UlfNorell/agda-prelude | 4230566d3ae229b6a00258587651ac7bfd38d088 | ||
isInfinite = primFloatIsInfinite | function | isInfinite | Builtin | src/Builtin/Float.agda | [
"Prelude",
"Prelude.Equality.Unsafe",
"Agda.Builtin.Float"
] | [] | https://github.com/UlfNorell/agda-prelude | 4230566d3ae229b6a00258587651ac7bfd38d088 | ||
a ** x = exp (x * ln a) | function | a | Builtin | src/Builtin/Float.agda | [
"Prelude",
"Prelude.Equality.Unsafe",
"Agda.Builtin.Float"
] | [
"exp",
"ln"
] | https://github.com/UlfNorell/agda-prelude | 4230566d3ae229b6a00258587651ac7bfd38d088 | ||
LessName (x y : Name) : Set where
less-name : primQNameLess x y ≡ true → LessName x y | data | LessName | Builtin | src/Builtin/Reflection.agda | [
"Prelude",
"Prelude.Equality.Unsafe",
"Builtin.Float",
"Container.Traversable",
"Control.Monad.Zero",
"Prelude.Variables",
"Agda.Builtin.Reflection"
] | [
"true"
] | https://github.com/UlfNorell/agda-prelude | 4230566d3ae229b6a00258587651ac7bfd38d088 | ||
LessMeta (x y : Meta) : Set where
less-meta : primMetaLess x y ≡ true → LessMeta x y | data | LessMeta | Builtin | src/Builtin/Reflection.agda | [
"Prelude",
"Prelude.Equality.Unsafe",
"Builtin.Float",
"Container.Traversable",
"Control.Monad.Zero",
"Prelude.Variables",
"Agda.Builtin.Reflection"
] | [
"true"
] | https://github.com/UlfNorell/agda-prelude | 4230566d3ae229b6a00258587651ac7bfd38d088 | ||
ShowName : Show Name | function | ShowName | Builtin | src/Builtin/Reflection.agda | [
"Prelude",
"Prelude.Equality.Unsafe",
"Builtin.Float",
"Container.Traversable",
"Control.Monad.Zero",
"Prelude.Variables",
"Agda.Builtin.Reflection"
] | [
"Show"
] | https://github.com/UlfNorell/agda-prelude | 4230566d3ae229b6a00258587651ac7bfd38d088 | ||
EqName : Eq Name | function | EqName | Builtin | src/Builtin/Reflection.agda | [
"Prelude",
"Prelude.Equality.Unsafe",
"Builtin.Float",
"Container.Traversable",
"Control.Monad.Zero",
"Prelude.Variables",
"Agda.Builtin.Reflection"
] | [
"Eq"
] | https://github.com/UlfNorell/agda-prelude | 4230566d3ae229b6a00258587651ac7bfd38d088 | ||
cmpName : ∀ x y → Comparison LessName x y | function | cmpName | Builtin | src/Builtin/Reflection.agda | [
"Prelude",
"Prelude.Equality.Unsafe",
"Builtin.Float",
"Container.Traversable",
"Control.Monad.Zero",
"Prelude.Variables",
"Agda.Builtin.Reflection"
] | [
"Comparison",
"LessName"
] | https://github.com/UlfNorell/agda-prelude | 4230566d3ae229b6a00258587651ac7bfd38d088 | ||
ShowMeta : Show Meta | function | ShowMeta | Builtin | src/Builtin/Reflection.agda | [
"Prelude",
"Prelude.Equality.Unsafe",
"Builtin.Float",
"Container.Traversable",
"Control.Monad.Zero",
"Prelude.Variables",
"Agda.Builtin.Reflection"
] | [
"Show"
] | https://github.com/UlfNorell/agda-prelude | 4230566d3ae229b6a00258587651ac7bfd38d088 | ||
EqMeta : Eq Meta | function | EqMeta | Builtin | src/Builtin/Reflection.agda | [
"Prelude",
"Prelude.Equality.Unsafe",
"Builtin.Float",
"Container.Traversable",
"Control.Monad.Zero",
"Prelude.Variables",
"Agda.Builtin.Reflection"
] | [
"Eq"
] | https://github.com/UlfNorell/agda-prelude | 4230566d3ae229b6a00258587651ac7bfd38d088 | ||
cmpMeta : ∀ x y → Comparison LessMeta x y | function | cmpMeta | Builtin | src/Builtin/Reflection.agda | [
