Proof Assistant Projects
Collection
Digesting proof assistant libraries for AI ingestion.
•
84 items
•
Updated
•
2
fact
stringlengths 1
4.3k
| type
stringclasses 3
values | library
stringclasses 11
values | imports
listlengths 0
62
| filename
stringclasses 673
values | symbolic_name
stringlengths 1
34
| docstring
stringlengths 6
1.33k
⌀ |
|---|---|---|---|---|---|---|
insert : Ord a => a -> BTree a -> BTree a
|
function
|
samples
|
[] |
samples/BTree.idr
|
insert
| null |
toList : BTree a -> List a
|
function
|
samples
|
[] |
samples/BTree.idr
|
toList
| null |
toTree : Ord a => List a -> BTree a
|
function
|
samples
|
[] |
samples/BTree.idr
|
toTree
| null |
BTree a = Leaf
| Node (BTree a) a (BTree a)
export
insert : Ord a => a -> BTree a -> BTree a
|
data
|
samples
|
[] |
samples/BTree.idr
|
BTree
| null |
RigCount : Type
|
function
|
compiler
|
[
"Algebra.ZeroOneOmega",
"Algebra.Semiring",
"Algebra.Preorder"
] |
src/Algebra.idr
|
RigCount
| null |
showCount : RigCount -> String
|
function
|
compiler
|
[
"Algebra.ZeroOneOmega",
"Algebra.Semiring",
"Algebra.Preorder"
] |
src/Algebra.idr
|
showCount
| null |
insert : Ord a => a -> BTree a -> BTree a
|
function
|
benchmark
|
[] |
benchmark/benchmarks/treeInt/BTree.idr
|
insert
| null |
toList : BTree a -> List a
|
function
|
benchmark
|
[] |
benchmark/benchmarks/treeInt/BTree.idr
|
toList
| null |
toTree : Ord a => List a -> BTree a
|
function
|
benchmark
|
[] |
benchmark/benchmarks/treeInt/BTree.idr
|
toTree
| null |
BTree a = Leaf
| Node (BTree a) a (BTree a)
export
insert : Ord a => a -> BTree a -> BTree a
|
data
|
benchmark
|
[] |
benchmark/benchmarks/treeInt/BTree.idr
|
BTree
| null |
sleep : HasIO io => (sec : Int) -> io ()
|
function
|
base
|
[
"Data.So",
"Data.String",
"System.Escape",
"System.File"
] |
libs/base/System.idr
|
sleep
|
Sleep for the specified number of seconds or, if signals are supported, until an un-ignored signal arrives. The exact wall-clock time slept might slightly differ depending on how busy the system is and the resolution of the system's clock. @ sec the number of seconds to sleep for
|
usleep : HasIO io => (usec : Int) -> So (usec >= 0) => io ()
|
function
|
base
|
[
"Data.So",
"Data.String",
"System.Escape",
"System.File"
] |
libs/base/System.idr
|
usleep
|
Sleep for the specified number of microseconds or, if signals are supported, until an un-ignored signal arrives. The exact wall-clock time slept might slighly differ depending on how busy the system is and the resolution of the system's clock. @ usec the number of microseconds to sleep for
|
getArgs : HasIO io => io (List String)
|
function
|
base
|
[
"Data.So",
"Data.String",
"System.Escape",
"System.File"
] |
libs/base/System.idr
|
getArgs
|
Retrieve the arguments to the program call, if there were any.
|
enableRawMode : HasIO io => io (Either FileError ())
|
function
|
base
|
[
"Data.So",
"Data.String",
"System.Escape",
"System.File"
] |
libs/base/System.idr
|
enableRawMode
|
`enableRawMode` enables raw mode for stdin, allowing characters to be read one at a time, without buffering or echoing. If `enableRawMode` is used, the program should call `resetRawMode` before exiting. Consider using `withRawMode` instead to ensure the tty is reset. This is not supported on windows.
