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logic and minimizing global knowledge","#leanpub-auto-separating-logic-and-minimizing-global-knowledge","No duplicate record fields","#leanpub-auto-no-duplicate-record-fields","14.1 What are classy lenses and when do I need them?","#leanpub-auto-what-are-classy-lenses-and-when-do-i-need-them","14 Classy Lenses","#leanpub-auto-classy-lenses","13.3 Magnify & Zoom","#leanpub-auto-magnify--zoom","13.2 State Monad Combinators","#leanpub-auto-state-monad-combinators","13.1 Reader Monad and View","#leanpub-auto-reader-monad-and-view","13 Optics and Monads","#leanpub-auto-optics-and-monads","#questions-error-lenses-7","Level 6 Higher Order Beast","#questions-error-lenses-6","#questions-error-lenses-5","#questions-error-lenses-4","#questions-error-lenses-3","#questions-error-lenses-2","#questions-error-lenses-1","12.2 Type Error Arena","#leanpub-auto-type-error-arena","12.1 Interpreting expanded optics types","#leanpub-auto-interpreting-expanded-optics-types","12 Dealing with Type Errors","#leanpub-auto-dealing-with-type-errors","11.5 Index-preserving optics","#leanpub-auto-index-preserving-optics","Exercises – Custom Indexed Optics","#questions-custom-indexed-optics","Index helpers","#leanpub-auto-index-helpers","Custom IndexedTraversals","#leanpub-auto-custom-indexedtraversals","Custom IndexedFolds","#leanpub-auto-custom-indexedfolds","11.4 Custom indexed optics","#leanpub-auto-custom-indexed-optics","Exercises – Index Filters","#questions-index-filters","11.3 Filtering by index","#leanpub-auto-filtering-by-index","Exercises – Indexed Optics","#questions-indexed-optics","Custom index composition","#leanpub-auto-custom-index-composition","11.2 Index Composition","#leanpub-auto-index-composition","11.1 What are indexed optics?","#leanpub-auto-what-are-indexed-optics","11 Indexed Optics","#leanpub-auto-indexed-optics","Exercises – Iso Laws","#questions-iso-laws","The one and only law: Reversibility","#leanpub-auto-the-one-and-only-law-reversibility","10.8 Laws","#leanpub-auto-laws-1","Newtype wrapper isos","#leanpub-auto-newtype-wrapper-isos","Coercing with isos","#leanpub-auto-coercing-with-isos","10.7 Isos and newtypes","#leanpub-auto-isos-and-newtypes","Exercises – Projected Isos","#questions-projected-isos","10.6 Projecting Isos","#leanpub-auto-projecting-isos","Exercises – Intro to Isos","#questions-intro-to-isos","Composing isos","#leanpub-auto-composing-isos","10.5 Varieties of isomorphisms","#leanpub-auto-varieties-of-isomorphisms","10.4 Modification under isomorphism","#leanpub-auto-modification-under-isomorphism","10.3 Flipping isos with from","#leanpub-auto-flipping-isos-with-from","10.2 Building Isos","#leanpub-auto-building-isos","There and back again","#leanpub-auto-there-and-back-again","How do Isos fit into the hierarchy?","#leanpub-auto-how-do-isos-fit-into-the-hierarchy","10.1 Introduction to Isos","#leanpub-auto-introduction-to-isos","10 Isos","#leanpub-auto-isos","Matching on HTTP Verb","#leanpub-auto-matching-on-http-verb","Altering sub-sets of functions","#leanpub-auto-altering-sub-sets-of-functions","Path prefix matching","#leanpub-auto-path-prefix-matching","9.4 Case Study: Simple Server","#leanpub-auto-case-study-simple-server","Exercises – Prism Laws","#questions-prism-laws","Summary","#leanpub-auto-summary","Law Three: Pass-through Reversion","#leanpub-auto-law-three-pass-through-reversion","Law Two: Prism Complement","#leanpub-auto-law-two-prism-complement","Law One: Review-Preview","#leanpub-auto-law-one-review-preview","9.3 Laws","#leanpub-auto-laws","Exercises – Custom Prisms","#questions-custom-prisms","Cracking the coding interview: