Refutable



verb (used with object), refuted, refuting.
1.
to prove to be false or erroneous, as an opinion or charge.
2.
to prove (a person) to be in error.
verb
1.
(transitive) to prove (a statement, theory, charge, etc) of (a person) to be false or incorrect; disprove
2.
to deny (a claim, charge, allegation, etc)

In lazy functional languages, a refutable pattern is one which may fail to match. An expression being matched against a refutable pattern is first evaluated to head normal form (which may fail to terminate) and then the top-level constructor of the result is compared with that of the pattern. If they are the same then any arguments are matched against the pattern’s arguments otherwise the match fails.
An irrefutable pattern is one which always matches. An attempt to evaluate any variable in the pattern forces the pattern to be matched as though it were refutable which may fail to match (resulting in an error) or fail to terminate.
Patterns in Haskell are normally refutable but may be made irrefutable by prefixing them with a tilde (~). For example,
(\ (x,y) -> 1) undefined ==> undefined (\ ~(x,y) -> 1) undefined ==> 1
Patterns in Miranda are refutable, except for tuples which are irrefutable. Thus
g [x] = 2 g undefined ==> undefined
f (x,y) = 1 f undefined ==> 1
Pattern bindings in local definitions are irrefutable in both languages:
h = 1 where [x] = undefined ==> 1 Irrefutable patterns can be used to simulate unlifted products because they effectively ignore the top-level constructor of the expression being matched and consider only its components.

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  • Refutal

    noun 1. an act of refuting a statement, charge, etc.; disproof. noun 1. the act or process of refuting 2. something that refutes; disproof

  • Refutation

    noun 1. an act of refuting a statement, charge, etc.; disproof. noun 1. the act or process of refuting 2. something that refutes; disproof



  • Refutative

    adjective 1. tending to refute; pertaining to refutation: refutative evidence.

  • Refute

    verb (used with object), refuted, refuting. 1. to prove to be false or erroneous, as an opinion or charge. 2. to prove (a person) to be in error. verb 1. (transitive) to prove (a statement, theory, charge, etc) of (a person) to be false or incorrect; disprove 2. to deny (a claim, charge, allegation, etc)



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