|
resetRawMode : HasIO io => io ()
|
function
|
base
|
[
"Data.So",
"Data.String",
"System.Escape",
"System.File"
] |
libs/base/System.idr
|
resetRawMode
|
`resetRawMode` resets stdin raw mode to original state if `enableRawMode` had been previously called.
|
withRawMode : HasIO io => (onError : FileError -> io a) -> (onSuccess : () -> io a) -> io a
|
function
|
base
|
[
"Data.So",
"Data.String",
"System.Escape",
"System.File"
] |
libs/base/System.idr
|
withRawMode
|
`withRawMode` performs a given operation after setting stdin to raw mode and ensure that stdin is reset to its original state afterwards. This is not supported on windows.
|
getEnv : HasIO io => (var : String) -> io (Maybe String)
|
function
|
base
|
[
"Data.So",
"Data.String",
"System.Escape",
"System.File"
] |
libs/base/System.idr
|
getEnv
|
Retrieve the specified environment variable's value string, or `Nothing` if there is no such environment variable. @ var the name of the environment variable to look up
|
setEnv : HasIO io => (var : String) -> (val : String) -> (overwrite : Bool) -> io Bool
|
function
|
base
|
[
"Data.So",
"Data.String",
"System.Escape",
"System.File"
] |
libs/base/System.idr
|
setEnv
|
Add the specified variable with the given value string to the environment, optionally overwriting any existing environment variable with the same name. Returns True whether the value is set, overwritten, or not overwritten because overwrite was False. Returns False if a system error occurred. You can `getErrno` to check the error. @ var the name of the environment variable to set @ val the value string to set the environment variable to @ overwrite whether to overwrite the existing value if an environment variable with the specified name already exists
|
unsetEnv : HasIO io => (var : String) -> io Bool
|
function
|
base
|
[
"Data.So",
"Data.String",
"System.Escape",
"System.File"
] |
libs/base/System.idr
|
unsetEnv
|
Delete the specified environment variable. Returns `True` either if the value was deleted or if the value was not defined/didn't exist. Returns `False` if a system error occurred. You can `getErrno` to check the error.
|
system : HasIO io => String -> io Int
|
function
|
base
|
[
"Data.So",
"Data.String",
"System.Escape",
"System.File"
] |
libs/base/System.idr
|
system
|
Execute a shell command, returning its termination status or -1 if an error occurred.
|
system : HasIO io => List String -> io Int system
|
function
|
base
|
[
"Data.So",
"Data.String",
"System.Escape",
"System.File"
] |
libs/base/System.idr
|
system
| null |
time : HasIO io => io Integer
|
function
|
base
|
[
"Data.So",
"Data.String",
"System.Escape",
"System.File"
] |
libs/base/System.idr
|
time
|
Return the number of seconds since epoch.
|
getPID : HasIO io => io Int
|
function
|
base
|
[
"Data.So",
"Data.String",
"System.Escape",
"System.File"
] |
libs/base/System.idr
|
getPID
|
Get the ID of the currently running process.
|
exitWith : HasIO io => ExitCode -> io a
|
function
|
base
|
[
"Data.So",
"Data.String",
"System.Escape",
"System.File"
] |
libs/base/System.idr
|
exitWith
|
Exit the program normally, with the specified status.
|
exitFailure : HasIO io => io a
|
function
|
base
|
[
"Data.So",
"Data.String",
"System.Escape",
"System.File"
] |
libs/base/System.idr
|
exitFailure
|
Exit the program with status value 1, indicating failure. If you want to specify a custom status value, see `exitWith`.
|
exitSuccess : HasIO io => io a
|
function
|
base
|
[
"Data.So",
"Data.String",
"System.Escape",
"System.File"
] |
libs/base/System.idr
|
exitSuccess
|
Exit the program after a successful run.
|
die : HasIO io => String -> io a
|
function
|
base
|
[
"Data.So",
"Data.String",
"System.Escape",
"System.File"
] |
libs/base/System.idr
|
die
|
Print the error message and call exitFailure
|
ExitCode : Type where
|
data
|
base
|
[
"Data.So",
"Data.String",
"System.Escape",
"System.File"
] |
libs/base/System.idr
|
ExitCode
|
Programs can either terminate successfully, or end in a caught failure.
