diff --git a/docs/reference/dinfrirst.md b/docs/reference/dinfrirst.md index 0139037..4b945c1 100644 --- a/docs/reference/dinfrirst.md +++ b/docs/reference/dinfrirst.md @@ -2,28 +2,11 @@ ## dinfrirst -Basis Function Combinator +Combinator -dip infrst - -Gentzen diagram. +Specialist function (that means I forgot what it does and why.) ### Definition -if not basis. +> [dip] [infrst] -### Derivation - -if not basis. - -### Source - -if basis - -### Discussion - -Lorem ipsum. - -### Crosslinks - -Lorem ipsum. diff --git a/docs/reference/dip.md b/docs/reference/dip.md index 28fb88a..e94ffee 100644 --- a/docs/reference/dip.md +++ b/docs/reference/dip.md @@ -2,34 +2,38 @@ ## dip -Basis Function Combinator +Basis Combinator -The dip combinator expects a quoted program on the stack and below it +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. : +on the rest of the stack. - ... x [Q] dip - ------------------- - ... Q x - -Gentzen diagram. - -### Definition - -if not basis. - -### Derivation - -if not basis. - -### Source - -if basis + ... x [Q] . dip + --------------------- + ... . Q x ### Discussion -Lorem ipsum. +This along with [infra] are enough to update any datastructure. +See the ["Traversing Datastructures with Zippers" notebook](https://joypy.osdn.io/notebooks/Zipper.html). + +Note that the item that was on the top of the stack (`x` in the example above) +will not be treated specially by the interpreter when it is reached +again. This is something of a footgun. My advice is to avoid putting +bare unquoted symbols onto the stack, but then you can't use symbols as +"atoms" and also use `dip` and `infra` to operate on compound +datastructures with atoms in them. This is a kind of side-effect of the +Continuation-Passing Style. The `dip` combinator could "set aside" the +item and replace it after running `Q` but that means that there is an +"extra space" where the item resides while `Q` runs. One of the nice +things about CPS is that the whole state is recorded in the stack and +pending expression (not counting modifications to the dictionary.) ### Crosslinks -Lorem ipsum. +[dipd] +[dipdd] +[dupdip] +[dupdipd] +[infra] + diff --git a/docs/reference/dipd.md b/docs/reference/dipd.md index 72f2973..aae4e24 100644 --- a/docs/reference/dipd.md +++ b/docs/reference/dipd.md @@ -2,32 +2,22 @@ ## dipd -Basis Function Combinator +Combinator -Like dip but expects two items. : +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 + ... y x [Q] . dipd + ------------------------- + ... . Q y x ### Discussion -Lorem ipsum. +See [dip]. ### Crosslinks -Lorem ipsum. +[dip] +[dipdd] +[dupdip] +[dupdipd] +[infra] diff --git a/docs/reference/dipdd.md b/docs/reference/dipdd.md index de355b8..e373e9d 100644 --- a/docs/reference/dipdd.md +++ b/docs/reference/dipdd.md @@ -2,32 +2,22 @@ ## dipdd -Basis Function Combinator +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 +Like [dip] but expects three items. : + ... z y x [Q] . dip + ----------------------------- + ... . Q z y x ### Discussion -Lorem ipsum. +See [dip]. ### Crosslinks -Lorem ipsum. +[dip] +[dipd] +[dupdip] +[dupdipd] +[infra] + diff --git a/docs/reference/disenstacken.md b/docs/reference/disenstacken.md index 8a188e2..3fed85c 100644 --- a/docs/reference/disenstacken.md +++ b/docs/reference/disenstacken.md @@ -2,29 +2,28 @@ ## disenstacken -Basis Function Combinator +Function -The disenstacken operator expects a list on top of the stack and makes +The `disenstacken` function expects a list on top of the stack and makes that the stack discarding the rest of the stack. -Gentzen diagram. + 1 2 3 [4 5 6] disenstacken + -------------------------------- + 6 5 4 ### Definition -if not basis. - -### Derivation - -if not basis. - -### Source - -if basis +> \[[clear]\] [dip] [reverse] [unstack](#unstack) ### Discussion -Lorem ipsum. +Note that the order of the list is not changed, it just looks that way +because the stack is printed with the top on the right while lists are +printed with the top or head on the left. ### Crosslinks -Lorem ipsum. +[enstacken] +[stack] +[unstack](#unstack) + diff --git a/docs/reference/divmod.md b/docs/reference/divmod.md index 6e8a6da..528a3cd 100644 --- a/docs/reference/divmod.md +++ b/docs/reference/divmod.md @@ -2,30 +2,17 @@ ## divmod -Basis Function Combinator +Function -divmod(x, y) -\> (quotient, remainder) + x y divmod + ------------------ + q r + (x/y) (x%y) -Return the tuple (x//y, x%y). Invariant: q \* y + r == x. +Invariant: `qy + r = x`. -Gentzen diagram. ### Definition -if not basis. +> \[[floordiv]\] \[[mod]\] [clop] -### Derivation - -if not basis. - -### Source - -if basis - -### Discussion - -Lorem ipsum. - -### Crosslinks - -Lorem ipsum. diff --git a/docs/reference/down_to_zero.md b/docs/reference/down_to_zero.md index cda1d4c..c83c0f1 100644 --- a/docs/reference/down_to_zero.md +++ b/docs/reference/down_to_zero.md @@ -2,28 +2,22 @@ ## down_to_zero -Basis Function Combinator +Function -\[0 \>\] \[dup \--\] while +Given a number greater than zero put all the Natural numbers (including +zero) less than that onto the stack. -Gentzen diagram. +### Example + + 3 down_to_zero + -------------------- + 3 2 1 0 ### Definition -if not basis. - -### Derivation - -if not basis. - -### Source - -if basis - -### Discussion - -Lorem ipsum. +> \[0 \>\] \[[dup] [--]\] [while] ### Crosslinks -Lorem ipsum. +[range] + diff --git a/docs/reference/drop.md b/docs/reference/drop.md index f085d2b..e332e2a 100644 --- a/docs/reference/drop.md +++ b/docs/reference/drop.md @@ -2,35 +2,22 @@ ## drop -Basis Function Combinator - - drop == [rest] times +Function Expects an integer and a quote on the stack and returns the quote with n -items removed off the top. : +items removed off the top. - [a b c d] 2 drop +### Example + + [a b c d] 2 drop ---------------------- - [c d] - -Gentzen diagram. + [c d] ### Definition -if not basis. - -### Derivation - -if not basis. - -### Source - -if basis - -### Discussion - -Lorem ipsum. +> \[[rest]\] [times] ### Crosslinks -Lorem ipsum. +[take] + diff --git a/docs/reference/dup.md b/docs/reference/dup.md index 8d34e93..69c1369 100644 --- a/docs/reference/dup.md +++ b/docs/reference/dup.md @@ -2,28 +2,18 @@ ## dup -Basis Function Combinator +Basis Function - (a1 -- a1 a1) +"Dup"licate the top item on the stack. -Gentzen diagram. - -### Definition - -if not basis. - -### Derivation - -if not basis. - -### Source - -if basis - -### Discussion - -Lorem ipsum. + a dup + ----------- + a a ### Crosslinks -Lorem ipsum. +[dupd] +[dupdd] +[dupdip] +[dupdipd] + diff --git a/docs/reference/dupd.md b/docs/reference/dupd.md index 4190c23..df2c6b0 100644 --- a/docs/reference/dupd.md +++ b/docs/reference/dupd.md @@ -2,28 +2,22 @@ ## dupd -Basis Function Combinator +Function - (a2 a1 -- a2 a2 a1) +[dup] the second item down on the stack. -Gentzen diagram. + a b dupd + -------------- + a a b ### Definition -if not basis. - -### Derivation - -if not basis. - -### Source - -if basis - -### Discussion - -Lorem ipsum. +> \[[dup]\] [dip] ### Crosslinks -Lorem ipsum. +[dup] +[dupdd] +[dupdip] +[dupdipd] + diff --git a/docs/reference/dupdd.md b/docs/reference/dupdd.md index ad3d58a..5f4f495 100644 --- a/docs/reference/dupdd.md +++ b/docs/reference/dupdd.md @@ -2,28 +2,22 @@ ## dupdd -Basis Function Combinator +Function - (a3 a2 a1 -- a3 a3 a2 a1) +[dup] the third item down on the stack. -Gentzen diagram. + a b c dupdd + ----------------- + a a b c ### Definition -if not basis. - -### Derivation - -if not basis. - -### Source - -if basis - -### Discussion - -Lorem ipsum. +> \[[dup]\] [dipd] ### Crosslinks -Lorem ipsum. +[dup] +[dupd] +[dupdip] +[dupdipd] + diff --git a/docs/reference/dupdip.md b/docs/reference/dupdip.md index 131b568..38a138b 100644 --- a/docs/reference/dupdip.md +++ b/docs/reference/dupdip.md @@ -2,33 +2,32 @@ ## dupdip -Basis Function Combinator +Combinator - [F] dupdip == dup [F] dip +Apply a function `F` and [dup] the item under it on the stack. - ... a [F] dupdip - ... a dup [F] dip - ... a a [F] dip - ... a F a - -Gentzen diagram. + a [F] dupdip + ------------------ + a F a ### Definition -if not basis. +> [dupd] [dip] ### Derivation -if not basis. - -### Source - -if basis + a [F] dupdip + a [F] dupd dip + a [F] [dup] dip dip + a dup [F] dip + a a [F] dip + a F a ### Discussion -Lorem ipsum. +A very common and useful combinator. ### Crosslinks -Lorem ipsum. +[dupdipd] + diff --git a/docs/reference/dupdipd.md b/docs/reference/dupdipd.md index 30aa73d..1d28291 100644 --- a/docs/reference/dupdipd.md +++ b/docs/reference/dupdipd.md @@ -2,28 +2,19 @@ ## dupdipd -Basis Function Combinator +Combinator -dup dipd +Run a copy of program `F` under the next item down on the stack. -Gentzen diagram. + a [F] dupdipd + ------------------- + F a [F] ### Definition -if not basis. - -### Derivation - -if not basis. - -### Source - -if basis - -### Discussion - -Lorem ipsum. +> [dup] [dipd] ### Crosslinks -Lorem ipsum. +[dupdip] + diff --git a/docs/reference/mkref/FuncRef.html b/docs/reference/mkref/FuncRef.html index c9d424d..ef560ac 100644 --- a/docs/reference/mkref/FuncRef.html +++ b/docs/reference/mkref/FuncRef.html @@ -866,295 +866,248 @@ cond

