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 Lorem ipsum. ### Crosslinks Lorem ipsum. -------------- ## << See [lshift](#lshift). ------------------------------------------------------------------------ ## \<\<{} Basis Function Combinator \[\] rollup Gentzen diagram. ### Definition if not basis. ### Derivation if not basis. ### Source if basis ### Discussion Lorem ipsum. ### Crosslinks Lorem ipsum. -------------- ## % See [mod](#mod). -------------- ## + See [add](#add). -------------- ## ++ See [succ](#succ). ------------------------------------------------------------------------ ## ? Basis Function Combinator dup bool Gentzen diagram. ### Definition if not basis. ### Derivation if not basis. ### Source if basis ### Discussion Lorem ipsum. ### Crosslinks Lorem ipsum. -------------- ## / See [floordiv](#floordiv). -------------- ## // See [floordiv](#floordiv). -------------- ## /floor See [floordiv](#floordiv). ------------------------------------------------------------------------ ## \|\| Basis Function Combinator nulco \[nullary\] dip \[true\] branch Gentzen diagram. ### Definition if not basis. ### Derivation if not basis. ### Source if basis ### Discussion Lorem ipsum. ### Crosslinks Lorem ipsum. ------------------------------------------------------------------------ ## abs Basis Function Combinator Return the absolute value of the argument. Gentzen diagram. ### Definition if not basis. ### Derivation if not basis. ### Source if basis ### Discussion Lorem ipsum. ### Crosslinks Lorem ipsum. ------------------------------------------------------------------------ ## add 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. ------------------------------------------------------------------------ ## anamorphism Basis Function Combinator \[pop \[\]\] swap \[dip swons\] genrec Gentzen diagram. ### Definition if not basis. ### Derivation if not basis. ### Source if basis ### Discussion Lorem ipsum. ### Crosslinks Lorem ipsum. ------------------------------------------------------------------------ ## and 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. -------------------- ## 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 ### Definition nullary popd ### Discussion Just a specialization of `nullary` really. Its parallelizable cousins are more useful. ------------------------------------------------------------------------ ## app2 Basis Function Combinator Like app1 with two items. : ... y x [Q] . app2 ----------------------------------- ... [y ...] [Q] . infra first [x ...] [Q] infra first Gentzen diagram. ### Definition if not basis. ### Derivation if not basis. ### Source if basis ### Discussion Lorem ipsum. ### Crosslinks Lorem ipsum. ------------------------------------------------------------------------ ## app3 Basis Function Combinator Like app1 with three items. : ... z y x [Q] . app3 ----------------------------------- ... [z ...] [Q] . infra first [y ...] [Q] infra first [x ...] [Q] infra first Gentzen diagram. ### Definition if not basis. ### Derivation if not basis. ### Source if basis ### Discussion Lorem ipsum. ### Crosslinks Lorem ipsum. ------------------------------------------------------------------------ ## appN Basis Function Combinator \[grabN\] codi map disenstacken Gentzen diagram. ### Definition if not basis. ### Derivation if not basis. ### Source if basis ### Discussion Lorem ipsum. ### Crosslinks Lorem ipsum. -------------- ## at See [getitem](#getitem). ------------------------------------------------------------------------ ## average Basis Function Combinator \[sum\] \[size\] cleave / Gentzen diagram. ### Definition if not basis. ### Derivation if not basis. ### Source if basis ### Discussion Lorem ipsum. ### Crosslinks Lorem ipsum. -------------------- ## b (Combinator) Run two quoted programs [P] [Q] b --------------- P Q ### Definition [i] dip i ### Derivation [P] [Q] b [P] [Q] [i] dip i [P] i [Q] i P [Q] i P Q ### Discussion This combinator 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 Combinator bool(x) -\> bool Returns True when the argument x is true, False otherwise. The builtins True and False are the only two instances of the class bool. The class bool is a subclass of the class int, and cannot be subclassed. Gentzen diagram. ### Definition