sforman
/
Thun
1
0
Fork 0
Code Issues Pull Requests Packages Projects Releases Wiki Activity

T's and U's.

This commit is contained in:
Simon Forman 2022-03-29 12:57:41 -07:00
parent 81f8ade4be
commit a722f90072
15 changed files with 335 additions and 559 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

310
docs/reference/mkref/FuncRef.html
View File

@ -2276,256 +2276,226 @@ a F a</code></pre>
</blockquote>
<hr />
<h2 id="tailrec">tailrec</h2>
<p>Basis Function Combinator</p>
<p>[i] genrec</p>
<p>Gentzen diagram.</p>
<p>Combinator</p>
<p>A specialization of the <a href="#genrec">genrec</a> combinator.</p>
<h3 id="definition-92">Definition</h3>
<p>if not basis.</p>
<h3 id="derivation-3">Derivation</h3>
<p>if not basis.</p>
<h3 id="source">Source</h3>
<p>if basis</p>
<blockquote>
<p>[<a href="#i">i</a>] <a href="#genrec">genrec</a></p>
</blockquote>
<h3 id="discussion-69">Discussion</h3>
<p>Lorem ipsum.</p>
<p>Some recursive functions do not need to store additional data or pending actions per-call. These are called <a href="https://en.wikipedia.org/wiki/Tail_recursive">&#x201C;tail recursive&#x201D; functions</a>. In Joy, they appear as <a href="#genrec">genrec</a> definitions that have <a href="#i">i</a> for the second half of their recursive branch.</p>
<p>See the <a href="https://joypy.osdn.io/notebooks/Recursion_Combinators.html">Recursion Combinators notebook</a>.</p>
<h3 id="crosslinks-109">Crosslinks</h3>
<p>Lorem ipsum.</p>
<p><a href="#genrec">genrec</a></p>
<hr />
<h2 id="take">take</h2>
<p>Basis Function Combinator</p>
<p>Expects an integer and a quote on the stack and returns the quote with just the top n items in reverse order (because that's easier and you can use reverse if needed.) :</p>
<pre><code>[a b c d] 2 take
<p>Function</p>
<p>Expects an integer <code>n</code> and a list on the stack and replace them with a list with just the top <code>n</code> items in reverse order.</p>
<pre><code> [a b c d] 2 take
----------------------
[b a]</code></pre>
<p>Gentzen diagram.</p>
[b a]</code></pre>
<h3 id="definition-93">Definition</h3>
<p>if not basis.</p>
<h3 id="derivation-4">Derivation</h3>
<p>if not basis.</p>
<h3 id="source-1">Source</h3>
<p>if basis</p>
<h3 id="discussion-70">Discussion</h3>
<p>Lorem ipsum.</p>
<h3 id="crosslinks-110">Crosslinks</h3>
<p>Lorem ipsum.</p>
<blockquote>
<p><a href="#section-18">&lt;&lt;{}</a> [<a href="#shift">shift</a>] <a href="#times">times</a> <a href="#pop">pop</a></p>
</blockquote>
<hr />
<h2 id="ternary">ternary</h2>
<p>(Combinator)</p>
<p>Combinator</p>
<p>Run a quoted program using exactly three stack values and leave the first item of the result on the stack.</p>
<pre><code> ... z y x [P] unary
<pre><code> ... z y x [P] ternary
-------------------------
... A</code></pre>
... a</code></pre>
<h3 id="definition-94">Definition</h3>
<pre><code>binary popd</code></pre>
<h3 id="discussion-71">Discussion</h3>
<blockquote>
<p><a href="#binary">binary</a> <a href="#popd">popd</a></p>
</blockquote>
<h3 id="discussion-70">Discussion</h3>
<p>Runs any other quoted function and returns its first result while consuming exactly three items from the stack.</p>
<h3 id="crosslinks-111">Crosslinks</h3>
<h3 id="crosslinks-110">Crosslinks</h3>
<p><a href="#binary">binary</a> <a href="#nullary">nullary</a> <a href="#unary">unary</a></p>
<hr />
<h2 id="third">third</h2>
<p>Basis Function Combinator</p>
<pre><code>([a1 a2 a3 ...1] -- a3)</code></pre>
<p>Gentzen diagram.</p>
<p>Function</p>
<pre><code> [a b c ...] third
-----------------------
c</code></pre>
<h3 id="definition-95">Definition</h3>
<p>if not basis.</p>
<h3 id="derivation-5">Derivation</h3>
<p>if not basis.</p>
<h3 id="source-2">Source</h3>
<p>if basis</p>
<h3 id="discussion-72">Discussion</h3>