uncons

dinfrirst

-

Basis Function Combinator

-

dip infrst

-

Gentzen diagram.

+

Combinator

+

Specialist function (that means I forgot what it does and why.)

Definition

-

if not basis.

-

Derivation

-

if not basis.

-

Source

-

if basis

-

Discussion

-

Lorem ipsum.

- -

Lorem ipsum.

+
+

dip infrst

+

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.

- -

Lorem ipsum.

+

Basis Combinator

+

The dip combinator expects a quoted program on the stack and below it some item, it hoists the item into the expression and runs the program on the rest of the stack.

+
   ... x [Q] . dip
+---------------------
+         ... . Q x
+

Discussion

+

This along with infra are enough to update any datastructure. See the “Traversing Datastructures with Zippers” notebook.

+

Note that the item that was on the top of the stack (x in the example above) will not be treated specially by the interpreter when it is reached again. This is something of a footgun. My advice is to avoid putting bare unquoted symbols onto the stack, but then you can’t use symbols as “atoms” and also use dip and infra to operate on compound datastructures with atoms in them. This is a kind of side-effect of the Continuation-Passing Style. The dip combinator could “set aside” the item and replace it after running Q but that means that there is an “extra space” where the item resides while Q runs. One of the nice things about CPS is that the whole state is recorded in the stack and pending expression (not counting modifications to the dictionary.)

+ +

dipd dipdd dupdip dupdipd infra

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.

- -

Lorem ipsum.

+

Combinator

+

Like dip but expects two items.

+
   ... y x [Q] . dipd
+-------------------------
+           ... . Q y x
+

Discussion

+

See dip.

+ +

dip dipdd dupdip dupdipd infra

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.

- -

Lorem ipsum.

+

Combinator

+

Like dip but expects three items. :

+
   ... z y x [Q] . dip
+-----------------------------
+             ... . Q z y x
+

Discussion

+

See dip.

+ +

dip dipd dupdip dupdipd infra

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.

- -

Lorem ipsum.