if not basis. ### Derivation if not basis. ### Source if basis ### Discussion Lorem ipsum. ### Crosslinks Lorem ipsum. ------------------------------------------------------------------------ ## branch Basis Function Combinator Use a Boolean value to select one of two quoted programs to run. branch == roll< choice i False [F] [T] branch -------------------------- F True [F] [T] branch ------------------------- T Gentzen diagram. ### Definition if not basis. ### Derivation if not basis. ### Source if basis ### Discussion Lorem ipsum. ### Crosslinks Lorem ipsum. ------------------------------------------------------------------------ ## ccccons Basis Function Combinator ccons ccons Gentzen diagram. ### Definition if not basis. ### Derivation if not basis. ### Source if basis ### Discussion Lorem ipsum. ### Crosslinks Lorem ipsum. -------------------- ## ccons (Function) Given two items and a list, append the items to the list to make a new list. B A [...] ccons --------------------- [B A ...] ### Definition cons cons ### Discussion Does `cons` twice. ### Crosslinks [cons](#cons) ------------------------------------------------------------------------ ## choice Basis Function Combinator Use a Boolean value to select one of two items. : A B false choice ---------------------- A A B true choice --------------------- B 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. ------------------------------------------------------------------------ ## clear Basis Function Combinator Clear everything from the stack. : clear == stack [pop stack] loop ... clear --------------- Gentzen diagram. ### Definition if not basis. ### Derivation if not basis. ### Source if basis ### Discussion Lorem ipsum. ### Crosslinks Lorem ipsum. ------------------------------------------------------------------------ ## cleave Basis Function Combinator fork popdd Gentzen diagram. ### Definition if not basis. ### Derivation if not basis. ### Source if basis ### Discussion Lorem ipsum. ### Crosslinks Lorem ipsum. ------------------------------------------------------------------------ ## clop Basis Function Combinator cleave popdd Gentzen diagram. ### Definition if not basis. ### Derivation if not basis. ### Source if basis ### Discussion Lorem ipsum. ### Crosslinks Lorem ipsum. ------------------------------------------------------------------------ ## cmp Basis Function Combinator cmp takes two values and three quoted programs on the stack and runs 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 Gentzen diagram. ### Definition if not basis. ### Derivation if not basis. ### Source if basis ### Discussion Lorem ipsum. ### Crosslinks Lorem ipsum. ------------------------------------------------------------------------ ## codi Basis Function Combinator cons dip Gentzen diagram. ### Definition if not basis. ### Derivation if not basis. ### Source if basis ### Discussion Lorem ipsum. ### Crosslinks Lorem ipsum. ------------------------------------------------------------------------ ## codireco Basis Function Combinator codi reco Gentzen diagram. ### Definition if not basis. ### Derivation if not basis. ### Source if basis ### Discussion Lorem ipsum. ### Crosslinks Lorem ipsum. ------------------------------------------------------------------------ ## concat Basis Function Combinator Concatinate the two lists on the top of the stack. : [a b c] [d e f] concat ---------------------------- [a b c d e f] Gentzen diagram. ### Definition if not basis. ### Derivation if not basis. ### Source if basis ### Discussion Lorem ipsum. ### Crosslinks Lorem ipsum. ------------------------------------------------------------------------ ## cond Basis Function 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 clause 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. 