<p>Lorem ipsum.</p>
<h3 id="crosslinks-112">Crosslinks</h3>
<p>Lorem ipsum.</p>
<blockquote>
<p><a href="#rest">rest</a> <a href="#second">second</a></p>
</blockquote>
<h3 id="crosslinks-111">Crosslinks</h3>
<p><a href="#first">first</a> <a href="#second">second</a> <a href="#fourth">fourth</a> <a href="#rest">rest</a></p>
<hr />
<h2 id="times">times</h2>
<p>Basis Function Combinator</p>
<p>times == [-- dip] cons [swap] infra [0 &gt;] swap while pop :</p>
<pre><code>... n [Q] . times
--------------------- w/ n &lt;= 0
... .
<p>Combinator</p>
<p>Expect a quoted program and an integer <code>n</code> on the stack and do the program <code>n</code> times.</p>
<pre><code> ... n [Q] . times
----------------------- w/ n &lt;= 0
... .
... 1 [Q] . times
... 1 [Q] . times
-----------------------
... . Q
... . Q
... n [Q] . times
... n [Q] . times
------------------------------------- w/ n &gt; 1
... . Q (n - 1) [Q] times</code></pre>
<p>Gentzen diagram.</p>
... . Q (n-1) [Q] times</code></pre>
<h3 id="definition-96">Definition</h3>
<p>if not basis.</p>
<h3 id="derivation-6">Derivation</h3>
<p>if not basis.</p>
<h3 id="source-3">Source</h3>
<p>if basis</p>
<h3 id="discussion-73">Discussion</h3>
<p>Lorem ipsum.</p>
<h3 id="crosslinks-113">Crosslinks</h3>
<p>Lorem ipsum.</p>
<blockquote>
<p>[-- dip] cons [swap] infra [0 &gt;] swap while pop :</p>
</blockquote>
<h3 id="discussion-71">Discussion</h3>
<p>This works by building a little <a href="#while">while</a> program and running it:</p>
<pre><code> 1 3 [++] &#x2022; [-- dip] cons [swap] infra [0 &gt;] swap while pop
1 3 [++] [-- dip] &#x2022; cons [swap] infra [0 &gt;] swap while pop
1 3 [[++] -- dip] &#x2022; [swap] infra [0 &gt;] swap while pop
1 3 [[++] -- dip] [swap] &#x2022; infra [0 &gt;] swap while pop
dip -- [++] &#x2022; swap [3 1] swaack [0 &gt;] swap while pop
dip [++] -- &#x2022; [3 1] swaack [0 &gt;] swap while pop
dip [++] -- [3 1] &#x2022; swaack [0 &gt;] swap while pop
1 3 [-- [++] dip] &#x2022; [0 &gt;] swap while pop
1 3 [-- [++] dip] [0 &gt;] &#x2022; swap while pop
1 3 [0 &gt;] [-- [++] dip] &#x2022; while pop </code></pre>
<p>This is a common pattern in Joy. You accept some parameters from the stack which typically include qouted programs and use them to build another program which does the actual work. This is kind of like macros in Lisp, or preprocessor directives in C.</p>
<hr />
<h2 id="truthy">truthy</h2>
<p>See <a href="#bool">bool</a>.</p>
<hr />
<h2 id="tuck">tuck</h2>
<p>Basis Function Combinator</p>
<pre><code>(a2 a1 -- a1 a2 a1)</code></pre>
<p>Gentzen diagram.</p>
<p>Function</p>
<p><a href="#dup">dup</a> the item on the top of the stack under the second item on the stack.</p>
<pre><code> a b tuck
--------------
b a b</code></pre>
<h3 id="definition-97">Definition</h3>
<p>if not basis.</p>
<h3 id="derivation-7">Derivation</h3>
<p>if not basis.</p>
<h3 id="source-4">Source</h3>
<p>if basis</p>
<h3 id="discussion-74">Discussion</h3>
<p>Lorem ipsum.</p>
<h3 id="crosslinks-114">Crosslinks</h3>
<p>Lorem ipsum.</p>
<blockquote>
<p><a href="#dup">dup</a> [<a href="#swap">swap</a>] <a href="#dip">dip</a></p>
</blockquote>
<h3 id="crosslinks-112">Crosslinks</h3>
<p><a href="#over">over</a></p>
<hr />
<h2 id="unary">unary</h2>
<p>(Combinator)</p>
<p>Run a quoted program using exactly one stack value and leave the first item of the result on the stack.</p>
<pre><code> ... x [P] unary
---------------------
... A</code></pre>
... a</code></pre>
<h3 id="definition-98">Definition</h3>
<pre><code>nullary popd</code></pre>
<h3 id="discussion-75">Discussion</h3>
<blockquote>
<p><a href="#nullary">nullary</a> <a href="#popd">popd</a></p>
</blockquote>
<h3 id="discussion-72">Discussion</h3>