Prisms style!","#leanpub-auto-cracking-the-coding-interview-prisms-style","Matching String Prefixes","#leanpub-auto-matching-string-prefixes","Rebuilding _Just and _Nothing","#leanpub-auto-rebuilding-just-and-nothing","9.2 Writing Custom Prisms","#leanpub-auto-writing-custom-prisms","Exercises – Prisms","#questions-prisms","Other types of patterns","#leanpub-auto-other-types-of-patterns","Embedding values with prisms","#leanpub-auto-embedding-values-with-prisms","Generating prisms with makePrisms","#leanpub-auto-generating-prisms-with-makeprisms","Checking pattern matches with prisms","#leanpub-auto-checking-pattern-matches-with-prisms","Simple Pattern-Matching Prisms","#leanpub-auto-simple-pattern-matching-prisms","How do Prisms fit into the hierarchy?","#leanpub-auto-how-do-prisms-fit-into-the-hierarchy","9.1 Introduction to Prisms","#leanpub-auto-introduction-to-prisms","9 Prisms","#leanpub-auto-prisms","Exercises – Missing Values","#questions-missing-values","Checking fold success/failure","#leanpub-auto-checking-fold-successfailure","Default elements","#leanpub-auto-default-elements","Fallbacks with ‘failing’","#leanpub-auto-fallbacks-with-failing","Checking whether updates succeed","#leanpub-auto-checking-whether-updates-succeed","8.5 Handling missing values","#leanpub-auto-handling-missing-values","Exercises – Custom Indexed Structures","#questions-custom-indexed-structures","Custom At: Address indexing","#leanpub-auto-custom-at-address-indexing","Custom Ixed: Cyclical indexing","#leanpub-auto-custom-ixed-cyclical-indexing","8.4 Custom Indexed Data Structures","#leanpub-auto-custom-indexed-data-structures","Exercises – Indexable Structures","#questions-indexable-structures","Manipulating Sets","#leanpub-auto-manipulating-sets","Map-like structures","#leanpub-auto-map-like-structures","8.3 Inserting & Deleting with ‘At’","#leanpub-auto-inserting--deleting-with-at","Indexing stranger structures","#leanpub-auto-indexing-stranger-structures","Indexing monomorphic types","#leanpub-auto-indexing-monomorphic-types","Indexed Structures","#leanpub-auto-indexed-structures","Accessing and setting values with ix","#leanpub-auto-accessing-and-setting-values-with-ix","The Ixed Class","#leanpub-auto-the-ixed-class","8.2 Accessing and updating values with ‘Ixed’","#leanpub-auto-accessing-and-updating-values-with-ixed","8.1 What’s an “indexable” structure?","#leanpub-auto-whats-an-indexable-structure","8 Indexable Structures","#leanpub-auto-indexable-structures","Exercises – partsOf","#questions-partsof","partsOf and other data structures","#leanpub-auto-partsof-and-other-data-structures","Polymorphic partsOf","#leanpub-auto-polymorphic-partsof","partsOf","#leanpub-auto-partsof","7.7 Advanced manipulation","#leanpub-auto-advanced-manipulation","Exercises – Traversal Laws","#questions-traversal-laws","Good Traversal Bad Traversal","#leanpub-auto-good-traversal-bad-traversal","Law Two: Consistent Focuses","#leanpub-auto-law-two-consistent-focuses","Law One: Respect Purity","#leanpub-auto-law-one-respect-purity","7.6 Traversal Laws","#leanpub-auto-traversal-laws","Exercises – Custom Traversals","#questions-custom-traversals","Case Study: Transaction Traversal","#leanpub-auto-case-study-transaction-traversal","Traversals with custom logic","#leanpub-auto-traversals-with-custom-logic","Our first custom traversal","#leanpub-auto-our-first-custom-traversal","Optics look like traverse","#leanpub-auto-optics-look-like-traverse","7.5 Custom traversals","#custom-traversals","Exercises – Traversal Actions","#questions-traversal-actions","Using Traversals directly","#leanpub-auto-using-traversals-directly","Infix