pure functional programming Folder 6 functional programming immutable values NO x := x+1 pure functions (stateless) same output on same input always side effect free == no change to the global state of the real world not dependent on context (code position, evaluation time) code is substitutable IO monad order of code lines carries no meaning order of code lines choosable for best human comprehensability first class citisen functions higher order functions (functions as arguments) recursion instead of loops (no i++) tail recursion stack overflow issue explicit looptypes map, fold, ... currying "purely functional programming is poorly functional" declarative and not imperative specify the "what" and not the "how" isolated !! imperative programming comprehensability [2] modularity [1] comprehensability [2] loops are low level like "goto" syntay cleanlyness minimal "syntactic shugar" comprehensability [2] avoidance of global state variables (hidden state) memoization and sharing of data breaking loopholes unwrapped exceptions unsafePerformIO strong typing Folder 1 encapsulation of functional code by type kills segfaults incremental type inference system kills runtime errors number parameterized types strong typed programming typed types "wrapper types" type polymorphism typeclasses type families category theory monads applicative functor logic programming modularity [1] automatic differentiation correctness [3] linear typing functional reactive programming (FRP) Folder 2 functional reactive programming (FRP) time independence by mapping time to space declarative data streams architecture: model update view signals first order no join => no monad conversion of dynamic to static problem plain callbacks are low level like goto comprehensability [2] modularity [1] higher order FRP Asynchronous FRP (imerative) Arrowized FRP generating functions (symmetries) total programming Folder 3 total programming maybe type either type curry howard isomorphism provability of correctness to type specification there are outputs for all possible inputs kills runtime errors correctness [3] total functions not partial ones lazy evaluation Folder 4 lazy evaluation call by need simplified garbage collector memory management naive implementations create space leaks strictness analysis evaluation order short cut fusion loop fusion deforrestation map f . map g == map (f.g) non-strict evaluation more freedome in choice of evaluation order for the compiler infinite datastructures possible modularity [1] normal order applicative order WHNF transfinite (multidimensional) automatic differentiation (multilinear taylor) automatic proof systems reversible computation Folder 5 mapping to reversible logic no thermalisation energy efficient computation no overwriting no irreversible data destruction retractile cascades reversible logic gates usage for nanofactory design Folder 7 code maintainability nanofactory runtime code declarative / functional CSG - 3D modelling (scenegraph) big nanofactory system development [1] modularity composability extendability scalability [2] comprehensability easier to reason about code composable physical building blocks modelled as immutable pieces of data [3] correctness programmable matter -> materializable program logistics for nanoscale building blocks promoting code reuse interactive quantum computation Folder 8 quantum mechanic unitary reversaible "timeless" wave propagation quantum computation data management Folder 9 diffing generalized algebraic datatypes (GADTs) records differentials of datastructures zippers integration of object oriented programming basic datastructures naive copy updates create space leaks purely functional datastructures modularity [1] persistence beyond volatile RAM -> serialisation parallel programming Folder 10 software transactional memory easier concurrency management par & seq modularity [1] "pointfree style is pointless style" 2015 - CC BY - Lukas M. Süss