Question

I am having trouble groking F#’s Map class. I created a simple, naive lambda calculus evaluation function,

type Name = string type Term =     |   Var of Name      |   Lit of int     |   App of Term * Term     |   Lam of Name * Term  let rec lookup(v, e) =     match e with     |   (v1, t)::tl         -> if v1 = v then t else lookup(v, tl)     |   []                  -> failwith 'unknown variable %s' v  let rec eval(x, e) =      match x with     |   Var x               -> lookup(x, e)     |   Lit x               -> Lit x     |   App (Lam(v, f), t2) -> eval(f, ((v, t2)::e))     |   _                   -> failwith 'Invalid' 

The obvious optimization to this is to change the list to a Map so I came up with,

let rec eval2(x, e: Map<Name,Term>) =     match x with     |   Var v               -> e.[v]     |   Lit l               -> x     |   App (Lam (v, f), t) -> eval2(f, e.Add(v, t))     |   _                   -> failwith 'Invalid term' 

Given the values,

let ident = Lam ('x', Var 'x') let prog = App (ident, Lit 3) 

why does,

let x = eval(prog, []) 

succeed but,

let x2 = eval2(prog, Map []) 

throw a key not found exception?

Answer 1

I don’t repro this behavior (using F# 1.9.6.2, it works for me):

#light  type Name = string type Term =     |   Var of Name     |   Lit of int     |   App of Term * Term     |   Lam of Name * Term  let rec eval2(x, e: Map<Name,Term>) =     match x with     |   Var v               -> e.[v]     |   Lit l               -> x     |   App (Lam (v, f), t) -> eval2(f, e.Add(v, t))     |   _                   -> failwith 'Invalid term'  let ident = Lam ('x', Var 'x') let prog = App (ident, Lit 3) let x2 = eval2(prog, Map []) printfn '%A' x2   // Lit 3