<p>Runs any other quoted function and returns its first result while consuming exactly one item from the stack.</p>
<h3 id="crosslinks-115">Crosslinks</h3>
<h3 id="crosslinks-113">Crosslinks</h3>
<p><a href="#binary">binary</a> <a href="#nullary">nullary</a> <a href="#ternary">ternary</a></p>
<hr />
<h2 id="uncons">uncons</h2>
<p>(Basis Function)</p>
<p>Basis Function</p>
<p>Removes an item from a list and leaves it on the stack under the rest of the list. You cannot <code>uncons</code> an item from an empty list.</p>
<pre><code> [A ...] uncons
<pre><code> [a ...] uncons
--------------------
A [...]</code></pre>
<h3 id="source-5">Source</h3>
<pre><code>func(uncons, Si, So) :- func(cons, So, Si).</code></pre>
<h3 id="discussion-76">Discussion</h3>
<p>This is the inverse of <code>cons</code>.</p>
<h3 id="crosslinks-116">Crosslinks</h3>
a [...]</code></pre>
<h3 id="discussion-73">Discussion</h3>
<p>This is the inverse of <a href="#cons">cons</a>.</p>
<h3 id="crosslinks-114">Crosslinks</h3>
<p><a href="#cons">cons</a></p>
<hr />
<h2 id="unique">unique</h2>
<p>Basis Function Combinator</p>
<p>Function</p>
<p>Given a list remove duplicate items.</p>
<p>Gentzen diagram.</p>
<h3 id="definition-99">Definition</h3>
<p>if not basis.</p>
<h3 id="derivation-8">Derivation</h3>
<p>if not basis.</p>
<h3 id="source-6">Source</h3>
<p>if basis</p>
<h3 id="discussion-77">Discussion</h3>
<p>Lorem ipsum.</p>
<h3 id="crosslinks-117">Crosslinks</h3>
<p>Lorem ipsum.</p>
<hr />
<h2 id="unit">unit</h2>
<p>Basis Function Combinator</p>
<pre><code>(a1 -- [a1 ])</code></pre>
<p>Gentzen diagram.</p>
<h3 id="definition-100">Definition</h3>
<p>if not basis.</p>
<h3 id="derivation-9">Derivation</h3>
<p>if not basis.</p>
<h3 id="source-7">Source</h3>
<p>if basis</p>
<h3 id="discussion-78">Discussion</h3>
<p>Lorem ipsum.</p>
<h3 id="crosslinks-118">Crosslinks</h3>
<p>Lorem ipsum.</p>
<p>Function</p>
<pre><code> a unit
------------
[a]</code></pre>
<h3 id="definition-99">Definition</h3>
<blockquote>
<p>[] <a href="#cons">cons</a></p>
</blockquote>
<hr />
<h2 id="unquoted">unquoted</h2>
<p>Basis Function Combinator</p>
<p>[i] dip</p>
<p>Gentzen diagram.</p>
<h3 id="definition-101">Definition</h3>
<p>if not basis.</p>
<h3 id="derivation-10">Derivation</h3>
<p>if not basis.</p>
<h3 id="source-8">Source</h3>
<p>if basis</p>
<h3 id="discussion-79">Discussion</h3>
<p>Lorem ipsum.</p>
<h3 id="crosslinks-119">Crosslinks</h3>
<p>Lorem ipsum.</p>
<p>Combinator</p>
<p>Unquote (using <a href="#i">i</a>) the list that is second on the stack.</p>
<h3 id="example-31">Example</h3>
<pre><code> 1 2 [3 4] 5 unquoted
--------------------------
1 2 3 4 5</code></pre>
<h3 id="definition-100">Definition</h3>
<blockquote>
<p>[<a href="#i">i</a>] <a href="#dip">dip</a></p>
</blockquote>
<h3 id="crosslinks-115">Crosslinks</h3>
<p><a href="#unit">unit</a></p>
<hr />
<h2 id="unswons">unswons</h2>
<p>Basis Function Combinator</p>
<pre><code>([a1 ...1] -- [...1] a1)</code></pre>
<p>Gentzen diagram.</p>
<h3 id="definition-102">Definition</h3>
<p>if not basis.</p>
<h3 id="derivation-11">Derivation</h3>
<p>if not basis.</p>
<h3 id="source-9">Source</h3>
<p>if basis</p>
<h3 id="discussion-80">Discussion</h3>
<p>Lorem ipsum.</p>
<h3 id="crosslinks-120">Crosslinks</h3>
<p>Lorem ipsum.</p>
<p>Function</p>
<pre><code> [a ...] unswons
---------------------
[...] a</code></pre>
<h3 id="definition-101">Definition</h3>
<blockquote>
<p><a href="#uncons">uncons</a> <a href="#swap">swap</a></p>
</blockquote>
<hr />
<h2 id="void">void</h2>
<p>Basis Function Combinator</p>
<p>True if the form on TOS is void otherwise False.</p>
<p>Gentzen diagram.</p>
<h3 id="definition-103">Definition</h3>
<h3 id="definition-102">Definition</h3>
<p>if not basis.</p>
<h3 id="derivation-12">Derivation</h3>
<h3 id="derivation-3">Derivation</h3>