|
assert_total : (1 _ : a) -> a
|
function
|
prelude
|
[] |
libs/prelude/Builtin.idr
|
assert_total
| null |
assert_smaller : (0 x : a) -> (1 y : b) -> b
|
function
|
prelude
|
[] |
libs/prelude/Builtin.idr
|
assert_smaller
| null |
fst : {0 a, b : Type} -> (a, b) -> a
|
function
|
prelude
|
[] |
libs/prelude/Builtin.idr
|
fst
|
Return the first element of a pair.
|
snd : {0 a, b : Type} -> (a, b) -> b
|
function
|
prelude
|
[] |
libs/prelude/Builtin.idr
|
snd
|
Return the second element of a pair.
|
swap : (a, b) -> (b, a)
|
function
|
prelude
|
[] |
libs/prelude/Builtin.idr
|
swap
|
Swap the elements in a pair
|
rewrite__impl : {0 x, y : a} -> (0 p : _) -> (0 rule : x
|
function
|
prelude
|
[] |
libs/prelude/Builtin.idr
|
rewrite__impl
| null |
replace : forall x, y, p . (0 rule : x = y) -> (1 _ : p x) -> p y
|
function
|
prelude
|
[] |
libs/prelude/Builtin.idr
|
replace
| null |
sym : (0 rule : x ~=~ y) -> y ~=~ x
|
function
|
prelude
|
[] |
libs/prelude/Builtin.idr
|
sym
| null |
trans : forall a, b, c . (0 l : a = b) -> (0 r : b = c) -> a = c
|
function
|
prelude
|
[] |
libs/prelude/Builtin.idr
|
trans
| null |
mkDPairInjectiveFst : MkDPair a pa === MkDPair b qb -> a === b
|
function
|
prelude
|
[] |
libs/prelude/Builtin.idr
|
mkDPairInjectiveFst
|
Injectivity of MkDPair (first components)
|
mkDPairInjectiveSnd : MkDPair a pa === MkDPair a qa -> pa === qa
|
function
|
prelude
|
[] |
libs/prelude/Builtin.idr
|
mkDPairInjectiveSnd
|
Injectivity of MkDPair (snd components)
|
defaultString : FromString String
|
function
|
prelude
|
[] |
libs/prelude/Builtin.idr
|
defaultString
| null |
defaultChar : FromChar Char
|
function
|
prelude
|
[] |
libs/prelude/Builtin.idr
|
defaultChar
| null |
defaultDouble : FromDouble Double
|
function
|
prelude
|
[] |
libs/prelude/Builtin.idr
|
defaultDouble
| null |
Unit =
||| The trivial constructor for `()`.
MkUnit
||| The non-dependent pair type, also known as conjunction.
public export
data Pair : Type -> Type -> Type where
|
data
|
prelude
|
[] |
libs/prelude/Builtin.idr
|
Unit
|
The canonical single-element type, also known as the trivially true proposition.
|
LPair : Type -> Type -> Type where
|
data
|
prelude
|
[] |
libs/prelude/Builtin.idr
|
LPair
|
A pair type where each component is linear
|
Res : (a : Type) -> (a -> Type) -> Type where
|
data
|
prelude
|
[] |
libs/prelude/Builtin.idr
|
Res
| null |
Void : Type where
|
data
|
prelude
|
[] |
libs/prelude/Builtin.idr
|
Void
|
The empty type, also known as the trivially false proposition. Use `void` or `absurd` to prove anything if you have a variable of type `Void` in scope.
|
Equal : forall a, b . a -> b -> Type where
|
data
|
prelude
|
[] |
libs/prelude/Builtin.idr
|
Equal
| null |
DPair a (p : a -> Type)
|
record
|
prelude
|
[] |
libs/prelude/Builtin.idr
|
DPair
| null |
PrimIO : Type -> Type
|
function
|
prelude
|
[
"Builtin"
] |
libs/prelude/PrimIO.idr
|
PrimIO
|
Idris's primitive IO, for building abstractions on top of.