+

Function

+

The disenstacken function expects a list on top of the stack and makes that the stack discarding the rest of the stack.

+
   1 2 3 [4 5 6] disenstacken
+--------------------------------
+            6 5 4
+

Definition

+
+

[clear] dip reverse unstack

+
+

Discussion

+

Note that the order of the list is not changed, it just looks that way because the stack is printed with the top on the right while lists are printed with the top or head on the left.

+ +

enstacken stack unstack

div

See 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.

- -

Lorem ipsum.

+

Function

+
    x y divmod
+------------------
+     q      r
+   (x/y)  (x%y)
+

Invariant: qy + r = x.

+

Definition

+
+

[floordiv] [mod] clop

+

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.

- -

Lorem ipsum.

+

Function

+

Given a number greater than zero put all the Natural numbers (including zero) less than that onto the stack.

+

Example

+
   3 down_to_zero
+--------------------
+      3 2 1 0
+

Definition

+
+

[0 >] [dup –] while

+
+ +

range

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
+
Function

+
Expects an integer and a quote on the stack and returns the quote with n items removed off the top.

+
Example

+
   [a b c d] 2 drop
 ----------------------
-    [c d]

-
Gentzen diagram.

-
Definition

-
if not basis.

-
Derivation

-
if not basis.

-
Source

-
if basis

-
Discussion

-
Lorem ipsum.

-
-
Lorem ipsum.

+       [c d]
+

Definition

+
+

[rest] times

+
+ +

take

dup

-

Basis Function Combinator

-
(a1 -- a1 a1)
-

Gentzen diagram.

-

Definition

-

if not basis.

-

Derivation

-

if not basis.

-

Source

-

if basis

-

Discussion

-

Lorem ipsum.

- -

Lorem ipsum.

+

Basis Function

+

“Dup”licate the top item on the stack.

+
   a dup
+-----------
+    a a
+ +

dupd dupdd dupdip dupdipd

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.

- -

Lorem ipsum.

+

Function

+

dup the second item down on the stack.

+
   a b dupd
+--------------
+    a a b
+

Definition

+
+

[dup] dip

+
+ +

dup dupdd dupdip dupdipd

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.

- -

Lorem ipsum.

+

Function

+

dup the third item down on the stack.

+
   a b c dupdd
+-----------------
+     a a b c
+

Definition

+
+

[dup] dipd

+
+ +

dup dupd dupdip dupdipd

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.

- -

Lorem ipsum.

+

Combinator

+

Apply a function F and dup the item under it on the stack.

+
   a [F] dupdip
+------------------
+      a F a
+

Definition

+
+

dupd dip

+
+

Derivation

+
a [F] dupdip
+a [F] dupd dip
+a [F] [dup] dip dip
+a dup [F] dip
+a a [F] dip
+a F a
+

Discussion

+

A very common and useful combinator.

+ +

dupdipd

dupdipd

-

Basis Function Combinator

-

dup dipd

-

Gentzen diagram.

-

Definition

-

if not basis.

-

Derivation

-

if not basis.

-

Source

-

if basis

-

Discussion

-

Lorem ipsum.

- -

Lorem ipsum.

+

Combinator

+

Run a copy of program F under the next item down on the stack.

+
   a [F] dupdipd
+-------------------
+      F a [F]
+

Definition

+
+

dup dipd

+
+ +

dupdip

enstacken

Basis Function Combinator

stack [clear] dip

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

- +

Lorem ipsum.

eq

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.

first

Basis Function Combinator

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

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

- +

Lorem ipsum.

first_two

Basis Function Combinator

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

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

- +

Lorem ipsum.

flatten

Basis Function Combinator

<{} [concat] step

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

- +

Lorem ipsum.

floor

@@ -1162,105 +1115,105 @@ cond

Return the floor of x as an Integral.

This is the largest integer <= x.

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

- +

Lorem ipsum.

floordiv

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.

fork

Basis Function Combinator

[i] app2

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

- +

Lorem ipsum.

fourth

Basis Function Combinator

([a1 a2 a3 a4 ...1] -- a4)

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

- +

Lorem ipsum.

gcd

Basis Function Combinator

true [tuck mod dup 0 >] loop pop

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

- +

Lorem ipsum.

gcd2

Basis Function Combinator

Compiled GCD function.