<p>if not basis.</p>
<h3 id="source-10">Source</h3>
<h3 id="source">Source</h3>
<p>if basis</p>
<h3 id="discussion-81">Discussion</h3>
<h3 id="discussion-74">Discussion</h3>
<p>Lorem ipsum.</p>
<h3 id="crosslinks-121">Crosslinks</h3>
<h3 id="crosslinks-116">Crosslinks</h3>
<p>Lorem ipsum.</p>
<hr />
<h2 id="warranty">warranty</h2>
<p>Basis Function Combinator</p>
<p>Print warranty information.</p>
<p>Gentzen diagram.</p>
<h3 id="definition-104">Definition</h3>
<h3 id="definition-103">Definition</h3>
<p>if not basis.</p>
<h3 id="derivation-13">Derivation</h3>
<h3 id="derivation-4">Derivation</h3>
<p>if not basis.</p>
<h3 id="source-11">Source</h3>
<h3 id="source-1">Source</h3>
<p>if basis</p>
<h3 id="discussion-82">Discussion</h3>
<h3 id="discussion-75">Discussion</h3>
<p>Lorem ipsum.</p>
<h3 id="crosslinks-122">Crosslinks</h3>
<h3 id="crosslinks-117">Crosslinks</h3>
<p>Lorem ipsum.</p>
<hr />
<h2 id="while">while</h2>
<p>Basis Function Combinator</p>
<p>swap nulco dupdipd concat loop</p>
<p>Gentzen diagram.</p>
<h3 id="definition-105">Definition</h3>
<h3 id="definition-104">Definition</h3>
<p>if not basis.</p>
<h3 id="derivation-14">Derivation</h3>
<h3 id="derivation-5">Derivation</h3>
<p>if not basis.</p>
<h3 id="source-12">Source</h3>
<h3 id="source-2">Source</h3>
<p>if basis</p>
<h3 id="discussion-83">Discussion</h3>
<h3 id="discussion-76">Discussion</h3>
<p>Lorem ipsum.</p>
<h3 id="crosslinks-123">Crosslinks</h3>
<h3 id="crosslinks-118">Crosslinks</h3>
<p>Lorem ipsum.</p>
<hr />
<h2 id="words">words</h2>
<p>Basis Function Combinator</p>
<p>Print all the words in alphabetical order.</p>
<p>Gentzen diagram.</p>
<h3 id="definition-106">Definition</h3>
<h3 id="definition-105">Definition</h3>
<p>if not basis.</p>
<h3 id="derivation-15">Derivation</h3>
<h3 id="derivation-6">Derivation</h3>
<p>if not basis.</p>
<h3 id="source-13">Source</h3>
<h3 id="source-3">Source</h3>
<p>if basis</p>
<h3 id="discussion-84">Discussion</h3>
<h3 id="discussion-77">Discussion</h3>
<p>Lorem ipsum.</p>
<h3 id="crosslinks-124">Crosslinks</h3>
<h3 id="crosslinks-119">Crosslinks</h3>
<p>Lorem ipsum.</p>
<hr />
<h2 id="x">x</h2>
@ -2533,39 +2503,39 @@ a F a</code></pre>
<pre><code> [F] x
-----------
[F] F</code></pre>
<h3 id="definition-107">Definition</h3>
<h3 id="definition-106">Definition</h3>
<pre><code>dup i</code></pre>
<h3 id="discussion-85">Discussion</h3>
<h3 id="discussion-78">Discussion</h3>
<p>The <code>x</code> combinator &#x2026;</p>
<hr />
<h2 id="xor">xor</h2>
<p>Basis Function Combinator</p>
<p>Same as a ^ b.</p>
<p>Gentzen diagram.</p>
<h3 id="definition-108">Definition</h3>
<h3 id="definition-107">Definition</h3>
<p>if not basis.</p>
<h3 id="derivation-16">Derivation</h3>
<h3 id="derivation-7">Derivation</h3>
<p>if not basis.</p>
<h3 id="source-14">Source</h3>
<h3 id="source-4">Source</h3>
<p>if basis</p>
<h3 id="discussion-86">Discussion</h3>
<h3 id="discussion-79">Discussion</h3>
<p>Lorem ipsum.</p>
<h3 id="crosslinks-125">Crosslinks</h3>
<h3 id="crosslinks-120">Crosslinks</h3>
<p>Lorem ipsum.</p>
<hr />
<h2 id="zip">zip</h2>
<p>Basis Function Combinator</p>
<p>Replace the two lists on the top of the stack with a list of the pairs from each list. The smallest list sets the length of the result list.</p>
<p>Gentzen diagram.</p>
<h3 id="definition-109">Definition</h3>
<h3 id="definition-108">Definition</h3>
<p>if not basis.</p>
<h3 id="derivation-17">Derivation</h3>
<h3 id="derivation-8">Derivation</h3>
<p>if not basis.</p>
<h3 id="source-15">Source</h3>
<h3 id="source-5">Source</h3>
<p>if basis</p>
<h3 id="discussion-87">Discussion</h3>
<h3 id="discussion-80">Discussion</h3>
<p>Lorem ipsum.</p>
<h3 id="crosslinks-126">Crosslinks</h3>
<h3 id="crosslinks-121">Crosslinks</h3>
<p>Lorem ipsum.</p>
</body>
</html>

