Two L's.
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Simon Forman
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@ -2,28 +2,22 @@
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## le
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Basis Function Combinator
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Basis Function
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Same as a \<= b.
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Gentzen diagram.
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Less-Than-or-Equal-to comparison of the two items on the top of the
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stack, replacing them with a Boolean value.
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### Definition
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if not basis.
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### Derivation
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if not basis.
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### Source
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if basis
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### Discussion
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Lorem ipsum.
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a b eq
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-------------
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Boolean
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(a <= b)
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### Crosslinks
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Lorem ipsum.
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[cmp]
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[eq]
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[ge]
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[gt]
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[lt]
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[ne]
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@ -2,36 +2,35 @@
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## loop
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Basis Function Combinator
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Basis Combinator
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Basic loop combinator. :
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Expect a quoted program `Q` and a Boolean value on the stack. If the value is false
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discard the quoted program, otherwise run a copy of `Q` and `loop` again.
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... True [Q] loop
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-----------------------
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... Q [Q] loop
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false [Q] loop
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--------------------
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... False [Q] loop
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------------------------
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...
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Gentzen diagram.
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### Definition
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if not basis.
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### Derivation
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if not basis.
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### Source
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if basis
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true [Q] . loop
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--------------------------
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. Q [Q] loop
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### Discussion
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Lorem ipsum.
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This, along with [branch] and [fork], is one of the four main combinators
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of all programming. The fourth, sequence, is implied by juxtaposition.
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That is to say, in Joy `F G` is like `G(F(...))` in a language bassed on
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function application. Or again, to quote the [Joy Wikipedia
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entry](https://en.wikipedia.org/wiki/Joy_(programming_language)#Mathematical_purity),
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> In Joy, the meaning function is a homomorphism from the syntactic monoid onto the semantic monoid. That is, the syntactic relation of concatenation of symbols maps directly onto the semantic relation of composition of functions.
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Anyway, [branch], [fork], amd [loop] are the fundamental combinators in Joy.
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Just as [branch] has it's more common and convenient form [ifte],
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[loop] has [while].
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### Crosslinks
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Lorem ipsum.
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[branch]
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[fork]
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[while]
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File diff suppressed because it is too large
Load Diff
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@ -2024,69 +2024,62 @@ know what you're doing.
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## le
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Basis Function Combinator
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Basis Function
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Same as a \<= b.
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Gentzen diagram.
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Less-Than-or-Equal-to comparison of the two items on the top of the
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stack, replacing them with a Boolean value.
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### Definition
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if not basis.
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### Derivation
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if not basis.
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### Source
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if basis
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### Discussion
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Lorem ipsum.
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a b eq
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-------------
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Boolean
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(a <= b)
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### Crosslinks
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Lorem ipsum.
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[cmp]
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[eq]
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[ge]
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[gt]
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[lt]
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[ne]
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------------------------------------------------------------------------
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## loop
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Basis Function Combinator
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Basis Combinator
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Basic loop combinator. :
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Expect a quoted program `Q` and a Boolean value on the stack. If the value is false
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discard the quoted program, otherwise run a copy of `Q` and `loop` again.
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... True [Q] loop
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-----------------------
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... Q [Q] loop
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false [Q] loop
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--------------------
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... False [Q] loop
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------------------------
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...
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Gentzen diagram.
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### Definition
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if not basis.
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### Derivation
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if not basis.
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### Source
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if basis
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true [Q] . loop
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--------------------------
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. Q [Q] loop
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### Discussion
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Lorem ipsum.
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This, along with [branch] and [fork], is one of the four main combinators
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of all programming. The fourth, sequence, is implied by juxtaposition.
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That is to say, in Joy `F G` is like `G(F(...))` in a language bassed on
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function application. Or again, to quote the [Joy Wikipedia
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entry](https://en.wikipedia.org/wiki/Joy_(programming_language)#Mathematical_purity),
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> In Joy, the meaning function is a homomorphism from the syntactic monoid onto the semantic monoid. That is, the syntactic relation of concatenation of symbols maps directly onto the semantic relation of composition of functions.
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Anyway, [branch], [fork], amd [loop] are the fundamental combinators in Joy.
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Just as [branch] has it's more common and convenient form [ifte],
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[loop] has [while].
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### Crosslinks
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Lorem ipsum.
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[branch]
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[fork]
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[while]
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------------------------------------------------------------------------
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