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

- +

Lorem ipsum.

ge

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.

genrec

@@ -1283,15 +1236,15 @@ cond == [I] [T] [R [P] i] ifte == [I] [T] [R P] ifte

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

- +

Lorem ipsum.

getitem

@@ -1302,90 +1255,90 @@ cond ------------------------- a

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

- +

Lorem ipsum.

grabN

Basis Function Combinator

<{} [cons] times

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

- +

Lorem ipsum.

grba

Basis Function Combinator

[stack popd] dip

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

- +

Lorem ipsum.

gt

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.

help

Basis Function Combinator

Accepts a quoted symbol on the top of the stack and prints its docs.

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

- +

Lorem ipsum.

hypot

Basis Function Combinator

[sqr] ii + sqrt

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

- +

Lorem ipsum.

i

@@ -1394,24 +1347,24 @@ cond 
   [Q] i
 -----------
     Q
-

Source

+

Source

combo(i, [list(P)|S], S, Ei, Eo) :- append(P, Ei, Eo).
-

Discussion

+

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

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

- +

Lorem ipsum.

ifte

@@ -1429,15 +1382,15 @@ cond ... [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

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

- +

Lorem ipsum.

ii

@@ -1446,15 +1399,15 @@ cond ------------------ ... Q a Q

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

- +

Lorem ipsum.

infra

@@ -1463,26 +1416,26 @@ cond 
   ... [a b c] [Q] infra
 ---------------------------
     c b a Q [...] swaack
-

Definition

+

Definition

swons swaack [i] dip swaack
-

Discussion

+

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.

- +

swaack

infrst

Basis Function Combinator

infra first

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

- +

Lorem ipsum.

inscribe

@@ -1492,30 +1445,30 @@ cond

[sqr dup mul] inscribe

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

- +

Lorem ipsum.

le

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.

loop

@@ -1529,120 +1482,120 @@ cond ------------------------ ...

Gentzen diagram.

-

Definition

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

- +

Lorem ipsum.

lshift

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.

lt

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.

make_generator

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.

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

+

Definition

if not basis.

-

Derivation

+

Derivation

if not basis.

-

Source

+

Source

if basis

-

Discussion

+

Discussion

Lorem ipsum.

- +

Lorem ipsum.

max

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.

min

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.

mod

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.

modulus

@@ -1652,60 +1605,60 @@ cond

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.

ne

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.

neg

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.

not

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.

!-

@@ -1719,22 +1672,22 @@ cond 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.

nullary

@@ -1743,78 +1696,78 @@ cond 
   ... [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

of

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.

or

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.

over

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.

pam

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.

pick

@@ -1827,150 +1780,150 @@ cond ------------- 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.

pop

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.

popd

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.

popdd

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.

popop

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.

popopd

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.

popopdd

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.

popopop

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.

pow

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.

pred

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.

primrec

@@ -1989,90 +1942,90 @@ 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.

product

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.

quoted

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.

range

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.

range_to_zero

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.

reco

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.

rem

@@ -2088,30 +2041,30 @@ 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.

rest

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.

reverse

@@ -2119,45 +2072,45 @@ 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.

rolldown

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.

rollup

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.

roll>

@@ -2171,75 +2124,75 @@ 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.

rrest

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.

rshift

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.

run

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.

second

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.

select

@@ -2255,45 +2208,45 @@ 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.

sharing

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.

shift

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.

shunt

@@ -2305,150 +2258,150 @@ 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.

size

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.

sort

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.

spiral_next

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.

split_at

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.

split_list

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.

sqr

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.

sqrt

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.

stack

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.

stackd

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.

step

@@ -2469,90 +2422,90 @@ 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.

step_zero

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.

stuncons

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.

stununcons

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.

sub

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.

succ

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.

sum

@@ -2560,105 +2513,105 @@ 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.

swaack

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.

swap

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.

swapd

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.

swoncat

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.

swons

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.

tailrec

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.

take

@@ -2668,15 +2621,15 @@ 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.

ternary

@@ -2685,26 +2638,26 @@ 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

third

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.

times

@@ -2724,15 +2677,15 @@ 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.

truthy

@@ -2742,15 +2695,15 @@ 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.

unary

@@ -2759,11 +2712,11 @@ 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

uncons

@@ -2772,131 +2725,131 @@ 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

unique

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.

unit

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.

unquoted

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.

unswons

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.

