Version -10.0.0 Each function, combinator, or definition should be documented here. -------------- ## & See [and](#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.) [A] [B] && ---------------- 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. ### Discussion This is seldom useful, I suspect, but this way you have it. ### Crosslinks [||](#section-25) -------------- ## * See [mul](#mul). -------------- ## • See [id](#id). -------------- ## ^ See [xor](#xor). -------------- ## = See [eq](#eq). -------------- ## != See [ne](#ne). ------------------------------------------------------------------------ ## !- Function Not negative. n !- ----------- n < 0 false n !- ---------- n >= 0 true ### Definition 0 \>= ### Discussion Return a Boolean value indicating if a number is greater than or equal to zero. -------------- ## > See [gt](#gt). -------------- ## >= See [ge](#ge). -------------- ## >> See [rshift](#rshift). -------------- ## - See [sub](#sub). -------------- ## -- See [pred](#pred). -------------- ## < See [lt](#lt). -------------- ## <= See [le](#le). -------------- ## <> See [ne](#ne). ------------------------------------------------------------------------ ## \<\{\} Function ... a <{} ---------------- ... [] a ### Definition [] swap ### Discussion Tuck an empty list just under the first item on the stack. ### Crosslinks [<<{}](#section-18) -------------- ## << See [lshift](#lshift). ------------------------------------------------------------------------ ## \<\<\{\} Function ... b a <{} ----------------- ... [] b a ### Definition [] rollup ### Discussion Tuck an empty list just under the first two items on the stack. ### Crosslinks [<{}](#section-16) -------------- ## % See [mod](#mod). -------------- ## + See [add](#add). -------------- ## ++ See [succ](#succ). ------------------------------------------------------------------------ ## ? Function Is the item on the top of the stack "truthy"? ### Definition > [dup](#dup) [bool](#bool) ### Discussion You often want to test the truth value of an item on the stack without consuming the item. ### Crosslinks [bool](#bool) -------------- ## / See [floordiv](#floordiv). -------------- ## // See [floordiv](#floordiv). -------------- ## /floor See [floordiv](#floordiv). ------------------------------------------------------------------------ ## \|\| Combinator Short-circuiting Boolean OR ### Definition > [nulco](#nulco) \[[nullary](#nullary)\] [dip](#dip) \[true\] [branch](#branch) ### Discussion 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 true ### Crosslinks [&&](#section-1) ------------------------------------------------------------------------ ## abs Function Return the absolute value of the argument. ### Definition > [dup](#dup) 0 < [] \[[neg](#neg)\] [branch](#branch) ------------------------------------------------------------------------ ## add Basis Function Add two numbers together: a + b. ------------------------------------------------------------------------ ## anamorphism 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 ### Definition > \[[pop](#pop) \[\]\] [swap](#swap) \[[dip](#dip) [swons](#swons)\] [genrec](#genrec) ### Example The `range` function generates a list of the integers from 0 to n - 1: > \[0 <=\] \[\-\- dup\] anamorphism ### Discussion See the [Recursion Combinators notebook](https://joypy.osdn.io/notebooks/Recursion_Combinators.html). ------------------------------------------------------------------------ ## and Basis Function Logical bit-wise AND. ### Crosslinks [or](#or) [xor](#xor) -------------------- ## app1 "apply one" Combinator 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. ... x [Q] app1 --------------------------------- ... [x ...] [Q] infra first This is the same effect as the [unary](#unary) combinator. ### Definition > [nullary](#nullary) [popd](#popd) ### Discussion Just a specialization of `nullary` really. Its parallelizable cousins are more useful. ### Crosslinks [app2](#app2) [app3](#app3) [appN](#appN) [unary](#unary) ------------------------------------------------------------------------ ## app2 Combinator Like [app1](#app1) with two items. ... y x [Q] . app2 ----------------------------------- ... [y ...] [Q] . infra first [x ...] [Q] infra first ### Definition > \[[grba] [swap] [grba] [swap]\] [dip] \[[infrst]\] [cons] [ii] ### Discussion Unlike [app1](#app1), which is essentially an alias for [unary](#unary), this function is not the same as [binary](#binary). Instead of running one program using exactly two items from the stack and pushing one result (as [binary](#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. ### Crosslinks [app1](#app1) [app3](#app3) [appN](#appN) [unary](#unary) ------------------------------------------------------------------------ ## app3 Combinator Like [app1] with three items. ... z y x [Q] . app3 ----------------------------------- ... [z ...] [Q] . infra first [y ...] [Q] infra first [x ...] [Q] infra first ### Definition > 3 [appN] ### Discussion See [app2]. ### Crosslinks [app1](#app1) [app2](#app2) [appN](#appN) [unary](#unary) ------------------------------------------------------------------------ ## appN 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 ### Definition > \[[grabN]\] [codi] [map] [disenstacken] ### Discussion 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]. ### Crosslinks [app1](#app1) [app2](#app2) [app3](#app3) [unary](#unary) -------------- ## at See [getitem](#getitem). ------------------------------------------------------------------------ ## average Function Compute the average of a list of numbers. (Currently broken until I can figure out what to do about "numeric tower" in Thun.) ### Definition > \[[sum]\] \[[size]\] [cleave] [/] ### Discussion 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](https://joypy.osdn.io/notebooks/Recursion_Combinators.html). -------------------- ## b Combinator Run two quoted programs [P] [Q] b --------------- P Q ### Definition > \[[i]\] [dip] [i] ### Discussion This combinator may seem trivial but it comes in handy. ### Crosslinks [dupdip](#dupdip) [ii](#ii) -------------------- ## binary 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 ### Definition > [unary] [popd] ### Discussion Runs any other quoted function and returns its first result while consuming exactly two items from the stack. ### Crosslinks [nullary](#nullary) [ternary](#ternary) [unary](#unary) ------------------------------------------------------------------------ ## bool Basis Function Convert the item on the top of the stack to a Boolean value. ### Discussion For integers 0 is `false` and any other number is `true`; for lists the empty list is `false` and all other lists are `true`. ### Crosslinks [not] ------------------------------------------------------------------------ ## branch Basis Combinator Use a Boolean value to select and run one of two quoted programs. false [F] [T] branch -------------------------- F true [F] [T] branch ------------------------- T ### Definition > [rolldown] [choice] [i] ### Discussion This 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]. ### Crosslinks [choice] [ifte] [select] ------------------------------------------------------------------------ ## ccccons Function a b c d [...] ccccons --------------------------- [a b c d ...] Do [cons] four times. ### Definition > [ccons] [ccons] ### Crosslinks [ccons] [cons] [times] -------------------- ## ccons Function a b [...] ccons --------------------- [a b ...] Do [cons] two times. ### Definition > [cons] [cons] ### Crosslinks [cons] [ccons] ------------------------------------------------------------------------ ## choice Basis Function Use a Boolean value to select one of two items. a b false choice ---------------------- a a b true choice --------------------- b ### Definition > \[[pop]\] \[[popd]\] [branch] ### Discussion It's a matter of taste whether you implement this in terms of [branch] or the other way around. ### Crosslinks [branch] [select] ------------------------------------------------------------------------ ## clear Basis Function Clear everything from the stack. ### Definition > [stack] [bool] \[[pop] [stack] [bool]\] [loop] ### Crosslinks [stack] [swaack] ------------------------------------------------------------------------ ## cleave Combinator Run two programs in parallel, consuming one additional item, and put their results on the stack. ... x [A] [B] cleave ------------------------ ... a b ### Derivation > [fork] [popdd] ### Example 1 2 3 [+] [-] cleave -------------------------- 1 2 5 -1 ### Discussion One of a handful of useful parallel combinators. ### Crosslinks [clop] [fork] [map] ------------------------------------------------------------------------ ## clop Combinator Run two programs in parallel, consuming two additional items, and put their results on the stack. ... x y [A] [B] clop -------------------------- ... a b ### Definition > [cleave] [popdd] ### Discussion Like [cleave] but consumes an additional item from the stack. 1 2 3 4 [+] [-] clop -------------------------- 1 2 7 -1 ### Crosslinks [cleave] [fork] [map] ------------------------------------------------------------------------ ## cmp 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 [G] [E] [L] cmp ------------------------- a > b G a b [G] [E] [L] cmp ------------------------- a = b E a b [G] [E] [L] cmp ------------------------- a < b L ### Discussion 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] [LE] dup cmp [GE] [L] dupd cmp Or even: [GL] [E] over cmp ### Crosslinks TODO: link to tree notebooks where this was used. ------------------------------------------------------------------------ ## codi 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. a b [F] . codi -------------------- b . F a ### Definition > [cons] [dip] ### Discussion This is one of those weirdly specific functions that turns out to be useful in a few places. ### Crosslinks [appN] [codireco] ------------------------------------------------------------------------ ## codireco Combinator This is part of the [make_generator] function. You would not use this combinator directly. ### Definition > [codi] [reco] ### Discussion See [make_generator] and the ["Using `x` to Generate Values" notebook](https://joypy.osdn.io/notebooks/Generator_Programs.html#an-interesting-variation) as well as [Recursion Theory and Joy](https://www.kevinalbrecht.com/code/joy-mirror/j05cmp.html) by Manfred von Thun. ### Crosslinks [make_generator] ------------------------------------------------------------------------ ## concat Function Concatinate two lists. [a b c] [d e f] concat ---------------------------- [a b c d e f] ### Crosslinks [first] [first_two] [flatten] [fourth] [getitem] [remove] [rest] [reverse] [rrest] [second] [shift] [shunt] [size] [sort] [split_at] [split_list] [swaack] [third] [zip] ------------------------------------------------------------------------ ## cond 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 ] ... [ [PredicateN] FunctionN ] [Default] ] cond ### Discussion It works by rewriting into a chain of nested [ifte]{.title-ref} expressions, e.g.: [[[B0] T0] [[B1] T1] [D]] cond ----------------------------------------- [B0] [T0] [[B1] [T1] [D] ifte] ifte ### Crosslinks [ifte] -------------------- ## cons Basis Function Given an item and a list, append the item to the list to make a new list. a [...] cons ------------------ [a ...] ### Discussion Cons is a [venerable old function from Lisp](https://en.wikipedia.org/wiki/Cons#Lists). Its inverse operation is [uncons]. ### Crosslinks [uncons] ------------------------------------------------------------------------ ## dinfrirst Combinator Specialist function (that means I forgot what it does and why.) ### Definition > [dip] [infrst] ------------------------------------------------------------------------ ## dip Basis 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 x ### Discussion This along with [infra] are enough to update any datastructure. See the ["Traversing Datastructures with Zippers" notebook](https://joypy.osdn.io/notebooks/Zipper.html). 