# Functor Reference Version -10.0.0 Each function, combinator, or definition should be documented here. ------------------------------------------------------------------------ # & Basis Function Combinator Same as a & b. Gentzen diagram. ## Definition if not basis. ## Derivation if not basis. ## Source if basis ## Discussion Lorem ipsum. ## Crosslinks ------------------------------------------------------------------------ # && Basis Function Combinator nulco \[nullary \[false\]\] dip branch Gentzen diagram. ## Definition if not basis. ## Derivation if not basis. ## Source if basis ## Discussion Lorem ipsum. ## Crosslinks ------------------------------------------------------------------------ # \* Basis Function Combinator Same as a \* b. Gentzen diagram. ## Definition if not basis. ## Derivation if not basis. ## Source if basis ## Discussion Lorem ipsum. ## Crosslinks ------------------------------------------------------------------------ # • Basis Function Combinator The identity function. Gentzen diagram. ## Definition if not basis. ## Derivation if not basis. ## Source if basis ## Discussion Lorem ipsum. ## Crosslinks ------------------------------------------------------------------------ # \^ Basis Function Combinator Same as a \^ b. Gentzen diagram. ## Definition if not basis. ## Derivation if not basis. ## Source if basis ## Discussion Lorem ipsum. ## Crosslinks ------------------------------------------------------------------------ # = Basis Function Combinator Same as a == b. Gentzen diagram. ## Definition if not basis. ## Derivation if not basis. ## Source if basis ## Discussion Lorem ipsum. ## Crosslinks ------------------------------------------------------------------------ # != Basis Function Combinator Same as a != b. Gentzen diagram. ## Definition if not basis. ## Derivation if not basis. ## Source if basis ## Discussion Lorem ipsum. ## Crosslinks ------------------------------------------------------------------------ !-\^\^\^\^ Basis Function Combinator 0 \>= Gentzen diagram. # Definition if not basis. # Derivation if not basis. # Source if basis # Discussion Lorem ipsum. # Crosslinks ------------------------------------------------------------------------ # \> Basis Function Combinator Same as a \> b. Gentzen diagram. ## Definition if not basis. ## Derivation if not basis. ## Source if basis ## Discussion Lorem ipsum. ## Crosslinks ------------------------------------------------------------------------ # \>= Basis Function Combinator Same as a \>= b. Gentzen diagram. ## Definition if not basis. ## Derivation if not basis. ## Source if basis ## Discussion Lorem ipsum. ## Crosslinks ------------------------------------------------------------------------ # \>\> Basis Function Combinator Same as a \>\> b. Gentzen diagram. ## Definition if not basis. ## Derivation if not basis. ## Source if basis ## Discussion Lorem ipsum. ## Crosslinks # Functor Reference Version -10.0.0 Each function, combinator, or definition should be documented here. ------------------------------------------------------------------------ -\^\^\^ Basis Function Combinator Same as a - b. Gentzen diagram. # Definition if not basis. # Derivation if not basis. # Source if basis # Discussion Lorem ipsum. # Crosslinks ------------------------------------------------------------------------ \--\^\^\^\^ Basis Function Combinator Decrement TOS. Gentzen diagram. # Definition if not basis. # Derivation if not basis. # Source if basis # Discussion Lorem ipsum. # Crosslinks ------------------------------------------------------------------------ # \< Basis Function Combinator Same as a \< b. Gentzen diagram. ## Definition if not basis. ## Derivation if not basis. ## Source if basis ## Discussion Lorem ipsum. ## Crosslinks ------------------------------------------------------------------------ # \<= Basis Function Combinator Same as a \<= b. Gentzen diagram. ## Definition if not basis. ## Derivation if not basis. ## Source if basis ## Discussion Lorem ipsum. ## Crosslinks ------------------------------------------------------------------------ # \<\> Basis Function Combinator Same as a != b. Gentzen diagram. ## Definition if not basis. ## Derivation if not basis. ## Source if basis ## Discussion Lorem ipsum. ## Crosslinks ------------------------------------------------------------------------ # \<{} Basis Function Combinator \[\] swap Gentzen diagram. ## Definition if not basis. ## Derivation if not basis. ## Source if basis ## Discussion Lorem ipsum. ## Crosslinks ------------------------------------------------------------------------ # \<\< Basis Function Combinator Same as a \<\< b. Gentzen diagram. ## Definition if not basis. ## Derivation if not basis. ## Source if basis ## Discussion Lorem ipsum. ## Crosslinks ------------------------------------------------------------------------ # \<\<{} Basis Function Combinator \[\] rollup Gentzen diagram. ## Definition if not basis. ## Derivation if not basis. ## Source if basis ## Discussion Lorem ipsum. ## Crosslinks ------------------------------------------------------------------------ # % Basis Function Combinator Same as a % b. Gentzen diagram. ## Definition if not basis. ## Derivation if not basis. ## Source if basis ## Discussion Lorem ipsum. ## Crosslinks ------------------------------------------------------------------------ # + Basis Function Combinator Same as a + b. Gentzen diagram. ## Definition if not basis. ## Derivation if not basis. ## Source if basis ## Discussion Lorem ipsum. ## Crosslinks ------------------------------------------------------------------------ # ++ Basis Function Combinator Increment TOS. Gentzen diagram. ## Definition if not basis. ## Derivation if not basis. ## Source if basis ## Discussion Lorem ipsum. ## Crosslinks ------------------------------------------------------------------------ # ? Basis Function Combinator dup bool Gentzen diagram. ## Definition if not basis. ## Derivation if not basis. ## Source if basis ## Discussion Lorem ipsum. ## Crosslinks ------------------------------------------------------------------------ # / Basis Function Combinator Same as a // b. Gentzen diagram. ## Definition if not basis. ## Derivation if not basis. ## Source if basis ## Discussion Lorem ipsum. ## Crosslinks ------------------------------------------------------------------------ # // Basis Function Combinator Same as a // b. Gentzen diagram. ## Definition if not basis. ## Derivation if not basis. ## Source if basis ## Discussion Lorem ipsum. ## Crosslinks ------------------------------------------------------------------------ # /floor Basis Function Combinator Same as a // b. Gentzen diagram. ## Definition if not basis. ## Derivation if not basis. ## Source if basis ## Discussion Lorem ipsum. ## Crosslinks ------------------------------------------------------------------------ # \|\| 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 ------------------------------------------------------------------------ # 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 ## Crosslinks ------------------------------------------------------------------------ # add Basis Function Combinator Same as a + b. Gentzen diagram. ## Definition if not basis. ## Derivation if not basis. ## Source if basis ## Discussion ## Crosslinks ------------------------------------------------------------------------ # anamorphism Basis Function Combinator \[pop \[\]\] swap \[dip swons\] genrec Gentzen diagram. ## Definition if not basis. ## Derivation if not basis. ## Source if basis ## Discussion ## Crosslinks ------------------------------------------------------------------------ # and Basis Function Combinator Same as a & b. Gentzen diagram. ## Definition if not basis. ## Derivation if not basis. ## Source if basis ## Discussion ## Crosslinks -------------------- ## 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 ## Crosslinks ------------------------------------------------------------------------ # 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 ## Crosslinks ------------------------------------------------------------------------ # appN Basis Function Combinator \[grabN\] codi map disenstacken Gentzen diagram. ## Definition if not basis. ## Derivation if not basis. ## Source if basis ## Discussion ## Crosslinks ------------------------------------------------------------------------ # at 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 ## Crosslinks ------------------------------------------------------------------------ # average Basis Function Combinator \[sum\] \[size\] cleave / Gentzen diagram. ## Definition if not basis. ## Derivation if not basis. ## Source if basis ## Discussion ## Crosslinks -------------------- ## 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 ## Crosslinks ------------------------------------------------------------------------ # 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 ## Crosslinks ------------------------------------------------------------------------ # ccccons Basis Function Combinator ccons ccons Gentzen diagram. ## Definition if not basis. ## Derivation if not basis. ## Source if basis ## Discussion ## Crosslinks -------------------- ## 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 ## Crosslinks ------------------------------------------------------------------------ # 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 ## Crosslinks ------------------------------------------------------------------------ # cleave Basis Function Combinator fork popdd Gentzen diagram. ## Definition if not basis. ## Derivation if not basis. ## Source if basis ## Discussion ## Crosslinks ------------------------------------------------------------------------ # clop Basis Function Combinator cleave popdd Gentzen diagram. ## Definition if not basis. ## Derivation if not basis. ## Source if basis ## Discussion ## Crosslinks ------------------------------------------------------------------------ # 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 ## Crosslinks ------------------------------------------------------------------------ # codi Basis Function Combinator cons dip Gentzen diagram. ## Definition if not basis. ## Derivation if not basis. ## Source if basis ## Discussion ## Crosslinks ------------------------------------------------------------------------ # codireco Basis Function Combinator codi reco Gentzen diagram. ## Definition if not basis. ## Derivation if not basis. ## Source if basis ## Discussion ## Crosslinks ------------------------------------------------------------------------ # 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 ## Crosslinks ------------------------------------------------------------------------ # 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 ## Crosslinks -------------------- ## 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 ## Crosslinks ------------------------------------------------------------------------ # 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 ## Crosslinks ------------------------------------------------------------------------ # 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 ## Crosslinks ------------------------------------------------------------------------ # 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 ## Crosslinks ------------------------------------------------------------------------ # 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 ## Crosslinks ------------------------------------------------------------------------ # div Basis Function Combinator Same as a // b. Gentzen diagram. ## Definition if not basis. ## Derivation if not basis. ## Source if basis ## Discussion ## Crosslinks ------------------------------------------------------------------------ # 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 ## Crosslinks ------------------------------------------------------------------------ # down_to_zero Basis Function Combinator \[0 \>\] \[dup \--\] while Gentzen diagram. ## Definition if not basis. ## Derivation if not basis. ## Source if basis ## Discussion ## Crosslinks ------------------------------------------------------------------------ # 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 ## Crosslinks ------------------------------------------------------------------------ # dup Basis Function Combinator (a1 -- a1 a1) Gentzen diagram. ## Definition if not basis. ## Derivation if not basis. ## Source if basis ## Discussion ## Crosslinks ------------------------------------------------------------------------ # dupd Basis Function Combinator (a2 a1 -- a2 a2 a1) Gentzen diagram. ## Definition if not basis. ## Derivation if not basis. ## Source if basis ## Discussion ## Crosslinks ------------------------------------------------------------------------ # 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 ## Crosslinks ------------------------------------------------------------------------ # 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 ## Crosslinks ------------------------------------------------------------------------ # dupdipd Basis Function Combinator dup dipd Gentzen diagram. ## Definition if not basis. ## Derivation if not basis. ## Source if basis ## Discussion ## Crosslinks ------------------------------------------------------------------------ # enstacken Basis Function Combinator stack \[clear\] dip Gentzen diagram. ## Definition if not basis. ## Derivation if not basis. ## Source if basis ## Discussion ## Crosslinks ------------------------------------------------------------------------ # eq Basis Function Combinator Same as a == b. Gentzen diagram. ## Definition if not basis. ## Derivation if not basis. ## Source if basis ## Discussion ## Crosslinks ------------------------------------------------------------------------ # first Basis Function Combinator ([a1 ...1] -- a1) Gentzen diagram. ## Definition if not basis. ## Derivation if not basis. ## Source if basis ## Discussion ## Crosslinks ------------------------------------------------------------------------ # first_two Basis Function Combinator ([a1 a2 ...1] -- a1 a2) Gentzen diagram. ## Definition if not basis. ## Derivation if not basis. ## Source if basis ## Discussion ## Crosslinks ------------------------------------------------------------------------ # flatten Basis Function Combinator \<{} \[concat\] step Gentzen diagram. ## Definition if not basis. ## Derivation if not basis. ## Source if basis ## Discussion ## Crosslinks ------------------------------------------------------------------------ # 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 ## Crosslinks ------------------------------------------------------------------------ # floordiv Basis Function Combinator Same as a // b. Gentzen diagram. ## Definition if not basis. ## Derivation if not basis. ## Source if basis ## Discussion ## Crosslinks ------------------------------------------------------------------------ # fork Basis Function Combinator \[i\] app2 Gentzen diagram. ## Definition if not basis. ## Derivation if not basis. ## Source if basis ## Discussion ## Crosslinks ------------------------------------------------------------------------ # fourth Basis Function Combinator ([a1 a2 a3 a4 ...1] -- a4) Gentzen diagram. ## Definition if not basis. ## Derivation if not basis. ## Source if basis ## Discussion ## Crosslinks ------------------------------------------------------------------------ # 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 ## Crosslinks ------------------------------------------------------------------------ # gcd2 Basis Function Combinator Compiled GCD function. Gentzen diagram. ## Definition if not basis. ## Derivation if not basis. ## Source if basis ## Discussion ## Crosslinks ------------------------------------------------------------------------ # ge Basis Function Combinator Same as a \>= b. Gentzen diagram. ## Definition if not basis. ## Derivation if not basis. ## Source if basis ## Discussion ## Crosslinks ------------------------------------------------------------------------ # 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 ## Crosslinks ------------------------------------------------------------------------ # 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 ## Crosslinks ------------------------------------------------------------------------ # grabN Basis Function Combinator \<{} \[cons\] times Gentzen diagram. ## Definition if not basis. ## Derivation if not basis. ## Source if basis ## Discussion ## Crosslinks ------------------------------------------------------------------------ # grba Basis Function Combinator \[stack popd\] dip Gentzen diagram. ## Definition if not basis. ## Derivation if not basis. ## Source if basis ## Discussion ## Crosslinks ------------------------------------------------------------------------ # gt Basis Function Combinator Same as a \> b. Gentzen diagram. ## Definition if not basis. ## Derivation if not basis. ## Source if basis ## Discussion ## Crosslinks ------------------------------------------------------------------------ # 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 ## Crosslinks ------------------------------------------------------------------------ # hypot Basis Function Combinator \[sqr\] ii + sqrt Gentzen diagram. ## Definition if not basis. ## Derivation if not basis. ## Source if basis ## Discussion ## Crosslinks -------------------- ## 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 ## Crosslinks ------------------------------------------------------------------------ # 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 ## Crosslinks ------------------------------------------------------------------------ # ii Basis Function Combinator ... a [Q] ii ------------------ ... Q a Q Gentzen diagram. ## Definition if not basis. ## Derivation if not basis. ## Source if basis ## Discussion ## Crosslinks -------------------- ## 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 ## Crosslinks ------------------------------------------------------------------------ # 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 ## Crosslinks ------------------------------------------------------------------------ # le Basis Function Combinator Same as a \<= b. Gentzen diagram. ## Definition if not basis. ## Derivation if not basis. ## Source if basis ## Discussion ## Crosslinks ------------------------------------------------------------------------ # 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 ## Crosslinks ------------------------------------------------------------------------ # lshift Basis Function Combinator Same as a \<\< b. Gentzen diagram. ## Definition if not basis. ## Derivation if not basis. ## Source if basis ## Discussion ## Crosslinks ------------------------------------------------------------------------ # lt Basis Function Combinator Same as a \< b. Gentzen diagram. ## Definition if not basis. ## Derivation if not basis. ## Source if basis ## Discussion ## Crosslinks ------------------------------------------------------------------------ # make_generator Basis Function Combinator \[codireco\] ccons Gentzen diagram. ## Definition if not basis. ## Derivation if not basis. ## Source if basis ## Discussion ## Crosslinks ------------------------------------------------------------------------ # 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 ## Crosslinks ------------------------------------------------------------------------ # max Basis Function Combinator Given a list find the maximum. Gentzen diagram. ## Definition if not basis. ## Derivation if not basis. ## Source if basis ## Discussion ## Crosslinks ------------------------------------------------------------------------ # min Basis Function Combinator Given a list find the minimum. Gentzen diagram. ## Definition if not basis. ## Derivation if not basis. ## Source if basis ## Discussion ## Crosslinks ------------------------------------------------------------------------ # mod Basis Function Combinator Same as a % b. Gentzen diagram. ## Definition if not basis. ## Derivation if not basis. ## Source if basis ## Discussion ## Crosslinks ------------------------------------------------------------------------ # modulus Basis Function Combinator Same as a % b. Gentzen diagram. ## Definition if not basis. ## Derivation if not basis. ## Source if basis ## Discussion ## Crosslinks ------------------------------------------------------------------------ # mul Basis Function Combinator Same as a \* b. Gentzen diagram. ## Definition if not basis. ## Derivation if not basis. ## Source if basis ## Discussion ## Crosslinks ------------------------------------------------------------------------ # ne Basis Function Combinator Same as a != b. Gentzen diagram. ## Definition if not basis. ## Derivation if not basis. ## Source if basis ## Discussion ## Crosslinks ------------------------------------------------------------------------ # neg Basis Function Combinator Same as -a. Gentzen diagram. ## Definition if not basis. ## Derivation if not basis. ## Source if basis ## Discussion ## Crosslinks ------------------------------------------------------------------------ # not Basis Function Combinator Same as not a. Gentzen diagram. ## Definition if not basis. ## Derivation if not basis. ## Source if basis ## Discussion ## Crosslinks -------------------- ## !- "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 ## Crosslinks -------------------- ## 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 ## Crosslinks ------------------------------------------------------------------------ # or Basis Function Combinator Same as a \| b. Gentzen diagram. ## Definition if not basis. ## Derivation if not basis. ## Source if basis ## Discussion ## Crosslinks ------------------------------------------------------------------------ # over Basis Function Combinator (a2 a1 -- a2 a1 a2) Gentzen diagram. ## Definition if not basis. ## Derivation if not basis. ## Source if basis ## Discussion ## Crosslinks ------------------------------------------------------------------------ # pam Basis Function Combinator \[i\] map Gentzen diagram. ## Definition if not basis. ## Derivation if not basis. ## Source if basis ## Discussion ## Crosslinks ------------------------------------------------------------------------ # pick 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 ## Crosslinks ------------------------------------------------------------------------ # 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 ## Crosslinks ------------------------------------------------------------------------ # pop Basis Function Combinator (a1 --) Gentzen diagram. ## Definition if not basis. ## Derivation if not basis. ## Source if basis ## Discussion ## Crosslinks ------------------------------------------------------------------------ # popd Basis Function Combinator (a2 a1 -- a1) Gentzen diagram. ## Definition if not basis. ## Derivation if not basis. ## Source if basis ## Discussion ## Crosslinks ------------------------------------------------------------------------ # popdd Basis Function Combinator (a3 a2 a1 -- a2 a1) Gentzen diagram. ## Definition if not basis. ## Derivation if not basis. ## Source if basis ## Discussion ## Crosslinks ------------------------------------------------------------------------ # popop Basis Function Combinator (a2 a1 --) Gentzen diagram. ## Definition if not basis. ## Derivation if not basis. ## Source if basis ## Discussion ## Crosslinks ------------------------------------------------------------------------ # popopd Basis Function Combinator (a3 a2 a1 -- a1) Gentzen diagram. ## Definition if not basis. ## Derivation if not basis. ## Source if basis ## Discussion ## Crosslinks ------------------------------------------------------------------------ # popopdd Basis Function Combinator (a4 a3 a2 a1 -- a2 a1) Gentzen diagram. ## Definition if not basis. ## Derivation if not basis. ## Source if basis ## Discussion ## Crosslinks ------------------------------------------------------------------------ # popopop Basis Function Combinator pop popop Gentzen diagram. ## Definition if not basis. ## Derivation if not basis. ## Source if basis ## Discussion ## Crosslinks ------------------------------------------------------------------------ # pow Basis Function Combinator Same as a \*\* b. Gentzen diagram. ## Definition if not basis. ## Derivation if not basis. ## Source if basis ## Discussion ## Crosslinks ------------------------------------------------------------------------ # pred Basis Function Combinator Decrement TOS. Gentzen diagram. ## Definition if not basis. ## Derivation if not basis. ## Source if basis ## Discussion ## Crosslinks ------------------------------------------------------------------------ # 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 ## Crosslinks ------------------------------------------------------------------------ # product Basis Function Combinator 1 swap \[\*\] step Gentzen diagram. ## Definition if not basis. ## Derivation if not basis. ## Source if basis ## Discussion ## Crosslinks ------------------------------------------------------------------------ # quoted Basis Function Combinator \[unit\] dip Gentzen diagram. ## Definition if not basis. ## Derivation if not basis. ## Source if basis ## Discussion ## Crosslinks ------------------------------------------------------------------------ # range Basis Function Combinator \[0 \<=\] \[1 - dup\] anamorphism Gentzen diagram. ## Definition if not basis. ## Derivation if not basis. ## Source if basis ## Discussion ## Crosslinks ------------------------------------------------------------------------ # 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 ## Crosslinks ------------------------------------------------------------------------ # reco Basis Function Combinator rest cons Gentzen diagram. ## Definition if not basis. ## Derivation if not basis. ## Source if basis ## Discussion ## Crosslinks ------------------------------------------------------------------------ # rem Basis Function Combinator Same as a % b. Gentzen diagram. ## Definition if not basis. ## Derivation if not basis. ## Source if basis ## Discussion ## Crosslinks ------------------------------------------------------------------------ # remainder Basis Function Combinator Same as a % b. Gentzen diagram. ## Definition if not basis. ## Derivation if not basis. ## Source if basis ## Discussion ## Crosslinks ------------------------------------------------------------------------ # 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 ## Crosslinks ------------------------------------------------------------------------ # rest Basis Function Combinator ([a1 ...0] -- [...0]) Gentzen diagram. ## Definition if not basis. ## Derivation if not basis. ## Source if basis ## Discussion ## Crosslinks ------------------------------------------------------------------------ # 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 ## Crosslinks ------------------------------------------------------------------------ # rolldown Basis Function Combinator (a1 a2 a3 -- a2 a3 a1) Gentzen diagram. ## Definition if not basis. ## Derivation if not basis. ## Source if basis ## Discussion ## Crosslinks ------------------------------------------------------------------------ # rollup Basis Function Combinator (a1 a2 a3 -- a3 a1 a2) Gentzen diagram. ## Definition if not basis. ## Derivation if not basis. ## Source if basis ## Discussion ## Crosslinks ------------------------------------------------------------------------ # roll> 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 ------------------------------------------------------------------------ # roll\< 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 ------------------------------------------------------------------------ # 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 ## Crosslinks ------------------------------------------------------------------------ # rrest Basis Function Combinator ([a1 a2 ...1] -- [...1]) Gentzen diagram. ## Definition if not basis. ## Derivation if not basis. ## Source if basis ## Discussion ## Crosslinks ------------------------------------------------------------------------ # rshift Basis Function Combinator Same as a \>\> b. Gentzen diagram. ## Definition if not basis. ## Derivation if not basis. ## Source if basis ## Discussion ## Crosslinks ------------------------------------------------------------------------ # run Basis Function Combinator \<{} infra Gentzen diagram. ## Definition if not basis. ## Derivation if not basis. ## Source if basis ## Discussion ## Crosslinks ------------------------------------------------------------------------ # second Basis Function Combinator ([a1 a2 ...1] -- a2) Gentzen diagram. ## Definition if not basis. ## Derivation if not basis. ## Source if basis ## Discussion ## Crosslinks ------------------------------------------------------------------------ # 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 ## Crosslinks ------------------------------------------------------------------------ # sharing Basis Function Combinator Print redistribution information. Gentzen diagram. ## Definition if not basis. ## Derivation if not basis. ## Source if basis ## Discussion ## Crosslinks ------------------------------------------------------------------------ # shift Basis Function Combinator uncons \[swons\] dip Gentzen diagram. ## Definition if not basis. ## Derivation if not basis. ## Source if basis ## Discussion ## Crosslinks ------------------------------------------------------------------------ # 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 ## Crosslinks ------------------------------------------------------------------------ # size Basis Function Combinator \[pop ++\] step_zero Gentzen diagram. ## Definition if not basis. ## Derivation if not basis. ## Source if basis ## Discussion ## Crosslinks ------------------------------------------------------------------------ # sort Basis Function Combinator Given a list return it sorted. Gentzen diagram. ## Definition if not basis. ## Derivation if not basis. ## Source if basis ## Discussion ## Crosslinks ------------------------------------------------------------------------ # 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 ## Crosslinks ------------------------------------------------------------------------ # split_at Basis Function Combinator \[drop\] \[take\] clop Gentzen diagram. ## Definition if not basis. ## Derivation if not basis. ## Source if basis ## Discussion ## Crosslinks ------------------------------------------------------------------------ # split_list Basis Function Combinator \[take reverse\] \[drop\] clop Gentzen diagram. ## Definition if not basis. ## Derivation if not basis. ## Source if basis ## Discussion ## Crosslinks ------------------------------------------------------------------------ # sqr Basis Function Combinator dup \* Gentzen diagram. ## Definition if not basis. ## Derivation if not basis. ## Source if basis ## Discussion ## Crosslinks ------------------------------------------------------------------------ # 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 ## Crosslinks ------------------------------------------------------------------------ # stack Basis Function Combinator (... -- ... [...]) Gentzen diagram. ## Definition if not basis. ## Derivation if not basis. ## Source if basis ## Discussion ## Crosslinks ------------------------------------------------------------------------ # stackd Basis Function Combinator \[stack\] dip Gentzen diagram. ## Definition if not basis. ## Derivation if not basis. ## Source if basis ## Discussion ## Crosslinks ------------------------------------------------------------------------ # 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 ## Crosslinks ------------------------------------------------------------------------ # step_zero Basis Function Combinator 0 roll> step Gentzen diagram. ## Definition