- +

Lorem ipsum.

void

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.

- +

Lorem ipsum.

warranty

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.

- +

Lorem ipsum.

while

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.

- +

Lorem ipsum.

words

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.

- +

Lorem ipsum.

x

@@ -2904,39 +2857,39 @@ 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.

- +

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

+

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 4e9d47e..b424c7a 100644 --- a/docs/reference/mkref/Functor-Reference.md +++ b/docs/reference/mkref/Functor-Reference.md @@ -1013,166 +1013,132 @@ Its inverse operation is [uncons]. ## dinfrirst -Basis Function Combinator +Combinator -dip infrst - -Gentzen diagram. +Specialist function (that means I forgot what it does and why.) ### Definition -if not basis. +> [dip] [infrst] -### Derivation - -if not basis. - -### Source - -if basis - -### Discussion - -Lorem ipsum. - -### Crosslinks - -Lorem ipsum. ------------------------------------------------------------------------ ## dip -Basis Function Combinator +Basis Combinator -The dip combinator expects a quoted program on the stack and below it +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. : +on the rest of the stack. - ... x [Q] dip - ------------------- - ... Q x - -Gentzen diagram. - -### Definition - -if not basis. - -### Derivation - -if not basis. - -### Source - -if basis + ... x [Q] . dip + --------------------- + ... . Q x ### Discussion -Lorem ipsum. +This along with [infra] are enough to update any datastructure. +See the ["Traversing Datastructures with Zippers" notebook](https://joypy.osdn.io/notebooks/Zipper.html). + +Note that the item that was on the top of the stack (`x` in the example above) +will not be treated specially by the interpreter when it is reached +again. This is something of a footgun. My advice is to avoid putting +bare unquoted symbols onto the stack, but then you can't use symbols as +"atoms" and also use `dip` and `infra` to operate on compound +datastructures with atoms in them. This is a kind of side-effect of the +Continuation-Passing Style. The `dip` combinator could "set aside" the +item and replace it after running `Q` but that means that there is an +"extra space" where the item resides while `Q` runs. One of the nice +things about CPS is that the whole state is recorded in the stack and +pending expression (not counting modifications to the dictionary.) ### Crosslinks -Lorem ipsum. +[dipd] +[dipdd] +[dupdip] +[dupdipd] +[infra] + ------------------------------------------------------------------------ ## dipd -Basis Function Combinator +Combinator -Like dip but expects two items. : +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 + ... y x [Q] . dipd + ------------------------- + ... . Q y x ### Discussion -Lorem ipsum. +See [dip]. ### Crosslinks -Lorem ipsum. +[dip] +[dipdd] +[dupdip] +[dupdipd] +[infra] ------------------------------------------------------------------------ ## dipdd -Basis Function Combinator +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 +Like [dip] but expects three items. : + ... z y x [Q] . dip + ----------------------------- + ... . Q z y x ### Discussion -Lorem ipsum. +See [dip]. ### Crosslinks -Lorem ipsum. +[dip] +[dipd] +[dupdip] +[dupdipd] +[infra] + ------------------------------------------------------------------------ ## disenstacken -Basis Function Combinator +Function -The disenstacken operator expects a list on top of the stack and makes +The `disenstacken` function expects a list on top of the stack and makes that the stack discarding the rest of the stack. -Gentzen diagram. + 1 2 3 [4 5 6] disenstacken + -------------------------------- + 6 5 4 ### Definition -if not basis. - -### Derivation - -if not basis. - -### Source - -if basis +> \[[clear]\] [dip] [reverse] [unstack](#unstack) ### Discussion -Lorem ipsum. +Note that the order of the list is not changed, it just looks that way +because the stack is printed with the top on the right while lists are +printed with the top or head on the left. ### Crosslinks -Lorem