From aae78523d366ee0355d81fc846b8d578a7b32799 Mon Sep 17 00:00:00 2001 From: Simon Forman Date: Sun, 27 Mar 2022 11:11:20 -0700 Subject: [PATCH] The N's. --- docs/reference/mkref/FuncRef.html | 815 +++++++++++----------- docs/reference/mkref/Functor-Reference.md | 112 +-- docs/reference/neg.md | 26 +- docs/reference/not.md | 30 +- docs/reference/nulco.md | 24 +- docs/reference/nullary.md | 15 +- 6 files changed, 470 insertions(+), 552 deletions(-) diff --git a/docs/reference/mkref/FuncRef.html b/docs/reference/mkref/FuncRef.html index 94fe2e4..6e1027c 100644 --- a/docs/reference/mkref/FuncRef.html +++ b/docs/reference/mkref/FuncRef.html @@ -262,7 +262,6 @@
  • ne
  • neg
  • not
  • -
  • !-
  • nulco
  • nullary
  • of
  • @@ -1509,142 +1508,128 @@ a F a

    cmp eq ge gt le lt


    neg

    -

    Basis Function Combinator

    -

    Same as -a.

    -

    Gentzen diagram.

    +

    Function

    +

    Invert the sign of a number.

    +
       a neg
    +-----------
    +    -a

    Definition

    -

    if not basis.

    -

    Derivation

    -

    if not basis.

    -

    Source

    -

    if basis

    -

    Discussion

    -

    Lorem ipsum.

    - -

    Lorem ipsum.

    +
    +

    0 swap -

    +

    not

    -

    Basis Function Combinator

    -

    Same as not a.

    -

    Gentzen diagram.

    -

    Definition

    -

    if not basis.

    -

    Derivation

    -

    if not basis.

    -

    Source

    -

    if basis

    -

    Discussion

    -

    Lorem ipsum.

    - -

    Lorem ipsum.

    -
    -

    !-

    -

    “not negative”

    -

    (Function, Boolean Predicate)

    -

    Integer on top of stack is replaced by Boolean value indicating whether it is non-negative.

    -
        N !-
    ------------  N < 0
    -   false
    +

    Function

    +

    Like bool but convert the item on the top of the stack to the inverse Boolean value.

    +
       true not
    +--------------
    +    false
     
    -   N !-
    -----------  N >= 0
    -   true
    -

    Definition

    -
    0 >=
    + false not +--------------- + true
    +

    Definition

    +
    +

    bool [true] [false] branch

    +
    + +

    bool


    nulco

    -

    Basis Function Combinator

    -

    [nullary] cons

    -

    Gentzen diagram.

    -

    Definition

    -

    if not basis.

    -

    Derivation

    -

    if not basis.

    -

    Source

    -

    if basis

    -

    Discussion

    -

    Lorem ipsum.

    - -

    Lorem ipsum.

    +

    Function

    +

    Take the item on the top of the stack and cons it onto [nullary].

    +
         [F] nulco
    +-------------------
    +   [[F] nullary]
    +

    Definition

    +
    +

    [nullary] cons

    +
    +

    Discussion

    +

    Helper function for || and &&.

    + +

    && ||


    nullary

    -

    (Combinator)

    +

    Combinator

    Run a quoted program without using any stack values and leave the first item of the result on the stack.

       ... [P] nullary
     ---------------------
             ... A
    -

    Definition

    -
    [stack] dip infra first
    -

    Derivation

    +

    Definition

    +
    +

    [stack] dip infra first

    +
    +

    Example

    ... [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

    @@ -1657,150 +1642,150 @@ 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.


    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

    @@ -1819,90 +1804,90 @@ 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

    @@ -1918,30 +1903,30 @@ 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

    @@ -1949,45 +1934,45 @@ 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>

    @@ -2001,30 +1986,30 @@ 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

    @@ -2033,37 +2018,37 @@ a+b a-b
       a n rshift
     ----------------
          (a∕2ⁿ)
    - +