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.) ### Crosslinks [dipd] [dipdd] [dupdip] [dupdipd] [infra] ------------------------------------------------------------------------ ## dipd Combinator Like [dip] but expects two items. ... y x [Q] . dipd ------------------------- ... . Q y x ### Discussion See [dip]. ### Crosslinks [dip] [dipdd] [dupdip] [dupdipd] [infra] ------------------------------------------------------------------------ ## dipdd Combinator Like [dip] but expects three items. : ... z y x [Q] . dip ----------------------------- ... . Q z y x ### Discussion See [dip]. ### Crosslinks [dip] [dipd] [dupdip] [dupdipd] [infra] ------------------------------------------------------------------------ ## disenstacken Function 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 ### Definition > \[[clear]\] [dip] [reverse] [unstack](#unstack) ### Discussion Note 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. ### Crosslinks [enstacken] [stack] [unstack](#unstack) -------------- ## div See [floordiv](#floordiv). ------------------------------------------------------------------------ ## divmod Function x y divmod ------------------ q r (x/y) (x%y) Invariant: `qy + r = x`. ### Definition > \[[floordiv]\] \[[mod]\] [clop] ------------------------------------------------------------------------ ## down_to_zero Function Given a number greater than zero put all the Natural numbers (including zero) less than that onto the stack. ### Example 3 down_to_zero -------------------- 3 2 1 0 ### Definition > \[0 \>\] \[[dup] [--]\] [while] ### Crosslinks [range] ------------------------------------------------------------------------ ## drop Function Expects an integer and a quote on the stack and returns the quote with n items removed off the top. ### Example [a b c d] 2 drop ---------------------- [c d] ### Definition > \[[rest]\] [times] ### Crosslinks [take] ------------------------------------------------------------------------ ## dup Basis Function "Dup"licate the top item on the stack. a dup ----------- a a ### Crosslinks [dupd] [dupdd] [dupdip] [dupdipd] ------------------------------------------------------------------------ ## dupd Function [dup] the second item down on the stack. a b dupd -------------- a a b ### Definition > \[[dup]\] [dip] ### Crosslinks [dup] [dupdd] [dupdip] [dupdipd] ------------------------------------------------------------------------ ## dupdd Function [dup] the third item down on the stack. a b c dupdd ----------------- a a b c ### Definition > \[[dup]\] [dipd] ### Crosslinks [dup] [dupd] [dupdip] [dupdipd] ------------------------------------------------------------------------ ## dupdip Combinator Apply a function `F` and [dup] the item under it on the stack. a [F] dupdip ------------------ a F a ### Definition > [dupd] [dip] ### Derivation a [F] dupdip a [F] dupd dip a [F] [dup] dip dip a dup [F] dip a a [F] dip a F a ### Discussion A very common and useful combinator. ### Crosslinks [dupdipd] ------------------------------------------------------------------------ ## dupdipd Combinator Run a copy of program `F` under the next item down on the stack. a [F] dupdipd ------------------- F a [F] ### Definition > [dup] [dipd] ### Crosslinks [dupdip] ------------------------------------------------------------------------ ## enstacken Basis Function Combinator stack \[clear\] dip Gentzen diagram. ### Definition if not basis. ### Derivation if not basis. ### Source if basis ### Discussion Lorem ipsum. ### Crosslinks Lorem ipsum. ------------------------------------------------------------------------ ## eq Basis Function Combinator Same as a == b. Gentzen diagram. ### Definition if not basis. ### Derivation if not basis. ### Source if basis ### Discussion Lorem ipsum. ### Crosslinks Lorem ipsum. ------------------------------------------------------------------------ ## first Basis Function Combinator ([a1 ...1] -- a1) Gentzen diagram. ### Definition if not basis. ### Derivation if not basis. ### Source if basis ### Discussion Lorem ipsum. ### Crosslinks Lorem ipsum. ------------------------------------------------------------------------ ## first_two Basis Function Combinator ([a1 a2 ...1] -- a1 a2) Gentzen diagram. ### Definition if not basis. ### Derivation if not basis. ### Source if basis ### Discussion Lorem ipsum. ### Crosslinks Lorem ipsum. ------------------------------------------------------------------------ ## flatten Basis Function Combinator \<{} \[concat\] step Gentzen diagram. ### Definition if not basis. ### Derivation if not basis. ### Source if basis ### Discussion Lorem ipsum. ### Crosslinks Lorem ipsum. ------------------------------------------------------------------------ ## floor Basis Function Combinator Return the floor of x as an Integral. This is the largest integer \<= x. Gentzen diagram. ### Definition if not basis. ### Derivation if not basis. ### Source if basis ### Discussion Lorem ipsum. ### Crosslinks Lorem ipsum. ------------------------------------------------------------------------ ## floordiv Basis Function Combinator Same as a // b. Gentzen diagram. ### Definition if not basis. ### Derivation if not basis. ### Source if basis ### Discussion Lorem ipsum. ### Crosslinks Lorem ipsum. ------------------------------------------------------------------------ ## fork Basis Function Combinator \[i\] app2 Gentzen diagram. ### Definition if not basis. ### Derivation if not basis. ### Source if basis ### Discussion Lorem ipsum. ### Crosslinks Lorem ipsum. ------------------------------------------------------------------------ ## fourth Basis Function Combinator ([a1 a2 a3 a4 ...1] -- a4) Gentzen diagram. ### Definition if not basis. ### Derivation if not basis. ### Source if basis ### Discussion Lorem ipsum. ### Crosslinks Lorem ipsum. ------------------------------------------------------------------------ ## gcd Basis Function Combinator true \[tuck mod dup 0 \>\] loop pop Gentzen diagram. ### Definition if not basis. ### Derivation if not basis. ### Source if basis ### Discussion Lorem ipsum. ### Crosslinks Lorem ipsum. ------------------------------------------------------------------------ ## gcd2 Basis Function Combinator Compiled GCD function. Gentzen diagram. ### Definition if not basis. ### Derivation if not basis. ### Source if basis ### Discussion Lorem ipsum. ### Crosslinks Lorem ipsum. ------------------------------------------------------------------------ ## ge Basis Function Combinator Same as a \>= b. Gentzen diagram. ### Definition if not basis. ### Derivation if not basis. ### Source if basis ### Discussion Lorem ipsum. ### Crosslinks Lorem ipsum. ------------------------------------------------------------------------ ## genrec Basis Function Combinator General Recursion Combinator. : [if] [then] [rec1] [rec2] genrec --------------------------------------------------------------------- [if] [then] [rec1 [[if] [then] [rec1] [rec2] genrec] rec2] ifte From \"Recursion Theory and Joy\" (j05cmp.html) 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] genrec If the \[I\] if-part fails you must derive R1 and R2 from: : ... R1 [F] R2 Just 