fix doc example

Author: sunxd3

docs/src/state_interface.md

@@ -17,7 +17,7 @@ Base.vec(state)
 This function takes the state and returns a vector of the parameter values stored in the state.
 
 ```julia
-state = StateType(state, logp)
+state = StateType(state::StateType, logp)
 ```
 
 This function takes an existing `state` and a log probability value `logp`, and returns a new state of the same type with the updated log probability.
@@ -42,7 +42,17 @@ x_i &\sim \text{Normal}(\mu, \sqrt{\tau^2})
 
 We can write the log joint probability function as follows, where for the sake of simplicity for the following steps, we will assume that the `mu` and `tau2` parameters are one-element vectors. And `x` is the data.
 
-```julia
+```@example gibbs_example
+using AbstractMCMC: AbstractMCMC, LogDensityProblems # hide
+using Distributions # hide
+using Random # hide
+using AbstractMCMC: AbstractMCMC # hide 
+using AbstractPPL: AbstractPPL # hide
+using BangBang: constructorof # hide
+using AbstractPPL: AbstractPPL
+```
+
+```@example gibbs_example
 function log_joint(; mu::Vector{Float64}, tau2::Vector{Float64}, x::Vector{Float64})
     # mu is the mean
     # tau2 is the variance
@@ -71,7 +81,7 @@ end
 
 To make using `LogDensityProblems` interface, we create a simple type for this model.
 
-```julia
+```@example gibbs_example
 abstract type AbstractHierNormal end
 
 struct HierNormal{Tdata<:NamedTuple} <: AbstractHierNormal
@@ -89,15 +99,15 @@ end
 
 where `ConditionedHierNormal` is a type that represents the model conditioned on some variables, and
 
-```julia
+```@example gibbs_example
 function AbstractPPL.condition(hn::HierNormal, conditioned_values::NamedTuple)
     return ConditionedHierNormal(hn.data, conditioned_values)
 end
 ```
 
 then we can simply write down the `LogDensityProblems` interface for this model.
 
-```julia
+```@example gibbs_example
 function LogDensityProblems.logdensity(
     hier_normal_model::ConditionedHierNormal{Tdata,Tconditioned_vars},
     params::AbstractVector,
@@ -132,7 +142,7 @@ Although the interface doesn't force the sampler to implement `Transition` and `
 
 Here we define some bare minimum types to represent the transitions and states.
 
-```julia
+```@example gibbs_example
 struct MHTransition{T}
     params::Vector{T}
 end
@@ -145,7 +155,7 @@ end
 
 Next we define the  `state` interface functions mentioned at the beginning of this section.
 
-```julia
+```@example gibbs_example
 # Interface 1: LogDensityProblems.logdensity
 # This function takes the logdensity function and the state (state is defined by the sampler package)
 # and returns the logdensity. It allows for optional recomputation of the log probability.
@@ -168,15 +178,14 @@ Base.vec(state::MHState) = state.params
 
 # Interface 3: constructorof and MHState(state::MHState, logp::Float64)
 # This function allows the state to be updated with a new log probability.
-BangBang.constructorof(state::MHState{T}) where {T} = MHState
 function MHState(state::MHState, logp::Float64)
     return MHState(state.params, logp)
 end
 ```
 
 It is very simple to implement the samplers according to the `AbstractMCMC` interface, where we can use `LogDensityProblems.logdensity` to easily read the log probability of the current state.
 
-```julia
+```@example gibbs_example
 """
     RandomWalkMH{T} <: AbstractMCMC.AbstractSampler
 
@@ -264,7 +273,7 @@ end
 
 At last, we can proceed to implement a very simple Gibbs sampler.
 
-```julia
+```@example gibbs_example
 struct Gibbs{T<:NamedTuple} <: AbstractMCMC.AbstractSampler
     "Maps variables to their samplers."
     sampler_map::T
@@ -440,7 +449,7 @@ The Gibbs sampler operates in two main phases:
    b. Update current variable:
       - Recompute the log probability of the current state, as other variables may have changed:
         - Use `LogDensityProblems.logdensity(cond_logdensity_model, sub_state)` to get the new log probability.
-        - Update the state with `sub_state = sub_state(logp)` to incorporate the new log probability.
+        - Update the state with `sub_state = constructorof(typeof(sub_state))(sub_state, logp)` to incorporate the new log probability.
       - Perform a sampling step for the current conditional probability problem:
         - Use `AbstractMCMC.step(rng, cond_logdensity_model, sub_sampler, sub_state; kwargs...)` to generate a new state.
       - Update the global trace: