generic type variable
(Also known as a "schematic type variable"). Different occurrences of a generic type variable in a type expression may be instantiated to different types. Thus, in the expression let id x = x in (id True, id 1) id' s type is (for all a: a -> a). The universal quantifier "for all a:" means that a is a generic type variable. For the two uses of id, a is instantiated to Bool and Int. Compare this with let id x = x in let f g = (g True, g 1) in f id This looks similar but f has no legal Hindley-Milner type. If we say f :: (a -> b) -> (b, b) this would permit g' s type to be any instance of (a -> b) rather than requiring it to be at least as general as (a -> b). Furthermore, it constrains both instances of g to have the same result type whereas they do not. The type variables a and b in the above are implicitly quantified at the top level: f :: for all a: for all b: (a -> b) -> (b, b) so instantiating them (removing the quantifiers) can only be done once, at the top level. To correctly describe the type of f requires that they be locally quantified: f :: ((for all a: a) -> (for all b: b)) -> (c, d) which means that each time g is applied, a and b may be instantiated differently. f' s actual argument must have a type at least as general as ((for all a: a) -> (for all b: b)), and may not be some less general instance of this type. Type variables c and d are still implicitly quantified at the top level and, now that g' s result type is a generic type variable, any types chosen for c and d are guaranteed to be instances of it. This type for f does not express the fact that b only needs to be at least as general as the types c and d. For example, if c and d were both Bool then any function of type (for all a: a -> Bool) would be a suitable argument to f but it would not match the above type for f. In addition suitable contents:
[ = ] [ actual argument ] [ ai ] [ al ] [ am ] [ an ] [ app ] [ ar ] [ arc ] [ arg ] [ argument ] [ as ] [ at ] [ av ] [ B ] [ b ] [ be ] [ bo ] [ bot ] [ C ] [ ca ] [ cc ] [ ch ] [ ci ] [ co ] [ con ] [ cons ] [ cr ] [ cu ] [ D ] [ de ] [ diff ] [ do ] [ du ] [ ec ] [ ed ] [ ee ] [ eg ] [ er ] [ era ] [ es ] [ et ] [ expression ] [ fact ] [ fi ] [ file ] [ fo ] [ for ] [ function ] [ ga ] [ ge ] [ gen ] [ gr ] [ gu ] [ h ] [ hat ] [ hose ] [ hr ] [ hu ] [ id ] [ ie ] [ iff ] [ il ] [ in ] [ instance ] [ instantiate ] [ io ] [ ir ] [ is ] [ it ] [ kn ] [ la ] [ ld ] [ legal ] [ Lex ] [ li ] [ ls ] [ lt ] [ ly ] [ M ] [ ma ] [ mil ] [ mm ] [ mo ] [ mod ] [ module ] [ mp ] [ mu ] [ na ] [ nc ] [ ne ] [ ng ] [ ni ] [ nl ] [ no ] [ ns ] [ om ] [ op ] [ pa ] [ pe ] [ ph ] [ pl ] [ pr ] [ program ] [ programming ] [ quantifier ] [ query ] [ rc ] [ re ] [ ro ] [ ru ] [ sa ] [ sam ] [ say ] [ sc ] [ schematic type variable ] [ se ] [ si ] [ so ] [ st ] [ su ] [ suit ] [ T ] [ table ] [ tc ] [ tee ] [ th ] [ to ] [ tr ] [ tw ] [ type ] [ ua ] [ um ] [ us ] [ va ] [ var ] [ variable ] [ ve ] [ vi ]
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