Version -10.0.0
Each function, combinator, or definition should be documented here.
Not negative.
- n !-
------------ n < 0
- false
-
-
- n !-
----------- n >= 0
- true
-combinator
Short-circuiting Boolean AND
-Accept two quoted programs, run the first and expect a Boolean value, if
-it's true pop it and run the second program (which should also return a
-Boolean value) otherwise pop the second program (leaving false on the
-stack.)
[A] [B] &&
----------------- true
+
+
+
+
+
+
+ Thun Function Reference
+
+
+
+
+
+
+Thun Function Reference
+
+
+
+Version -10.0.0
+Each function, combinator, or definition should be documented here.
+
+abs
+Take an integer from the stack and replace it with its absolute value.
+
+add
+Take two integers from the stack and replace them with their sum.
+
+and
+Combinator
+Short-circuiting Boolean AND
+Accept two quoted programs, run the first and expect a Boolean value, if it’s true pop it and run the second program (which should also return a Boolean value) otherwise pop the second program (leaving false on the stack.) The quoted programs are run with nullary.
+ [A] [B] and
+----------------- A -> true
B
- [A] [B] &&
----------------- false
- false
-
-Definition
-nulco [nullary [false]] dip branch
-
-Derivation
-TODO: this is derived in one of the notebooks I think, look it up and
-link to it, or copy the content here.
... b a <{}
------------------
- ... [] b a
-[] rollup
... a <{}
-----------------
- ... [] a
-[] swap
Is the item on the top of the stack "truthy"?
Add two numbers together: a + b.
combinator
Build a list of values from a generator program G and a stopping
-predicate P.
TODO: this is derived in one of the notebooks I think, look it up and link to it, or copy the content here.
+Combinator
+Build a list of values from a generator program G and a stopping predicate P.
[P] [G] anamorphism
-----------------------------------------
- [P] [pop []] [G] [dip swons] genrec
-The range function generates a list of the integers from 0 to n - 1:
[0 <=] [-- dup] anamorphism-[0 <=] [-- dup] anamorphism
-
combinator
"apply one"
-Given a quoted program on TOS and anything as the second stack item run -the program without disturbing the stack and replace the two args with -the first result of the program.
+joy? 5
+5
+joy? [0 <=] [– dup]
+5 [0 <=] [– dup]
+joy? anamorphism
+[4 3 2 1 0]
+ +Note that the last value generated (0) is at the bottom of the list. See the Recursion Combinators notebook.
+“apply one”
+Combinator
+Given a quoted program on TOS and anything as the second stack item run the program without disturbing the rest of the stack and replace the two args with the first result of the program.
... x [Q] app1
---------------------------------
- ... [x ...] [Q] infra first
-This is the same effect as the unary combinator.
combinator
Like app1 with two items.
+ ... [x ...] [Q] infra first +This is the same effect as the unary combinator.
+Just a specialization of nullary really. Its parallelizable cousins are more useful.
Combinator
+Like app1 with two items.
... y x [Q] . app2
-----------------------------------
... [y ...] [Q] . infra first
- [x ...] [Q] infra first
-combinator
Like [app1] with three items.
+ [x ...] [Q] infra first +Unlike app1, which is essentially an alias for unary, this function is not the same as binary. Instead of running one program using exactly two items from the stack and pushing one result (as binary does) this function takes two items from the stack and runs the program twice, separately for each of the items, then puts both results onto the stack.
+This is not currently implemented as parallel processes but it can (and should) be done.
+Combinator
+Like app1 with three items.
... z y x [Q] . app3
-----------------------------------
... [z ...] [Q] . infra first
[y ...] [Q] infra first
- [x ...] [Q] infra first
-combinator
Like [app1] with any number of items.
+ [x ...] [Q] infra first +See app2.
+Combinator
+Like app1 with any number of items.
... xN ... x2 x1 x0 [Q] n . appN
--------------------------------------
... [xN ...] [Q] . infra first
...
[x2 ...] [Q] infra first
[x1 ...] [Q] infra first
- [x0 ...] [Q] infra first
-[grabN] codi map reverse disenstacken
Compute the average of a list of numbers. -(Currently broken until I can figure out what to do about "numeric tower" -in Thun.)
combinator
Run two quoted programs
- [P] [Q] b
----------------
- P Q
-combinator
Run a quoted program using exactly two stack values and leave the first -item of the result on the stack.
+ [x0 ...] [Q] infra first +This function takes a quoted function Q and an integer and runs the function that many times on that many stack items. See also app2.
See mul.
+See getitem.
+Compute the average of a list of numbers. (Currently broken until I can figure out what to do about “numeric tower” in Thun.)
+Theoretically this function would compute the sum and the size in two separate threads, then divide. This works but a compiled version would probably do better to sum and count the list once, in one thread, eh?
+As an exercise in Functional Programming in Joy it would be fun to convert this into a catamorphism. See the Recursion Combinators notebook.
+Combinator
+Run a quoted program using exactly two stack values and leave the first item of the result on the stack.
... y x [P] binary
-----------------------
- ... a
-Convert the item on the top of the stack to a Boolean value.
combinator built-in
Use a Boolean value to select and run one of two quoted programs.
+ ... a +Runs any other quoted function and returns its first result while consuming exactly two items from the stack.
+Combinator
+Run two quoted programs
+ [P] [Q] b
+---------------
+ P QThis combinator may seem trivial but it comes in handy.
+Convert the item on the top of the stack to a Boolean value.
