mirror of
https://github.com/idris-lang/Idris2.git
synced 2024-12-30 15:13:37 +03:00
48 lines
1.6 KiB
Idris
48 lines
1.6 KiB
Idris
module Data.Path
|
|
|
|
%default total
|
|
|
|
||| Paths in a typed graph as a sequence of edges with source and target nodes matching up domino-style.
|
|
||| AKA reflexive-transitive closure.
|
|
public export
|
|
data Path : (t -> t -> Type) -> t -> t -> Type where
|
|
Nil : Path g i i
|
|
(::) : {0 i, j, k : t} ->
|
|
g i j -> Path g j k -> Path g i k
|
|
|
|
export
|
|
joinPath : Path g i j -> Path g j k -> Path g i k
|
|
joinPath [] jk = jk
|
|
joinPath (e::ij) jk = e :: joinPath ij jk
|
|
|
|
export
|
|
snocPath : Path g i j -> g j k -> Path g i k
|
|
snocPath [] f = [f]
|
|
snocPath (e::ij) f = e :: snocPath ij f
|
|
|
|
export
|
|
lengthPath : Path g i j -> Nat
|
|
lengthPath [] = Z
|
|
lengthPath (_::p) = S $ lengthPath p
|
|
|
|
export
|
|
mapPath : {0 gt : t -> t -> Type} -> {0 gu : u -> u -> Type} -> {0 f : t -> u}
|
|
-> ({0 i, j : t} -> gt i j -> gu (f i) (f j))
|
|
-> {0 i, j : t} -> Path gt i j -> Path gu (f i) (f j)
|
|
mapPath gf [] = []
|
|
mapPath gf (e::p) = gf e :: mapPath gf p
|
|
|
|
export
|
|
foldPath : {0 gt : t -> t -> Type} -> {0 gu : u -> u -> Type} -> {0 f : t -> u}
|
|
-> ({0 i, j, k : t} -> gt i j -> gu (f j) (f k) -> gu (f i) (f k))
|
|
-> {0 i, j, k : t} -> Path gt i j -> gu (f j) (f k) -> gu (f i) (f k)
|
|
foldPath gf [] jk = jk
|
|
foldPath gf (e::ij) jk = gf e (foldPath {gu} gf ij jk)
|
|
|
|
export
|
|
foldlPath : {0 gt : t -> t -> Type} -> {0 gu : u -> u -> Type} -> {0 f : t -> u}
|
|
-> ({0 i, j, k : t} -> gu (f i) (f j) -> gt j k -> gu (f i) (f k))
|
|
-> {0 i, j, k : t} -> gu (f i) (f j) -> Path gt j k -> gu (f i) (f k)
|
|
foldlPath gf ij [] = ij
|
|
foldlPath gf ij (e::jk) = foldlPath {gu} gf (gf ij e) jk
|