Example of idea(How We Used category theory to solve a problem in java) presented in http://techblog.realestate.com.au/how-we-used-category-theory-to-solve-a-problem-in-java/?utm_medium=email&utm_source=flipboard

ExtensionTester.java

import java.util.ArrayList;
import java.util.HashMap;
import java.util.List;
import java.util.Map;
import java.util.function.Function;
import java.util.stream.Stream;

public class ExtensionTester {

    //================================ Supporting classes  ======================================
    interface Request {
        String getDecider();
        String getCity();
        Map<String, String> getFakeHttpRequest();
    }

    static class RequestImpl implements Request{
        private String decider;
        private String city;
        private Map<String, String> fakeHttpRequest;

        public RequestImpl(String decider, String city) {
            this.decider = decider;
            this.city = city;
            this.fakeHttpRequest = new HashMap<>();
        }

        @Override
        public String getDecider() {
            return decider;
        }

        @Override
        public String getCity() {
            return city;
        }

        @Override
        public Map<String, String> getFakeHttpRequest() {
            return fakeHttpRequest;
        }
    }

    static class RequestDifferent implements Request{
        private String decider;
        private String city;
        private String color;
        private Map<String, String> fakeHttpRequest;

        RequestDifferent(String decider, String city) {
            this.decider = decider;
            this.city = city;
        }

        @Override
        public String getDecider() {
            return decider;
        }

        @Override
        public String getCity() {
            return city;
        }

        @Override
        public Map<String, String> getFakeHttpRequest() {
            return fakeHttpRequest;
        }

        public void setFakeHttpRequest(Map<String, String> fakeHttpRequest) {
            this.fakeHttpRequest = fakeHttpRequest;
        }

        public void setColor(String color) {
            this.color = color;
        }

        public String getColor() {
            return color;
        }
    }

    interface Response {
        String getData();
        void setData(String s);
        boolean isCityClose();
        void setIsCityClose(boolean b);
        String getColor();
        void setColor(String color);
    }

    static class ResponseImpl implements Response {
        private String data;
        private boolean isCityClose;
        private String color;

        public ResponseImpl(String data, boolean isClose) {
            this.data = data;
            this.isCityClose = isClose;
        }

        @Override
        public String getData() {
            return data;
        }

        @Override
        public void setData(String s) {
            this.data = s;
        }

        @Override
        public boolean isCityClose() {
            return isCityClose;
        }

        @Override
        public void setIsCityClose(boolean isClose) {
            this.isCityClose = isClose;
        }

        @Override
        public String getColor() {
            return color;
        }

        @Override
        public void setColor(String color) {
            this.color = color;
        }
    }

    static class DifferentResponseImpl implements Response {
        private String data;
        private boolean isClose;
        private String color;
        private String shape;

        public DifferentResponseImpl(String data, boolean isClose) {
            this.data = data;
            this.isClose = isClose;
        }

        @Override
        public String getData() {
            return data;
        }

        @Override
        public void setData(String s) {
            this.data = s;
        }

        @Override
        public boolean isCityClose() {
            return isClose;
        }

        @Override
        public void setIsCityClose(boolean isClose) {
            this.isClose = isClose;
        }

        @Override
        public String getColor() {
            return color;
        }

        @Override
        public void setColor(String color) {
            this.color = color;
        }

        public String getShape() {
            return shape;
        }

        public void setShape(String shape) {
            this.shape = shape;
        }
    }


    //================================ Extension classes  ======================================
    interface Extension<S> {

        Response apply(S source, Response response);

        default Extension<S> compose(Extension<S> extension) {
            return (source, response) -> extension.apply(source, Extension.this.apply(source, response));
        }

        static final Extension IDENTITY = (s, r) -> r;

        static <S> Extension<S> composeAll(Extension<S>... extensions) {
            return Stream.of(extensions).reduce(IDENTITY, Extension::compose);
        }

        default <T> Extension<T> contraMap(Function<T, S> function) {
            return (T source, Response response) -> Extension.this.apply(function.apply(source), response);
        }
    }

    static class ExtensionImpl implements Extension<Request> {

        @Override
        public Response apply(Request source, Response response) {
            System.out.println("In Extension 1");
            if (source.getDecider().equals("chris")) {
                String data = response.getData();
                data += " extension 1 ";
                response.setData(data);
            }
            return response;
        }
    }

    static class ExtensionImpl2 implements Extension<Request> {

        @Override
        public Response apply(Request source, Response response) {
            System.out.println("In Extension 2");
            if (source.getCity().equals("chicago")) {
                response.setIsCityClose(true);
            } else {
                response.setIsCityClose(false);
            }

            return response;
        }
    }

    static class ExtensionImpl3 implements Extension<RequestDifferent> {

        @Override
        public Response apply(RequestDifferent source, Response response) {
            System.out.println("In Extension 3");
                response.setColor(source.getColor());
            return response;
        }
    }

    public static void main(String[] args) {
        //Set up the request and response - this mimics what comes out of the original RESTful call
        Request request = new RequestImpl("chris", "chicago");
        request.getFakeHttpRequest().put("color", "red");
        Response response = new ResponseImpl("Original_response", false);
        System.out.println("original response color: " + response.getColor());
        System.out.println("original response data: " + response.getData());
        System.out.println("original response isclose: " + response.isCityClose());


        //Customizations - i.e. Extensions
        Extension<Request> extension = new ExtensionImpl();
        Extension<Request> extension2 = new ExtensionImpl2();
        Extension<RequestDifferent> extension3 = new ExtensionImpl3();

        //Function to contra-vert the child
//        Function<Request, RequestDifferent> convert = r -> (RequestDifferent) r;
        Function<Request, RequestDifferent> convert = r -> {
            String color = r.getFakeHttpRequest().get("color");
            RequestDifferent rd = new RequestDifferent(r.getDecider(), r.getCity());
            rd.setFakeHttpRequest(r.getFakeHttpRequest());
            rd.setColor(color);
            return rd;
        };

        List<Extension<Request>> extensionList = new ArrayList<Extension<Request>>() {{
            add(extension);
            add(extension2);
            add(extension3.contraMap(convert));
        }};
        Extension<Request> [] extensions = extensionList.toArray(new Extension[extensionList.size()]);

        //compose all the extensions
        Response result = Extension.composeAll(extensions).apply(request, response);

        //check data to see if it is changed
        System.out.println(result.getData());
        System.out.println("Is city close: " + result.isCityClose());
        System.out.println("The color is: " + result.getColor());
        System.out.println("The data is: " + result.getData());


    }
}

this.isCityClose = isClose needed after https://gist.github.com/calam1/6f011d434def52a33af2#file-extensiontester-java-L97 ?

(Edited:
And also after https://gist.github.com/calam1/6f011d434def52a33af2#file-extensiontester-java-L138 )