+For integers 0 is false and any other number is true; for lists the empty list is false and all other lists are true.
Combinator
+Use a Boolean value to select and run one of two quoted programs.
false [F] [T] branch
--------------------------
F
true [F] [T] branch
-------------------------
- T
- a b c d [...] ccccons
+ TThis is one of the fundamental operations (although it can be defined in terms of choice as above). The more common “if..then..else” construct ifte adds a predicate function that is evaluated nullary.
+ a b c d [...] ccccons
---------------------------
- [a b c d ...]
-Do [cons] four times.
a b [...] ccons
+ [a b c d ...]Do cons four times.
+ a b [...] ccons
---------------------
- [a b ...]
-Do [cons] two times.
Use a Boolean value to select one of two items.
+ [a b ...] +Do cons two times.
+Use a Boolean value to select one of two items.
a b false choice
----------------------
a
a b true choice
---------------------
- b
-combinator
Run two programs in parallel, consuming one additional item, and put their -results on the stack.
+ b +It’s a matter of taste whether you implement this in terms of branch or the other way around.
+See xor.
+Clear everything from the stack.
+Combinator
+Run two programs in parallel, consuming one additional item, and put their results on the stack.
... x [A] [B] cleave
------------------------
- ... a b
---[fork] [popdd]
+
1 2 3 [+] [-] cleave
--------------------------
- 1 2 5 -1
-combinator
Run two programs in parallel, consuming two additional items, and put their results on the stack.
+ 1 2 5 -1 +One of a handful of useful parallel combinators.
+Combinator
+Run two programs in parallel, consuming two additional items, and put their results on the stack.
... x y [A] [B] clop
--------------------------
- ... a b
-combinator
Take two values and three quoted programs on the stack and run one -of the three depending on the results of comparing the two values.
+ ... a b +Like cleave but consumes an additional item from the stack.
+ 1 2 3 4 [+] [-] clop
+--------------------------
+ 1 2 7 -1Combinator
+Take two values and three quoted programs on the stack and run one of the three depending on the results of comparing the two values.
a b [G] [E] [L] cmp
------------------------- a > b
G
@@ -158,32 +449,45 @@ of the three depending on the results of comparing the two values.
a b [G] [E] [L] cmp
------------------------- a < b
- L
-combinator
Take a quoted program from the stack, [cons] the next item onto it, then -[dip] the whole thing under what was the third item on the stack.
+ L +This is useful sometimes, and you can dup or dupd with two quoted programs to handle the cases when you just want to deal with <= or >= and not all three possibilities, e.g.:
+[G] [EL] dup cmp
+
+[GE] [L] dupd cmpOr even:
+[GL] [E] over cmpCombinator
+Take a quoted program from the stack, cons the next item onto it, then dip the whole thing under what was the third item on the stack.
a b [F] . codi
--------------------
- b . F a
-combinator
This is part of the [make_generator] function. You would not use this -combinator directly.
Concatinate two lists.
+ b . F a +This is one of those weirdly specific functions that turns out to be useful in a few places.
+Combinator
+This is part of the make_generator function. You would not use this combinator directly.
+See make_generator and the “Using x to Generate Values” notebook as well as Recursion Theory and Joy by Manfred von Thun.
Concatinate two lists.
[a b c] [d e f] concat
----------------------------
- [a b c d e f]
-combinator
This combinator works like a case statement. It expects a single quote
-on the stack that must contain zero or more condition quotes and a
-default quote. Each condition quote should contain a quoted predicate
-followed by the function expression to run if that predicate returns
-true. If no predicates return true the default function runs.
first first_two flatten fourth getitem remove rest reverse rrest second shift shunt size sort split_at split_list swaack third zip
+Combinator
+This combinator works like a case statement. It expects a single quote on the stack that must contain zero or more condition quotes and a default quote. Each condition quote should contain a quoted predicate followed by the function expression to run if that predicate returns true. If no predicates return true the default function runs.
[
[ [Predicate0] Function0 ]
[ [Predicate1] Function1 ]
@@ -191,243 +495,424 @@ followed by the function expression to run if that predicate returns
[ [PredicateN] FunctionN ]
[Default]
]
-cond
-built-in
Given an item and a list, append the item to the list to make a new list.
+cond +It works by rewriting into a chain of nested ifte expressions, e.g.:
+ [[[B0] T0] [[B1] T1] [D]] cond
+-----------------------------------------
+ [B0] [T0] [[B1] [T1] [D] ifte] ifteGiven an item and a list, append the item to the list to make a new list.
a [...] cons
------------------
- [a ...]
-combinator built-in
The dip combinator expects a quoted program on the stack and below it
-some item, it hoists the item into the expression and runs the program
-on the rest of the stack.
... x [Q] . dip
----------------------
- ... . Q x
-combinator
Like [dip] but expects two items.
- ... y x [Q] . dipd
--------------------------
- ... . Q y x
-combinator
Like [dip] but expects three items. :
+ [a ...] +Cons is a venerable old function from Lisp. Its inverse operation is uncons.
+Combinator
+Specialist function (that means I forgot what it does and why.)
+Combinator
+Like dip but expects three items. :
... z y x [Q] . dip
-----------------------------
- ... . Q z y x
-The disenstacken function expects a list on top of the stack and makes
-that the stack discarding the rest of the stack.
See dip.
+Combinator
+Like dip but expects two items.
+ ... y x [Q] . dipd
+-------------------------
+ ... . Q y xSee dip.
