Super combinator
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| - | A | + | A supercombinator is either a constant, or a [[combinator]] which contains only supercombinators as [[subexpression]]s. |
To get a fuller idea of what a supercombinator is, it may help to use the following equivalent definition: | To get a fuller idea of what a supercombinator is, it may help to use the following equivalent definition: | ||
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* <code>\f g -> f (\x -> g x 2)</code> | * <code>\f g -> f (\x -> g x 2)</code> | ||
| - | + | Any lambda calculus expression (or, indeed, Haskell program) with no free variables can be converted into supercombinators using [[lambda lifting]]. For example, the last example can be expressed as: | |
| - | + | * <code>\f g -> f ((\h x -> h x 2) g)</code> | |
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| + | Because supercombinators have no free variables, they can always be given their own names and [[lifting pattern|let floated]] to the top level. The last example, for example, can be rewritten as: | ||
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| + | * <code>let { scF h x = h x 2; scE f g = f (scF g) } in scE</code> | ||
| + | |||
| + | Some older compilers for Haskell-like languages, such as [[Gofer]], used this as part of the compilation process. Converting a whole program into supercombinators leaves no internal lambda abstractions left, and each supercombinator can then be compiled more or less directly into a lower-level language, such as the [[G machine]]. | ||
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| + | A supercombinator which is not a lambda abstraction (i.e. for which n=0) is called a [[constant applicative form]]. | ||
[[Category:Glossary]] | [[Category:Glossary]] | ||
[[Category:Combinators]] | [[Category:Combinators]] | ||
Current revision
A supercombinator is either a constant, or a combinator which contains only supercombinators as subexpressions.
To get a fuller idea of what a supercombinator is, it may help to use the following equivalent definition:
Any lambda expression is of the form \x1 x2 .. xn -> E, where E is not a lambda abstraction and n≥0. (Note that if the expression is not a lambda abstraction, n=0.) This is a supercombinator if and only if:
- the only free variables in E are x1..xn, and
- every lambda abstraction in E is a supercombinator.
So these are supercombinators:
-
0 -
\x y -> x + y -
\f -> f (\x -> x + x)
These are not combinators, let alone supercombinators, because in each case, the variable y occurs free:
-
\x -> y -
\x -> y + x
This is a combinator, but not a supercombinator, because the inner lambda abstraction is not a combinator:
-
\f g -> f (\x -> g x 2)
Any lambda calculus expression (or, indeed, Haskell program) with no free variables can be converted into supercombinators using lambda lifting. For example, the last example can be expressed as:
-
\f g -> f ((\h x -> h x 2) g)
Because supercombinators have no free variables, they can always be given their own names and let floated to the top level. The last example, for example, can be rewritten as:
-
let { scF h x = h x 2; scE f g = f (scF g) } in scE
Some older compilers for Haskell-like languages, such as Gofer, used this as part of the compilation process. Converting a whole program into supercombinators leaves no internal lambda abstractions left, and each supercombinator can then be compiled more or less directly into a lower-level language, such as the G machine.
A supercombinator which is not a lambda abstraction (i.e. for which n=0) is called a constant applicative form.
