Programming Languages (CS302 2006S)

Homework 2: Denotational Semantics of D

Assigned: Wednesday, March 1, 2006
Due: Monday, March 13, 2006 (flexible)

The Assignment

Consider a simple programming language that contains

The language will only operate on natural numbers (integers). Let's call this language D, for the grade it deserves. In the following sections, I define the key domains and type equations for the language. Your goal is to define a semantics for that language. For example, the meaning of the sequence

read(a);
read(b);
write(a+b);

should be a function from the a list of numbers (the input) to a list that contains the sum of the first two numbers on the input list.

Syntactic Domains

P in Prog
L in SL
S in Stat
E in Exp
V in Val
I in Ide

Abstract Syntax

// Programs
Prog => L
// Lists of statements
SL => S
    |  S ; L
// Statements
Stat => I = E
      |  if E then L fi
      |  if E then L0 else L1 fi
      |  read(I)
      |  write(E)
// Expressions
Exp => E1 + E2
     |  E1 * E2
     |  E1 - E2
     |  E1 / E2
     |  (E)
     |  V
     |  I

Semantic Domains

n in N                   Natural Numbers
env in U = Id -> N    Environments
inp in I = N*            Input (a sequence of numbers)
out in O = N*            Output (a sequence of numbers)
cont in C = U -> I -> O  Continuations

Types of the Semantic Functions

meaningProg : Prog -> I -> O
meaningSL : SL -> C-> U -> I -> O
meaningStat : Stat -> C -> U -> I -> O
meaningExp : Exp -> U -> N
meaningVal : Val -> N

Helper Functions

Here are some helper functions that you might find useful.

// Build a basic environment that assigns 0 to every variable.
basicEnv : U
basicEnv = \x . 0
// A continuation used to clean up at the end of the program.
cleanup : C
cleanup = \env . \inp . nil
// Set the value associated with an identifier in an environment.
setenv : U -> Id -> N -> U
setenv env id num =
  \x . (x == id) -> num , (env id)

Disclaimer: I usually create these pages on the fly, which means that I rarely proofread them and they may contain bad grammar and incorrect details. It also means that I tend to update them regularly (see the history for more details). Feel free to contact me with any suggestions for changes.

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The source to the document was last modified on Wed Apr 12 15:22:13 2006.
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Samuel A. Rebelsky, rebelsky@grinnell.edu