+dip dipdd dupdip dupdipd infra
+Combinator
+The dip combinator expects a quoted program on the stack and below it some item, it hoists the item into the expression and runs the program on the rest of the stack.
... x [Q] . dip
+---------------------
+ ... . Q xThis along with infra are enough to update any datastructure. See the “Traversing Datastructures with Zippers” notebook.
+Note that the item that was on the top of the stack (x in the example above) will not be treated specially by the interpreter when it is reached again. This is something of a footgun. My advice is to avoid putting bare unquoted symbols onto the stack, but then you can’t use symbols as “atoms” and also use dip and infra to operate on compound datastructures with atoms in them. This is a kind of side-effect of the Continuation-Passing Style. The dip combinator could “set aside” the item and replace it after running Q but that means that there is an “extra space” where the item resides while Q runs. One of the nice things about CPS is that the whole state is recorded in the stack and pending expression (not counting modifications to the dictionary.)
dipd dipdd dupdip dupdipd infra
+The disenstacken function expects a list on top of the stack and makes that the stack discarding the rest of the stack.
1 2 3 [4 5 6] disenstacken
--------------------------------
- 6 5 4
- x y divmod
+ 6 5 4Note that the order of the list is not changed, it just looks that way because the stack is printed with the top on the right while lists are printed with the top or head on the left.
+See floordiv.
+ x y divmod
------------------
q r
- (x/y) (x%y)
-Invariant: qy + r = x.
Given a number greater than zero put all the Natural numbers (including -zero) less than that onto the stack.
-Invariant: qy + r = x.
Given a number greater than zero put all the Natural numbers (including zero) less than that onto the stack.
+ 3 down_to_zero
--------------------
- 3 2 1 0
-Expects an integer and a quote on the stack and returns the quote with n -items removed off the top.
-Expects an integer and a quote on the stack and returns the quote with n items removed off the top.
+ [a b c d] 2 drop
----------------------
- [c d]
-[dup] the third item down on the stack.
+ [c d] +dup the third item down on the stack.
a b c dupdd
-----------------
- a a b c
-combinator
Apply a function F and [dup] the item under it on the stack.
Combinator
+Run a copy of program F under the next item down on the stack.
a [F] dupdipd
+-------------------
+ F a [F]Combinator
+Apply a function F and dup the item under it on the stack.
a [F] dupdip
------------------
- a F a
-a [F] dupdip
a [F] dupd dip
a [F] [dup] dip dip
a dup [F] dip
a a [F] dip
-a F a
-combinator
Run a copy of program F under the next item down on the stack.
a [F] dupdipd
--------------------
- F a [F]
-Put the stack onto the stack replacing the contents of the stack.
+a F a +A very common and useful combinator.
+dup the second item down on the stack.
+ a b dupd
+--------------
+ a a b“Dup”licate the top item on the stack.
+ a dup
+-----------
+ a aPut the stack onto the stack replacing the contents of the stack.
... a b c enstacken
-------------------------
- [c b a ...]
-Compare the two items on the top of the stack for equality and replace -them with a Boolean value.
+ [c b a ...] +This is a destructive version of stack. See the note under disenstacken about the apparent but illusory reversal of the stack.
+Compare the two items on the top of the stack for equality and replace them with a Boolean value.
a b eq
-------------
Boolean
- (a = b)
-built-in
Replace a list with its first item.
+ (a = b) +See eq.
+See ne.
+Not negative.
+ n !-
+----------- n < 0
+ false
+
+
+ n !-
+---------- n >= 0
+ trueReturn a Boolean value indicating if a number is greater than or equal to zero.
+Replace a list with its first item.
[a ...]
--------------
- a
-Replace a list with its first two items.
+ a +Replace a list with its first two items.
[a b ...] first_two
-------------------------
- a b
-Given a list of lists, concatinate them.
-first second third fourth rest
+Given a list of lists, concatinate them.
+ [[1 2] [3 [4] 5] [6 7]] flatten
-------------------------------------
- [1 2 3 [4] 5 6 7]
-Return the largest integer \<= x.
I don't know why this is called "floor" div, I think it rounds its -result down (not towards zero or up.)
+ [1 2 3 [4] 5 6 7] +Note that only one “level” of lists is flattened. In the example above [4] is not unquoted.
concat first first_two fourth getitem remove rest reverse rrest second shift shunt size sort split_at split_list swaack third zip
+I don’t know why this is called “floor” div, I think it rounds its result down (not towards zero or up.)
a b floordiv
------------------
- (a/b)
-combinator
Run two quoted programs in parallel and replace them with their results.
+ (a/b) +All the division commands need to be revisited when the “numeric tower” for Thun gets nailed down.
+Return the largest integer <= x.
+This function doesn’t make sense (yet) to have because there are (as yet) only integers in the system.
+Combinator
+Run two quoted programs in parallel and replace them with their results.
... [F] [G] fork
----------------------
- ... f g
-Replace a list with its fourth item.
+ ... f g +The basic parallelism combinator, the two programs are run independently.
+Replace a list with its fourth item.
[a b c d ...] fourth
--------------------------
- d
-Take two integers from the stack and replace them with their Greatest -Common Denominator.
Greater-than-or-equal-to comparison of two numbers.
+ d +Compiled GCD function.
+See gcd.
+Take two integers from the stack and replace them with their Greatest Common Denominator.
+Euclid’s Algorithm
+Greater-than-or-equal-to comparison of two numbers.
a b ge
--------------
Boolean
- (a >= b)
-combinator
General Recursion Combinator.
+ (a >= b) +Combinator
+General Recursion Combinator.
