As an example, the functional update of the record
{a = 13, b = 14, c = 15}
with c = 16 yields a new record
{a = 13, b = 14, c = 16}
Functional record update also makes sense with multiple simultaneous updates. For example, the functional update of the record above with a = 18, c = 19 yields a new record
{a = 18, b = 14, c = 19}
One could easily imagine an extension of the SML that supports functional record update. For example
e with {a = 16, b = 17}
would create a copy of the record denoted by e with field a replaced with 16 and b replaced with 17.
Since there is no such syntax in SML, we now show how to implement functional record update directly. We first give a simple implementation that has a number of problems. We then give an advanced implementation, that, while complex underneath, is a reusable library that admits simple use.
Simple implementation
To support functional record update on the record type
{a: 'a, b: 'b, c: 'c}
first, define an update function for each component.
fun withA ({a = _, b, c}, a) = {a = a, b = b, c = c}
fun withB ({a, b = _, c}, b) = {a = a, b = b, c = c}
fun withC ({a, b, c = _}, c) = {a = a, b = b, c = c}
Then, one can express e with {a = 16, b = 17} as
withB (withA (e, 16), 17)With infix notation
infix withA withB withCthe syntax is almost as concise as a language extension.
e withA 16 withB 17
This approach suffers from the fact that the amount of boilerplate code is quadratic in the number of record fields. Furthermore, changing, adding, or deleting a field requires time proportional to the number of fields (because each with function must be changed). It is also annoying to have to define a with function, possibly with a fixity declaration, for each field.
Fortunately, there is a solution to these problems.
Advanced implementation
Using Fold one can define a family of makeUpdate<N> functions and single update operator U so that one can define a functional record update function for any record type simply by specifying a (trivial) isomorphism between that type and function argument list. For example, suppose that we would like to do functional record update on records with fields a and b. Then one defines a function updateAB as follows.
val updateAB =
fn z =>
let
fun from v1 v2 = {a = v1, b = v2}
fun to f {a = v1, b = v2} = f v1 v2
in
makeUpdate2 (from, from, to)
end
z
The functions from (think from function arguments) and to (think to function arguements) specify an isomorphism between a,b records and function arguments. There is a second use of from to work around the lack of first-class polymorphism in SML.
With the definition of updateAB in place, the following expressions are valid.
updateAB {a = 13, b = "hello"} (set#b "goodbye") $
updateAB {a = 13.5, b = true} (set#b false) (set#a 12.5) $
As another example, suppose that we would like to do functional record update on records with fields b, c, and d. Then one defines a function updateBCD as follows.
val updateBCD =
fn z =>
let
fun from v1 v2 v3 = {b = v1, c = v2, d = v3}
fun to f {b = v1, c = v2, d = v3} = f v1 v2 v3
in
makeUpdate3 (from, from, to)
end
z
With the definition of updateBCD in place, the following expression is valid.
updateBCD {b = 1, c = 2, d = 3} (set#c 4) (set#c 5) $
Note that not all fields need be updated and that the same field may be updated multiple times. Further note that the same set operator is used for all update functions (in the above, for both updateAB and updateBCD).
In general, to define a functional-record-update function on records with fields f1, f2, ..., fN, use the following template.
val update =
fn z =>
let
fun from v1 v2 ... vn = {f1 = v1, f2 = v2, ..., fn = vn}
fun to f {f1 = v1, f2 = v2, ..., fn = vn} = v1 v2 ... vn
in
makeUpdateN (from, from, to)
end
z
With this, one can update a record as follows.
update {f1 = v1, ..., fn = vn} (set#fi1 vi1) ... (set#fim vim) $
The FunctionalRecordUpdate structure
Here is the implementation of functional record update.
structure FunctionalRecordUpdate =
struct
local
fun next g (f, z) x = g (f x, z)
fun f1 (f, z) x = f (z x)
fun f2 z = next f1 z
fun f3 z = next f2 z
fun c0 from = from
fun c1 from = c0 from f1
fun c2 from = c1 from f2
fun c3 from = c2 from f3
fun makeUpdate cX (from, from', to) record =
let
fun ops () = cX from'
fun vars f = to f record
in
Fold.fold ((vars, ops), fn (vars, _) => vars from)
end
in
fun makeUpdate0 z = makeUpdate c0 z
fun makeUpdate1 z = makeUpdate c1 z
fun makeUpdate2 z = makeUpdate c2 z
fun makeUpdate3 z = makeUpdate c3 z
fun upd z = Fold.step2 (fn (s, f, (vars, ops)) => (fn out => vars (s (ops ()) (out, f)), ops)) z
fun set z = Fold.step2 (fn (s, v, (vars, ops)) => (fn out => vars (s (ops ()) (out, fn _ => v)), ops)) z
end
end
The idea of makeUpdate is to build a record of functions which can replace the contents of one argument out of a list of arguments. The functions fX replace the 0th, 1st, ... argument with their argument z. The cX functions pass the first X f functions to the record constructor.
The #field notation of Standard ML allows us to select the map function which replaces the corresponding argument. By converting the record to an argument list, feeding that list through the selected map function and piping the list into the record constructor, functional record update is achieved.
Efficiency
With MLton, the efficiency of this approach is as good as one would expect with the special syntax. Namely a sequence of updates will be optimized into a single record construction that copies the unchanged fields and fills in the changed fields with their new values.
Before Sep 14, 2009, this page advocated an alternative implementation of FunctionalRecordUpdate. However, the old structure caused exponentially increasing compile times. We advise you to switch to the newer version.
Applications
Functional record update can be used to implement labelled optional arguments.