if not basis. ## Derivation if not basis. ## Source if basis ## Discussion ## Crosslinks ------------------------------------------------------------------------ # stuncons Basis Function Combinator (... a1 -- ... a1 a1 [...]) Gentzen diagram. ## Definition if not basis. ## Derivation if not basis. ## Source if basis ## Discussion ## Crosslinks ------------------------------------------------------------------------ # stununcons Basis Function Combinator (... a2 a1 -- ... a2 a1 a1 a2 [...]) Gentzen diagram. ## Definition if not basis. ## Derivation if not basis. ## Source if basis ## Discussion ## Crosslinks ------------------------------------------------------------------------ # sub Basis Function Combinator Same as a - b. Gentzen diagram. ## Definition if not basis. ## Derivation if not basis. ## Source if basis ## Discussion ## Crosslinks ------------------------------------------------------------------------ # succ Basis Function Combinator Increment TOS. Gentzen diagram. ## Definition if not basis. ## Derivation if not basis. ## Source if basis ## Discussion ## Crosslinks ------------------------------------------------------------------------ # 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 ## Crosslinks ------------------------------------------------------------------------ # swaack Basis Function Combinator ([...1] -- [...0]) Gentzen diagram. ## Definition if not basis. ## Derivation if not basis. ## Source if basis ## Discussion ## Crosslinks ------------------------------------------------------------------------ # swap Basis Function Combinator (a1 a2 -- a2 a1) Gentzen diagram. ## Definition if not basis. ## Derivation if not basis. ## Source if basis ## Discussion ## Crosslinks ------------------------------------------------------------------------ # swapd Basis Function Combinator \[swap\] dip Gentzen diagram. ## Definition if not basis. ## Derivation if not basis. ## Source if basis ## Discussion ## Crosslinks ------------------------------------------------------------------------ # swoncat Basis Function Combinator swap concat Gentzen diagram. ## Definition if not basis. ## Derivation if not basis. ## Source if basis ## Discussion ## Crosslinks ------------------------------------------------------------------------ # swons Basis Function Combinator ([...1] a1 -- [a1 ...1]) Gentzen diagram. ## Definition if not basis. ## Derivation if not basis. ## Source if basis ## Discussion ## Crosslinks ------------------------------------------------------------------------ # tailrec Basis Function Combinator \[i\] genrec Gentzen diagram. ## Definition if not basis. ## Derivation if not basis. ## Source if basis ## Discussion ## Crosslinks ------------------------------------------------------------------------ # 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 ## Crosslinks -------------------- ## 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 ## Crosslinks ------------------------------------------------------------------------ # 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 ## Crosslinks ------------------------------------------------------------------------ # truthy 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 ## Crosslinks ------------------------------------------------------------------------ # tuck Basis Function Combinator (a2 a1 -- a1 a2 a1) Gentzen diagram. ## Definition if not basis. ## Derivation if not basis. ## Source if basis ## Discussion ## Crosslinks -------------------- ## 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 ## Crosslinks ------------------------------------------------------------------------ # unit Basis Function Combinator (a1 -- [a1 ]) Gentzen diagram. ## Definition if not basis. ## Derivation if not basis. ## Source if basis ## Discussion ## Crosslinks ------------------------------------------------------------------------ # unquoted Basis Function Combinator \[i\] dip Gentzen diagram. ## Definition if not basis. ## Derivation if not basis. ## Source if basis ## Discussion ## Crosslinks ------------------------------------------------------------------------ # unswons Basis Function Combinator ([a1 ...1] -- [...1] a1) Gentzen diagram. ## Definition if not basis. ## Derivation if not basis. ## Source if basis ## Discussion ## Crosslinks ------------------------------------------------------------------------ # 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 ## Crosslinks ------------------------------------------------------------------------ # warranty Basis Function Combinator Print warranty information. Gentzen diagram. ## Definition if not basis. ## Derivation if not basis. ## Source if basis ## Discussion ## Crosslinks ------------------------------------------------------------------------ # while Basis Function Combinator swap nulco dupdipd concat loop Gentzen diagram. ## Definition if not basis. ## Derivation if not basis. ## Source if basis ## Discussion ## Crosslinks ------------------------------------------------------------------------ # 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 ## Crosslinks -------------------- ## 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 ## Crosslinks ------------------------------------------------------------------------ # 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 ## Crosslinks