291
docs/reference/mkref/Functor-Reference.md
View File

@ -3656,85 +3656,62 @@ Like [cons] but [swap] the item and list.
## tailrec
Basis Function Combinator
Combinator
\[i\] genrec
Gentzen diagram.
A specialization of the [genrec] combinator.
### Definition
if not basis.
### Derivation
if not basis.
### Source
if basis
> \[[i]\] [genrec]
### Discussion
Lorem ipsum.
Some recursive functions do not need to store additional data or pending
actions per-call. These are called ["tail recursive" functions](https://en.wikipedia.org/wiki/Tail_recursive). In Joy,
they appear as [genrec] definitions that have [i] for the second half of
their recursive branch.
See the [Recursion Combinators notebook](https://joypy.osdn.io/notebooks/Recursion_Combinators.html).
### Crosslinks
Lorem ipsum.
[genrec]
------------------------------------------------------------------------
## take
Basis Function Combinator
Function
Expects an integer and a quote on the stack and returns the quote with
just the top n items in reverse order (because that\'s easier and you
can use reverse if needed.) :
Expects an integer `n` and a list on the stack and replace them with a list
with just the top `n` items in reverse order.
[a b c d] 2 take
[a b c d] 2 take
----------------------
[b a]
Gentzen diagram.
[b a]
### Definition
if not basis.
> [\<\<\{\}] \[[shift]\] [times] [pop]
### Derivation
if not basis.
### Source
if basis
### Discussion
Lorem ipsum.
### Crosslinks
Lorem ipsum.
--------------------
## ternary
(Combinator)
Combinator
Run a quoted program using exactly three stack values and leave the first
item of the result on the stack.
... z y x [P] unary
... z y x [P] ternary
-------------------------
... A
... a
### Definition
binary popd
> [binary] [popd]
### Discussion
@ -3752,75 +3729,70 @@ consuming exactly three items from the stack.
## third
Basis Function Combinator
Function
([a1 a2 a3 ...1] -- a3)
Gentzen diagram.
[a b c ...] third
-----------------------
c
### Definition
if not basis.
### Derivation
if not basis.
### Source
if basis
### Discussion
Lorem ipsum.
> [rest] [second]
### Crosslinks
Lorem ipsum.
[first]
[second]
[fourth]
[rest]
------------------------------------------------------------------------
## times
Basis Function Combinator
Combinator
times == \[\-- dip\] cons \[swap\] infra \[0 \>\] swap while pop :
Expect a quoted program and an integer `n` on the stack and do the
program `n` times.
... n [Q] . times
--------------------- w/ n <= 0
... .
... n [Q] . times
----------------------- w/ n <= 0
... .
... 1 [Q] . times
... 1 [Q] . times
-----------------------
... . Q
... . Q
... n [Q] . times
... n [Q] . times
------------------------------------- w/ n > 1
... . Q (n - 1) [Q] times
Gentzen diagram.
... . Q (n-1) [Q] times
### Definition
if not basis.
> \[\-- dip\] cons \[swap\] infra \[0 \>\] swap while pop :
### Derivation
if not basis.
### Source
if basis
### Discussion
Lorem ipsum.
This works by building a little [while] program and running it:
### Crosslinks
1 3 [++] • [-- dip] cons [swap] infra [0 >] swap while pop
1 3 [++] [-- dip] • cons [swap] infra [0 >] swap while pop
1 3 [[++] -- dip] • [swap] infra [0 >] swap while pop
1 3 [[++] -- dip] [swap] • infra [0 >] swap while pop
dip -- [++] • swap [3 1] swaack [0 >] swap while pop