"Prelude",
"Prelude.Equality.Unsafe",
"Builtin.Float",
"Container.Traversable",
"Control.Monad.Zero",
"Prelude.Variables",
"Agda.Builtin.Reflection"
] | [
"Comparison",
"LessMeta"
] | https://github.com/UlfNorell/agda-prelude | 4230566d3ae229b6a00258587651ac7bfd38d088 | ||
unArg : Arg A → A | unArg (arg _ x) = x | function | unArg | Builtin | src/Builtin/Reflection.agda | [
"Prelude",
"Prelude.Equality.Unsafe",
"Builtin.Float",
"Container.Traversable",
"Control.Monad.Zero",
"Prelude.Variables",
"Agda.Builtin.Reflection"
] | [] | https://github.com/UlfNorell/agda-prelude | 4230566d3ae229b6a00258587651ac7bfd38d088 | |
getArgInfo : Arg A → ArgInfo | getArgInfo (arg i _) = i | function | getArgInfo | Builtin | src/Builtin/Reflection.agda | [
"Prelude",
"Prelude.Equality.Unsafe",
"Builtin.Float",
"Container.Traversable",
"Control.Monad.Zero",
"Prelude.Variables",
"Agda.Builtin.Reflection"
] | [] | https://github.com/UlfNorell/agda-prelude | 4230566d3ae229b6a00258587651ac7bfd38d088 | |
getVisibility : Arg A → Visibility | getVisibility (arg (arg-info v _) _) = v | function | getVisibility | Builtin | src/Builtin/Reflection.agda | [
"Prelude",
"Prelude.Equality.Unsafe",
"Builtin.Float",
"Container.Traversable",
"Control.Monad.Zero",
"Prelude.Variables",
"Agda.Builtin.Reflection"
] | [] | https://github.com/UlfNorell/agda-prelude | 4230566d3ae229b6a00258587651ac7bfd38d088 | |
getModality : Arg A → Modality | getModality (arg (arg-info _ m) _) = m | function | getModality | Builtin | src/Builtin/Reflection.agda | [
"Prelude",
"Prelude.Equality.Unsafe",
"Builtin.Float",
"Container.Traversable",
"Control.Monad.Zero",
"Prelude.Variables",
"Agda.Builtin.Reflection"
] | [] | https://github.com/UlfNorell/agda-prelude | 4230566d3ae229b6a00258587651ac7bfd38d088 | |
getRelevance : Arg A → Relevance | getRelevance (arg (arg-info _ (modality r _)) _) = r | function | getRelevance | Builtin | src/Builtin/Reflection.agda | [
"Prelude",
"Prelude.Equality.Unsafe",
"Builtin.Float",
"Container.Traversable",
"Control.Monad.Zero",
"Prelude.Variables",
"Agda.Builtin.Reflection"
] | [] | https://github.com/UlfNorell/agda-prelude | 4230566d3ae229b6a00258587651ac7bfd38d088 | |
getQuantity : Arg A → Quantity | getQuantity (arg (arg-info _ (modality _ q)) _) = q | function | getQuantity | Builtin | src/Builtin/Reflection.agda | [
"Prelude",
"Prelude.Equality.Unsafe",
"Builtin.Float",
"Container.Traversable",
"Control.Monad.Zero",
"Prelude.Variables",
"Agda.Builtin.Reflection"
] | [] | https://github.com/UlfNorell/agda-prelude | 4230566d3ae229b6a00258587651ac7bfd38d088 | |
isVisible : Arg A → Bool | isVisible (arg (arg-info visible _) _) = true
isVisible _ = false | function | isVisible | Builtin | src/Builtin/Reflection.agda | [
"Prelude",
"Prelude.Equality.Unsafe",
"Builtin.Float",
"Container.Traversable",
"Control.Monad.Zero",
"Prelude.Variables",
"Agda.Builtin.Reflection"
] | [
"false",
"true"
] | https://github.com/UlfNorell/agda-prelude | 4230566d3ae229b6a00258587651ac7bfd38d088 | |
FunctorArg : Functor {a = ℓ} Arg | function | FunctorArg | Builtin | src/Builtin/Reflection.agda | [
"Prelude",
"Prelude.Equality.Unsafe",
"Builtin.Float",
"Container.Traversable",
"Control.Monad.Zero",
"Prelude.Variables",
