There go the D's!
This is a slog, but it's great to be getting it done.
This commit is contained in:
Simon Forman
parent
6a71bfb003
commit
14554527b4
|
|
@ -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.
|
||||
|
|
|
|||
|
|
@ -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]
|
||||
|
||||
|
|
|
|||
|
|
@ -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]
|
||||
|
|
|
|||
|
|
@ -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]
|
||||
|
||||
|
|
|
|||
|
|
@ -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)
|
||||
|
||||
|
|
|
|||
|
|
@ -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.
|
||||
|
|
|
|||
|
|
@ -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]
|
||||
|
||||
|
|
|
|||
|
|
@ -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]
|
||||
|
||||
|
|
|
|||
|
|
@ -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]
|
||||
|
||||
|
|
|
|||
|
|
@ -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]
|
||||
|
||||
|
|
|
|||
|
|
@ -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]
|
||||
|
||||
|
|
|
|||
|
|
@ -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]
|
||||
|
||||
|
|
|
|||
|
|
@ -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]
|
||||
|
||||
|
|
|
|||
File diff suppressed because it is too large
Load Diff
|
|
@ -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]
|
||||
|
||||
|
||||
------------------------------------------------------------------------
|
||||
|
||||
|
|
|
|||
Loading…
Reference in New Issue