[if] [then] [rec1] [rec2] genrec
---------------------------------------------------------------------
- [if] [then] [rec1 [[if] [then] [rec1] [rec2] genrec] rec2] ifte
-Expects an integer and a quote on the stack and returns the item at the -nth position in the quote counting from 0.
-Note that this definition includes the genrec symbol itself, it is self-referential. This is possible because the definition machinery does not check that symbols in defs are in the dictionary. genrec is the only self-referential definition.
See the Recursion Combinators notebook.
+From “Recursion Theory and Joy” by Manfred von Thun:
+++“The genrec combinator takes four program parameters in addition to whatever data parameters it needs. Fourth from the top is an if-part, followed by a then-part. If the if-part yields true, then the then-part is executed and the combinator terminates. The other two parameters are the rec1-part and the rec2-part. If the if-part yields false, the rec1-part is executed. Following that the four program parameters and the combinator are again pushed onto the stack bundled up in a quoted form. Then the rec2-part is executed, where it will find the bundled form. Typically it will then execute the bundled form, either with i or with app2, or some other combinator.”
+
The way to design one of these is to fix your base case [then] and the test [if], and then treat rec1 and rec2 as an else-part “sandwiching” a quotation of the whole function.
For example, given a (general recursive) function F:
F == [I] [T] [R1] [R2] genrecIf the [I] if-part fails you must derive R1 and R2 from: :
... R1 [F] R2Just set the stack arguments in front, and figure out what R1 and R2 have to do to apply the quoted [F] in the proper way. In effect, the genrec combinator turns into an ifte combinator with a quoted copy of the original definition in the else-part:
F == [I] [T] [R1] [R2] genrec
+ == [I] [T] [R1 [F] R2] ifteTail recursive functions are those where R2 is the i combinator:
P == [I] [T] [R] tailrec
+ == [I] [T] [R [P] i] ifte
+ == [I] [T] [R P] ifteExpects an integer and a quote on the stack and returns the item at the nth position in the quote counting from 0.
+ [a b c d] 2 getitem
-------------------------
- c
-Expect a number on the top of the stack and [cons] that many items from under it onto a new list.
-If the number isn’t a valid index into the quote getitem will cause some sort of problem (the exact nature of which is implementation-dependant.)
concat first first_two flatten fourth remove rest reverse rrest second shift shunt size sort split_at split_list swaack third zip
+Expect a number on the top of the stack and cons that many items from under it onto a new list.
+ a b c d e 3 grabN
-----------------------
- a b [c d e]
-A weird function used in [app2] that does this:
+ a b [c d e] +A weird function used in app2 that does this:
... 1 2 3 4 5 grba
-------------------------------
- ... 1 2 3 [4 3 2 1 ...] 5
-It grabs the stack under the top item, and substitutes it for the second item down on the stack.
Greater-than comparison of two numbers.
+ ... 1 2 3 [4 3 2 1 ...] 5 +It grabs the stack under the top item, and substitutes it for the second item down on the stack.
+This function “grabs” an item from the stack along with a copy of the stack. It’s part of the app2 definition.
+See ge.
+See rshift.
+See gt.
+Greater-than comparison of two numbers.
a b gt
--------------
Boolean
- (a > b)
-Accepts a quoted symbol on the top of the stack and prints its -documentation.
+ (a > b) +Accepts a quoted symbol on the top of the stack and prints its documentation.
[foo] help
-----------------
- x y hypot
+----------------Technically this is equivalent to pop, but it will only work if the item on the top of the stack is a quoted symbol.
See pred.
+See sub.
+ x y hypot
---------------------------
- sqrt(sqr(x) + sqr(y))
-combinator built-in
Append a quoted expression onto the pending expression.
- [Q] . i
--------------
- . Q
-The identity function.
combinator
If-Then-Else combinator, a common and convenient specialization of [branch].
+ sqrt(sqr(x) + sqr(y)) +This is another function that has to wait on the numeric tower.
+The identity function.
+Does nothing. It’s kind of a mathematical thing, but it occasionally comes in handy.
+Combinator
+If-Then-Else combinator, a common and convenient specialization of branch.
[if] [then] [else] ifte
---------------------------------------
- [if] nullary [else] [then] branch
-combinator
Take a quoted program from the stack and run it twice, first under the -top item, then again with the top item.
+ [if] nullary [else] [then] branch +Combinator
+Take a quoted program from the stack and run it twice, first under the top item, then again with the top item.
... a [Q] ii
------------------
- ... Q a Q
-It's a little tricky to understand how this works so here's an example trace:
- 1 2 3 4 [++] • [dip] dupdip i
-1 2 3 4 [++] [dip] • dupdip i
- 1 2 3 4 [++] • dip [++] i
- 1 2 3 • ++ 4 [++] i
- 1 2 4 • 4 [++] i
- 1 2 4 4 • [++] i
- 1 2 4 4 [++] • i
- 1 2 4 4 • ++
- 1 2 4 5 •
-combinator
Accept a quoted program and a list on the stack and run the program with -the list as its stack. Does not affect the stack (below the list.)