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] ifte Primitive recursive functions are those where R2 == i. : P == [I] [T] [R] tailrec == [I] [T] [R [P] i] ifte == [I] [T] [R P] ifte Gentzen diagram. ### Definition if not basis. ### Derivation if not basis. ### Source if basis ### Discussion Lorem ipsum. ### Crosslinks Lorem ipsum. ------------------------------------------------------------------------ ## getitem Basis Function Combinator getitem == drop first Expects 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] 0 getitem ------------------------- a Gentzen diagram. ### Definition if not basis. ### Derivation if not basis. ### Source if basis ### Discussion Lorem ipsum. ### Crosslinks Lorem ipsum. ------------------------------------------------------------------------ ## grabN Basis Function Combinator \<{} \[cons\] times Gentzen diagram. ### Definition if not basis. ### Derivation if not basis. ### Source if basis ### Discussion Lorem ipsum. ### Crosslinks Lorem ipsum. ------------------------------------------------------------------------ ## grba Basis Function Combinator \[stack popd\] dip Gentzen diagram. ### Definition if not basis. ### Derivation if not basis. ### Source if basis ### Discussion Lorem ipsum. ### Crosslinks Lorem ipsum. ------------------------------------------------------------------------ ## gt Basis Function Combinator Same as a \> b. Gentzen diagram. ### Definition if not basis. ### Derivation if not basis. ### Source if basis ### Discussion Lorem ipsum. ### Crosslinks Lorem ipsum. ------------------------------------------------------------------------ ## help Basis Function Combinator Accepts a quoted symbol on the top of the stack and prints its docs. Gentzen diagram. ### Definition if not basis. ### Derivation if not basis. ### Source if basis ### Discussion Lorem ipsum. ### Crosslinks Lorem ipsum. ------------------------------------------------------------------------ ## hypot Basis Function Combinator \[sqr\] ii + sqrt Gentzen diagram. ### Definition if not basis. ### Derivation if not basis. ### Source if basis ### Discussion Lorem ipsum. ### Crosslinks Lorem ipsum. -------------------- ## i (Basis Combinator) Append a quoted expression onto the pending expression. [Q] i ----------- Q ### Source combo(i, [list(P)|S], S, Ei, Eo) :- append(P, Ei, Eo). ### Discussion This is probably the fundamental combinator. You wind up using it in all kinds of places (for example, the `x` combinator can be defined as `dup i`.) ------------------------------------------------------------------------ ## id Basis Function Combinator The identity function. Gentzen diagram. ### Definition if not basis. ### Derivation if not basis. ### Source if basis ### Discussion Lorem ipsum. ### Crosslinks Lorem ipsum. ------------------------------------------------------------------------ ## ifte Basis Function Combinator If-Then-Else Combinator : ... [if] [then] [else] ifte --------------------------------------------------- ... [[else] [then]] [...] [if] infra select i ... [if] [then] [else] ifte ------------------------------------------------------- ... [else] [then] [...] [if] infra first choice i Has the effect of grabbing a copy of the stack on which to run the if-part using infra. Gentzen diagram. ### Definition if not basis. ### Derivation if not basis. ### Source if basis ### Discussion Lorem ipsum. ### Crosslinks Lorem ipsum. ------------------------------------------------------------------------ ## ii Basis Function Combinator ... a [Q] ii ------------------ ... Q a Q Gentzen diagram. ### Definition if not basis. ### Derivation if not basis. ### Source if basis ### Discussion Lorem ipsum. ### Crosslinks Lorem ipsum. -------------------- ## infra (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.) ... [a b c] [Q] infra --------------------------- c b a Q [...] swaack ### Definition swons swaack [i] dip swaack ### Discussion 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. ### Crosslinks [swaack](#swaack) ------------------------------------------------------------------------ ## infrst Basis Function Combinator infra first Gentzen diagram. ### Definition if not basis. ### Derivation if not basis. ### Source if basis ### Discussion Lorem ipsum. ### Crosslinks Lorem ipsum. ------------------------------------------------------------------------ ## inscribe Basis Function Combinator 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. for example: > \[sqr dup mul\] inscribe Gentzen diagram. ### Definition if not basis. ### Derivation if not basis. ### Source if basis ### Discussion Lorem ipsum. ### Crosslinks Lorem ipsum. ------------------------------------------------------------------------ ## le Basis Function Combinator Same as a \<= b. Gentzen diagram. ### Definition if not basis. ### Derivation if not basis. ### Source if basis ### Discussion Lorem ipsum. ### Crosslinks Lorem ipsum. ------------------------------------------------------------------------ ## loop Basis Function Combinator Basic loop combinator. : ... True [Q] loop ----------------------- ... Q [Q] loop ... False [Q] loop ------------------------ ... Gentzen diagram. ### Definition if not basis. ### Derivation if not basis. ### Source if basis ### Discussion Lorem ipsum. ### Crosslinks Lorem ipsum. ------------------------------------------------------------------------ ## lshift Basis Function Combinator Same as a \<\< b. Gentzen diagram. ### Definition if not basis. ### Derivation if not basis. ### Source if basis ### Discussion Lorem ipsum. ### Crosslinks Lorem ipsum. ------------------------------------------------------------------------ ## lt Basis Function Combinator Same as a \< b. Gentzen diagram. ### Definition if not basis. ### Derivation if not basis. ### Source if basis ### Discussion Lorem ipsum. ### Crosslinks Lorem ipsum. ------------------------------------------------------------------------ ## make_generator Basis Function Combinator \[codireco\] ccons Gentzen diagram. ### Definition if not basis. ### Derivation if not basis. ### Source if basis ### Discussion Lorem ipsum. ### Crosslinks Lorem ipsum. ------------------------------------------------------------------------ ## map Basis Function Combinator Run the quoted program on TOS on the items in the list under it, push a new list with the results in place of the program and original list. Gentzen diagram. ### Definition if not