Lecture05InferenceRules

# Lecture05InferenceRules - Lecture 5 - CS 2603 Applied Logic...

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CS2603 Applied Logic for Hardware and Software Rex Page – University of Oklahoma 1 Lecture 5 —CS 2603 Applied Logic for Hardware and Software Inference Rules … Dude

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CS2603 Applied Logic for Hardware and Software Rex Page – University of Oklahoma 2 Proof-Checker Notation prefix vsinfix -equivalent forms thm = Theorem [And A B] (And B A) thm = Theorem [A `And` B] (B `And` A) prfB = AndER (Assume(And A B)) B prfB = (Assume(A `And` B)) `AndER` B prfA = AndEL (Assume(And A B)) A prfA = (Assume(A `And` B)) `AndEL` A prf = AndI (prfB , prfA) (And B A) prefix infix
CS2603 Applied Logic for Hardware and Software Rex Page – University of Oklahoma 3 Proof-Checker Notation prefix vsinfix -equivalent forms thm = Theorem [And A B] (And B A) prfB = AndER (Assume(And A B)) B prfA = AndEL (Assume(And A B)) A prf = AndI (prfB , prfA) (And B A) prefix infix thm = Theorem [A `And` B] (B `And` A) prfB = (Assume(A `And` B)) `AndER` B prfA = (Assume(A `And` B)) `AndEL` A prf = (prfB , prfA) `AndI` (B `And` A)

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CS2603 Applied Logic for Hardware and Software Rex Page – University of Oklahoma 4 Proof-Checker Notation prefix vsinfix -equivalent forms thm = Theorem [A `And` B] (B `And` A) prfB = Assume(A `And` B) {--------------------------}`AndER` B prfA = Assume(A `And` B) {-------------------------}`AndEL` A prf = (prfB , prfA) {----------------}`AndI` (B `And` A) infix thm = Theorem [A `And` B] (B `And` A) prfB = (Assume(A `And` B)) `AndER` B prfA = (Assume(A `And` B)) `AndEL` A prf = (prfB , prfA) `AndI` (B `And` A) infix with commentary
CS2603 Applied Logic for Hardware and Software Rex Page – University of Oklahoma 5 Proof-Checker Notation prefix vsinfix -equivalent forms infix with commentary and anonymoussubformulas thm = Theorem [A `And` B] (B `And` A) prf = (Assume(A `And` B) {-------------------------}`AndER` B , Assume(A `And` B) {------------------------}`AndEL` A) {-------------------------------------}`AndI` (B `And` A) thm = Theorem [A `And` B] (B `And` A) prfB = Assume(A `And` B) {--------------------------}`AndER` B prfA = Assume(A `And` B) {-------------------------}`AndEL` A prf = (prfB , prfA) {----------------}`AndI` (B `And` A)

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CS2603 Applied Logic for Hardware and Software Rex Page – University of Oklahoma 6 Using Haskell from Windows import Stdm thm = Theorem [A `And` B] (B `And` A) prf = (Assume(A `And` B) {-------------------------}`AndER` B, Assume(A `And` B) {------------------------}`AndEL` A) {-------------------------------------}`AndI` (B `And` A) Editor window __ __ __ __ ____ ___ || || || || || || ||__ ||___|| ||__|| ||__|| __|| ||---|| ___|| || || || || Version: Nov 2003 Haskell 98 mode: Restart with Type :? for help Main>
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## This note was uploaded on 04/08/2008 for the course CS 2603 taught by Professor Rexpage during the Spring '08 term at The University of Oklahoma.

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Lecture05InferenceRules - Lecture 5 - CS 2603 Applied Logic...

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