"Agda.Builtin.Reflection"
] | [
"Functor"
] | https://github.com/UlfNorell/agda-prelude | 4230566d3ae229b6a00258587651ac7bfd38d088 | ||
TraversableArg : Traversable {a = ℓ} Arg | function | TraversableArg | Builtin | src/Builtin/Reflection.agda | [
"Prelude",
"Prelude.Equality.Unsafe",
"Builtin.Float",
"Container.Traversable",
"Control.Monad.Zero",
"Prelude.Variables",
"Agda.Builtin.Reflection"
] | [
"Traversable"
] | https://github.com/UlfNorell/agda-prelude | 4230566d3ae229b6a00258587651ac7bfd38d088 | ||
unAbs : Abs A → A | unAbs (abs _ x) = x | function | unAbs | Builtin | src/Builtin/Reflection.agda | [
"Prelude",
"Prelude.Equality.Unsafe",
"Builtin.Float",
"Container.Traversable",
"Control.Monad.Zero",
"Prelude.Variables",
"Agda.Builtin.Reflection"
] | [
"abs"
] | https://github.com/UlfNorell/agda-prelude | 4230566d3ae229b6a00258587651ac7bfd38d088 | |
FunctorAbs : Functor {a = ℓ} Abs | function | FunctorAbs | Builtin | src/Builtin/Reflection.agda | [
"Prelude",
"Prelude.Equality.Unsafe",
"Builtin.Float",
"Container.Traversable",
"Control.Monad.Zero",
"Prelude.Variables",
"Agda.Builtin.Reflection"
] | [
"Functor"
] | https://github.com/UlfNorell/agda-prelude | 4230566d3ae229b6a00258587651ac7bfd38d088 | ||
TraversableAbs : Traversable {a = ℓ} Abs | function | TraversableAbs | Builtin | src/Builtin/Reflection.agda | [
"Prelude",
"Prelude.Equality.Unsafe",
"Builtin.Float",
"Container.Traversable",
"Control.Monad.Zero",
"Prelude.Variables",
"Agda.Builtin.Reflection"
] | [
"Traversable"
] | https://github.com/UlfNorell/agda-prelude | 4230566d3ae229b6a00258587651ac7bfd38d088 | ||
absurd-lam : Term | absurd-lam = pat-lam (absurd-clause (("()" , vArg unknown) ∷ []) (vArg (absurd 0) ∷ []) ∷ []) []
--- TC monad --- | function | absurd-lam | Builtin | src/Builtin/Reflection.agda | [
"Prelude",
"Prelude.Equality.Unsafe",
"Builtin.Float",
"Container.Traversable",
"Control.Monad.Zero",
"Prelude.Variables",
"Agda.Builtin.Reflection"
] | [
"[]"
] | https://github.com/UlfNorell/agda-prelude | 4230566d3ae229b6a00258587651ac7bfd38d088 | |
mapTC : (A → B) → TC A → TC B | mapTC f m = bindTC m λ x → returnTC (f x) | function | mapTC | Builtin | src/Builtin/Reflection.agda | [
"Prelude",
"Prelude.Equality.Unsafe",
"Builtin.Float",
"Container.Traversable",
"Control.Monad.Zero",
"Prelude.Variables",
"Agda.Builtin.Reflection"
] | [] | https://github.com/UlfNorell/agda-prelude | 4230566d3ae229b6a00258587651ac7bfd38d088 | |
FunctorTC : Functor {ℓ} TC | function | FunctorTC | Builtin | src/Builtin/Reflection.agda | [
"Prelude",
"Prelude.Equality.Unsafe",
"Builtin.Float",
"Container.Traversable",
"Control.Monad.Zero",
"Prelude.Variables",
"Agda.Builtin.Reflection"
] | [
"Functor"
] | https://github.com/UlfNorell/agda-prelude | 4230566d3ae229b6a00258587651ac7bfd38d088 | ||
ApplicativeTC : Applicative {ℓ} TC | function | ApplicativeTC | Builtin | src/Builtin/Reflection.agda | [
"Prelude",
"Prelude.Equality.Unsafe",
"Builtin.Float",
"Container.Traversable",
"Control.Monad.Zero",
"Prelude.Variables",
"Agda.Builtin.Reflection"
] | [
"Applicative"
] | https://github.com/UlfNorell/agda-prelude | 4230566d3ae229b6a00258587651ac7bfd38d088 | ||
MonadTC : Monad {ℓ} TC | function | MonadTC | Builtin | src/Builtin/Reflection.agda | [