basis. ### Derivation if not basis. ### Source if basis ### Discussion Lorem ipsum. ### Crosslinks Lorem ipsum. ------------------------------------------------------------------------ ## max Basis Function Combinator Given a list find the maximum. Gentzen diagram. ### Definition if not basis. ### Derivation if not basis. ### Source if basis ### Discussion Lorem ipsum. ### Crosslinks Lorem ipsum. ------------------------------------------------------------------------ ## min Basis Function Combinator Given a list find the minimum. Gentzen diagram. ### Definition if not basis. ### Derivation if not basis. ### Source if basis ### Discussion Lorem ipsum. ### Crosslinks Lorem ipsum. ------------------------------------------------------------------------ ## mod Basis Function Combinator Same as a % b. Gentzen diagram. ### Definition if not basis. ### Derivation if not basis. ### Source if basis ### Discussion Lorem ipsum. ### Crosslinks Lorem ipsum. -------------- ## modulus See [mod](#mod). ------------------------------------------------------------------------ ## mul Basis Function Combinator Same as a \* b. Gentzen diagram. ### Definition if not basis. ### Derivation if not basis. ### Source if basis ### Discussion Lorem ipsum. ### Crosslinks Lorem ipsum. ------------------------------------------------------------------------ ## ne Basis Function Combinator Same as a != b. Gentzen diagram. ### Definition if not basis. ### Derivation if not basis. ### Source if basis ### Discussion Lorem ipsum. ### Crosslinks Lorem ipsum. ------------------------------------------------------------------------ ## neg Basis Function Combinator Same as -a. Gentzen diagram. ### Definition if not basis. ### Derivation if not basis. ### Source if basis ### Discussion Lorem ipsum. ### Crosslinks Lorem ipsum. ------------------------------------------------------------------------ ## not Basis Function Combinator Same as not a. Gentzen diagram. ### Definition if not basis. ### Derivation if not basis. ### Source if basis ### Discussion Lorem ipsum. ### Crosslinks Lorem ipsum. -------------------- ## !- "not negative" (Function, Boolean Predicate) Integer on top of stack is replaced by Boolean value indicating whether it is non-negative. N !- ----------- N < 0 false N !- ---------- N >= 0 true ### Definition 0 >= ------------------------------------------------------------------------ ## nulco Basis Function Combinator \[nullary\] cons Gentzen diagram. ### Definition if not basis. ### Derivation if not basis. ### Source if basis ### Discussion Lorem ipsum. ### Crosslinks Lorem ipsum. -------------------- ## nullary (Combinator) Run a quoted program without using any stack values and leave the first item of the result on the stack. ... [P] nullary --------------------- ... A ### Definition [stack] dip infra first ### Derivation ... [P] nullary ... [P] [stack] dip infra first ... stack [P] infra first ... [...] [P] infra first ... [A ...] first ... A ### Discussion A very useful function that runs any other quoted function and returns it's first result without disturbing the stack (under the quoted program.) ### Crosslinks [unary](#unary) [binary](#binary) [ternary](#ternary) ------------------------------------------------------------------------ ## of Basis Function Combinator swap at Gentzen diagram. ### Definition if not basis. ### Derivation if not basis. ### Source if basis ### Discussion Lorem ipsum. ### Crosslinks Lorem ipsum. ------------------------------------------------------------------------ ## or Basis Function Combinator Same as a \| b. Gentzen diagram. ### Definition if not basis. ### Derivation if not basis. ### Source if basis ### Discussion Lorem ipsum. ### Crosslinks Lorem ipsum. ------------------------------------------------------------------------ ## over Basis Function Combinator (a2 a1 -- a2 a1 a2) Gentzen diagram. ### Definition if not basis. ### Derivation if not basis. ### Source if basis ### Discussion Lorem ipsum. ### Crosslinks Lorem ipsum. ------------------------------------------------------------------------ ## pam Basis Function Combinator \[i\] map Gentzen diagram. ### Definition if not basis. ### Derivation if not basis. ### Source if basis ### Discussion Lorem ipsum. ### Crosslinks Lorem ipsum. -------------- ## pick See [getitem](#getitem). ------------------------------------------------------------------------ ## pm Basis Function Combinator Plus or minus : a b pm ------------- a+b a-b Gentzen diagram. ### Definition if not basis. ### Derivation if not basis. ### Source if basis ### Discussion Lorem ipsum. ### Crosslinks Lorem ipsum. ------------------------------------------------------------------------ ## pop Basis Function Combinator (a1 --) Gentzen diagram. ### Definition if not basis. ### Derivation if not basis. ### Source if basis ### Discussion Lorem ipsum. ### Crosslinks Lorem ipsum. ------------------------------------------------------------------------ ## popd Basis Function Combinator (a2 a1 -- a1) Gentzen diagram. ### Definition if not basis. ### Derivation if not basis. ### Source if basis ### Discussion Lorem ipsum. ### Crosslinks Lorem ipsum. ------------------------------------------------------------------------ ## popdd Basis Function Combinator (a3 a2 a1 -- a2 a1) Gentzen diagram. ### Definition if not basis. ### Derivation if not basis. ### Source if basis ### Discussion Lorem ipsum. ### Crosslinks Lorem ipsum. ------------------------------------------------------------------------ ## popop Basis Function Combinator (a2 a1 --) Gentzen diagram. ### Definition if not basis. ### Derivation if not basis. ### Source if basis ### Discussion Lorem ipsum. ### Crosslinks Lorem ipsum. ------------------------------------------------------------------------ ## popopd Basis Function Combinator (a3 a2 a1 -- a1) Gentzen diagram. ### Definition if not basis. ### Derivation if not basis. ### Source if basis ### Discussion Lorem ipsum. ### Crosslinks Lorem ipsum. ------------------------------------------------------------------------ ## popopdd Basis Function Combinator (a4 a3 a2 a1 -- a2 a1) Gentzen diagram. ### Definition if not basis. ### Derivation if not basis. ### Source if basis ### Discussion Lorem ipsum. ### Crosslinks Lorem ipsum. ------------------------------------------------------------------------ ## popopop Basis Function Combinator pop popop Gentzen diagram. ### Definition