Creating a Function Representation for Environments in SML -

okay, working on creating function representation environments in sml:

type name = string type 'a fenv = name -> 'a 

i'm little stuck on how proceed this. first thing need define value fenvempty of type 'a fenv, represents empty environment (the environment not bind names). far, have this:

val fenvempty =      let         fun empty (name) = ???     in         empty     end 

i'm not sure if i'm on right track or anything. supposed return function empty? putting in 0, null, or none won't work.

later, have write functions returns data associated particular name in environment (a find function), , function binds data particular name in environment ( bind function), i'm stuck on fenvempty part.

i presume teacher wants raise exception when attempting unbound value:

type name = string type 'a fenv = name -> 'a  exception unboundname of name  fun fenvempty name = raise unboundname name 

but think more if first try use version of fenv returns none unbound variables. believe because, opposed exceptions, there's more type structure program guide while writing implementation (see below). so, first try write implementation fenv is:

type 'a fenv = name -> 'a option 

now, later part of question, you'll have define function associating name value existing environment. function's type:

val fenvassoc : 'a fenv -> name -> 'a -> 'a fenv 

notice above returns result of type 'a fenv. remember fenv is. it's "just" function:

type 'a fenv = name -> 'a 

so, returned value, function, needs somehow "remember" name , value have been associated it. how functions "remember" things they've "seen" in context they've been defined?

to name's value, need third function, takes existing environment , name , returns value name, if any:

val fenvlookup : 'a fenv -> name -> 'a 

again, remember type of 'a fenv is:

type 'a fenv = name -> 'a 

i'm emphasizing because type of 'a fenv restricts in operations can apply it. can either: a) create function or b) apply one.