CSc 520 - Principles of Programming Languages
25 : Names, Scope, Bindings -- Closures

Christian Collberg

Department of Computer Science

University of Arizona

1 Subroutine Closures

A closure is a structure
(procedure_addr,environment).
To pass C() to A we construct a closure consisting of C's address and the static link that would have been used if C would have been called directly:
1#1

When a reference to a procedure is created (for example by passing it as a reference to another procedure), when are scope rules applied?
1. When the reference is first created?
2. When the routine is first called?
Early binding of a referencing environment (what Pascal uses) is called deep binding.

2#2

dynamic1

A closure was created for B when A(2,B) was closed, hence B will print 1.

A language construct is first-class if it can be passed as a parameter, returned from a subroutine, or assigned to a variable.
A language construct is second-class if it can be passed as a parameter but not be returned from a subroutine, or assigned to a variable.
A language construct is third-class if it can't even be passed as a parameter.
Procedures are second-class in most imperative languages.

If a procedure can be returned as the result of a function we could reference an environment that has gone out of scope:
3#3

In functional languages functions are first-class.
Functional languages specify that local variables have unlimited extent -- they exist for as long as someone references them.
Algol-like languages specify that local variables have limited extent -- they exist until the scope in which they are declared is exited.
Objects with limited extent can be stored on a stack. Objects with unlimited extent must be stored on the heap.

C and C++ do not have nested scope -- no problem.
Modula-2 -- global procedures are first-class (can be stored), local procedures are third-class.
Modula-3 -- global procedures are first-class, local procedures are second-class (can be passed as parameters).
Ada 83 -- procedures are third class.
Ada 95 -- nested procedures can be returned if the scope in which it was declared is at least as wide as that of the declared return type. I.e. a procedure can only be propagated to an area of the program where the referencing environment is active.

The Scheme built-in function call-with-current-continuation (also called call/cc) takes a function as argument:
4#4
foo takes a continuation as argument.
(call/cc foo) calls foo, passing it the current continuation.
A continuation is a closure that holds the current program counter and environment.

foo can invoke the continuation and immediately return to the situation as it was when the call was made.
Any intermediate stack frames are popped off.
Continuations are first-class: you can store them in variables, return them from functions, etc.
call/cc can be used as a general building-block to construct a variety of control structures, such as iterators and coroutines.
Continuations can, for example, be used to quickly exit a tree-search procedure once the node we're looking for has been found.

The function throws the continuation the value 99 which makes it pop out of the current evaluation and return 99:
5#5
The expression (* [] 76) is never executed. Rather, the function pops out and returns 99:
6#6

Christian Collberg 2008-04-21