if not basis. ### Derivation if not basis. ### Source if basis ### Discussion Lorem ipsum. ### Crosslinks Lorem ipsum. ------------------------------------------------------------------------ ## pow Basis Function Combinator Same as a \*\* b. Gentzen diagram. ### Definition if not basis. ### Derivation if not basis. ### Source if basis ### Discussion Lorem ipsum. ### Crosslinks Lorem ipsum. ------------------------------------------------------------------------ ## pred Basis Function Combinator Decrement TOS. Gentzen diagram. ### Definition if not basis. ### Derivation if not basis. ### Source if basis ### Discussion Lorem ipsum. ### Crosslinks Lorem ipsum. ------------------------------------------------------------------------ ## primrec Basis Function 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.: n [Base] [Recur] primrec 0 [Base] [Recur] primrec ------------------------------ Base n [Base] [Recur] primrec ------------------------------------------ n > 0 n (n-1) [Base] [Recur] primrec Recur Gentzen diagram. ### Definition if not basis. ### Derivation if not basis. ### Source if basis ### Discussion Lorem ipsum. ### Crosslinks Lorem ipsum. ------------------------------------------------------------------------ ## product Basis Function Combinator 1 swap \[\*\] step Gentzen diagram. ### Definition if not basis. ### Derivation if not basis. ### Source if basis ### Discussion Lorem ipsum. ### Crosslinks Lorem ipsum. ------------------------------------------------------------------------ ## quoted Basis Function Combinator \[unit\] dip Gentzen diagram. ### Definition if not basis. ### Derivation if not basis. ### Source if basis ### Discussion Lorem ipsum. ### Crosslinks Lorem ipsum. ------------------------------------------------------------------------ ## range Basis Function Combinator \[0 \<=\] \[1 - dup\] anamorphism Gentzen diagram. ### Definition if not basis. ### Derivation if not basis. ### Source if basis ### Discussion Lorem ipsum. ### Crosslinks Lorem ipsum. ------------------------------------------------------------------------ ## range_to_zero Basis Function Combinator unit \[down_to_zero\] infra Gentzen diagram. ### Definition if not basis. ### Derivation if not basis. ### Source if basis ### Discussion Lorem ipsum. ### Crosslinks Lorem ipsum. ------------------------------------------------------------------------ ## reco Basis Function Combinator rest cons Gentzen diagram. ### Definition if not basis. ### Derivation if not basis. ### Source if basis ### Discussion Lorem ipsum. ### Crosslinks Lorem ipsum. -------------- ## rem See [mod](#mod). -------------- ## remainder See [mod](#mod). ------------------------------------------------------------------------ ## remove Basis Function Combinator 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] Gentzen diagram. ### Definition if not basis. ### Derivation if not basis. ### Source if basis ### Discussion Lorem ipsum. ### Crosslinks Lorem ipsum. ------------------------------------------------------------------------ ## rest Basis Function Combinator ([a1 ...0] -- [...0]) Gentzen diagram. ### Definition if not basis. ### Derivation if not basis. ### Source if basis ### Discussion Lorem ipsum. ### Crosslinks Lorem ipsum. ------------------------------------------------------------------------ ## reverse Basis Function Combinator Reverse the list on the top of the stack. : reverse == [] swap shunt Gentzen diagram. ### Definition if not basis. ### Derivation if not basis. ### Source if basis ### Discussion Lorem ipsum. ### Crosslinks Lorem ipsum. ------------------------------------------------------------------------ ## rolldown Basis Function Combinator (a1 a2 a3 -- a2 a3 a1) Gentzen diagram. ### Definition if not basis. ### Derivation if not basis. ### Source if basis ### Discussion Lorem ipsum. ### Crosslinks Lorem ipsum. ------------------------------------------------------------------------ ## rollup Basis Function Combinator (a1 a2 a3 -- a3 a1 a2) Gentzen diagram. ### Definition if not basis. ### Derivation if not basis. ### Source if basis ### Discussion Lorem ipsum. ### Crosslinks Lorem ipsum. -------------- ## roll> See [rollup](#rollup). -------------- ## roll< See [rolldown](#rolldown). ------------------------------------------------------------------------ ## round Basis Function Combinator Round a number to a given precision in decimal digits. The return value is an integer if ndigits is omitted or None. Otherwise the return value has the same type as the number. ndigits may be negative. Gentzen diagram. ### Definition if not basis. ### Derivation if not basis. ### Source if basis ### Discussion Lorem ipsum. ### Crosslinks Lorem ipsum. ------------------------------------------------------------------------ ## rrest Basis Function Combinator ([a1 a2 ...1] -- [...1]) Gentzen diagram. ### Definition if not basis. ### Derivation if not basis. ### Source if basis ### Discussion Lorem ipsum. ### Crosslinks Lorem ipsum. ------------------------------------------------------------------------ ## rshift Basis Function Combinator Same as a \>\> b. Gentzen diagram. ### Definition if not basis. ### Derivation if not basis. ### Source if basis ### Discussion Lorem ipsum. ### Crosslinks Lorem ipsum. ------------------------------------------------------------------------ ## run Basis Function Combinator \<{} infra Gentzen diagram. ### Definition if not basis. ### Derivation if not basis. ### Source if basis ### Discussion Lorem ipsum. ### Crosslinks Lorem ipsum. ------------------------------------------------------------------------ ## second Basis Function Combinator ([a1 a2 ...1] -- a2) Gentzen diagram. ### Definition if not basis. ### Derivation if not basis. ### Source if basis ### Discussion Lorem ipsum. ### Crosslinks Lorem ipsum. ------------------------------------------------------------------------ ## select Basis Function Combinator Use a Boolean value to select one of two items from a sequence. : [A B] false select ------------------------ A [A B] true select ----------------------- B The sequence can contain more than two items but not fewer. Currently Python semantics are used to evaluate the \"truthiness\" of the Boolean value (so empty string, zero, etc. are counted as false, etc.) Gentzen diagram. ### Definition if not basis. ### Derivation if not basis. ### Source if basis ### Discussion Lorem ipsum. ### Crosslinks