1. Introduction to RPAL
Module 10.1 COP4020 – Programming Language Concepts Dr. Manuel E. Bermudez

2. Topics The RPAL Language “Turing complete” No assignment No sequencing
No iteration
No “memory”
Only expressions: every RPAL program is an expression.
To run an RPAL program is to evaluate it.
“Turing complete”

3. RPAL is a subset of PAL PAL: Pedagogic Algorithmic Language.
Developed by J. Wozencraft and A. Evans at MIT, early 70's.
R(ight-reference)PAL ⊂ L(eft-reference)PAL ⊂ J(ump) PAL
Intellectual ancestor of Scheme, (Guy Steele, mid-70's)
Steele (Sun Microsystems): principal contributor to Java.
Google: 'Guy Steele Scheme‘.
Why Study RPAL ?
Generic, “plain vanilla” functional language.
Unknown language (to you) 
Paradigm shift !!

4. Simple one-line RPAL programs
3 //comment: value is 3, print nothing
(3+1)*4**2 // arithmetic: value is 64, prints nothing
’Hello World’ // value is ’Hello World’
Print(’Hello World’) // Prints ’Hello World’, value is dummy
Print(Conc ’Hello ’ ’World’) // same
4*6 < 27 // value is true (not ’true’)
2 < 0 -> 3 | 6 // conditional (like the ?: operator)
true or false // value is true
true & false // value is false, & is the ‘and’ operator

5. data types and operators
Integer operations:
+, -, *, /, **, eq, ne, ls, <, gr, >, le, <=, ge, >=
Truthvalue (boolean) operations:
or, &, not, eq, ne
String operations:
eq, ne, Stem S, Stern S, Conc S T
Conditional operator:
-> |
Elementary values: <int>, <id>, true, false

6. operator Precedence
Operator Precedence Associativity
-> Low Right
or Left
& Left
not None
gr ge le ls eq ne None
+ - (unary and binary) Left
* / Left
** Right
() High Embedded
Elements: <id>, <int>, <str>, true, false, dummy

7. New data type: function (fn x. B)
Has a ’bound variable’ (parameter), and a body. Example:
fn X. Print(X**2)
It’s value: “Nameless, typeless function with typeless parameter X, that prints X squared.”
fn N. N ls 0 -> -N | N
Value: “Nameless, typeless function with typeless parameter N, that returns |N|.”
fn x. fn y.x+y or, equivalently
fn x y.x+y
Value: “Nameless, typeless function that takes typeless parameter x, and returns nameless,
typeless function that take typeless parameter y, and returns x+y.”

8. Function application Function application is by juxtaposition.
Example: (fn X. Print(X**2)) 3
Function is applied to 3.
3 replaces X in expression Print(X**2), yielding
Print(3**2), yielding
Print(9), yielding
dummy (and prints 9).

9. Function application Example: (fn N. N ls 0 -> -N | N) (-3)
(-3) replaces N in (N ls 0 -> -N | N), yielding
((-3) ls 0 -> -(-3)|(-3)) ), yielding
–(-3) = 3
Function application is left associative:
Example: (fn x. fn y.x+y) 3 2 yielding
(fn y.3+y) 2 yielding
yielding 5

10. Type Identification Functions
Intrinsic functions.
Applied to a value, return true or false:
Isinteger x
Istruthvalue x
Isstring x
Istuple x
Isfunction x
Isdummy x

11. Rpal constructs Operators Function definitions
Constant definitions (parameterless function)
Conditional expressions
Function application
Recursion

12. RPAL Has Six Data Types:
Integer
Truthvalue (boolean)
String
Tuple (coming soon)
Function
Dummy (value: dummy)
RPAL is dynamically typed:
the type of an expression is determined at run-time.
Example: let Funny = (B -> 1 | ’January’) in Print(Funny)

13. summary RPAL Language of expressions To run it, evaluate it.
Arithmetic, boolean, string operations.
New data type: function.
New operation: function application.