diff --git a/docs/reference/le.md b/docs/reference/le.md index 9b9d5a5..cc95121 100644 --- a/docs/reference/le.md +++ b/docs/reference/le.md @@ -2,28 +2,22 @@ ## le -Basis Function Combinator +Basis Function -Same as a \<= b. -Gentzen diagram. +Less-Than-or-Equal-to comparison of the two items on the top of the +stack, replacing them with a Boolean value. -### Definition - -if not basis. - -### Derivation - -if not basis. - -### Source - -if basis - -### Discussion - -Lorem ipsum. + a b eq + ------------- + Boolean + (a <= b) ### Crosslinks -Lorem ipsum. +[cmp] +[eq] +[ge] +[gt] +[lt] +[ne] diff --git a/docs/reference/loop.md b/docs/reference/loop.md index fa661fa..c6a6cf5 100644 --- a/docs/reference/loop.md +++ b/docs/reference/loop.md @@ -2,36 +2,35 @@ ## loop -Basis Function Combinator +Basis Combinator -Basic loop combinator. : +Expect a quoted program `Q` and a Boolean value on the stack. If the value is false +discard the quoted program, otherwise run a copy of `Q` and `loop` again. - ... True [Q] loop - ----------------------- - ... Q [Q] loop + false [Q] loop + -------------------- - ... False [Q] loop - ------------------------ - ... -Gentzen diagram. - -### Definition - -if not basis. - -### Derivation - -if not basis. - -### Source - -if basis + true [Q] . loop + -------------------------- + . Q [Q] loop ### Discussion -Lorem ipsum. +This, along with [branch] and [fork], is one of the four main combinators +of all programming. The fourth, sequence, is implied by juxtaposition. +That is to say, in Joy `F G` is like `G(F(...))` in a language bassed on +function application. Or again, to quote the [Joy Wikipedia +entry](https://en.wikipedia.org/wiki/Joy_(programming_language)#Mathematical_purity), + +> In Joy, the meaning function is a homomorphism from the syntactic monoid onto the semantic monoid. That is, the syntactic relation of concatenation of symbols maps directly onto the semantic relation of composition of functions. + +Anyway, [branch], [fork], amd [loop] are the fundamental combinators in Joy. +Just as [branch] has it's more common and convenient form [ifte], +[loop] has [while]. ### Crosslinks -Lorem ipsum. +[branch] +[fork] +[while] diff --git a/docs/reference/mkref/FuncRef.html b/docs/reference/mkref/FuncRef.html index c78dba0..33010a3 100644 --- a/docs/reference/mkref/FuncRef.html +++ b/docs/reference/mkref/FuncRef.html @@ -1375,8 +1375,37 @@ a F a

This is the only function that modifies the dictionary. It’s provided as a convenience, for tinkering with new definitions before entering them into the defs.txt file. It can be abused, which you should avoid unless you know what you’re doing.

le

+

Basis Function

+

Less-Than-or-Equal-to comparison of the two items on the top of the stack, replacing them with a Boolean value.

+
   a b eq
+-------------
+   Boolean
+   (a <= b)
+ +

cmp eq ge gt lt ne

+
+

loop

+

Basis Combinator

+

Expect a quoted program Q and a Boolean value on the stack. If the value is false discard the quoted program, otherwise run a copy of Q and loop again.

+
   false [Q] loop
+--------------------
+
+
+   true [Q] . loop
+--------------------------
+            . Q [Q] loop
+

Discussion

+

This, along with branch and fork, is one of the four main combinators of all programming. The fourth, sequence, is implied by juxtaposition. That is to say, in Joy F G is like G(F(...)) in a language bassed on function application. Or again, to quote the Joy Wikipedia entry,

+
+

In Joy, the meaning function is a homomorphism from the syntactic monoid onto the semantic monoid. That is, the syntactic relation of concatenation of symbols maps directly onto the semantic relation of composition of functions.

+
+

Anyway, branch, fork, amd loop are the fundamental combinators in Joy. Just as branch has it’s more common and convenient form ifte, loop has while.

+ +

branch fork while

+
+

lshift

Basis Function Combinator

-

Same as a <= b.

+

Same as a << b.

Gentzen diagram.

Definition

if not basis.

@@ -1384,45 +1413,8 @@ a F a

if not basis.

Source

if basis

-

Discussion

-

Lorem ipsum.

- -

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.

- -

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.

Lorem ipsum.

@@ -1430,13 +1422,13 @@ a F a

Basis Function Combinator

Same as a < b.

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -1445,13 +1437,13 @@ a F a

Basis Function Combinator

[codireco] ccons

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -1460,13 +1452,13 @@ a F a

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

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -1475,13 +1467,13 @@ a F a

Basis Function Combinator

Given a list find the maximum.

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -1490,13 +1482,13 @@ a F a

Basis Function Combinator

Given a list find the minimum.

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -1505,13 +1497,13 @@ a F a

Basis Function Combinator

Same as a % b.

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -1523,13 +1515,13 @@ a F a

Basis Function Combinator

Same as a * b.

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -1538,13 +1530,13 @@ a F a

Basis Function Combinator

Same as a != b.

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -1553,13 +1545,13 @@ a F a

Basis Function Combinator

Same as -a.

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -1568,13 +1560,13 @@ a F a

Basis Function Combinator

Same as not a.

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -1590,20 +1582,20 @@ a F a N !- ---------- N >= 0 true -

Definition

+

Definition

0 >=

nulco

Basis Function Combinator

[nullary] cons

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -1614,16 +1606,16 @@ a F a 
   ... [P] nullary
 ---------------------
         ... A
-

Definition

+

Definition

[stack] dip infra first
-

Derivation

+

Derivation

... [P] nullary
 ... [P] [stack] dip infra first
 ... stack [P] infra first
 ... [...] [P] infra first
 ... [A ...] first
 ...  A
-

Discussion

+

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.)

unary binary ternary

@@ -1632,13 +1624,13 @@ a F a

Basis Function Combinator

swap at

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -1647,13 +1639,13 @@ a F a

Basis Function Combinator

Same as a | b.

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -1662,13 +1654,13 @@ a F a

Basis Function Combinator

(a2 a1 -- a2 a1 a2)

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -1677,13 +1669,13 @@ a F a

Basis Function Combinator

[i] map

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -1698,13 +1690,13 @@ a F a ------------- a+b a-b

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -1713,13 +1705,13 @@ a+b a-b

Basis Function Combinator

(a1 --)

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -1728,13 +1720,13 @@ a+b a-b

Basis Function Combinator

(a2 a1 -- a1)

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -1743,13 +1735,13 @@ a+b a-b

Basis Function Combinator

(a3 a2 a1 -- a2 a1)

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -1758,13 +1750,13 @@ a+b a-b

Basis Function Combinator

(a2 a1 --)

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -1773,13 +1765,13 @@ a+b a-b

Basis Function Combinator

(a3 a2 a1 -- a1)

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -1788,13 +1780,13 @@ a+b a-b

Basis Function Combinator

(a4 a3 a2 a1 -- a2 a1)

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -1803,13 +1795,13 @@ a+b a-b

Basis Function Combinator

pop popop

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -1818,13 +1810,13 @@ a+b a-b

Basis Function Combinator

Same as a ** b.

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -1833,13 +1825,13 @@ a+b a-b

Basis Function Combinator

Decrement TOS.

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -1860,13 +1852,13 @@ a+b a-b ------------------------------------------ n > 0 n (n-1) [Base] [Recur] primrec Recur

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -1875,13 +1867,13 @@ a+b a-b

Basis Function Combinator

1 swap [*] step

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -1890,13 +1882,13 @@ a+b a-b

Basis Function Combinator

[unit] dip

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -1905,13 +1897,13 @@ a+b a-b

Basis Function Combinator

[0 <=] [1 - dup] anamorphism

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -1920,13 +1912,13 @@ a+b a-b

Basis Function Combinator

unit [down_to_zero] infra

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -1935,13 +1927,13 @@ a+b a-b

Basis Function Combinator

rest cons

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -1959,13 +1951,13 @@ a+b a-b ------------------------ [2 3 1]

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -1974,13 +1966,13 @@ a+b a-b

Basis Function Combinator

([a1 ...0] -- [...0])

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -1990,13 +1982,13 @@ a+b a-b

Reverse the list on the top of the stack. :

reverse == [] swap shunt

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -2005,13 +1997,13 @@ a+b a-b

Basis Function Combinator

(a1 a2 a3 -- a2 a3 a1)

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -2020,13 +2012,13 @@ a+b a-b

Basis Function Combinator

(a1 a2 a3 -- a3 a1 a2)

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -2042,13 +2034,13 @@ a+b a-b

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

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -2057,13 +2049,13 @@ a+b a-b

Basis Function Combinator

([a1 a2 ...1] -- [...1])

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -2072,13 +2064,13 @@ a+b a-b

Basis Function Combinator

Same as a >> b.

