1. RPAL Function definitions
Module 10.2 COP4020 – Programming Language Concepts Dr. Manuel E. Bermudez

2. Topics RPAL Function definitions Functions are first-class objects
let, where constructs
Nesting and scopes
Simultaneous definitions
Cascading definitions
@: infix use of a function.
Functions are first-class objects

3. Function definitions – let D in E
Example (simple definition):
let X=3
in Print(X,X**2) // Prints (3,9)
Example (function form):
let Abs N = N ls 0 -> -N | N
in Print(Abs (-3)) // Prints 3
X=3 is not an assignment.
Equivalent to:
(fn X. Print(X,X**2))3
Equivalent to:
let Abs = fn N. N ls 0 -> -N | N in Print (Abs (-3))
(fn Abs. Print(Abs (-3)) (fn N. N ls 0 -> -N | N)
Print((fn N. N ls 0 -> -N | N) (-3)))

4. Nesting Definitions Scope of ‘let’ parameter is expression after ‘in’.
Nested scopes are as expected.
let X = 3 in
let Sqr X = X**2
Print (X, Sqr X, X * Sqr X, Sqr (X+2))
Scope of X=3, except for
Scope of Sqr

5. Function definitions – E where D
Example (simple definition):
Print(X,X**2) where X=3
// Prints (3,9)
Example (function form):
Print(Abs (-3)) where
Abs N = N ls 0 -> -N | N
// Prints 3
X=3 is not an assignment.
Equivalent to:
(fn X. Print(X,X**2))3
Equivalent to:
(fn Abs. Print(Abs (-3))) (fn N. N ls 0 -> -N | N)
Print((fn N. N ls 0 -> -N | N) (-3))

6. Nesting definitions vs. let X = 3 in let Sqr X = X**2 in
Print (X, Sqr X, X * Sqr X, Sqr (X+2))
vs.
( Print (X, Sqr X, X * Sqr X, Sqr (X+2))
where Sqr X = X**2 )
where X = 3
Parentheses required ! Otherwise
Sqr X = (X**2 where X=3)

7. Simultaneous Definitions
Join definitions with ’and’.
Example:
let X=3 and Y=5 in Print(X+Y)
Keyword and: not a boolean operator (we have &).
Both definitions come into scope at once, in Print(X+Y).
Different from
let X=3 in let Y=5 in Print(X+Y)
let X=3 in let Y=5+X in Print(X+Y)
Scope of X=3

8. cascading function definitions
’within’: make one definition visible inside other(s).
Example:
let c=3 within f x = x + c
in Print(f 3)
vs.
let c=3 in
let f x = x + c
Scope of c=3
Primitive form of information hiding

9. The ‘@’ operator Allows infix use of a function. Example:
let Add x y = x + y
in Print 4)
Equivalent to:
in Print (Add (Add 2 3) 4)
Useful for concatenating strings:
’c’)

10. Functions are first-class objects
Can do (almost) anything with a function.
Name it: let Inc x = x+1 in Inc (3)
Pass it as a parameter:
let f g = g 3 in let h x = x + 1
in Print(f h)
Return it from a function:
let f x = fn y. x+y
in Print (f 3 2)
Print it! let Inc x = x+1 in Print (Inc)

11. Functions are first-class objects
Select it using a conditional:
let B=true in
let f = B -> (fn y.y+1) | (fn y.y+2)
in Print (f 3)
Store it in a tuple:
let T=((fn x.x+1),(fn x.x+2))
in Print (T 1 3, T 2 3)
Apply it to a tuple (n-ary function):
let Add (x,y) = x+y
in Print (Add(3,4))

12. summary RPAL Function definitions Functions are first-class objects
let, where constructs
Nesting and scopes
Simultaneous definitions
Cascading definitions
@: infix use of a function.
Functions are first-class objects