dip [++] -- • [3 1] swaack [0 >] swap while pop
dip [++] -- [3 1] • swaack [0 >] swap while pop
1 3 [-- [++] dip] • [0 >] swap while pop
1 3 [-- [++] dip] [0 >] • swap while pop
1 3 [0 >] [-- [++] dip] • while pop
This is a common pattern in Joy. You accept some parameters from the
stack which typically include qouted programs and use them to build
another program which does the actual work. This is kind of like macros
in Lisp, or preprocessor directives in C.
Lorem ipsum.
--------------
@ -3833,31 +3805,23 @@ See [bool](#bool).
## tuck
Basis Function Combinator
Function
(a2 a1 -- a1 a2 a1)
[dup] the item on the top of the stack under the second item on the
stack.
Gentzen diagram.
a b tuck
--------------
b a b
### Definition
if not basis.
### Derivation
if not basis.
### Source
if basis
### Discussion
Lorem ipsum.
> [dup] \[[swap]\] [dip]
### Crosslinks
Lorem ipsum.
[over]
--------------------
@ -3865,15 +3829,16 @@ Lorem ipsum.
(Combinator)
Run a quoted program using exactly one stack value and leave the first item of the result on the stack.
Run a quoted program using exactly one stack value and leave the first
item of the result on the stack.
... x [P] unary
---------------------
... A
... a
### Definition
nullary popd
> [nullary] [popd]
### Discussion
@ -3891,147 +3856,85 @@ consuming exactly one item from the stack.
## uncons
(Basis Function)
Basis Function
Removes an item from a list and leaves it on the stack under the rest of
the list. You cannot `uncons` an item from an empty list.
[A ...] uncons
[a ...] uncons
--------------------
A [...]
### Source
func(uncons, Si, So) :- func(cons, So, Si).
a [...]
### Discussion
This is the inverse of `cons`.
This is the inverse of [cons].
### Crosslinks
[cons](#cons)
[cons]
------------------------------------------------------------------------
## unique
Basis Function Combinator
Function
Given a list remove duplicate items.
Gentzen diagram.
### Definition
if not basis.
### Derivation
if not basis.
### Source
if basis
### Discussion
Lorem ipsum.
### Crosslinks
Lorem ipsum.
------------------------------------------------------------------------
## unit
Basis Function Combinator
Function
(a1 -- [a1 ])
Gentzen diagram.
a unit
------------
[a]
### Definition
if not basis.
> \[\] [cons]
### Derivation
if not basis.
### Source
if basis
### Discussion
Lorem ipsum.
### Crosslinks
Lorem ipsum.
------------------------------------------------------------------------
## unquoted
Basis Function Combinator
Combinator
\[i\] dip
Unquote (using [i]) the list that is second on the stack.
Gentzen diagram.
### Example
1 2 [3 4] 5 unquoted
--------------------------
1 2 3 4 5
### Definition
if not basis.
### Derivation
if not basis.
### Source
if basis
### Discussion
Lorem ipsum.
> \[[i]\] [dip]
### Crosslinks
Lorem ipsum.
[unit]
------------------------------------------------------------------------
## unswons
Basis Function Combinator
Function
([a1 ...1] -- [...1] a1)
Gentzen diagram.
[a ...] unswons
---------------------
[...] a
### Definition
if not basis.
> [uncons] [swap]
### Derivation
if not basis.
### Source
if basis
### Discussion
Lorem ipsum.
### Crosslinks
Lorem ipsum.
------------------------------------------------------------------------