+ ... Q a Q +It’s a little tricky to understand how this works so here’s an example trace:
+ 1 2 3 4 [++] • [dip] dupdip i
+1 2 3 4 [++] [dip] • dupdip i
+ 1 2 3 4 [++] • dip [++] i
+ 1 2 3 • ++ 4 [++] i
+ 1 2 4 • 4 [++] i
+ 1 2 4 4 • [++] i
+ 1 2 4 4 [++] • i
+ 1 2 4 4 • ++
+ 1 2 4 5 •In some cases (like the example above) this is the same effect as using app2 but most of the time it’s not:
+ 1 2 3 4 [+] ii
+--------------------
+ 1 9
+
+ 1 2 3 4 [+] app2
+----------------------
+ 1 2 5 6Combinator
+Append a quoted expression onto the pending expression.
+ [Q] . i
+-------------
+ . QThis is a fundamental combinator. It is used in all kinds of places. For example, the x combinator can be defined as dup i.
Combinator
+Accept a quoted program and a list on the stack and run the program with the list as its stack. Does not affect the stack (below the list.)
... x y z [a b c] [Q] infra
---------------------------------
c b a Q [z y x ...] swaack
@@ -440,210 +925,370 @@ c b a [F] [...] [i] dip swaack
c b a [F] i [...] swaack
c b a F [...] swaack
d e [...] swaack
-... [e d]
-Create a new Joy function definition in the Joy dictionary. A definition -is given as a quote with a name followed by a Joy expression.
-[sqr dup mul] inscribe
-Less-Than-or-Equal-to comparison of the two items on the top of the -stack, replacing them with a Boolean value.
+... [e d] +This is one of the more useful combinators. It allows a quoted expression to serve as a stack for a program, effectively running it in a kind of “pocket universe”. If the list represents a datastructure then infra lets you work on its internal structure.
Combinator
+Does infra and then extracts the first item from the resulting list.
+Create a new Joy function definition in the Joy dictionary. A definition is given as a quote with a name followed by a Joy expression.
+[sqr dup mul] inscribeThis is the only function that modifies the dictionary. It’s provided as a convenience, for tinkering with new definitions before entering them into the defs.txt file. It can be abused, which you should avoid unless you know what you’re doing.
Less-Than-or-Equal-to comparison of the two items on the top of the stack, replacing them with a Boolean value.
a b le
-------------
Boolean
- (a <= b)
-combinator built-in
Expect a quoted program Q and a Boolean value on the stack. If the value is false
-discard the quoted program, otherwise run a copy of Q and loop again.
See le.
+See ne.
+ ... a <{}
+----------------
+ ... [] aTuck an empty list just under the first item on the stack.
+ ... b a <{}
+-----------------
+ ... [] b aTuck an empty list just under the first two items on the stack.
+See lshift.
+See lt.
+Combinator
+Expect a quoted program Q and a Boolean value on the stack. If the value is false discard the quoted program, otherwise run a copy of Q and loop again.
false [Q] loop
--------------------
true [Q] . loop
--------------------------
- . Q [Q] loop
-This, along with branch and fork, is one of the four main combinators of all programming. The fourth, sequence, is implied by juxtaposition. That is to say, in Joy F G is like G(F(...)) in a language bassed on function application. Or again, to quote the Joy Wikipedia entry,
++In Joy, the meaning function is a homomorphism from the syntactic monoid onto the semantic monoid. That is, the syntactic relation of concatenation of symbols maps directly onto the semantic relation of composition of functions.
+
Anyway, branch, fork, amd loop are the fundamental combinators in Joy. Just as branch has it’s more common and convenient form ifte, loop has while.
+ a n lshift
----------------
- (a×2ⁿ)
-Less-Than comparison of the two items on the top of the -stack, replacing them with a Boolean value.
+ (a×2ⁿ) +Less-Than comparison of the two items on the top of the stack, replacing them with a Boolean value.
a b lt
-------------
Boolean
- (a < b)
-Given an initial state value and a quoted generator function build a -generator quote.
+ (a < b) +Given an initial state value and a quoted generator function build a generator quote.
state [generator function] make_generator
-----------------------------------------------
- [state [generator function] codireco]
- 230 [dup ++] make_generator
---------------------------------
- [230 [dup ++] codireco]
-And then:
[230 [dup ++] codireco] 5 [x] times pop
---------------------------------------------
- 230 231 232 233 234
-combinator
Given a list of items and a quoted program run the program for each item -in the list (with the rest of the stack) and replace the old list and the -program with a list of the results.
-See the “Using x to Generate Values” notebook.
Combinator
+Given a list of items and a quoted program run the program for each item in the list (with the rest of the stack) and replace the old list and the program with a list of the results.
+ 5 [1 2 3] [++ *] map
--------------------------
- 5 [10 15 20]
-Given a list find the maximum.
-This is a common operation in many languages. In Joy it can be a parallelism combinator due to the “pure” nature of the language.
+Given a list find the maximum.
+ [1 2 3 4] max
-------------------
- 4
-Given a list find the minimum.
-Given a list find the minimum.
+ [1 2 3 4] min
-------------------
- 1
-Return the remainder of a divided by b.
Return the remainder of a divided by b.
a b mod
-------------
- (a%b)
-%
Multiply two numbers.
+ (a%b) +See mod.
+Multiply two numbers.
a b mul
-------------
- (a×b)
-Not-Equal comparison of the two items on the top of the -stack, replacing them with a Boolean value.
+ (a×b) +Invert the sign of a number.
+ a neg
+-----------
+ -aNot-Equal comparison of the two items on the top of the stack, replacing them with a Boolean value.
a b ne
-------------
Boolean
- (a = b)
-Like [bool] but convert the item on the top of the stack to the inverse -Boolean value.
+ (a = b) +Like bool but convert the item on the top of the stack to the inverse Boolean value.
true not
--------------
false
false not
---------------
- true
-Take the item on the top of the stack and [cons] it onto [nullary].