Lorem ipsum. ------------------------------------------------------------------------ ## sharing Basis Function Combinator Print redistribution information. Gentzen diagram. ### Definition if not basis. ### Derivation if not basis. ### Source if basis ### Discussion Lorem ipsum. ### Crosslinks Lorem ipsum. ------------------------------------------------------------------------ ## shift Basis Function Combinator uncons \[swons\] dip Gentzen diagram. ### Definition if not basis. ### Derivation if not basis. ### Source if basis ### Discussion Lorem ipsum. ### Crosslinks Lorem ipsum. ------------------------------------------------------------------------ ## shunt Basis Function Combinator Like concat but reverses the top list into the second. : shunt == [swons] step == reverse swap concat [a b c] [d e f] shunt --------------------------- [f e d a b c] Gentzen diagram. ### Definition if not basis. ### Derivation if not basis. ### Source if basis ### Discussion Lorem ipsum. ### Crosslinks Lorem ipsum. ------------------------------------------------------------------------ ## size Basis Function Combinator \[pop ++\] step_zero Gentzen diagram. ### Definition if not basis. ### Derivation if not basis. ### Source if basis ### Discussion Lorem ipsum. ### Crosslinks Lorem ipsum. ------------------------------------------------------------------------ ## sort Basis Function Combinator Given a list return it sorted. Gentzen diagram. ### Definition if not basis. ### Derivation if not basis. ### Source if basis ### Discussion Lorem ipsum. ### Crosslinks Lorem ipsum. ------------------------------------------------------------------------ ## spiral_next Basis Function Combinator \[\[\[abs\] ii \<=\] \[\[\<\>\] \[pop !-\] \|\|\] &&\] \[\[!-\] \[\[++\]\] \[\[\--\]\] ifte dip\] \[\[pop !-\] \[\--\] \[++\] ifte\] ifte Gentzen diagram. ### Definition if not basis. ### Derivation if not basis. ### Source if basis ### Discussion Lorem ipsum. ### Crosslinks Lorem ipsum. ------------------------------------------------------------------------ ## split_at Basis Function Combinator \[drop\] \[take\] clop Gentzen diagram. ### Definition if not basis. ### Derivation if not basis. ### Source if basis ### Discussion Lorem ipsum. ### Crosslinks Lorem ipsum. ------------------------------------------------------------------------ ## split_list Basis Function Combinator \[take reverse\] \[drop\] clop Gentzen diagram. ### Definition if not basis. ### Derivation if not basis. ### Source if basis ### Discussion Lorem ipsum. ### Crosslinks Lorem ipsum. ------------------------------------------------------------------------ ## sqr Basis Function Combinator dup \* Gentzen diagram. ### Definition if not basis. ### Derivation if not basis. ### Source if basis ### Discussion Lorem ipsum. ### Crosslinks Lorem ipsum. ------------------------------------------------------------------------ ## sqrt Basis Function Combinator Return the square root of the number a. Negative numbers return complex roots. Gentzen diagram. ### Definition if not basis. ### Derivation if not basis. ### Source if basis ### Discussion Lorem ipsum. ### Crosslinks Lorem ipsum. ------------------------------------------------------------------------ ## stack Basis Function Combinator (... -- ... [...]) Gentzen diagram. ### Definition if not basis. ### Derivation if not basis. ### Source if basis ### Discussion Lorem ipsum. ### Crosslinks Lorem ipsum. ------------------------------------------------------------------------ ## stackd Basis Function Combinator \[stack\] dip Gentzen diagram. ### Definition if not basis. ### Derivation if not basis. ### Source if basis ### Discussion Lorem ipsum. ### Crosslinks Lorem ipsum. ------------------------------------------------------------------------ ## step Basis Function Combinator Run a quoted program on each item in a sequence. : ... [] [Q] . step ----------------------- ... . ... [a] [Q] . step ------------------------ ... a . Q ... [a b c] [Q] . step ---------------------------------------- ... a . Q [b c] [Q] step The step combinator executes the quotation on each member of the list on top of the stack. Gentzen diagram. ### Definition if not basis. ### Derivation if not basis. ### Source if basis ### Discussion Lorem ipsum. ### Crosslinks Lorem ipsum. ------------------------------------------------------------------------ ## step_zero Basis Function Combinator 0 roll> step Gentzen diagram. ### Definition if not basis. ### Derivation if not basis. ### Source if basis ### Discussion Lorem ipsum. ### Crosslinks Lorem ipsum. ------------------------------------------------------------------------ ## stuncons Basis Function Combinator (... a1 -- ... a1 a1 [...]) Gentzen diagram. ### Definition if not basis. ### Derivation if not basis. ### Source if basis ### Discussion Lorem ipsum. ### Crosslinks Lorem ipsum. ------------------------------------------------------------------------ ## stununcons Basis Function Combinator (... a2 a1 -- ... a2 a1 a1 a2 [...]) Gentzen diagram. ### Definition if not basis. ### Derivation if not basis. ### Source if basis ### Discussion Lorem ipsum. ### Crosslinks Lorem ipsum. ------------------------------------------------------------------------ ## sub Basis Function Combinator Same as a - b. Gentzen diagram. ### Definition if not basis. ### Derivation if not basis. ### Source if basis ### Discussion Lorem ipsum. ### Crosslinks Lorem ipsum. ------------------------------------------------------------------------ ## succ Basis Function Combinator Increment TOS. Gentzen diagram. ### Definition if not basis. ### Derivation if not basis. ### Source if basis ### Discussion Lorem ipsum. ### Crosslinks Lorem ipsum. ------------------------------------------------------------------------ ## sum Basis Function Combinator Given a quoted sequence of numbers return the sum. : sum == 0 swap [+] step Gentzen diagram. ### Definition if not basis. ### Derivation if not basis. ### Source if basis ### Discussion Lorem ipsum. ### Crosslinks Lorem ipsum. ------------------------------------------------------------------------ ## swaack Basis Function Combinator ([...1] -- [...0]) Gentzen diagram. ### Definition if not basis. ### Derivation if not basis. ### Source if basis ### Discussion Lorem ipsum. ### Crosslinks Lorem ipsum. ------------------------------------------------------------------------ ## swap Basis Function