react-redux搜索过滤器的麻烦

这是我的第一个react-redux项目（课程列表），我对redux有一些麻烦。我需要按课程名称进行搜索，我的代码基于此answer，我可以在redux-devtool中看到操作，但不能在ui上看到。请帮助我了解我在做什么错

    //action    
    export function search (value) {
        return {type: SEARCH, value};
    }

    //reducer
    import { COURSES } from '../../constants';
    const initialState = COURSES;    
    export default function reducer(state = initialState, action) {
        switch(action.type) {
            case SEARCH: {
                const {value} = action;
                const course = state.filter((val) => val.includes(value));
                return {...state, value, course};
            }
            default:
                return state;
        }
    }

//search component

    import React, {Component} from 'react';
    import {connect} from 'react-redux';
    import {deleteCourse, search} from '../../redux/actions';

    class SearchInput extends Component {
        render() {
            const {search, value} = this.props;
            return (
                <div className={classes.SearchInput}>
                    <input
                        placeholder='Search'
                        onChange={(e) => search(e.target.value)}
                        value={value}
                    />
                </div>
            )
        }
    }

    export default connect (state => ({
        courses: state.courses,
    }), {search})(SearchInput);


//Courses Component
import Form from '../Form/Form';
    import { deleteCourse, search } from '../../redux/actions';

    const Courses = ({ courses, deleteCourse }) => {
        console.log(courses)
        return (
            <div className={classes.Courses}>
                <SearchInput />
                <Button title='Add course' />
                <CourseList
                    courses={courses}
                    deleteCourse={deleteCourse}
                    search={search}
                />
                <Form />
            </div>
        )
    }

    export default connect (state => ({
        courses: state.courses,
    }), {deleteCourse})(Courses);

image-from-redux-devtool