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Updated notes to reflect new rule shorthand syntax

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This commit is contained in:
Lawrence Bethlenfalvy
2022-07-06 20:18:39 +02:00
parent ec7ad81fac
commit 5d8d515c28
2 changed files with 22 additions and 22 deletions
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README.md
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@@ -7,14 +7,14 @@ Hello World in Orchid
```orchid
import std::io::(println, out)
main = println out "Hello World!"
main == println out "Hello World!"
```
Basic command line calculator
```orchid
import std::io::(readln, printf, in, out)
main = (
main == (
readln in >>= int |> \a.
readln in >>= \op.
readln in >>= int |> \b.
@@ -31,7 +31,7 @@ Grep
```orchid
import std::io::(readln, println, in, out, getarg)
main = loop \r. (
main == loop \r. (
readln in >>= \line.
if (substring (getarg 1) line)
then (println out ln >>= r)
@@ -41,7 +41,7 @@ main = loop \r. (
Filter through an arbitrary collection
```orchid
filter = @C:Type -> Type. @:Map C. @T. \f:T -> Bool. \coll:C T. (
filter == @C:Type -> Type. @:Map C. @T. \f:T -> Bool. \coll:C T. (
coll >> \el. if (f el) then (Some el) else Nil
):(C T)
```
@@ -122,9 +122,9 @@ types whose defaults have implmentations based on your defaults.
For a demonstration, here's a sample implementation of the Option monad.
```orchid
--[[ The definition of Monad ]]--
Bind = \M:Type -> Type. @T -> @U -> (T -> M U) -> M T -> M U
Return = \M:Type -> Type. @T -> T -> M T
Monad = \M:Type -> Type. (
Bind == \M:Type -> Type. @T -> @U -> (T -> M U) -> M T -> M U
Return == \M:Type -> Type. @T -> T -> M T
Monad == \M:Type -> Type. (
@:Bind M.
@:Return M.
0 --[ Note that empty expressions are forbidden so those that exist
@@ -134,19 +134,19 @@ Monad = \M:Type -> Type. (
)
--[[ The definition of Option ]]--
export Option = \T:Type. @U -> U -> (T -> U) -> U
export Option == \T:Type. @U -> U -> (T -> U) -> U
--[ Constructors ]--
export Some = @T. \data:T. ( \default. \map. map data ):(Option T)
export None = @T. ( \default. \map. default ):(Option T)
export Some == @T. \data:T. ( \default. \map. map data ):(Option T)
export None == @T. ( \default. \map. default ):(Option T)
--[ Implement Monad ]--
default returnOption = Some:(Return Option)
default bindOption = ( @T:Type. @U:Type.
default returnOption == Some:(Return Option)
default bindOption == ( @T:Type. @U:Type.
\f:T -> U. \opt:Option T. opt None f
):(Bind Option)
--[ Sample function that works on unknown monad to demonstrate HKTs.
Turns (Option (M T)) into (M (Option T)), "raising" the unknown monad
out of the Option ]--
export raise = @M:Type -> Type. @T:Type. @:Monad M. \opt:Option (M T). (
export raise == @M:Type -> Type. @T:Type. @:Monad M. \opt:Option (M T). (
opt (return None) (\m. bind m (\x. Some x))
):(M (Option T))
```
@@ -162,7 +162,7 @@ Add has three arguments, two are the types of the operands and one is
the result:
```orchid
default concatListAdd replacing applicativeAdd = @T. (
default concatListAdd replacing applicativeAdd == @T. (
...
):(Add (List T) (List T) (List T))
```
@@ -170,7 +170,7 @@ default concatListAdd replacing applicativeAdd = @T. (
For completeness' sake, the original definition might look like this:
```orchid
default elementwiseAdd = @C:Type -> Type. @T. @U. @V. @:(Applicative C). @:(Add T U V). (
default elementwiseAdd == @C:Type -> Type. @T. @U. @V. @:(Applicative C). @:(Add T U V). (
...
):(Add (C T) (C U) (C V))
```
@@ -179,7 +179,7 @@ With the use of autos, here's what the recursive multiplication
implementation looks like:
```orchid
default iterativeMultiply = @T. @:(Add T T T). (
default iterativeMultiply == @T. @:(Add T T T). (
\a:int.\b:T. loop \r. (\i.
ifthenelse (ieq i 0)
b
@@ -191,7 +191,7 @@ default iterativeMultiply = @T. @:(Add T T T). (
This could then be applied to any type that's closed over addition
```orchid
aroundTheWorldLyrics = (
aroundTheWorldLyrics == (
mult 18 (add (mult 4 "Around the World\n") "\n")
)
```
@@ -231,9 +231,9 @@ $a - $b =10=> (sub $a $b)
The recursive addition function now looks like this
```orchid
default iterativeMultiply = @T. @:(Add T T T). (
default iterativeMultiply == @T. @:(Add T T T). (
\a:int.\b:T. loop \r. (\i.
if (i == 0) then b
if (i = 0) then b
else (b + (r (i - 1)))
) a
):(Multiply T int T)