Functional Programming Functional Programming and Theorem Proving - PowerPoint PPT Presentation

Functional Programming Functional Programming and Theorem Proving and Theorem Proving for Undergraduates for Undergraduates A Progress Report A Progress Report Carl Carl Eastlund Eastlund and Matthias and Matthias Felleisen Felleisen Northeastern University Northeastern University Rex Page Rex Page University of Oklahoma University of Oklahoma Functional Programming and Theorem Proving for Undergraduates 1 1 FDPE 2008 - Rex Page / Carl Eastlund / Matthias Felleisen

History History � Before 2003 � Traditional SE at OU (2-course sequence, 4 th yr) � Process Design Testing/Validation 60% 20% 20% � � 2003-2005 � SE course using ACL2 (FDPE 2005 report) � Process Design Testing/Validation 30% 35% 35% � � Successful despite crude programming env � 2006 - present � SE course with Dracula/ACL2 environment � 1 st year course at NU using Dracula/ACL2 Functional Programming and Theorem Proving for Undergraduates 2 FDPE 2008 - Rex Page / Carl Eastlund / Matthias Felleisen

Mantra Mantra Engineering is the application of � Before 2003 principles of science and mathematics � Traditional SE at OU (2-course sequence, 4 th yr) � Process Design Testing/Validation to the design of useful things 60% 20% 20% � � 2003-2005 � SE course using ACL2 (FDPE 2005 report) � Process Design Testing/Validation 30% 35% 35% � � Successful despite crude programming env � 2006 - present � SE course with Dracula/ACL2 environment � 1 st year course at NU using Dracula/ACL2 Functional Programming and Theorem Proving for Undergraduates 3 FDPE 2008 - Rex Page / Carl Eastlund / Matthias Felleisen

ACL2 ;; sqr : Int -> Int (defun sqr (x) (* x x)) ;; All squares are nonnegative. (defthm sqr>=0 (implies (integerp x) (>= (sqr x) 0))) Functional Programming and Theorem Proving for Undergraduates 4 FDPE 2008 - Rex Page / Carl Eastlund / Matthias Felleisen

ACL2 Functional Programming & Theorem Proving for Undergrads - FDPE 2008 5 Rex Page / Carl Eastlund / Matthias Felleisen

Dracula Functional Programming and Theorem Proving for Undergraduates 8 FDPE 2008 - Rex Page / Carl Eastlund / Matthias Felleisen

Dracula ;; sqr : Int -> Int (defun sqr (x) (* x x)) ;; All squares are nonnegative. (defthm sqr>=0 (implies (integerp x) (>= (sqr x) 0))) Functional Programming and Theorem Proving for Undergraduates 18 FDPE 2008 - Rex Page / Carl Eastlund / Matthias Felleisen

Dracula ;; sqr : Int -> Int (defun sqr (x) x) ;; All squares are nonnegative. (defthm sqr>=0 (implies (integerp x) (>= (sqr x) 0))) Functional Programming and Theorem Proving for Undergraduates 19 FDPE 2008 - Rex Page / Carl Eastlund / Matthias Felleisen

Program Design � How to Design Programs code: ;; sqr : Int -> Int (define (sqr x) (* x x)) ;; Unit tests: (check-expect (sqr 0) 0) (check-expect (sqr 2) 4) Functional Programming and Theorem Proving for Undergraduates 21 FDPE 2008 - Rex Page / Carl Eastlund / Matthias Felleisen

Program Design � Dracula code: Dracula code: ;; sqr : Int -> Int (defun sqr (x) (* x x)) ;; Unit tests: (check-expect (sqr 0) 0) (check-expect (sqr 2) 4) Functional Programming and Theorem Proving for Undergraduates 22 FDPE 2008 - Rex Page / Carl Eastlund / Matthias Felleisen

Unit Tests � Dracula code: Dracula code: ;; sqr : Int -> Int (defun sqr (x) (* x x)) ;; Unit tests: (==> assert-event) (check-expect (sqr 0) 0) (check-expect (sqr 2) 4) Functional Programming and Theorem Proving for Undergraduates 23 FDPE 2008 - Rex Page / Carl Eastlund / Matthias Felleisen

Unit Tests Functional Programming and Theorem Proving for Undergraduates 24 FDPE 2008 - Rex Page / Carl Eastlund / Matthias Felleisen

Unit Tests Functional Programming and Theorem Proving for Undergraduates 25 FDPE 2008 - Rex Page / Carl Eastlund / Matthias Felleisen

Beyond Unit Tests ;; sqr : Int -> Int (defun sqr (x) (+ x x)) ;; Unit tests: (check-expect (sqr 0) 0) (check-expect (sqr 2) 4) Functional Programming and Theorem Proving for Undergraduates 26 FDPE 2008 - Rex Page / Carl Eastlund / Matthias Felleisen