"Prelude",
"Prelude.Equality.Unsafe",
"Builtin.Float",
"Container.Traversable",
"Control.Monad.Zero",
"Prelude.Variables",
"Agda.Builtin.Reflection"
] | [
"Monad"
] | https://github.com/UlfNorell/agda-prelude | 4230566d3ae229b6a00258587651ac7bfd38d088 | ||
FunctorTC′ : Functor′ {ℓ₁} {ℓ₂} TC | function | FunctorTC′ | Builtin | src/Builtin/Reflection.agda | [
"Prelude",
"Prelude.Equality.Unsafe",
"Builtin.Float",
"Container.Traversable",
"Control.Monad.Zero",
"Prelude.Variables",
"Agda.Builtin.Reflection"
] | [
"Functor′"
] | https://github.com/UlfNorell/agda-prelude | 4230566d3ae229b6a00258587651ac7bfd38d088 | ||
ApplicativeTC′ : Applicative′ {ℓ₁} {ℓ₂} TC | function | ApplicativeTC′ | Builtin | src/Builtin/Reflection.agda | [
"Prelude",
"Prelude.Equality.Unsafe",
"Builtin.Float",
"Container.Traversable",
"Control.Monad.Zero",
"Prelude.Variables",
"Agda.Builtin.Reflection"
] | [
"Applicative′"
] | https://github.com/UlfNorell/agda-prelude | 4230566d3ae229b6a00258587651ac7bfd38d088 | ||
MonadTC′ : Monad′ {ℓ₁} {ℓ₂} TC | function | MonadTC′ | Builtin | src/Builtin/Reflection.agda | [
"Prelude",
"Prelude.Equality.Unsafe",
"Builtin.Float",
"Container.Traversable",
"Control.Monad.Zero",
"Prelude.Variables",
"Agda.Builtin.Reflection"
] | [
"Monad′"
] | https://github.com/UlfNorell/agda-prelude | 4230566d3ae229b6a00258587651ac7bfd38d088 | ||
FunctorZeroTC : FunctorZero {ℓ} TC | function | FunctorZeroTC | Builtin | src/Builtin/Reflection.agda | [
"Prelude",
"Prelude.Equality.Unsafe",
"Builtin.Float",
"Container.Traversable",
"Control.Monad.Zero",
"Prelude.Variables",
"Agda.Builtin.Reflection"
] | [] | https://github.com/UlfNorell/agda-prelude | 4230566d3ae229b6a00258587651ac7bfd38d088 | ||
AlternativeTC : Alternative {ℓ} TC | function | AlternativeTC | Builtin | src/Builtin/Reflection.agda | [
"Prelude",
"Prelude.Equality.Unsafe",
"Builtin.Float",
"Container.Traversable",
"Control.Monad.Zero",
"Prelude.Variables",
"Agda.Builtin.Reflection"
] | [] | https://github.com/UlfNorell/agda-prelude | 4230566d3ae229b6a00258587651ac7bfd38d088 | ||
give : Term → Tactic | give v = λ hole → unify hole v | function | give | Builtin | src/Builtin/Reflection.agda | [
"Prelude",
"Prelude.Equality.Unsafe",
"Builtin.Float",
"Container.Traversable",
"Control.Monad.Zero",
"Prelude.Variables",
"Agda.Builtin.Reflection"
] | [
"Tactic",
"unify"
] | https://github.com/UlfNorell/agda-prelude | 4230566d3ae229b6a00258587651ac7bfd38d088 | |
define : Arg Name → Type → List Clause → TC ⊤ | define f a cs = declareDef f a >> defineFun (unArg f) cs | function | define | Builtin | src/Builtin/Reflection.agda | [
"Prelude",
"Prelude.Equality.Unsafe",
"Builtin.Float",
"Container.Traversable",
"Control.Monad.Zero",
"Prelude.Variables",
"Agda.Builtin.Reflection"
] | [
"unArg"
] | https://github.com/UlfNorell/agda-prelude | 4230566d3ae229b6a00258587651ac7bfd38d088 | |
newMeta : Type → TC Term | newMeta = checkType unknown | function | newMeta | Builtin | src/Builtin/Reflection.agda | [
"Prelude",
"Prelude.Equality.Unsafe",
"Builtin.Float",
"Container.Traversable",
"Control.Monad.Zero",
"Prelude.Variables",
"Agda.Builtin.Reflection"