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 Gentzen diagram. ### Definition if not basis. ### Derivation if not basis. ### Source if basis ### Discussion Lorem ipsum. ### Crosslinks Lorem ipsum. -------------------- ## cons (Basis Function) Given an item and a list, append the item to the list to make a new list. A [...] cons ------------------ [A ...] ### Source func(cons, [list(A), B|S], [list([B|A])|S]). ### Discussion Cons is a venerable old function from Lisp. It doesn't inspect the item but it will not cons onto a non-list. It's inverse operation is called `uncons`. ### Crosslinks [ccons](#ccons) [uncons](#uncons) ------------------------------------------------------------------------ ## dinfrirst Basis Function Combinator dip infrst Gentzen diagram. ### Definition if not basis. ### Derivation if not basis. ### Source if basis ### Discussion Lorem ipsum. ### Crosslinks Lorem ipsum. ------------------------------------------------------------------------ ## dip Basis Function 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 Gentzen diagram. ### Definition if not basis. ### Derivation if not basis. ### Source if basis ### Discussion Lorem ipsum. ### Crosslinks Lorem ipsum. ------------------------------------------------------------------------ ## dipd Basis Function Combinator Like dip but expects two items. : ... y x [Q] dip --------------------- ... Q y x Gentzen diagram. ### Definition if not basis. ### Derivation if not basis. ### Source if basis ### Discussion Lorem ipsum. ### Crosslinks Lorem ipsum. ------------------------------------------------------------------------ ## dipdd Basis Function Combinator Like dip but expects three items. : ... z y x [Q] dip ----------------------- ... Q z y x Gentzen diagram. ### Definition if not basis. ### Derivation if not basis. ### Source if basis ### Discussion Lorem ipsum. ### Crosslinks Lorem ipsum. ------------------------------------------------------------------------ ## disenstacken Basis Function Combinator The disenstacken operator expects a list on top of the stack and makes that the stack discarding the rest of the stack. Gentzen diagram. ### Definition if not basis. ### Derivation if not basis. ### Source if basis ### Discussion Lorem ipsum. ### Crosslinks Lorem ipsum. -------------- ## div See [floordiv](#floordiv). ------------------------------------------------------------------------ ## divmod Basis Function Combinator divmod(x, y) -\> (quotient, remainder) Return the tuple (x//y, x%y). Invariant: q \* y + r == x. Gentzen diagram. ### Definition if not basis. ### Derivation if not basis. ### Source if basis ### Discussion Lorem ipsum. ### Crosslinks Lorem ipsum. ------------------------------------------------------------------------ ## down_to_zero Basis Function Combinator \[0 \>\] \[dup \--\] while Gentzen diagram. ### Definition if not basis. ### Derivation if not basis. ### Source if basis ### Discussion Lorem ipsum. ### Crosslinks Lorem ipsum. ------------------------------------------------------------------------ ## drop Basis Function Combinator drop == [rest] times 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] Gentzen diagram. ### Definition if not basis. ### Derivation if not basis. ### Source if basis ### Discussion Lorem ipsum. ### Crosslinks Lorem ipsum. ------------------------------------------------------------------------ ## dup 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. ------------------------------------------------------------------------ ## dupd Basis Function Combinator (a2 a1 -- a2 a2 a1) Gentzen diagram. ### Definition if not basis. ### Derivation if not basis. ### Source if basis ### Discussion Lorem ipsum. ### Crosslinks Lorem ipsum. ------------------------------------------------------------------------ ## dupdd Basis Function Combinator (a3 a2 a1 -- a3 a3 a2 a1) Gentzen diagram. ### Definition if not basis. ### Derivation if not basis. ### Source if basis ### Discussion Lorem ipsum. ### Crosslinks Lorem ipsum. ------------------------------------------------------------------------ ## dupdip Basis Function Combinator [F] dupdip == dup [F] dip ... a [F] dupdip ... a dup [F] dip ... a a [F] dip ... a F a Gentzen diagram. ### Definition if not basis. ### Derivation if not basis. ### Source if basis ### Discussion Lorem ipsum. ### Crosslinks Lorem ipsum. ------------------------------------------------------------------------ ## dupdipd Basis Function Combinator dup dipd Gentzen diagram. ### Definition if not basis. ### Derivation if not basis. ### Source if basis ### Discussion Lorem ipsum. ### Crosslinks Lorem ipsum. ------------------------------------------------------------------------ ## 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.