Beyond Unit Tests Functional Programming and Theorem Proving for Undergraduates 27 FDPE 2008 - Rex Page / Carl Eastlund / Matthias Felleisen

DoubleCheck ;; ACL2 theorem: (defthm name (implies (and precondition ... ) postcondition ))) ;; DoubleCheck property: (defproperty name ( x [:where precondition] [:value distribution] ... ) postcondition ) Functional Programming and Theorem Proving for Undergraduates 28 FDPE 2008 - Rex Page / Carl Eastlund / Matthias Felleisen

DoubleCheck ;; ACL2 theorem: (defthm sqr>=0 (implies (integerp x) (>= (sqr x) 0))) ;; DoubleCheck property: (defproperty sqr>=0 (x) (implies (integerp x) (>= (sqr x) 0))) Functional Programming and Theorem Proving for Undergraduates 29 FDPE 2008 - Rex Page / Carl Eastlund / Matthias Felleisen

DoubleCheck ;; ACL2 theorem: (defthm sqr>=0 (implies (integerp x) (>= (sqr x) 0))) ;; DoubleCheck property: (defproperty sqr>=0 (x :where (integerp x)) (>= (sqr x) 0)) Functional Programming and Theorem Proving for Undergraduates 30 FDPE 2008 - Rex Page / Carl Eastlund / Matthias Felleisen

DoubleCheck ;; ACL2 theorem: (defthm sqr>=0 (implies (integerp x) (>= (sqr x) 0))) ;; DoubleCheck property: (defproperty sqr>=0 (x :where (integerp x) :value (random-integer)) (>= (sqr x) 0)) Functional Programming and Theorem Proving for Undergraduates 31 FDPE 2008 - Rex Page / Carl Eastlund / Matthias Felleisen

DoubleCheck ;; Simple distributions: (random-string) (random-integer) ;; Parameterized distributions: (random-between low high ) (random-list-of dist [:size size] ) ;; Write new distributions: (defrandom name ( arg ... ) expr ) Functional Programming and Theorem Proving for Undergraduates 32 FDPE 2008 - Rex Page / Carl Eastlund / Matthias Felleisen

DoubleCheck ;; ACL2 theorem: (defthm sqr>=0 (implies (integerp x) (>= (sqr x) 0))) ;; DoubleCheck property:(==> defthm) (defproperty sqr>=0 (x :where (integerp x) :value (random-integer)) (>= (sqr x) 0)) Functional Programming and Theorem Proving for Undergraduates 33 FDPE 2008 - Rex Page / Carl Eastlund / Matthias Felleisen

DoubleCheck ;; ACL2 theorem: (defthm sqr>=0 (implies (integerp x) (>= (sqr x) 0))) ;; Ideal syntax (future work): (defproperty sqr>=0 (implies (integerp x) (>= (sqr x) 0))) Functional Programming and Theorem Proving for Undergraduates 34 FDPE 2008 - Rex Page / Carl Eastlund / Matthias Felleisen

DoubleCheck Functional Programming and Theorem Proving for Undergraduates 35 FDPE 2008 - Rex Page / Carl Eastlund / Matthias Felleisen

DoubleCheck ;; sqr : Int -> Int (defun sqr (x) (+ x x)) ;; Unit tests: (check-expect (sqr 0) 0) (check-expect (sqr 2) 4) (check-expect (sqr -30) 900) Functional Programming and Theorem Proving for Undergraduates 38 FDPE 2008 - Rex Page / Carl Eastlund / Matthias Felleisen

DoubleCheck ;; sqr : Int -> Int (defun sqr (x) (* x x)) ;; Unit tests: (check-expect (sqr 0) 0) (check-expect (sqr 2) 4) (check-expect (sqr -30) 900) Functional Programming and Theorem Proving for Undergraduates 39 FDPE 2008 - Rex Page / Carl Eastlund / Matthias Felleisen

Functional Programming Functional Programming and Theorem Proving - PowerPoint PPT Presentation

Functional Programming Functional Programming and Theorem Proving and Theorem Proving for Undergraduates for Undergraduates A Progress Report A Progress Report Carl Carl Eastlund Eastlund and Matthias and Matthias Felleisen Felleisen

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Functional Programming Functional Programming and Theorem Proving - PowerPoint PPT Presentation

Functional Programming Functional Programming and Theorem Proving and Theorem Proving for Undergraduates for Undergraduates A Progress Report A Progress Report Carl Carl Eastlund Eastlund and Matthias and Matthias Felleisen Felleisen

+ f(x) = Python Functional Programming Python Functional Programming Functional Programming by

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Introduction to Functional Programming in Haskell 1 / 46 Outline Why learn functional

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Functional Systems Or: Functional Functional Programming Marius Eriksen Twitter Inc. @marius

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CSCI-2325 Functional Programming with Haskell Mohammad T . Irfan Functional Programming u

CSCI-2325 Functional Programming with Haskell Mohammad T . Irfan Functional Programming u

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