traverseOf","#leanpub-auto-infix-traverseof","Traverse on Traversals","#leanpub-auto-traverse-on-traversals","A Primer on Traversable","#leanpub-auto-a-primer-on-traversable","7.4 Traversal Actions","#leanpub-auto-traversal-actions","Exercises – Simple Traversals","#questions-simple-traversals","7.3 Traversal Composition","#leanpub-auto-traversal-composition","Focusing a specific traversal element","#leanpub-auto-focusing-a-specific-traversal-element","Traversing multiple paths at once","#leanpub-auto-traversing-multiple-paths-at-once","More Combinators","#leanpub-auto-more-combinators","Traversing each element of a container","#leanpub-auto-traversing-each-element-of-a-container","7.2 Traversal Combinators","#leanpub-auto-traversal-combinators","From fold to traversal","#leanpub-auto-from-fold-to-traversal","A bit of Nostalgia","#leanpub-auto-a-bit-of-nostalgia","How do Traversals fit into the hierarchy?","#leanpub-auto-how-do-traversals-fit-into-the-hierarchy","7.1 Introduction to Traversals","#leanpub-auto-introduction-to-traversals","7 Traversals","#leanpub-auto-traversals","6.6 Fold Laws","#leanpub-auto-fold-laws","Exercises – Filtering","#questions-filtering","Filtered","#leanpub-auto-filtered","6.5 Filtering folds","#leanpub-auto-filtering-folds","Exercises – Higher Order Folds","#questions-higher-order-folds","TakingWhile, DroppingWhile","#leanpub-auto-takingwhile-droppingwhile","Backwards","#leanpub-auto-backwards","Taking, Dropping","#leanpub-auto-taking-dropping","6.4 Higher Order Folds","#leanpub-auto-higher-order-folds","Exercises – Fold Actions","#questions-fold-actions","Customizing monoidal folds","#leanpub-auto-customizing-monoidal-folds","Using ‘view’ on folds","#leanpub-auto-using-view-on-folds","Combining fold results","#leanpub-auto-combining-fold-results","Folding with effects","#leanpub-auto-folding-with-effects","Queries case study","#leanpub-auto-queries-case-study","Writing queries with folds","#leanpub-auto-writing-queries-with-folds","6.3 Fold Actions","#leanpub-auto-fold-actions","Exercises – Custom Folds","#questions-custom-folds","Combining multiple folds on the same structure","#leanpub-auto-combining-multiple-folds-on-the-same-structure","Mapping over folds","#leanpub-auto-mapping-over-folds","6.2 Custom Folds","#leanpub-auto-custom-folds","Exercises – Simple Folds","#questions-simple-folds","Foundational fold combinators","#leanpub-auto-foundational-fold-combinators","Composing folds","#leanpub-auto-composing-folds","Using lenses as folds","#leanpub-auto-using-lenses-as-folds","Collecting focuses as a list","#leanpub-auto-collecting-focuses-as-a-list","Collapsing the Set","#leanpub-auto-collapsing-the-set","Focusing all elements of a container","#leanpub-auto-focusing-all-elements-of-a-container","6.1 Introduction to Folds","#leanpub-auto-introduction-to-folds","6 Folds","#leanpub-auto-folds","5.9 Exercises – Operators","#questions-operators","5.8 When to use operators vs named actions?","#leanpub-auto-when-to-use-operators-vs-named-actions","5.7 Modifiers","#leanpub-auto-modifiers","5.6 Learning Hieroglyphics","#leanpub-auto-learning-hieroglyphics","5.5 Using %~ a.k.a. over","#leanpub-auto-using--aka-over","5.4 Chaining many operations","#leanpub-auto-chaining-many-operations","5.3 set a.k.a. .