Homework 2: Denotational Semantics of D

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

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

// 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)