Take the item on the top of the stack and cons it onto [nullary].
[F] nulco
-------------------
- [[F] nullary]
-combinator
Run a quoted program without using any stack values and leave the first -item of the result on the stack.
+ [[F] nullary] +Helper function for or and and.
+Combinator
+Run a quoted program without using any stack values and leave the first item of the result on the stack.
... [P] nullary
---------------------
- ... a
-... [P] nullary
... [P] [stack] dip infra first
... stack [P] infra first
... [...] [P] infra first
... [a ...] first
-... a
-Like [getitem] but [swap]s the order of arguments.
-A very useful function that runs any other quoted function and returns it’s first result without disturbing the stack (under the quoted program.)
+Like getitem but swaps the order of arguments.
+ 2 [a b c d] of
--------------------
- c
-[dup] the second item on the stack over the first.
Logical bit-wise OR.
+dup the second item on the stack over the first.
a b over
--------------
- a b a
-There are many many ways to define this function.
--[swap] [tuck]
-[[pop]] [nullary]
-[[dup]] [dip] [swap]
-[unit] [dupdip]
-[unit] [dupdipd] [first]
+
And so on...
combinator
Take a list of quoted functions from the stack and replace it with a list -of the [first] results from running those functions (on copies of the -rest of the stack.)
-+ ++
+ ++
+ ++
+ ++
And so on…
+A fine old word from Forth.
+Combinator
+Take a list of quoted functions from the stack and replace it with a list of the first results from running those functions (on copies of the rest of the stack.)
+ 5 7 [[+][-][*][/][%]] pam
-------------------------------
- 5 7 [12 -2 35 0 5]
-Plus or minus. Replace two numbers with their sum and difference.
+ 5 7 [12 -2 35 0 5] +A specialization of map that runs a list of functions in parallel (if the underlying map function is so implemented, of course.)
+See mod.
+See getitem.
+See add.
+See succ.
+Plus or minus. Replace two numbers with their sum and difference.
a b pm
-----------------
- (a+b) (a-b)
-[pop] the second item down on the stack.
- a b popd
---------------
- b
-[pop] the third item on the stack.
+ (a+b) (a-b) +pop the third item on the stack.
a b c popdd
-----------------
- b c
-[pop] two items from the stack.
- a b popop
----------------
-[pop] the second and third items from the stack.
+ b c +pop popd popop popopd popopdd popopop
+pop the second item down on the stack.
+ a b popd
+--------------
+ bpop popdd popop popopd popopdd popopop
+Pop the top item from the stack and discard it.
+ a pop
+-----------popd popdd popop popopd popopdd popopop
+ a b c d popopdd
+---------------------
+ c dpop popd popdd popop popopd popopop
+pop the second and third items from the stack.
a b c popopd
------------------
- c
- a b c d popopdd
----------------------
- c d
-Take two numbers a and n from the stack and raise a to the nth
-power. (n is on the top of the stack.)
pop popd popdd popop popopd popopdd
+Take two numbers a and n from the stack and raise a to the nth power. (n is on the top of the stack.)
a n pow
-------------
- (aⁿ)
- 2 [2 3 4 5 6 7 8 9] [pow] map
-----------------------------------
- 2 [4 8 16 32 64 128 256 512]
-combinator
From the "Overview of the language JOY"
+ 2 [4 8 16 32 64 128 256 512] +Predecessor. Decrement TOS.
+Combinator
+From the “Overview of the language JOY”
-+The primrec combinator expects two quoted programs in addition to a -data parameter. For an integer data parameter it works like this: If -the data parameter is zero, then the first quotation has to produce the -value to be returned. If the data parameter is positive then the second -has to combine the data parameter with the result of applying the -function to its predecessor.
-5 [1] [*] primrec
-Then primrec tests whether the top element on the stack (initially the -5) is equal to zero. If it is, it pops it off and executes one of the -quotations, the [1] which leaves 1 on the stack as the result. -Otherwise it pushes a decremented copy of the top element and recurses. -On the way back from the recursion it uses the other quotation, [*], -to multiply what is now a factorial on top of the stack by the second -element on the stack.
+The primrec combinator expects two quoted programs in addition to a data parameter. For an integer data parameter it works like this: If the data parameter is zero, then the first quotation has to produce the value to be returned. If the data parameter is positive then the second has to combine the data parameter with the result of applying the function to its predecessor.
+
++5 [1] [*] primrec
+
+Then primrec tests whether the top element on the stack (initially the 5) is equal to zero. If it is, it pops it off and executes one of the quotations, the [1] which leaves 1 on the stack as the result. Otherwise it pushes a decremented copy of the top element and recurses. On the way back from the recursion it uses the other quotation, [*], to multiply what is now a factorial on top of the stack by the second element on the stack.
0 [Base] [Recur] primrec
------------------------------
@@ -651,141 +1296,278 @@ element on the stack.
n [Base] [Recur] primrec
------------------------------------------ n > 0
- n (n-1) [Base] [Recur] primrec Recur
-Just as [sum] sums a list of numbers, this function multiplies them -together.
-Simple and useful specialization of the genrec combinator from the original Joy system.
+Just as sum sums a list of numbers, this function multiplies them together.
+-1 [swap] [[mul]] [step]
+
Or,
-[1] [[mul]] [primrec]
-
"Quote D" Wrap the second item on the stack in a list.
+ + +Is the item on the top of the stack “truthy”?
+You often want to test the truth value of an item on the stack without consuming the item.
