General Computer Science 320201 GenCS I & II Lecture ... - Kwarc

Needed Infrastructure: Environments
Need a structure to keep track of the values of declared identifiers.
(take shadowing into account)
Definition 470 An environment is a finite partial function from keys (identifiers) to values.
We will need the following operations on environments:
creation of an empty environment ( the empty function)
insertion of a key/value pair 〈k, v〉 into an environment ϕ: ( ϕ, [v/k])
lookup of the value v for a key k in ϕ ( ϕ(k))
Realization in SML by a structure with the following signature
type ’a env (* a is the value type *)
exception Unbound of id (* Unbound *)
val empty : ’a env
val insert : id * ’a * ’a env -> ’a env (* id is the key type *)
val lookup : id * ’a env -> ’a
c○: Michael Kohlhase 300
The next slide has the main SML function for compiling SW programs. Its argument is a SW program
(type program) and its result is an expression of type code, i.e. a list of L(VM) instructions. From
there, we only need to apply a simple conversion (which we omit) to numbers to obtain L(VM)
byte code.
Compiling SW programs
SML function from SW programs (type program) to L(VM) programs (type code).
uses three auxiliary functions for compiling declarations (compileD), statements (compileS),
and expressions (compileE).
these use an environment to relate variable names with their stack index.
the initial environment is created by the declarations.
(therefore compileD has an environment as return value)
type env = index env
fun compile ((ds,s,e) : program) : code =
let
val (cds, env) = compileD(ds, empty, ~1)
in
cds @ compileS(s,env) @ compileE(e,env) @ [halt]
end
c○: Michael Kohlhase 301
The next slide has the function for compiling SW expressions. It is realized as a case statement
over the structure of the expression.
Compiling SW Expressions
constants are pushed to the stack.
variables are looked up in the stack by the index determined by the environment (and pushed
to the stack).
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