|
prim__io_pure : a -> PrimIO a
|
function
|
prelude
|
[
"Builtin"
] |
libs/prelude/PrimIO.idr
|
prim__io_pure
| null |
io_pure : a -> IO a
|
function
|
prelude
|
[
"Builtin"
] |
libs/prelude/PrimIO.idr
|
io_pure
| null |
prim__io_bind : (1 act : PrimIO a) -> (1 k : a -> PrimIO b) -> PrimIO b
|
function
|
prelude
|
[
"Builtin"
] |
libs/prelude/PrimIO.idr
|
prim__io_bind
| null |
io_bind : (1 act : IO a) -> (1 k : a -> IO b) -> IO b
|
function
|
prelude
|
[
"Builtin"
] |
libs/prelude/PrimIO.idr
|
io_bind
| null |
prim__nullAnyPtr : AnyPtr -> Int %foreign "C:idris2_getNull, libidris2_support, idris_support.h"
|
function
|
prelude
|
[
"Builtin"
] |
libs/prelude/PrimIO.idr
|
prim__nullAnyPtr
| null |
prim__getNullAnyPtr : AnyPtr export
|
function
|
prelude
|
[
"Builtin"
] |
libs/prelude/PrimIO.idr
|
prim__getNullAnyPtr
| null |
prim__forgetPtr : Ptr t -> AnyPtr
|
function
|
prelude
|
[
"Builtin"
] |
libs/prelude/PrimIO.idr
|
prim__forgetPtr
| null |
unsafePerformIO : IO a -> a
|
function
|
prelude
|
[
"Builtin"
] |
libs/prelude/PrimIO.idr
|
unsafePerformIO
| null |
IORes : Type -> Type where
|
data
|
prelude
|
[
"Builtin"
] |
libs/prelude/PrimIO.idr
|
IORes
| null |
IO : Type -> Type where
|
data
|
prelude
|
[
"Builtin"
] |
libs/prelude/PrimIO.idr
|
IO
|
The internal representation of I/O computations.
|
Ptr : Type -> Type where [external]
|
data
|
prelude
|
[
"Builtin"
] |
libs/prelude/PrimIO.idr
|
Ptr
| null |
AnyPtr : Type where [external]
|
data
|
prelude
|
[
"Builtin"
] |
libs/prelude/PrimIO.idr
|
AnyPtr
| null |
GCPtr : Type -> Type where [external]
|
data
|
prelude
|
[
"Builtin"
] |
libs/prelude/PrimIO.idr
|
GCPtr
| null |
GCAnyPtr : Type where [external]
|
data
|
prelude
|
[
"Builtin"
] |
libs/prelude/PrimIO.idr
|
GCAnyPtr
| null |
ThreadID : Type where [external]
|
data
|
prelude
|
[
"Builtin"
] |
libs/prelude/PrimIO.idr
|
ThreadID
| null |
Error : Type
|
function
|
base
|
[
"Data.IORef"
] |
libs/base/Control/App.idr
|
Error
|
`Error` is a type synonym for `Type`, specify for exception handling.
