Assigned: Wednesday, March 1, 2006
Due: Monday, March 13, 2006 (flexible)
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.
P in Prog L in SL S in Stat E in Exp V in Val I in Ide
// 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
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
meaningProg : Prog -> I -> O meaningSL : SL -> C-> U -> I -> O meaningStat : Stat -> C -> U -> I -> O meaningExp : Exp -> U -> N meaningVal : Val -> N
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 toclean upat 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)
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.
This document was generated by
Siteweaver on Wed May 10 09:02:34 2006.
The source to the document was last modified on Wed Apr 12 15:22:13 2006.
This document may be found at