### Abstract

We give a formalization of affine forms as abstract representations of zonotopes. We provide affine operations as well as overapproximations of some non-affine operations like multiplication and division. Expressions involving those operations can automatically be turned into (executable) functions approximating the original expression in affine arithmetic.

### License

BSD License

### History

September 20, 2017
  linear approximations for all symbols from the floatarith data type
January 31, 2015
  added algorithm for zonotope/hyperplane intersection

### Topics

- Mathematics/Analysis

### Session Affine_Arithmetic

- Affine_Arithmetic_Auxiliarities
- Executable_Euclidean_Space
- Affine_Form
- Floatarith_Expression
- Straight_Line_Program
- Affine_Approximation
- Counterclockwise
- Counterclockwise_Vector
- Counterclockwise_2D_Strict
- Polygon
- Counterclockwise_2D_Arbitrary
- Intersection
- Affine_Code
- Optimize_Integer
- Optimize_Float
- Print
- Float_Real
- Ex_Affine_Approximation
- Ex_Ineqs
- Ex_Inter
- Affine_Arithmetic

### Depends on

- Deriving class instances for datatypes
- List Index
- Haskell’s Show Class in Isabelle/HOL

### Used by

- Taylor Models
- Ordinary Differential Equations

### Auto-related entries

- Ordinary Differential Equations

## Cite

×

Affine_Arithmetic-AFP

    @article{Affine_Arithmetic-AFP,
      author  = {Fabian Immler},
      title   = {Affine Arithmetic},
      journal = {Archive of Formal Proofs},
      month   = {February},
      year    = {2014},
      note    = {\url{https://isa-afp.org/entries/Affine_Arithmetic.html},
                 Formal proof development},
      ISSN    = {2150-914x},
    }

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