Combinator (a1 a2 -- a2 a1) Gentzen diagram. ### Definition if not basis. ### Derivation if not basis. ### Source if basis ### Discussion Lorem ipsum. ### Crosslinks Lorem ipsum. ------------------------------------------------------------------------ ## swapd Basis Function Combinator \[swap\] dip Gentzen diagram. ### Definition if not basis. ### Derivation if not basis. ### Source if basis ### Discussion Lorem ipsum. ### Crosslinks Lorem ipsum. ------------------------------------------------------------------------ ## swoncat Basis Function Combinator swap concat Gentzen diagram. ### Definition if not basis. ### Derivation if not basis. ### Source if basis ### Discussion Lorem ipsum. ### Crosslinks Lorem ipsum. ------------------------------------------------------------------------ ## swons Basis Function Combinator ([...1] a1 -- [a1 ...1]) Gentzen diagram. ### Definition if not basis. ### Derivation if not basis. ### Source if basis ### Discussion Lorem ipsum. ### Crosslinks Lorem ipsum. ------------------------------------------------------------------------ ## tailrec Basis Function Combinator \[i\] genrec Gentzen diagram. ### Definition if not basis. ### Derivation if not basis. ### Source if basis ### Discussion Lorem ipsum. ### Crosslinks Lorem ipsum. ------------------------------------------------------------------------ ## take Basis Function Combinator 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.) : [a b c d] 2 take ---------------------- [b a] Gentzen diagram. ### Definition if not basis. ### Derivation if not basis. ### Source if basis ### Discussion Lorem ipsum. ### Crosslinks Lorem ipsum. -------------------- ## ternary (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 ------------------------- ... A ### Definition binary popd ### Discussion Runs any other quoted function and returns its first result while consuming exactly three items from the stack. ### Crosslinks [binary](#binary) [nullary](#nullary) [unary](#unary) ------------------------------------------------------------------------ ## third Basis Function Combinator ([a1 a2 a3 ...1] -- a3) Gentzen diagram. ### Definition if not basis. ### Derivation if not basis. ### Source if basis ### Discussion Lorem ipsum. ### Crosslinks Lorem ipsum. ------------------------------------------------------------------------ ## times Basis Function Combinator times == \[\-- dip\] cons \[swap\] infra \[0 \>\] swap while pop : ... n [Q] . times --------------------- w/ n <= 0 ... . ... 1 [Q] . times ----------------------- ... . Q ... n [Q] . times ------------------------------------- w/ n > 1 ... . Q (n - 1) [Q] times Gentzen diagram. ### Definition if not basis. ### Derivation if not basis. ### Source if basis ### Discussion Lorem ipsum. ### Crosslinks Lorem ipsum. -------------- ## truthy See [bool](#bool). ------------------------------------------------------------------------ ## tuck Basis Function Combinator (a2 a1 -- a1 a2 a1) Gentzen diagram. ### Definition if not basis. ### Derivation if not basis. ### Source if basis ### Discussion Lorem ipsum. ### Crosslinks Lorem ipsum. -------------------- ## unary (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 ### Definition nullary popd ### Discussion Runs any other quoted function and returns its first result while consuming exactly one item from the stack. ### Crosslinks [binary](#binary) [nullary](#nullary) [ternary](#ternary) -------------------- ## uncons (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 [...] ### Source func(uncons, Si, So) :- func(cons, So, Si). ### Discussion This is the inverse of `cons`. ### Crosslinks [cons](#cons) ------------------------------------------------------------------------ ## unique Basis Function Combinator 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 (a1 -- [a1 ]) Gentzen diagram. ### Definition if not basis. ### Derivation if not basis. ### Source if basis ### Discussion Lorem ipsum. ### Crosslinks Lorem ipsum. ------------------------------------------------------------------------ ## unquoted Basis Function Combinator \[i\] dip Gentzen diagram. ### Definition if not basis. ### Derivation if not basis. ### Source if basis ### Discussion Lorem ipsum. ### Crosslinks Lorem ipsum. ------------------------------------------------------------------------ ## unswons Basis Function Combinator ([a1 ...1] -- [...1] a1) Gentzen diagram. ### Definition if not basis. ### Derivation if not basis. ### Source if basis ### Discussion Lorem ipsum. ### Crosslinks Lorem ipsum. ------------------------------------------------------------------------ ## void Basis Function Combinator True if the form on TOS is void otherwise False. Gentzen diagram. ### Definition if not basis. ### Derivation if not basis. ### Source if basis ### Discussion Lorem ipsum. ### Crosslinks Lorem ipsum. ------------------------------------------------------------------------ ## warranty Basis Function Combinator Print warranty information. Gentzen diagram. ### Definition if not basis. ### Derivation if not basis. ### Source if basis ### Discussion Lorem ipsum. ### Crosslinks Lorem ipsum. ------------------------------------------------------------------------ ## while Basis Function Combinator swap nulco dupdipd concat loop Gentzen diagram. ### Definition if not basis. ### Derivation if not basis. ### Source if basis ### Discussion Lorem ipsum. ### Crosslinks Lorem ipsum. ------------------------------------------------------------------------ ## words Basis Function Combinator Print all the words in alphabetical order. Gentzen diagram. ### Definition if not basis. ### Derivation if not basis. ### Source if basis ### Discussion Lorem ipsum. ### Crosslinks Lorem ipsum. -------------------- ## x (Combinator) [F] x ----------- [F] F ### Definition dup i ### Discussion The `x` combinator ... ------------------------------------------------------------------------ ## xor Basis Function Combinator Same as a \^ b. Gentzen diagram. ### Definition if not basis. ### Derivation if not basis. ### Source if basis ### Discussion Lorem ipsum. ### Crosslinks Lorem ipsum. ------------------------------------------------------------------------ ## zip Basis Function Combinator 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. Gentzen diagram. ### Definition if not basis. ### Derivation if not basis. ### Source if basis ### Discussion Lorem ipsum. ### Crosslinks Lorem ipsum.