--- layout: default title: "Functions" parent: Abstraction ancestor: Funcons-beta --- [Funcons-beta] : [Functions.cbs] ----------------------------- ### Functions 
[
  Datatype functions
  Funcon   function
  Funcon   apply
  Funcon   supply
  Funcon   compose
  Funcon   uncurry
  Funcon   curry
  Funcon   partial-apply
]
Meta-variables
  T, T′, T1, T2 <: values
Datatype
  functions(T,T′) ::= function(A:abstractions(T=>T′))
functions(T, T′) consists of abstractions whose bodies may depend on a given value of type T, and whose executions normally compute values of type T′. function(abstraction(X)) evaluates to a function with dynamic bindings, function(closure(X)) computes a function with static bindings. 
Funcon
  apply(_:functions(T, T′), _:T) : =>T′
apply(F, V) applies the function F to the argument value V. This corresponds to call by value; using thunks as argument values corresponds to call by name. Moreover, using tuples as argument values corresponds to application to multiple arguments. 
Rule
  apply(function(abstraction(X)), V:T) ~> give(V, X)
Funcon
  supply(_:functions(T, T′), _:T) : =>thunks(T′)
supply(F, V) determines the argument value of a function application, but returns a thunk that defers executing the body of the function. 
Rule
  supply(function(abstraction(X)), V:T) ~> thunk(abstraction(give(V, X)))
Funcon
  compose(_:functions(T2, T′), _:functions(T1, T2)) : =>functions(T1, T′)
compose(F2, F1) returns the function that applies F1 to its argument, then applies F2 to the result of F1. 
Rule
  compose(function(abstraction(Y)), function(abstraction(X)))
    ~> function(abstraction(give(X, Y)))
Funcon
  uncurry(F:functions(T1, functions(T2, T′))) : 
    =>functions(tuples(T1, T2), T′)
   ~> function(abstraction(
         apply(
           apply(F, checked index(1, tuple-elements given)),
           checked index(2, tuple-elements given))))
uncurry(F) takes a curried function F and returns a function that takes a pair of arguments.. 
Funcon
  curry(F:functions(tuples(T1, T2), T′)) : =>functions(T1, functions(T2, T′))
    ~> function(abstraction(partial-apply(F, given)))
curry(F) takes a function F that takes a pair of arguments, and returns the corresponding 'curried' function. 
Funcon
  partial-apply(F:functions(tuples(T1, T2), T′), V:T1) : =>functions(T2, T′)
    ~> function(abstraction(apply(F,tuple(V,given))))
partial-apply(F, V) takes a function F that takes a pair of arguments, and determines the first argument, returning a function of the second argument. ____ From the [PLanCompS Project] | [CBS-beta issues...] | [Suggest an improvement...] [Functions.cbs]: Functions.cbs "CBS SOURCE FILE" [Funcons-beta]: /CBS-beta/docs/Funcons-beta "FUNCONS-BETA" [Unstable-Funcons-beta]: /CBS-beta/docs/Unstable-Funcons-beta "UNSTABLE-FUNCONS-BETA" [Languages-beta]: /CBS-beta/docs/Languages-beta "LANGUAGES-BETA" [Unstable-Languages-beta]: /CBS-beta/docs/Unstable-Languages-beta "UNSTABLE-LANGUAGES-BETA" [CBS-beta]: /CBS-beta "CBS-BETA" [PLanCompS Project]: https://plancomps.github.io "PROGRAMMING LANGUAGE COMPONENTS AND SPECIFICATIONS PROJECT HOME PAGE" [CBS-beta issues...]: https://github.com/plancomps/CBS-beta/issues "CBS-BETA ISSUE REPORTS ON GITHUB" [Suggest an improvement...]: mailto:plancomps@gmail.com?Subject=CBS-beta%20-%20comment&Body=Re%3A%20CBS-beta%20specification%20at%20Values/Abstraction/Functions/Functions.cbs%0A%0AComment/Query/Issue/Suggestion%3A%0A%0A%0ASignature%3A%0A "GENERATE AN EMAIL TEMPLATE"