] | [] | https://github.com/UlfNorell/agda-prelude | 4230566d3ae229b6a00258587651ac7bfd38d088 | |
newMeta! : TC Term | newMeta! = newMeta unknown | function | newMeta! | Builtin | src/Builtin/Reflection.agda | [
"Prelude",
"Prelude.Equality.Unsafe",
"Builtin.Float",
"Container.Traversable",
"Control.Monad.Zero",
"Prelude.Variables",
"Agda.Builtin.Reflection"
] | [
"newMeta"
] | https://github.com/UlfNorell/agda-prelude | 4230566d3ae229b6a00258587651ac7bfd38d088 | |
typeErrorS : ∀ {a} {A : Set a} → String → TC A | typeErrorS s = typeError (strErr s ∷ []) | function | typeErrorS | Builtin | src/Builtin/Reflection.agda | [
"Prelude",
"Prelude.Equality.Unsafe",
"Builtin.Float",
"Container.Traversable",
"Control.Monad.Zero",
"Prelude.Variables",
"Agda.Builtin.Reflection"
] | [
"[]"
] | https://github.com/UlfNorell/agda-prelude | 4230566d3ae229b6a00258587651ac7bfd38d088 | |
blockOnMeta! : ∀ {a} {A : Set a} → Meta → TC A | blockOnMeta! x = commitTC >>=′ λ _ → blockOnMeta x | function | blockOnMeta! | Builtin | src/Builtin/Reflection.agda | [
"Prelude",
"Prelude.Equality.Unsafe",
"Builtin.Float",
"Container.Traversable",
"Control.Monad.Zero",
"Prelude.Variables",
"Agda.Builtin.Reflection"
] | [] | https://github.com/UlfNorell/agda-prelude | 4230566d3ae229b6a00258587651ac7bfd38d088 | |
inferNormalisedType : Term → TC Type | inferNormalisedType t = withNormalisation true (inferType t)
--- Convenient wrappers ---
-- Zero for non-datatypes | function | inferNormalisedType | Builtin | src/Builtin/Reflection.agda | [
"Prelude",
"Prelude.Equality.Unsafe",
"Builtin.Float",
"Container.Traversable",
"Control.Monad.Zero",
"Prelude.Variables",
"Agda.Builtin.Reflection"
] | [
"true"
] | https://github.com/UlfNorell/agda-prelude | 4230566d3ae229b6a00258587651ac7bfd38d088 | |
getParameters : Name → TC Nat | getParameters d =
caseM getDefinition d of λ
{ (data-type n _) → pure n
; _ → pure 0 } | function | getParameters | Builtin | src/Builtin/Reflection.agda | [
"Prelude",
"Prelude.Equality.Unsafe",
"Builtin.Float",
"Container.Traversable",
"Control.Monad.Zero",
"Prelude.Variables",
"Agda.Builtin.Reflection"
] | [
"pure"
] | https://github.com/UlfNorell/agda-prelude | 4230566d3ae229b6a00258587651ac7bfd38d088 | |
getConstructors : Name → TC (List Name) | getConstructors d =
caseM getDefinition d of λ
{ (data-type _ cs) → pure cs
; (record-type c _) → pure (c ∷ [])
; _ → typeError (strErr "Cannot get constructors of non-data or record type" ∷ nameErr d ∷ [])
} | function | getConstructors | Builtin | src/Builtin/Reflection.agda | [
"Prelude",
"Prelude.Equality.Unsafe",
"Builtin.Float",
"Container.Traversable",
"Control.Monad.Zero",
"Prelude.Variables",
"Agda.Builtin.Reflection"
] | [
"[]",
"pure"
] | https://github.com/UlfNorell/agda-prelude | 4230566d3ae229b6a00258587651ac7bfd38d088 | |
getClauses : Name → TC (List Clause) | getClauses d =
caseM getDefinition d of λ
{ (function cs) → pure cs
; _ → typeError (strErr "Cannot get constructors of non-function type" ∷ nameErr d ∷ [])
}
-- Get the constructor of a record type (or single-constructor data type) | function | getClauses | Builtin | src/Builtin/Reflection.agda | [
"Prelude",
"Prelude.Equality.Unsafe",
"Builtin.Float",
"Container.Traversable",
"Control.Monad.Zero",
"Prelude.Variables",