26
docs/reference/tailrec.md
View File

@ -2,28 +2,24 @@
## tailrec
Basis Function Combinator
Combinator
\[i\] genrec
Gentzen diagram.
A specialization of the [genrec] combinator.
### Definition
if not basis.
### Derivation
if not basis.
### Source
if basis
> \[[i]\] [genrec]
### Discussion
Lorem ipsum.
Some recursive functions do not need to store additional data or pending
actions per-call. These are called ["tail recursive" functions](https://en.wikipedia.org/wiki/Tail_recursive). In Joy,
they appear as [genrec] definitions that have [i] for the second half of
their recursive branch.
See the [Recursion Combinators notebook](https://joypy.osdn.io/notebooks/Recursion_Combinators.html).
### Crosslinks
Lorem ipsum.
[genrec]

30
docs/reference/take.md
View File

@ -2,34 +2,16 @@
## take
Basis Function Combinator
Function
Expects an integer and a quote on the stack and returns the quote with
just the top n items in reverse order (because that\'s easier and you
can use reverse if needed.) :
Expects an integer `n` and a list on the stack and replace them with a list
with just the top `n` items in reverse order.
[a b c d] 2 take
[a b c d] 2 take
----------------------
[b a]
Gentzen diagram.
[b a]
### Definition
if not basis.
> [\<\<\{\}] \[[shift]\] [times] [pop]
### Derivation
if not basis.
### Source
if basis
### Discussion
Lorem ipsum.
### Crosslinks
Lorem ipsum.

9
docs/reference/ternary.md
View File

@ -2,19 +2,18 @@
## ternary
(Combinator)
Combinator
Run a quoted program using exactly three stack values and leave the first
item of the result on the stack.
... z y x [P] unary
... z y x [P] ternary
-------------------------
... A
... a
### Definition
binary popd
> [binary] [popd]
### Discussion

28
docs/reference/third.md
View File

@ -2,28 +2,20 @@
## third
Basis Function Combinator
Function
([a1 a2 a3 ...1] -- a3)
Gentzen diagram.
[a b c ...] third
-----------------------
c
### Definition
if not basis.
### Derivation
if not basis.
### Source
if basis
### Discussion
Lorem ipsum.
> [rest] [second]
### Crosslinks
Lorem ipsum.
[first]
[second]
[fourth]
[rest]

