7 Essential Words of Fall
1510s, "refuse, reject," from Middle French réfuter (16c.) and directly from Latin refutare "drive back; rebut, disprove; repress, repel, resist, oppose," from re- "back" (see re-) + -futare "to beat," probably from PIE root *bhau- "to strike down" (see bat (n.1)).
Meaning "prove wrong" dates from 1540s. Since c.1964 linguists have frowned on the subtle shift in meaning towards "to deny," as it is used in connection with allegation. Related: Refuted; refuting.
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.