"Agda.Builtin.Reflection"
] | [
"[]",
"pure"
] | https://github.com/UlfNorell/agda-prelude | 4230566d3ae229b6a00258587651ac7bfd38d088 | |
recordConstructor : Name → TC Name | recordConstructor r =
caseM getConstructors r of λ
{ (c ∷ []) → pure c
; _ → typeError $ strErr "Cannot get constructor of non-record type" ∷ nameErr r ∷ [] }
-- Injectivity of constructors | function | recordConstructor | Builtin | src/Builtin/Reflection.agda | [
"Prelude",
"Prelude.Equality.Unsafe",
"Builtin.Float",
"Container.Traversable",
"Control.Monad.Zero",
"Prelude.Variables",
"Agda.Builtin.Reflection"
] | [
"[]",
"getConstructors",
"pure"
] | https://github.com/UlfNorell/agda-prelude | 4230566d3ae229b6a00258587651ac7bfd38d088 | |
arg-inj₁ : ∀ {i i′} {x x′ : A} → arg i x ≡ arg i′ x′ → i ≡ i′ | arg-inj₁ refl = refl | function | arg-inj₁ | Builtin | src/Builtin/Reflection.agda | [
"Prelude",
"Prelude.Equality.Unsafe",
"Builtin.Float",
"Container.Traversable",
"Control.Monad.Zero",
"Prelude.Variables",
"Agda.Builtin.Reflection"
] | [
"refl"
] | https://github.com/UlfNorell/agda-prelude | 4230566d3ae229b6a00258587651ac7bfd38d088 | |
arg-inj₂ : ∀ {i i′} {x x′ : A} → arg i x ≡ arg i′ x′ → x ≡ x′ | arg-inj₂ refl = refl | function | arg-inj₂ | Builtin | src/Builtin/Reflection.agda | [
"Prelude",
"Prelude.Equality.Unsafe",
"Builtin.Float",
"Container.Traversable",
"Control.Monad.Zero",
"Prelude.Variables",
"Agda.Builtin.Reflection"
] | [
"refl"
] | https://github.com/UlfNorell/agda-prelude | 4230566d3ae229b6a00258587651ac7bfd38d088 | |
arg-info-inj₁ : ∀ {v v′ r r′} → arg-info v r ≡ arg-info v′ r′ → v ≡ v′ | arg-info-inj₁ refl = refl | function | arg-info-inj₁ | Builtin | src/Builtin/Reflection.agda | [
"Prelude",
"Prelude.Equality.Unsafe",
"Builtin.Float",
"Container.Traversable",
"Control.Monad.Zero",
"Prelude.Variables",
"Agda.Builtin.Reflection"
] | [
"refl"
] | https://github.com/UlfNorell/agda-prelude | 4230566d3ae229b6a00258587651ac7bfd38d088 | |
arg-info-inj₂ : ∀ {v v′ r r′} → arg-info v r ≡ arg-info v′ r′ → r ≡ r′ | arg-info-inj₂ refl = refl | function | arg-info-inj₂ | Builtin | src/Builtin/Reflection.agda | [
"Prelude",
"Prelude.Equality.Unsafe",
"Builtin.Float",
"Container.Traversable",
"Control.Monad.Zero",
"Prelude.Variables",
"Agda.Builtin.Reflection"
] | [
"refl"
] | https://github.com/UlfNorell/agda-prelude | 4230566d3ae229b6a00258587651ac7bfd38d088 | |
modality-inj₁ : ∀ {r r′ q q′} → modality r q ≡ modality r′ q′ → r ≡ r′ | modality-inj₁ refl = refl | function | modality-inj₁ | Builtin | src/Builtin/Reflection.agda | [
"Prelude",
"Prelude.Equality.Unsafe",
"Builtin.Float",
"Container.Traversable",
"Control.Monad.Zero",
"Prelude.Variables",
"Agda.Builtin.Reflection"
] | [
"refl"
] | https://github.com/UlfNorell/agda-prelude | 4230566d3ae229b6a00258587651ac7bfd38d088 | |
modality-inj₂ : ∀ {r r′ q q′} → modality r q ≡ modality r′ q′ → q ≡ q′ | modality-inj₂ refl = refl | function | modality-inj₂ | Builtin | src/Builtin/Reflection.agda | [
"Prelude",
"Prelude.Equality.Unsafe",
"Builtin.Float",
"Container.Traversable",
"Control.Monad.Zero",
"Prelude.Variables",
"Agda.Builtin.Reflection"
] | [
"refl"
] | https://github.com/UlfNorell/agda-prelude | 4230566d3ae229b6a00258587651ac7bfd38d088 | |