ipsum. +[enstacken] +[stack] +[unstack](#unstack) + -------------- @@ -1185,255 +1151,191 @@ See [floordiv](#floordiv). ## divmod -Basis Function Combinator +Function -divmod(x, y) -\> (quotient, remainder) + x y divmod + ------------------ + q r + (x/y) (x%y) -Return the tuple (x//y, x%y). Invariant: q \* y + r == x. +Invariant: `qy + r = x`. -Gentzen diagram. ### Definition -if not basis. +> \[[floordiv]\] \[[mod]\] [clop] -### Derivation - -if not basis. - -### Source - -if basis - -### Discussion - -Lorem ipsum. - -### Crosslinks - -Lorem ipsum. ------------------------------------------------------------------------ ## down_to_zero -Basis Function Combinator +Function -\[0 \>\] \[dup \--\] while +Given a number greater than zero put all the Natural numbers (including +zero) less than that onto the stack. -Gentzen diagram. +### Example + + 3 down_to_zero + -------------------- + 3 2 1 0 ### Definition -if not basis. - -### Derivation - -if not basis. - -### Source - -if basis - -### Discussion - -Lorem ipsum. +> \[0 \>\] \[[dup] [--]\] [while] ### Crosslinks -Lorem ipsum. +[range] + ------------------------------------------------------------------------ ## drop -Basis Function Combinator - - drop == [rest] times +Function Expects an integer and a quote on the stack and returns the quote with n -items removed off the top. : +items removed off the top. - [a b c d] 2 drop +### Example + + [a b c d] 2 drop ---------------------- - [c d] - -Gentzen diagram. + [c d] ### Definition -if not basis. - -### Derivation - -if not basis. - -### Source - -if basis - -### Discussion - -Lorem ipsum. +> \[[rest]\] [times] ### Crosslinks -Lorem ipsum. +[take] + ------------------------------------------------------------------------ ## dup -Basis Function Combinator +Basis Function - (a1 -- a1 a1) +"Dup"licate the top item on the stack. -Gentzen diagram. - -### Definition - -if not basis. - -### Derivation - -if not basis. - -### Source - -if basis - -### Discussion - -Lorem ipsum. + a dup + ----------- + a a ### Crosslinks -Lorem ipsum. +[dupd] +[dupdd] +[dupdip] +[dupdipd] + ------------------------------------------------------------------------ ## dupd -Basis Function Combinator +Function - (a2 a1 -- a2 a2 a1) +[dup] the second item down on the stack. -Gentzen diagram. + a b dupd + -------------- + a a b ### Definition -if not basis. - -### Derivation - -if not basis. - -### Source - -if basis - -### Discussion - -Lorem ipsum. +> \[[dup]\] [dip] ### Crosslinks -Lorem ipsum. +[dup] +[dupdd] +[dupdip] +[dupdipd] + ------------------------------------------------------------------------ ## dupdd -Basis Function Combinator +Function - (a3 a2 a1 -- a3 a3 a2 a1) +[dup] the third item down on the stack. -Gentzen diagram. + a b c dupdd + ----------------- + a a b c ### Definition -if not basis. - -### Derivation - -if not basis. - -### Source - -if basis - -### Discussion - -Lorem ipsum. +> \[[dup]\] [dipd] ### Crosslinks -Lorem ipsum. +[dup] +[dupd] +[dupdip] +[dupdipd] + ------------------------------------------------------------------------ ## dupdip -Basis Function Combinator +Combinator - [F] dupdip == dup [F] dip +Apply a function `F` and [dup] the item under it on the stack. - ... a [F] dupdip - ... a dup [F] dip - ... a a [F] dip - ... a F a - -Gentzen diagram. + a [F] dupdip + ------------------ + a F a ### Definition -if not basis. +> [dupd] [dip] ### Derivation -if not basis. - -### Source - -if basis + a [F] dupdip + a [F] dupd dip + a [F] [dup] dip dip + a dup [F] dip + a a [F] dip + a F a ### Discussion -Lorem ipsum. +A very common and useful combinator. ### Crosslinks -Lorem ipsum. +[dupdipd] + ------------------------------------------------------------------------ ## dupdipd -Basis Function Combinator +Combinator -dup dipd +Run a copy of program `F` under the next item down on the stack. -Gentzen diagram. + a [F] dupdipd + ------------------- + F a [F] ### Definition -if not basis. - -### Derivation - -if not basis. - -### Source - -if basis - -### Discussion - -Lorem ipsum. +> [dup] [dipd] ### Crosslinks -Lorem ipsum. +[dupdip] + ------------------------------------------------------------------------