## State II

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## Continuations

Continuations can also be used to implement objects with state. A continuation is just a function, passed as a parameter, that represents a computation to be completed (i.e. continued with) at some later time. e.g.

γ : Cmd
σ : State
θ : Cont = State->Ans
C : Cmd->Cont->State->Ans = Cmd->Cont->Cont
C `γ12' θ σ = C γ1 (C γ2 θ) σ

Note how the rule for `γ12', can be read left-to-right as "to do γ12, first do γ1 and then do γ2", and replaces what would otherwise be functional composition (C' γ2)o(C' γ1). (Continuations are used in denotational semantics to describe the semantics of jumps and other sequencers found in imperative programming languages.)

```let Obj = lambda cmds.        { List Cmd -> Ans }
{ Cont = State -> Ans         -- continuation }
let rec
{ C : Cmd->Cont->State->Ans = Cmd->Cont->Cont }
C = lambda cmd. lambda cont. lambda state.
let rec tag   = fst cmd,
param = snd cmd
in if tag = set then { change State }
(pair ok nil)   :: cont param
else if tag = get then
(pair st state) :: cont state
else (pair err nil)  :: cont state,

Cs = lambda cmds. lambda state.
if null cmds then nil        {finished}
else C hd cmds (Cs tl cmds) state

in Cs cmds state0

```

Note that we have two functions, C and Cs, because (here) Cmd and Cmds = List Cmd are different types.

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λ ...
 :: list cons nil the [ ] list null predicate hd head (1st) tl tail (rest)

 © L. Allison   http://www.allisons.org/ll/   (or as otherwise indicated), Faculty of Information Technology (Clayton), Monash University, Australia 3800 (6/'05 was School of Computer Science and Software Engineering, Fac. Info. Tech., Monash University, was Department of Computer Science, Fac. Comp. & Info. Tech., '89 was Department of Computer Science, Fac. Sci., '68-'71 was Department of Information Science, Fac. Sci.) Created with "vi (Linux + Solaris)",  charset=iso-8859-1,  fetched Wednesday, 27-May-2020 21:42:48 AEST.