|
Cont1Type : Usage -> Type -> Usage -> List Error -> Type -> Type
|
function
|
base
|
[
"Data.IORef"
] |
libs/base/Control/App.idr
|
Cont1Type
| null |
bindApp1 : {u : _} -> (1 act : App1 {u} e a) -> (1 k : Cont1Type u a u' e b) -> App1 {u
|
function
|
base
|
[
"Data.IORef"
] |
libs/base/Control/App.idr
|
bindApp1
| null |
bindL : App {l=NoThrow} e a -> (1 k : a -> App {l} e b) -> App {l} e b
|
function
|
base
|
[
"Data.IORef"
] |
libs/base/Control/App.idr
|
bindL
| null |
seqL : App {l=NoThrow} e () -> (1 k : App {l} e b) -> App {l} e b
|
function
|
base
|
[
"Data.IORef"
] |
libs/base/Control/App.idr
|
seqL
| null |
app : (1 p : App {l=NoThrow} e a) -> App1 {u=Any} e a
|
function
|
base
|
[
"Data.IORef"
] |
libs/base/Control/App.idr
|
app
| null |
app1 : (1 p : App1 {u=Any} e a) -> App {l} e a
|
function
|
base
|
[
"Data.IORef"
] |
libs/base/Control/App.idr
|
app1
| null |
pure : (x : a) -> App1 {u=Any} e a pure x
|
function
|
base
|
[
"Data.IORef"
] |
libs/base/Control/App.idr
|
pure
| null |
pure1 : (1 x : a) -> App1 e a pure1 x
|
function
|
base
|
[
"Data.IORef"
] |
libs/base/Control/App.idr
|
pure1
| null |
mapState : State tag t e -> State tag t (eff :: e)
|
function
|
base
|
[
"Data.IORef"
] |
libs/base/Control/App.idr
|
mapState
| null |
get : (0 tag : _) -> State tag t e => App {l} e t
|
function
|
base
|
[
"Data.IORef"
] |
libs/base/Control/App.idr
|
get
| null |
put : (0 tag : _) -> State tag t e => (val : t) -> App {l} e ()
|
function
|
base
|
[
"Data.IORef"
] |
libs/base/Control/App.idr
|
put
| null |
modify : (0 tag : _) -> State tag t e => (p : t -> t) -> App {l} e ()
|
function
|
base
|
[
"Data.IORef"
] |
libs/base/Control/App.idr
|
modify
| null |
new : t -> (p : State tag t e => App {l} e a) -> App {l} e a
|
function
|
base
|
[
"Data.IORef"
] |
libs/base/Control/App.idr
|
new
| null |
Exception : Error -> List Error -> Type
|
function
|
base
|
[
"Data.IORef"
] |
libs/base/Control/App.idr
|
Exception
|
An alias for `HasErr`.
|
throw : HasErr err es => err -> App es a
|
function
|
base
|
[
"Data.IORef"
] |
libs/base/Control/App.idr
|
throw
| null |
catch : HasErr err es => App es a -> (err -> App es a) -> App es a
|
function
|
base
|
[
"Data.IORef"
] |
libs/base/Control/App.idr
|
catch
| null |
handle : App (err :: e) a -> (onok : a -> App e b) -> (onerr : err -> App e b) -> App e b
|
function
|
base
|
[
"Data.IORef"
] |
libs/base/Control/App.idr
|
handle
| null |
lift : App e a -> App (err :: e) a
|
function
|
base
|
[
"Data.IORef"
] |
libs/base/Control/App.idr
|
lift
| null |
Init : List Error
|
function
|
base
|
[
"Data.IORef"
] |
libs/base/Control/App.idr
|
Init
| null |
run : App {l} Init a -> IO a
|
function
|
base
|
[
"Data.IORef"
] |
libs/base/Control/App.idr
|
run
|
The only way provided by `Control.App` to run an App. @ Init A concrete list of errors.
|
noThrow : App Init a -> App Init {l=NoThrow} a
|
function
|
base
|
[
"Data.IORef"
] |
libs/base/Control/App.idr
|
noThrow
| null |
new1 : t -> (1 p : State tag t e => App1 {u} e a) -> App1 {u} e a
|
function
|
base
|
[
"Data.IORef"
] |
libs/base/Control/App.idr
|
new1
| null |
HasErr : Error -> List Error -> Type where
|
data
|
base
|
[
"Data.IORef"
] |
libs/base/Control/App.idr
|
HasErr
| null |
Path = MayThrow | NoThrow
public export
data Usage = One | Any
public export
0 Has : List (a -> Type) -> a -> Type
|
data
|
base
|
[
"Data.IORef"
] |
libs/base/Control/App.idr
|
Path
|
States whether the program's execution path is linear or might throw exceptions so that we can know whether it is safe to reference linear resources.