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -2087,13 +2079,13 @@ a+b a-b

Basis Function Combinator

<{} infra

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -2102,13 +2094,13 @@ a+b a-b

Basis Function Combinator

([a1 a2 ...1] -- a2)

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -2126,13 +2118,13 @@ a+b a-b 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

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -2141,13 +2133,13 @@ a+b a-b

Basis Function Combinator

Print redistribution information.

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -2156,13 +2148,13 @@ a+b a-b

Basis Function Combinator

uncons [swons] dip

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -2176,13 +2168,13 @@ a+b a-b --------------------------- [f e d a b c]

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -2191,13 +2183,13 @@ a+b a-b

Basis Function Combinator

[pop ++] step_zero

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -2206,13 +2198,13 @@ a+b a-b

Basis Function Combinator

Given a list return it sorted.

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -2221,13 +2213,13 @@ a+b a-b

Basis Function Combinator

[[[abs] ii <=] [[<>] [pop !-] ||] &&] [[!-] [[++]] [[--]] ifte dip] [[pop !-] [--] [++] ifte] ifte

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -2236,13 +2228,13 @@ a+b a-b

Basis Function Combinator

[drop] [take] clop

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -2251,13 +2243,13 @@ a+b a-b

Basis Function Combinator

[take reverse] [drop] clop

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -2266,13 +2258,13 @@ a+b a-b

Basis Function Combinator

dup *

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -2281,13 +2273,13 @@ a+b a-b

Basis Function Combinator

Return the square root of the number a. Negative numbers return complex roots.

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -2296,13 +2288,13 @@ a+b a-b

Basis Function Combinator

(... -- ... [...])

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -2311,13 +2303,13 @@ a+b a-b

Basis Function Combinator

[stack] dip

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -2340,13 +2332,13 @@ a+b a-b ... 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

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -2355,13 +2347,13 @@ a+b a-b

Basis Function Combinator

0 roll> step

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -2370,13 +2362,13 @@ a+b a-b

Basis Function Combinator

(... a1 -- ... a1 a1 [...])

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -2385,13 +2377,13 @@ a+b a-b

Basis Function Combinator

(... a2 a1 -- ... a2 a1 a1 a2 [...])

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -2400,13 +2392,13 @@ a+b a-b

Basis Function Combinator

Same as a - b.

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -2415,13 +2407,13 @@ a+b a-b

Basis Function Combinator

Increment TOS.

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -2431,13 +2423,13 @@ a+b a-b

Given a quoted sequence of numbers return the sum. :

sum == 0 swap [+] step

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -2446,13 +2438,13 @@ a+b a-b

Basis Function Combinator

([...1] -- [...0])

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -2461,13 +2453,13 @@ a+b a-b

Basis Function Combinator

(a1 a2 -- a2 a1)

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -2476,13 +2468,13 @@ a+b a-b

Basis Function Combinator

[swap] dip

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -2491,13 +2483,13 @@ a+b a-b

Basis Function Combinator

swap concat

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -2506,13 +2498,13 @@ a+b a-b

Basis Function Combinator

([...1] a1 -- [a1 ...1])

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -2521,13 +2513,13 @@ a+b a-b

Basis Function Combinator

[i] genrec

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -2539,13 +2531,13 @@ a+b a-b ---------------------- [b a]

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -2556,9 +2548,9 @@ a+b a-b 
   ... z y x [P] unary
 -------------------------
          ... A
-

Definition

+

Definition

binary popd
-

Discussion

+

Discussion

Runs any other quoted function and returns its first result while consuming exactly three items from the stack.

binary nullary unary

@@ -2567,13 +2559,13 @@ a+b a-b

Basis Function Combinator

([a1 a2 a3 ...1] -- a3)

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -2595,13 +2587,13 @@ a+b a-b ------------------------------------- w/ n > 1 ... . Q (n - 1) [Q] times

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -2613,13 +2605,13 @@ a+b a-b