51
docs/reference/times.md
View File

@ -2,42 +2,45 @@
## times
Basis Function Combinator
Combinator
times == \[\-- dip\] cons \[swap\] infra \[0 \>\] swap while pop :
Expect a quoted program and an integer `n` on the stack and do the
program `n` times.
... n [Q] . times
--------------------- w/ n <= 0
... .
... n [Q] . times
----------------------- w/ n <= 0
... .
... 1 [Q] . times
... 1 [Q] . times
-----------------------
... . Q
... . Q
... n [Q] . times
... n [Q] . times
------------------------------------- w/ n > 1
... . Q (n - 1) [Q] times
Gentzen diagram.
... . Q (n-1) [Q] times
### Definition
if not basis.
> \[\-- dip\] cons \[swap\] infra \[0 \>\] swap while pop :
### Derivation
if not basis.
### Source
if basis
### Discussion
Lorem ipsum.
This works by building a little [while] program and running it:
### Crosslinks
1 3 [++] • [-- dip] cons [swap] infra [0 >] swap while pop
1 3 [++] [-- dip] • cons [swap] infra [0 >] swap while pop
1 3 [[++] -- dip] • [swap] infra [0 >] swap while pop
1 3 [[++] -- dip] [swap] • infra [0 >] swap while pop
dip -- [++] • swap [3 1] swaack [0 >] swap while pop
dip [++] -- • [3 1] swaack [0 >] swap while pop
dip [++] -- [3 1] • swaack [0 >] swap while pop
1 3 [-- [++] dip] • [0 >] swap while pop
1 3 [-- [++] dip] [0 >] • swap while pop
1 3 [0 >] [-- [++] dip] • while pop
This is a common pattern in Joy. You accept some parameters from the
stack which typically include qouted programs and use them to build
another program which does the actual work. This is kind of like macros
in Lisp, or preprocessor directives in C.
Lorem ipsum.

26
docs/reference/tuck.md
View File

@ -2,28 +2,20 @@
## tuck
Basis Function Combinator
Function
(a2 a1 -- a1 a2 a1)
[dup] the item on the top of the stack under the second item on the
stack.
Gentzen diagram.
a b tuck
--------------
b a b
### Definition
if not basis.
### Derivation
if not basis.
### Source
if basis
### Discussion
Lorem ipsum.
> [dup] \[[swap]\] [dip]
### Crosslinks
Lorem ipsum.
[over]

7
docs/reference/unary.md
View File

@ -4,15 +4,16 @@
(Combinator)
Run a quoted program using exactly one stack value and leave the first item of the result on the stack.
Run a quoted program using exactly one stack value and leave the first
item of the result on the stack.
... x [P] unary
---------------------
... A
... a
### Definition
nullary popd
> [nullary] [popd]
### Discussion

14
docs/reference/uncons.md
View File

@ -2,24 +2,20 @@
## uncons
(Basis Function)
Basis Function
Removes an item from a list and leaves it on the stack under the rest of
the list. You cannot `uncons` an item from an empty list.
[A ...] uncons
[a ...] uncons
--------------------
A [...]
### Source
func(uncons, Si, So) :- func(cons, So, Si).
a [...]
### Discussion
This is the inverse of `cons`.
This is the inverse of [cons].
### Crosslinks
[cons](#cons)
[cons]

23
docs/reference/unique.md
View File

@ -2,28 +2,7 @@
## unique
Basis Function Combinator
Function
Given a list remove duplicate items.
Gentzen diagram.
### Definition
if not basis.
### Derivation
if not basis.
### Source
if basis
### Discussion
Lorem ipsum.
### Crosslinks
Lorem ipsum.

25
docs/reference/unit.md
View File

@ -2,28 +2,13 @@
## unit
Basis Function Combinator
Function
(a1 -- [a1 ])
Gentzen diagram.
a unit
------------
[a]
### Definition
if not basis.
> \[\] [cons]
### Derivation
if not basis.
### Source
if basis
### Discussion
Lorem ipsum.
### Crosslinks
Lorem ipsum.

27
docs/reference/unquoted.md
View File

@ -2,28 +2,21 @@
## unquoted
Basis Function Combinator
Combinator
\[i\] dip
Unquote (using [i]) the list that is second on the stack.
Gentzen diagram.
### Example
1 2 [3 4] 5 unquoted
--------------------------
1 2 3 4 5
### Definition
if not basis.
### Derivation
if not basis.
### Source
if basis
### Discussion
Lorem ipsum.
> \[[i]\] [dip]
### Crosslinks
Lorem ipsum.
[unit]

25
docs/reference/unswons.md
View File

@ -2,28 +2,13 @@
## unswons
Basis Function Combinator
Function
([a1 ...1] -- [...1] a1)
Gentzen diagram.
[a ...] unswons
---------------------
[...] a
### Definition
if not basis.
> [uncons] [swap]
### Derivation
if not basis.
### Source
if basis
### Discussion
Lorem ipsum.
### Crosslinks
Lorem ipsum.

2
implementations/defs.txt
View File

@ -90,7 +90,7 @@ swons swap cons
swoncat swap concat
sqr dup mul
tailrec [i] genrec
take [] roll> [shift] times pop
take <<{} [shift] times pop
ternary binary popd
third rest second
tuck dup swapd