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Miranda A Functional Language

Miranda A Functional Language. Dan Vasicek March 16, 2008. References. “Introduction to Functional Programming” Richard Bird, and Philip Wadler Prentice – Hall, 1988, 291 pages Structure and Interpretation of Computer Programs Abelson and Sussman MIT Press 1985. Historical.

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Miranda A Functional Language

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  1. Miranda A Functional Language Dan Vasicek March 16, 2008

  2. References • “Introduction to Functional Programming” • Richard Bird, and Philip Wadler • Prentice – Hall, 1988, 291 pages • Structure and Interpretation of Computer Programs • Abelson and Sussman • MIT Press 1985

  3. Historical • 1986 Study Scheme using Ableson and Sussman, Structure and Interpretation of Computer Programs • 1988 Miranda using Bird and Wadler • 1988 Study reservoir modeling problem • 100 Man*year Amoco Effort • 1990 Begin the Miranda Reservoir Model • Use Claris Works to organize the project • 1992 AMOCO cancels the project • 1992 Disk Crash destroys most records of the project

  4. Miranda • Miranda concepts • “Pure” functional language • Lazy evaluation (allows infinite lists) • Single assignment (Parallel Computation) • Reservoir Models • Darcy’s Law (Flow in porous media) • Constitutive relationships (pv=nrT) • Miranda Reservoir Experiment

  5. Synthesis of Programs from Specifications • Equational reasoning used to derive a program from a specification • Building definitions • Program Transformation • Constructing a function to solve a given problem • Without specification the sequence of steps in the process

  6. Miranda = a pure functional language • All computations are done by applying functions to data (purely functional) • The top level program is a function call that produces the desired result • Characteristics of functional languages • Order of execution is irrelevant • Each function call encapsulates the relationship between some inputs and outputs • Higher level of abstraction is available • Less development time • Less code

  7. Miranda does not • Provide iterative constructs such as the “for” or “do” loop • Provide any way to change the value of a “variable” (single assignment) • Once a “variable” has a value, it cannot change

  8. Procedural vs. Functional • Procedural Cake Recipe • Specifies the process • Specifies the sequence of steps for making a cake • Functional Cake Recipe • Specifies the steps but not the sequence • Abstract the steps from the sequence

  9. Recipe – Bake a Cake • Procedural Recipe (“Fortran” Program) • Buy cake mix, eggs, milk • Preheat oven to 350 • Beat eggs until frothy • Add milk • Fold in mix • Grease pan • Put batter in pan • Put pan in oven • Bake 350 degrees for 30 minutes

  10. Recipe – Bake a Cake • Functional recipe • Cake=Bake_a_cake(Cake_in_oven) • Cake_in_oven=batter_in_oven(hot_oven, b_in_pan) • hot_oven=heat_oven( turn_on_oven()) • b_in_pan=mix_ingredients(eggs, milk, c_mix)

  11. Recursion • Mathematical theorems are frequently proven using a recursive argument such as “Proof by Induction” • Recursion provides an alternative to iteration in programs • Factorial Example: • F(0)=1 • F(n)=n*F(n-1)

  12. List Processing • Miranda is a descendent of LISP • [1,2,3] :: [num] • [‘h’,’e’,’l’,’l’,’o’] :: [char] • [(+), (*)] ::[num  num  num] • [1,2,..4]=[1,2,3,4] • [1..] = infinite list of all positive digits

  13. LaTeX In-Line Documentation • Miranda allows one text file containing both the program and the documentation • Process the file with LaTeX  Document • Process the file with Miranda compiler  executable program

  14. Reservoir Model Ideas • Darcy’s Law • Compositional Relationships • Finite Differences • Linear Algebra • Reference: Page, Sexton, and Wainwright (1990 IEEE) • http://ieeexplore.ieee.org/xpl/freeabs_all.jsp?arnumber=82145

  15. Darcy’s Law for Flow in Porous Media • P=pressure, =permeability Tensor • q= fluid flux, =fluid viscosity

  16. Equations of State • Van der Waals • ( P + a / Vm2 )( Vm - b ) = R T • P = pressure • Vm = molar volume • R = ideal gas constant • T = temperature

  17. Discretization of the Reservoir • Continuous reservoir  Discrete 3 d grid • PDE  Linear Algebra • Derivatives  Finite differences • Large linear systems  sparse, iterative, system solvers • Conjugate gradient method

  18. Oil Reservoir Characterization • Seismic Data – location of layers • Exploration wells – measure properties in the layers (pressure, gas, oil, and water concentration, rock properties…) • Extrapolate between the wells using the seismically derived layers

  19. Oil Reservoir

  20. Fluid Velocity in a Reservoir

  21. Basic Ideas of the Model • 100 man years of programming effort to construct the Fortran version of the reservoir model • Many input data files existed for the Fortran version of the model • Difficult to achieve effective parallelism in the code • Huge effort in maintenance and development • Documentation difficult

  22. Miranda Reservoir Model • 2 man years of effort • Rex Page • Roger Wainwright • Julio Diaz • Dan Vasicek • LaTeX in-line documentation • Accepts existing structures intended for input to the Fortran reservoir model

  23. Functional Languages • “Pure” & Single Assignment constraints • Make explicit the dependence of the functions on the data • Allow a simple operating system to take advantage of the opportunities for parallel computation • High level language • Decreases the programming effort

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