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2. Recall in lambda calculus, logic connectives NOT and OR can be defined as: NOT = (Ax | xFT) OR= (Axy | xTy) where T (Axy | x) and F (Axy | y). In logic, that "x implies y" is written x Ɔ y (or in some textbooks, x → y or x = y). Denote this function by IMP (a) Give a lambda expression that defines IMP, i.e., write what is missing at the right hand side of the vertical bar below. IMP (Axy | .....) Make sure that your answer is a normal form, i.e., it cannot contain expressions that are still reducible. Hint: In logic, we know x Ɔ y = ¬x V y. (b) Using your definition, for each expression below, reduce it to a normal form. Here, the order of reduction is unimportant. • IMP TF • IMP FT

2. Recall in lambda calculus, logic connectives NOT and OR can be defined as: NOT = (Ax | xFT) OR= (Axy | xTy) where T (Axy | x) and F (Axy | y). In logic, that "x implies y" is written x Ɔ y (or in some textbooks, x → y or x = y). Denote this function by IMP (a) Give a lambda expression that defines IMP, i.e., write what is missing at the right hand side of the vertical bar below. IMP (Axy | .....) Make sure that your answer is a normal form, i.e., it cannot contain expressions that are still reducible. Hint: In logic, we know x Ɔ y = ¬x V y. (b) Using your definition, for each expression below, reduce it to a normal form. Here, the order of reduction is unimportant. • IMP TF • IMP FT

Computer Networking: A Top-Down Approach (7th Edition)
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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2. Recall in lambda calculus, logic connectives NOT and OR can be defined as: NOT = (Aæ | xFT) = (Axy | xTy) where T = (Axy | x) and F (Axy | y). In logic, that "x implies y" is written x ɔ y (or in some textbooks, x → y or x = y). Denote this function by IMP (a) Give a lambda expression that defines IMP, i.e., write what is missing at the right hand side of the vertical bar below. IMP = (Axy | ....) Make sure that your answer is a normal form, i.e., it cannot contain expressions that are still reducible. Hint: In logic, we know xƆy = ¬x V y. (b) Using your definition, for each expression below, reduce it to a normal form. Here, the order of reduction is unimportant. • IMP TF • IMP FT
Transcribed Image Text:2. Recall in lambda calculus, logic connectives NOT and OR can be defined as: NOT = (Aæ | xFT) = (Axy | xTy) where T = (Axy | x) and F (Axy | y). In logic, that "x implies y" is written x ɔ y (or in some textbooks, x → y or x = y). Denote this function by IMP (a) Give a lambda expression that defines IMP, i.e., write what is missing at the right hand side of the vertical bar below. IMP = (Axy | ....) Make sure that your answer is a normal form, i.e., it cannot contain expressions that are still reducible. Hint: In logic, we know xƆy = ¬x V y. (b) Using your definition, for each expression below, reduce it to a normal form. Here, the order of reduction is unimportant. • IMP TF • IMP FT
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