    lshift


    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

    @@ -2079,45 +2064,45 @@ 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

    @@ -2129,150 +2114,150 @@ 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

    @@ -2293,90 +2278,90 @@ 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

    @@ -2384,105 +2369,105 @@ 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

    @@ -2492,15 +2477,15 @@ 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

    @@ -2509,26 +2494,26 @@ 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

    @@ -2548,15 +2533,15 @@ 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

    @@ -2566,15 +2551,15 @@ 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

    @@ -2583,11 +2568,11 @@ 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

    @@ -2596,131 +2581,131 @@ 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

    @@ -2728,39 +2713,39 @@ 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 01432e1..6b2e399 100644 --- a/docs/reference/mkref/Functor-Reference.md +++ b/docs/reference/mkref/Functor-Reference.md @@ -2298,124 +2298,78 @@ stack, replacing them with a Boolean value. ## neg -Basis Function Combinator +Function -Same as -a. - -Gentzen diagram. +Invert the sign of a number. + a neg + ----------- + -a ### Definition -if not basis. +> 0 [swap] [-] -### Derivation - -if not basis. - -### Source - -if basis - -### Discussion - -Lorem ipsum. - -### Crosslinks - -Lorem ipsum. ------------------------------------------------------------------------ ## not -Basis Function Combinator +Function -Same as not a. +Like [bool] but convert the item on the top of the stack to the inverse +Boolean value. -Gentzen diagram. + true not + -------------- + false + false not + --------------- + true + ### Definition -if not basis. - -### Derivation - -if not basis. - -### Source - -if basis - -### Discussion - -Lorem ipsum. +> [bool] \[true\] \[false\] [branch] ### Crosslinks -Lorem ipsum. - --------------------- - -## !- - -"not negative" - -(Function, Boolean Predicate) - -Integer on top of stack is replaced by Boolean value indicating whether -it is non-negative. - - N !- - ----------- N < 0 - false - - N !- - ---------- N >= 0 - true - - -### Definition - - 0 >= +[bool] ------------------------------------------------------------------------ ## nulco -Basis Function Combinator +Function -\[nullary\] cons +Take the item on the top of the stack and [cons] it onto `[nullary]`. -Gentzen diagram. + [F] nulco + ------------------- + [[F] nullary] ### Definition -if not basis. - -### Derivation - -if not basis. - -### Source - -if basis +> \[[nullary]\] [cons] ### Discussion -Lorem ipsum. +Helper function for [\|\|] and [&&]. ### Crosslinks -Lorem ipsum. +[&&] +[\|\|] + -------------------- ## nullary -(Combinator) +Combinator -Run a quoted program without using any stack values and leave the first item of the result on the stack. +Run a quoted program without using any stack values and leave the first +item of the result on the stack. ... [P] nullary --------------------- @@ -2423,9 +2377,9 @@ Run a quoted program without using any stack values and leave the first item of ### Definition - [stack] dip infra first +> \[[stack]\] [dip] [infra] [first] -### Derivation +### Example ... [P] nullary ... [P] [stack] dip infra first diff --git a/docs/reference/neg.md b/docs/reference/neg.md index b1721e8..b62a88b 100644 --- a/docs/reference/neg.md +++ b/docs/reference/neg.md @@ -2,28 +2,14 @@ ## neg -Basis Function Combinator +Function -Same as -a. - -Gentzen diagram. +Invert the sign of a number. + a neg + ----------- + -a ### Definition -if not basis. +> 0 [swap] [-] -### Derivation - -if not basis. - -### Source - -if basis - -### Discussion - -Lorem ipsum. - -### Crosslinks - -Lorem ipsum. diff --git a/docs/reference/not.md b/docs/reference/not.md index bfd2a43..5ce78de 100644 --- a/docs/reference/not.md +++ b/docs/reference/not.md @@ -2,28 +2,24 @@ ## not -Basis Function Combinator +Function -Same as not a. +Like [bool] but convert the item on the top of the stack to the inverse +Boolean value. -Gentzen diagram. + true not + -------------- + false + false not + --------------- + true + ### Definition -if not basis. - -### Derivation - -if not basis. - -### Source - -if basis - -### Discussion - -Lorem ipsum. +> [bool] \[true\] \[false\] [branch] ### Crosslinks -Lorem ipsum. +[bool] + diff --git a/docs/reference/nulco.md b/docs/reference/nulco.md index 5b5f12e..4eda5be 100644 --- a/docs/reference/nulco.md +++ b/docs/reference/nulco.md @@ -2,28 +2,24 @@ ## nulco -Basis Function Combinator +Function -\[nullary\] cons +Take the item on the top of the stack and [cons] it onto `[nullary]`. -Gentzen diagram. + [F] nulco + ------------------- + [[F] nullary] ### Definition -if not basis. - -### Derivation - -if not basis. - -### Source - -if basis +> \[[nullary]\] [cons] ### Discussion -Lorem ipsum. +Helper function for [\|\|] and [&&]. ### Crosslinks -Lorem ipsum. +[&&] +[\|\|] + diff --git a/docs/reference/nullary.md b/docs/reference/nullary.md index b6eaeb4..b3beaf7 100644 --- a/docs/reference/nullary.md +++ b/docs/reference/nullary.md @@ -2,26 +2,27 @@ ## nullary -(Combinator) +Combinator -Run a quoted program without using any stack values and leave the first item of the result on the stack. +Run a quoted program without using any stack values and leave the first +item of the result on the stack. ... [P] nullary --------------------- - ... A + ... a ### Definition - [stack] dip infra first +> \[[stack]\] [dip] [infra] [first] -### Derivation +### Example ... [P] nullary ... [P] [stack] dip infra first ... stack [P] infra first ... [...] [P] infra first - ... [A ...] first - ... A + ... [a ...] first + ... a ### Discussion