+“Quote D” Wrap the second item on the stack in a list.
a b quoted
----------------
- [a] b
-Expect a number n on the stack and replace it with a list:
-[(n-1)...0].
This comes from the original Joy stuff.
+Expect a number n on the stack and replace it with a list: [(n-1)...0].
5 range
-----------------
[4 3 2 1 0]
-5 range
--------------
- []
-[0 <=] [-- dup] anamorphism
Take a number n from the stack and replace it with a list
-[0...n].
If n is less than 1 the resulting list is empty.
Take a number n from the stack and replace it with a list [0...n].
5 range_to_zero
---------------------
- [0 1 2 3 4 5]
-unit [down_to_zero] infra
Replace the first item in a list with the item under it.
+ [0 1 2 3 4 5] +Note that the order is reversed compared to range.
+Replace the first item in a list with the item under it.
a [b ...] reco
--------------------
- [a ...]
-Expects an item on the stack and a quote under it and removes that item -from the the quote. The item is only removed once. If the list is empty -or the item isn't in the list then the list is unchanged.
+ [a ...] +See mod.
+See mod.
+Expects an item on the stack and a quote under it and removes that item from the the quote. The item is only removed once. If the list is empty or the item isn’t in the list then the list is unchanged.
[1 2 3 1] 1 remove
------------------------
- [2 3 1]
-See the "Remove Function" notebook.
built-in
[a ...] rest
+ [2 3 1]See the “Remove Function” notebook.
+ [a ...] rest
------------------
- [...]
-Reverse the list on the top of the stack.
-Reverse the list on the top of the stack.
+ [1 2 3] reverse
---------------------
- [3 2 1]
- a b c rolldown
+ [3 2 1] a b c rolldown
--------------------
- b c a
-roll<
a b c rollup
+ b c aSee rollup.
+See rolldown.
+ a b c rollup
------------------
- c a b
-roll>
Round a number to a given precision in decimal digits.
[a b ...] rrest
+ c a bRound a number to a given precision in decimal digits.
+Another one that won’t make sense until the “numeric tower” is nailed down.
+ [a b ...] rrest
---------------------
- [...]
- a n rshift
----------------
- (a∕2ⁿ)
-Run a quoted program in a list.
-Run a quoted program in a list.
+ [1 2 +] run
-----------------
- [3]
- [a b ...] second
+ [3] [a b ...] second
----------------------
- b
-Use a Boolean value to select one of two items from a sequence. :
+ b +Use a Boolean value to select one of two items from a sequence. :
[a b] false select
------------------------
a
[a b] true select
-----------------------
- b
-Print redistribution information.
Move the top item from one list to another.
-The sequence can contain more than two items but not fewer.
+Print redistribution information.
+Mathematically this is a form of id, but it has the side-effect of printing out the GPL notice.
+Move the top item from one list to another.
+ [x y z] [a b c] shift
---------------------------
- [a x y z] [b c]
-Like [concat] but [reverse] the top list into the second.
-Like concat but reverse the top list into the second.
+ [a b c] [d e f] shunt
---------------------------
- [f e d a b c]
-Replace a list with its size.
-This is more efficient than concat so prefer it if you don’t need to preserve order.
+Replace a list with its size.
+ [23 [cats] 4] size
------------------------
- 3
-Example code.
[[[abs] ii <=] [[<>] [pop !-] or] and] [[!-] [[++]] [[--]] ifte dip] [[pop !-] [--] [++] ifte] ifte
Split a list (second on the stack) at the position given by the number on -the top of the stack.
-Example code.
+See the “Square Spiral Example Joy Code” notebook.
+Split a list (second on the stack) at the position given by the number on the top of the stack.
+ [1 2 3 4 5 6 7] 4 split_at
--------------------------------
- [5 6 7] [4 3 2 1]
-Split a list (second on the stack) at the position given by the number on -the top of the stack such that [concat] would reconstruct the original -list.
+ [5 6 7] [4 3 2 1] +Take a list and a number n from the stack, take n items from the top of the list and shunt them onto a new list that replaces the number n on the top of the stack.
Split a list (second on the stack) at the position given by the number on the top of the stack such that concat would reconstruct the original list.
[1 2 3 4 5 6 7] 4 split_list
----------------------------------
- [1 2 3 4] [5 6 7]
-Square the number on the top of the stack.
+ [1 2 3 4] [5 6 7] +Compare with split_at. This function does extra work to ensure that concat would reconstruct the original list.
+Square the number on the top of the stack.
n sqr
------------
- n²
-Function Combinator
-Return the square root of the number a. Negative numbers return complex -roots.
built-in
Put the stack onto the stack.
- ... c b a stack
----------------------------
- ... c b a [a b c ...]
-Grab the stack under the top item and put it onto the stack.
-Function Combinator
+Return the square root of the number a. Negative numbers return complex roots.
+Another “numeric tower” hatch…
+Grab the stack under the top item and put it onto the stack.
+ ... 1 2 3 stackd
------------------------
- ... 1 2 [2 1 ...] 3
-combinator
Run a quoted program on each item in a sequence.
+ ... 1 2 [2 1 ...] 3 +Put the stack onto the stack.
+ ... c b a stack
+---------------------------
+ ... c b a [a b c ...]This function forms a pair with [unstack], and together they form the complement to the “destructive” pair enstacken and disenstacken.
+Combinator
+Run a quoted program on each item in a sequence.
... [] [Q] step
---------------------
...