abs-inj₁ : ∀ {s s′} {x x′ : A} → abs s x ≡ abs s′ x′ → s ≡ s′ | abs-inj₁ refl = refl | function | abs-inj₁ | Builtin | src/Builtin/Reflection.agda | [
"Prelude",
"Prelude.Equality.Unsafe",
"Builtin.Float",
"Container.Traversable",
"Control.Monad.Zero",
"Prelude.Variables",
"Agda.Builtin.Reflection"
] | [
"abs",
"refl"
] | https://github.com/UlfNorell/agda-prelude | 4230566d3ae229b6a00258587651ac7bfd38d088 | |
abs-inj₂ : ∀ {s s′} {x x′ : A} → abs s x ≡ abs s′ x′ → x ≡ x′ | abs-inj₂ refl = refl
--- Terms --- | function | abs-inj₂ | Builtin | src/Builtin/Reflection.agda | [
"Prelude",
"Prelude.Equality.Unsafe",
"Builtin.Float",
"Container.Traversable",
"Control.Monad.Zero",
"Prelude.Variables",
"Agda.Builtin.Reflection"
] | [
"abs",
"refl"
] | https://github.com/UlfNorell/agda-prelude | 4230566d3ae229b6a00258587651ac7bfd38d088 | |
var-inj₁ : ∀ {x x′ args args′} → Term.var x args ≡ var x′ args′ → x ≡ x′ | var-inj₁ refl = refl | function | var-inj₁ | Builtin | src/Builtin/Reflection.agda | [
"Prelude",
"Prelude.Equality.Unsafe",
"Builtin.Float",
"Container.Traversable",
"Control.Monad.Zero",
"Prelude.Variables",
"Agda.Builtin.Reflection"
] | [
"refl"
] | https://github.com/UlfNorell/agda-prelude | 4230566d3ae229b6a00258587651ac7bfd38d088 |
End of preview. Expand in Data Studio
Agda-Prelude
Structured dataset from agda-prelude — Programming utilities by Ulf Norell.
Source
- Repository: https://github.com/UlfNorell/agda-prelude
- Commit:
4230566d3ae229b6a00258587651ac7bfd38d088 - Files: 139
- License: mit
Schema
| Column | Type | Description |
|---|---|---|
| statement | string | Declaration signature/claim with the leading keyword removed (verbatim slice); the full declaration minus its proof |
| proof | string | Verbatim proof/body, empty if the declaration has none |
| type | string | Declaration keyword |
| symbolic_name | string | Declaration identifier |
| library | string | Sub-library |
| filename | string | Repository-relative source path |
| imports | list[string] | File-level Require/Import modules |
| deps | list[string] | Intra-corpus identifiers referenced |
| docstring | string | Preceding documentation comment, empty if absent |
| source_url | string | Upstream repository |
| commit | string | Upstream commit extracted |
Statistics
- Entries: 1,654
- With proof: 1,086 (65.7%)
- With docstring: 0 (0.0%)
- Libraries: 35
By type
| Type | Count |
|---|---|
| function | 1,534 |
| data | 69 |
| record | 50 |
| postulate | 1 |
Example
intToFloat : Int → Float
intToFloat (pos x) = natToFloat x
intToFloat (negsuc x) = primFloatMinus -1.0 (natToFloat x)
- type: function | symbolic_name:
intToFloat| src/Builtin/Float.agda
Use
Each declaration is split into a statement (signature/claim) and a proof (body) that are disjoint
and together form the complete declaration, for proof modeling, autoformalization, retrieval, and
dependency analysis via deps.
Citation
@misc{agda_prelude_dataset,
title = {Agda-Prelude},
author = {Norton, Charles},
year = {2026},
note = {Extracted from https://github.com/UlfNorell/agda-prelude, commit 4230566d3ae2},
url = {https://huggingface.co/datasets/phanerozoic/Agda-Prelude}
}
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