计算机科学分类程序设计语言types-and functions

1、Programming LanguagesDan GrossmanPolymorphic Types and Functions As ArgumentsThe key pointHigher-order functions are often so “generic” and “reusable” that they have polymorphic types, i.e., types with type variablesBut there are higher-order functions that are not polymorphicAnd there are non-highe

2、r-order (first-order) functions that are polymorphicAlways a good idea to understand the type of a function, especially a higher-order function2Dan Grossman, Programming LanguagesTypesval n_times : (a - a) * int * a - aSimpler but less useful: (int - int) * int * int - intTwo of our examples instant

3、iated a with intOne of our examples instantiated a with int listThis polymorphism makes n_times more usefulType is inferred based on how arguments are used (later lecture) Describes which types must be exactly something (e.g., int) and which can be anything but the same (e.g., a)3Dan Grossman, Progr

4、amming Languagesfun n_times (f,n,x) = if n=0 then x else f (n_times(f,n-1,x)Polymorphism and higher-order functionsMany higher-order functions are polymorphic because they are so reusable that some types, “can be anything”But some polymorphic functions are not higher-orderExample: len : a list - intAnd some higher-order functions are not polymorphicExample: times_until_0 : (int - int) * int - int4Dan Grossman, Programming Languagesfun times_until_0 (f,x) = if x=0 then 0