@@ -798,70 +1580,136 @@ complement to the "destructive" pair [enstacken] and [disenstacken].combinator
Like [step] but with 0 as the initial value.
+ ... a . Q [b c] [Q] step +See the Recursion Combinators notebook.
+Combinator
+Like step but with 0 as the initial value.
[...] [F] step_zero
-------------------------
- 0 [...] [F] step
-Take the [stack] and [uncons] the top two items.
-Take the stack and uncons the top two items.
+ 1 2 3 stununcons
----------------------
- 1 2 3 3 2 [1]
-Subtract the number on the top of the stack from the number below it.
+ 1 2 3 3 2 [1] +Subtract the number on the top of the stack from the number below it.
a b sub
-------------
- (a-b)
-combinator
Given a quoted sequence of numbers return the sum.
-Successor. Increment TOS.
+Combinator
+Given a quoted sequence of numbers return the sum.
+ [1 2 3 4 5] sum
---------------------
- 15
-built-in
Swap stack. Take a list from the top of the stack, replace the stack -with the list, and put the old stack onto it.
-Swap stack. Take a list from the top of the stack, replace the stack with the list, and put the old stack onto it.
+ 1 2 3 [4 5 6] swaack
--------------------------
- 6 5 4 [3 2 1]
-Swap the second and third items on the stack.
+ 6 5 4 [3 2 1] +This function works as a kind of “context switch”. It’s used in the definition of infra.
+Swap the second and third items on the stack.
a b c swapd
-----------------
- b a c
-Like [cons] but [swap] the item and list.
+ b a c +Swap the top two items on the stack.
+ a b swap
+--------------
+ b aconcat two lists, but swap the lists first.
+Like cons but swap the item and list.
[...] a swons
-------------------
- [a ...]
-combinator
A specialization of the [genrec] combinator.
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.
Combinator
+A specialization of the genrec combinator.
+Some recursive functions do not need to store additional data or pending actions per-call. These are called “tail recursive” functions. In Joy, they appear as genrec definitions that have i for the second half of their recursive branch.
+See the Recursion Combinators notebook.
+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
----------------------
- [b a]
-combinator
Run a quoted program using exactly three stack values and leave the first -item of the result on the stack.
+ [b a] +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] ternary
-------------------------
- ... a
- [a b c ...] third
+ ... aRuns any other quoted function and returns its first result while consuming exactly three items from the stack.
+ [a b c ...] third
-----------------------
- c
-combinator
Expect a quoted program and an integer n on the stack and do the
-program n times.
Combinator
+Expect a quoted program and an integer n on the stack and do the program n times.
... n [Q] . times
----------------------- w/ n <= 0
... .
@@ -872,80 +1720,139 @@ program n times.
... n [Q] . times
------------------------------------- w/ n > 1
- ... . Q (n-1) [Q] times
-[dup] the item on the top of the stack under the second item on the -stack.
+ ... . Q (n-1) [Q] times +This works by building a little while program and running it:
+ 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 popThis 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.
+See bool.
+dup the item on the top of the stack under the second item on the stack.
a b tuck
--------------
- b a b
-(Combinator)
-Run a quoted program using exactly one stack value and leave the first -item of the result on the stack.
+ b a b +(Combinator)
+Run a quoted program using exactly one stack value and leave the first item of the result on the stack.
... x [P] unary
---------------------
- ... a
-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.
Runs any other quoted function and returns its first result while consuming exactly one item from the stack.
+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 [...]
-Given a list remove duplicate items.
a unit
+ a [...]This is the inverse of cons.
+Given a list remove duplicate items.
+ a unit
------------
- [a]
-[] cons
combinator
Unquote (using [i]) the list that is second on the stack.
-Combinator
+Unquote (using i) the list that is second on the stack.
+ 1 2 [3 4] 5 unquoted
--------------------------
- 1 2 3 4 5
- [a ...] unswons
+ 1 2 3 4 5 [a ...] unswons
---------------------
- [...] a
-True if the form on TOS is void otherwise False.
Print warranty information.
combinator
A specialization of [loop] that accepts a quoted predicate program P
-and runs it [nullary].
Combinator
+Short-circuiting Boolean OR
+Accept two quoted programs, run the first and expect a Boolean value, if it’s false pop it and run the second program (which should also return a Boolean value) otherwise pop the second program (leaving true on the stack.)
[A] [B] ||
+---------------- A -> false
+ B
+
+
+ [A] [B] ||
+---------------- A -> true
+ trueTrue if the form on TOS is void otherwise False.
+A form is any Joy expression composed solely of lists. This represents a binary Boolean logical formula in the arithmetic of the “Laws of Form”, see The Markable Mark
+Print warranty information.
+Combinator
+A specialization of loop that accepts a quoted predicate program P and runs it nullary.
[P] [F] while
------------------- P -> false
[P] [F] while
--------------------- P -> true
- F [P] [F] while
-Print all the words in alphabetical order.
combinator
Take a quoted function F and run it with itself as the first item on
-the stack.
Print all the words in alphabetical order.
+Mathematically this is a form of id.
+Combinator
+Take a quoted function F and run it with itself as the first item on the stack.
[F] x
-----------
- [F] F
-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.
-The simplest recursive pattern.
+See the Recursion Combinators notebook. as well as Recursion Theory and Joy by Manfred von
+Logical bit-wise eXclusive OR.
+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.
+ [1 2 3] [4 5 6] zip
-------------------------
- [[4 1] [5 2] [6 3]]
-combinator
Short-circuiting Boolean OR