Basis Function Combinator

(a2 a1 -- a1 a2 a1)

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -2630,9 +2622,9 @@ a+b a-b 
   ... x [P] unary
 ---------------------
        ... A
-

Definition

+

Definition

nullary popd
-

Discussion

+

Discussion

Runs any other quoted function and returns its first result while consuming exactly one item from the stack.

binary nullary ternary

@@ -2643,9 +2635,9 @@ a+b a-b 
   [A ...] uncons
 --------------------
       A [...]
-

Source

+

Source

func(uncons, Si, So) :- func(cons, So, Si).
-

Discussion

+

Discussion

This is the inverse of cons.

cons

@@ -2654,13 +2646,13 @@ a+b a-b

Basis Function Combinator

Given a list remove duplicate items.

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -2669,13 +2661,13 @@ a+b a-b

Basis Function Combinator

(a1 -- [a1 ])

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -2684,13 +2676,13 @@ a+b a-b

Basis Function Combinator

[i] dip

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

@@ -2699,13 +2691,13 @@ a+b a-b

Basis Function Combinator

([a1 ...1] -- [...1] a1)

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

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@@ -2714,13 +2706,13 @@ a+b a-b

Basis Function Combinator

True if the form on TOS is void otherwise False.

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

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@@ -2729,13 +2721,13 @@ a+b a-b

Basis Function Combinator

Print warranty information.

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

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@@ -2744,13 +2736,13 @@ a+b a-b

Basis Function Combinator

swap nulco dupdipd concat loop

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

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@@ -2759,13 +2751,13 @@ a+b a-b

Basis Function Combinator

Print all the words in alphabetical order.

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

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@@ -2775,22 +2767,22 @@ a+b a-b 
   [F] x
 -----------
    [F] F
-

Definition

+

Definition

dup i
-

Discussion

+

Discussion

The x combinator …

xor

Basis Function Combinator

Same as a ^ b.

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

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@@ -2799,13 +2791,13 @@ a+b a-b

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

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

Lorem ipsum.

diff --git a/docs/reference/mkref/Functor-Reference.md b/docs/reference/mkref/Functor-Reference.md index 68e8111..e4d42cd 100644 --- a/docs/reference/mkref/Functor-Reference.md +++ b/docs/reference/mkref/Functor-Reference.md @@ -2024,69 +2024,62 @@ know what you're doing. ## le -Basis Function Combinator +Basis Function -Same as a \<= b. -Gentzen diagram. +Less-Than-or-Equal-to comparison of the two items on the top of the +stack, replacing them with a Boolean value. -### Definition - -if not basis. - -### Derivation - -if not basis. - -### Source - -if basis - -### Discussion - -Lorem ipsum. + a b eq + ------------- + Boolean + (a <= b) ### Crosslinks -Lorem ipsum. +[cmp] +[eq] +[ge] +[gt] +[lt] +[ne] ------------------------------------------------------------------------ ## loop -Basis Function Combinator +Basis Combinator -Basic loop combinator. : +Expect a quoted program `Q` and a Boolean value on the stack. If the value is false +discard the quoted program, otherwise run a copy of `Q` and `loop` again. - ... True [Q] loop - ----------------------- - ... Q [Q] loop + false [Q] loop + -------------------- - ... False [Q] loop - ------------------------ - ... -Gentzen diagram. - -### Definition - -if not basis. - -### Derivation - -if not basis. - -### Source - -if basis + true [Q] . loop + -------------------------- + . Q [Q] loop ### Discussion -Lorem ipsum. +This, along with [branch] and [fork], is one of the four main combinators +of all programming. The fourth, sequence, is implied by juxtaposition. +That is to say, in Joy `F G` is like `G(F(...))` in a language bassed on +function application. Or again, to quote the [Joy Wikipedia +entry](https://en.wikipedia.org/wiki/Joy_(programming_language)#Mathematical_purity), + +> In Joy, the meaning function is a homomorphism from the syntactic monoid onto the semantic monoid. That is, the syntactic relation of concatenation of symbols maps directly onto the semantic relation of composition of functions. + +Anyway, [branch], [fork], amd [loop] are the fundamental combinators in Joy. +Just as [branch] has it's more common and convenient form [ifte], +[loop] has [while]. ### Crosslinks -Lorem ipsum. +[branch] +[fork] +[while] ------------------------------------------------------------------------