~","#leanpub-auto-set-aka-","5.2 view a.k.a. ^.","#leanpub-auto-view-aka-","5.1 Lens Operators","#leanpub-auto-lens-operators","5 Operators","#operators","Exercises – Lens Composition","#questions-lens-composition","How do Lens Types Compose?","#leanpub-auto-how-do-lens-types-compose","Composing Lenses","#leanpub-auto-composing-lenses","Composing update functions","#leanpub-auto-composing-update-functions","How do I update fields in deeply nested records?","#leanpub-auto-how-do-i-update-fields-in-deeply-nested-records","4.3 Composing Lenses","#composing-lenses","Exercises – Polymorphic Lenses","#questions-polymorphic-lenses","Changing type variables with polymorphic lenses","#leanpub-auto-changing-type-variables-with-polymorphic-lenses","Type-changing focuses","#leanpub-auto-type-changing-focuses","4.2 When do we need polymorphic lenses","#leanpub-auto-when-do-we-need-polymorphic-lenses","Simple vs Polymorphic optics","#leanpub-auto-simple-vs-polymorphic-optics","4.1 Introduction to polymorphic optics","#leanpub-auto-introduction-to-polymorphic-optics","4 Polymorphic Optics","#polymorphic-optics","Exercises – Self-Correcting Lenses","#questions-correction-lenses","Including correction logic in lenses","#leanpub-auto-including-correction-logic-in-lenses","3.7 Data correction and maintaining invariants","#leanpub-auto-data-correction-and-maintaining-invariants","Exercises – Virtual Fields","#questions-virtual-fields","Breakage-free refactoring","#leanpub-auto-breakage-free-refactoring","Writing a virtual field","#leanpub-auto-writing-a-virtual-field","What’s a virtual field","#leanpub-auto-whats-a-virtual-field","3.6 Virtual Fields","#leanpub-auto-virtual-fields","Exercises - Laws","#questions-laws","Case Study: lensProduct","#leanpub-auto-case-study-lensproduct","Case Study: msg","#leanpub-auto-case-study-msg","Case Study: _1","#leanpub-auto-case-study-1","The Laws","#leanpub-auto-the-laws","Why do optics have laws?","#leanpub-auto-why-do-optics-have-laws","3.5 Lens Laws","#leanpub-auto-lens-laws","Is it a Lens? – Answers","#answers-is-it-a-lens","Is it a Lens?","#leanpub-auto-is-it-a-lens","3.4 Limitations","#leanpub-auto-limitations","Exercises - Records Part Two","#questions-records-part-two","Automatically generating field lenses","#leanpub-auto-automatically-generating-field-lenses","Modifying fields with a lens","#leanpub-auto-modifying-fields-with-a-lens","Getting and setting with a field lens","#leanpub-auto-getting-and-setting-with-a-field-lens","Exercises - Records Part One","#questions-records-part-one","Building a lens for a record field","#leanpub-auto-building-a-lens-for-a-record-field","Lenses subsume the “accessor” pattern","#leanpub-auto-lenses-subsume-the-accessor-pattern","3.3 Lenses and records","#records","Exercises - Lens Actions","#questions-lens-actions","Setting through a lens","#leanpub-auto-setting-through-a-lens","Viewing through lenses","#leanpub-auto-viewing-through-lenses","3.2 Lens actions","#leanpub-auto-lens-actions","Exercises – Optic Anatomy","#questions-optic-anatomy","Anatomy","#leanpub-auto-anatomy","3.1 Introduction to Lenses","#leanpub-auto-introduction-to-lenses","3 Lenses","#leanpub-auto-lenses","2.5 Impractical optics at a glance","#leanpub-auto-impractical-optics-at-a-glance","2.4 Practical optics at a glance","#leanpub-auto-practical-optics-at-a-glance","2.3 Weaknesses","#leanpub-auto-weaknesses","2.2 Strengths","#optics-motivation","2.1 What are optics?","#leanpub-auto-what-are-optics","2 Optics","#leanpub-auto-optics","1.7 About the exercises","#about-exercises","1.6 About the type signatures","#leanpub-auto-about-the-type-signatures","1.5 Following examples","#following-examples","1.4 Your practice environment","#leanpub-auto-your-practice-environment","1.3 Chosen language and optics encodings","#leanpub-auto-chosen-language-and-optics-encodings","1.2 How to read this book","#leanpub-auto-how-to-read-this-book","1.1 Why should I read this book?","#leanpub-auto-why-should-i-read-this-book","1 Obligatory 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