|
SafeBind : Path -> (l' : Path) -> Type where
|
data
|
base
|
[
"Data.IORef"
] |
libs/base/Control/App.idr
|
SafeBind
| null |
App : {default MayThrow l : Path} ->
|
data
|
base
|
[
"Data.IORef"
] |
libs/base/Control/App.idr
|
App
|
A type supports throwing and catching exceptions. See `interface Exception err e` for details. @ l An implicit Path states whether the program's execution path is linear or might throw exceptions. The default value is `MayThrow` which represents that the program might throw. @ es A list of exception types that can be thrown. Constrained interfaces can be defined by parameterising with a list of errors `es`.
|
App1 : {default One u : Usage} ->
|
data
|
base
|
[
"Data.IORef"
] |
libs/base/Control/App.idr
|
App1
| null |
AppHasIO : Type where
|
data
|
base
|
[
"Data.IORef"
] |
libs/base/Control/App.idr
|
AppHasIO
|
When type is present in app "errors" list, app is allowed to perform I/O.
|
State : (tag : a) -> Type -> List Error -> Type where
|
data
|
base
|
[
"Data.IORef"
] |
libs/base/Control/App.idr
|
State
| null |
FileEx = GenericFileEx Int -- errno
| FileReadError
| FileWriteError
| FileNotFound
| PermissionDenied
| FileExists
export
Show FileEx where
show (GenericFileEx errno) = "File error : " ++ show errno
|
data
|
base
|
[
"Data.IORef"
] |
libs/base/Control/App.idr
|
FileEx
| null |
IOError
= GenericErr String
| FileErr FileEx
export
Show IOError where
show (GenericErr str) = "IO error : " ++ str
|
data
|
base
|
[
"Data.IORef"
] |
libs/base/Control/App.idr
|
IOError
| null |
inj : (0 f : a -> b) -> {auto 0 _ : Injective f} -> {0 x, y : a} -> (0 _ : f x = f y) -> x = y
|
function
|
base
|
[] |
libs/base/Control/Function.idr
|
inj
| null |
biinj : (0 f : _) -> (0 _ : Biinjective f) => (0 _ : f x v = f y w) -> (x = y, v = w)
|
function
|
base
|
[] |
libs/base/Control/Function.idr
|
biinj
| null |
leftmost : (0 rel : _) -> StronglyConnex ty rel => ty -> ty -> ty
|
function
|
base
|
[
"Control.Relation"
] |
libs/base/Control/Order.idr
|
leftmost
|
Gives the leftmost of a strongly connex relation among the given two elements, generalisation of `min`. That is, leftmost x y ~ x and leftmost x y ~ y, and `leftmost x y` is either `x` or `y`
|
rightmost : (0 rel : _) -> StronglyConnex ty rel => ty -> ty -> ty
|
function
|
base
|
[
"Control.Relation"
] |
libs/base/Control/Order.idr
|
rightmost
|
Gives the rightmost of a strongly connex relation among the given two elements, generalisation of `max`. That is, x ~ rightmost x y and y ~ rightmost x y, and `rightmost x y` is either `x` or `y`
|
A structured dataset of type declarations and definitions from Idris 2, a dependently typed functional programming language.
| Property | Value |
|---|---|
| Total Entries | 6,211 |
| Functions | 5,318 |
| Data types | 695 |
| Records | 198 |
| Docstring Coverage | 30.8% |
| Column | Type | Description |
|---|---|---|
fact |
string | Type signature or definition |
type |
string | "function", "data", or "record" |
library |
string | Idris library (base, contrib, etc.) |
imports |
list[string] | Module imports |
filename |
string | Source .idr file |
symbolic_name |
string | Declaration name |
docstring |
string | Documentation comment |
Idris 2 is a purely functional language with:
Charles Norton (phanerozoic)