Difference between revisions of "Weak head normal form"

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(Add a note about strict fields and note (inspired by Stack Overflow question) that the difference between builtin and defined functions is immaterial.)
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An expression is in weak head normal form (WHNF), if it is either:
 
An expression is in weak head normal form (WHNF), if it is either:
* a constructor (eventually applied to arguments) like True, Just (square 42) or (:) 1
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* a constructor (eventually applied to arguments) like <code>True</code>, <code>Just (square 42)</code> or <code>(:) 1</code>.
* a built-in function applied to too few arguments (perhaps none) like (+) 2 or sqrt.
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* a built-in function applied to too few arguments (perhaps none) like <code>(+) 2</code> or <code>sqrt</code>.
* or a lambda abstraction \x -> expression.
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* or a lambda abstraction <code>\x -> expression</code>.
   
Note that the arguments do not themselves have to be fully evaluated for an expression to be in weak head normal form; thus, while (square 42) can be reduced to (42 * 42), which can itself be reduced to a normal form of 1764, Just (square 42) is WHNF without further evaluation. Similarly, (+) (2 * 3 * 4) is WHNF, even though (2 * 3 * 4) could be reduced to the normal form 24.
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Note that the arguments do not themselves have to be fully evaluated for an expression to be in weak head normal form; thus, while <code>square 42</code> can be reduced to <code>42 * 42</code> (which can itself be reduced to a normal form of <code>1764</code>), <code>Just (square 42)</code> is in WHNF without further evaluation. Similarly, <code>(+) (2 * 3 * 4)</code> is in WHNF, even though <code>2 * 3 * 4</code> could be reduced to the normal form <code>24</code>.
   
 
An exception is the case of a fully applied constructor for a data type with some fields declared as strict; the arguments for these fields then also need to be in WHNF.
 
An exception is the case of a fully applied constructor for a data type with some fields declared as strict; the arguments for these fields then also need to be in WHNF.
   
The above definition might seem to treat built-in functions differently from functions defined via lambda abstraction. However, the distinction does not matter to semantics. If a lambda abstraction is applied to "too few arguments", then evaluating the application just means substituting arguments for some of the lambda abstraction's variables, which always halts with the result a now unapplied lambda abstraction.
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The above definition might seem to treat built-in functions differently from functions defined via lambda abstraction. However, the distinction does not matter to semantics. If a lambda abstraction is applied to "too few arguments", then evaluating the application just means substituting arguments for some of the lambda abstraction's variables, which always halts with the result a now-unapplied lambda abstraction.
   
 
== See also ==
 
== See also ==

Latest revision as of 22:16, 5 April 2021

An expression is in weak head normal form (WHNF), if it is either:

  • a constructor (eventually applied to arguments) like True, Just (square 42) or (:) 1.
  • a built-in function applied to too few arguments (perhaps none) like (+) 2 or sqrt.
  • or a lambda abstraction \x -> expression.

Note that the arguments do not themselves have to be fully evaluated for an expression to be in weak head normal form; thus, while square 42 can be reduced to 42 * 42 (which can itself be reduced to a normal form of 1764), Just (square 42) is in WHNF without further evaluation. Similarly, (+) (2 * 3 * 4) is in WHNF, even though 2 * 3 * 4 could be reduced to the normal form 24.

An exception is the case of a fully applied constructor for a data type with some fields declared as strict; the arguments for these fields then also need to be in WHNF.

The above definition might seem to treat built-in functions differently from functions defined via lambda abstraction. However, the distinction does not matter to semantics. If a lambda abstraction is applied to "too few arguments", then evaluating the application just means substituting arguments for some of the lambda abstraction's variables, which always halts with the result a now-unapplied lambda abstraction.

See also