COMP 356 Programming Language Structures Notes for Chapter 15
... The keyword if is used for if expressions. Syntax: (if )
Meaning: if condition is true, the value of the if expression is the value of the expression .
Otherwise, the value of the if expression is the value of the expression .
Example: an absolute value function.
(de ...
... The keyword if is used for if expressions. Syntax: (if
CLASSICAL LOGIC and FUZZY LOGIC
... Another example comes from ancient Greece. Does the liar from Crete lie when he claims, ‘‘All Cretians are liars?’’ If he is telling the truth, his statement is false. But if his statement is false, he is not telling the truth. A simpler form of this paradox is the two-word proposition, ‘‘I lie.’’ T ...
... Another example comes from ancient Greece. Does the liar from Crete lie when he claims, ‘‘All Cretians are liars?’’ If he is telling the truth, his statement is false. But if his statement is false, he is not telling the truth. A simpler form of this paradox is the two-word proposition, ‘‘I lie.’’ T ...
4 slides/page
... • epistemic logic: for reasoning about knowledge The simplest logic (on which all the rest are based) is propositional logic. It is intended to capture features of arguments such as the following: Borogroves are mimsy whenever it is brillig. It is now brillig and this thing is a borogrove. Hence thi ...
... • epistemic logic: for reasoning about knowledge The simplest logic (on which all the rest are based) is propositional logic. It is intended to capture features of arguments such as the following: Borogroves are mimsy whenever it is brillig. It is now brillig and this thing is a borogrove. Hence thi ...
Lect5-CombinationalLogic
... logic block that has n-bit input and 2n outputs, where only one output is asserted for each input combination If the input is i (in binary), A ...
... logic block that has n-bit input and 2n outputs, where only one output is asserted for each input combination If the input is i (in binary), A ...
Chapter 14a - McGraw Hill Higher Education
... In pure lambda calculus, expressions like (( x . x2)5) = 52 are uninterpreted. In a functional language, (( x . x2)5) is interpreted normally (25). ...
... In pure lambda calculus, expressions like (( x . x2)5) = 52 are uninterpreted. In a functional language, (( x . x2)5) is interpreted normally (25). ...
History of Lisp
... McCarthy, J. 1978. History of Lisp. In Preprints of Proceedings of ACM SIGPLAN History of Programming Languages Conference. SIGPLAN Notices, Vol. 13, pp. 217223 Wadler, Phillip. “Functional Programming: Why no one uses functional languages” ...
... McCarthy, J. 1978. History of Lisp. In Preprints of Proceedings of ACM SIGPLAN History of Programming Languages Conference. SIGPLAN Notices, Vol. 13, pp. 217223 Wadler, Phillip. “Functional Programming: Why no one uses functional languages” ...
mathematical logic: constructive and non
... However, if we agree here that a c proof ' of a sentence should be a finite linguistic construction, recognizable as being made in accordance with preassigned rules and whose existence assures the 'truth' of the sentence in the appropriate sense, we already have (II ), since the verification of (2) ...
... However, if we agree here that a c proof ' of a sentence should be a finite linguistic construction, recognizable as being made in accordance with preassigned rules and whose existence assures the 'truth' of the sentence in the appropriate sense, we already have (II ), since the verification of (2) ...
Lindenbaum lemma for infinitary logics
... If ∆ and Π are singletons, we obtain the well known proof by cases property which in finitary logics coincides with its strong form but not in general it differs, see [2]. ...
... If ∆ and Π are singletons, we obtain the well known proof by cases property which in finitary logics coincides with its strong form but not in general it differs, see [2]. ...
Functional Programming
... Functional programs are referentially transparent , that is, if a variable is set to be a certain value in a program; this value cannot be changed again. That is, there is no assignment but only a true mathematical equality. ...
... Functional programs are referentially transparent , that is, if a variable is set to be a certain value in a program; this value cannot be changed again. That is, there is no assignment but only a true mathematical equality. ...
Two Marks with Answer: all units 1. Describe the Four Categories
... B) Modus Tolens - If There Is An Axiom E F And An Axiom F, Then E Follows Logically. C) Resolution - If There Is An Axiom E F And An Axiom F G Then E G Follows Logically. In Fact, Resolution Can Subsume Both Modus Ponens And Modus Tolens. It Can Also Be Generalized So That There Can Be Any Number Of ...
... B) Modus Tolens - If There Is An Axiom E F And An Axiom F, Then E Follows Logically. C) Resolution - If There Is An Axiom E F And An Axiom F G Then E G Follows Logically. In Fact, Resolution Can Subsume Both Modus Ponens And Modus Tolens. It Can Also Be Generalized So That There Can Be Any Number Of ...
Declarative Programming
... - There were only two data types, atom and list - LISP lists are stored internally as singly-linked lists - Lambda notation is used to specify function applications and function definitions; functions and data all have the same form e.g., If the list (A B C) is interpreted as data, it is a simple li ...
... - There were only two data types, atom and list - LISP lists are stored internally as singly-linked lists - Lambda notation is used to specify function applications and function definitions; functions and data all have the same form e.g., If the list (A B C) is interpreted as data, it is a simple li ...
Functional Programming www.AssignmentPoint.com In computer
... Functional programming has its roots in lambda calculus, a formal system developed in the 1930s to investigate computability, the Entscheidungsproblem, function definition, function application, and recursion. Many functional programming languages can be viewed as elaborations on the lambda calculus ...
... Functional programming has its roots in lambda calculus, a formal system developed in the 1930s to investigate computability, the Entscheidungsproblem, function definition, function application, and recursion. Many functional programming languages can be viewed as elaborations on the lambda calculus ...
HW 12
... a. Provide a definitional axiom for A \ B (use a 2-place function symbol diff(x,y)) b. Construct a formal proof that shows that for any sets A, B, and C: A (B \ C) = (A B) \ C 5. Any set without any elements is an empty set a. Provide a definitional axiom that defines a 1-place predicate Empty(x ...
... a. Provide a definitional axiom for A \ B (use a 2-place function symbol diff(x,y)) b. Construct a formal proof that shows that for any sets A, B, and C: A (B \ C) = (A B) \ C 5. Any set without any elements is an empty set a. Provide a definitional axiom that defines a 1-place predicate Empty(x ...
Chapter_4
... application has priority over (:). For example, the following definition gives an error: head x:_ = x Hugs> hd [1, 2, 3] where hd x:_ = x ERROR - Syntax error in declaration (unexpected symbol ":") Hugs> hd [1, 2, 3] where hd (x:_) = x ...
... application has priority over (:). For example, the following definition gives an error: head x:_ = x Hugs> hd [1, 2, 3] where hd x:_ = x ERROR - Syntax error in declaration (unexpected symbol ":") Hugs> hd [1, 2, 3] where hd (x:_) = x ...
functional form
... have the same form. e.g., If the list (A B C) is interpreted as data it is a simple list of three atoms, A, B, and C If it is interpreted as a function application, it means that the function named A is applied to the two parameters, B and C • The first LISP interpreter appeared only as a demonstrat ...
... have the same form. e.g., If the list (A B C) is interpreted as data it is a simple list of three atoms, A, B, and C If it is interpreted as a function application, it means that the function named A is applied to the two parameters, B and C • The first LISP interpreter appeared only as a demonstrat ...
The origin of the technical use of "sound argument": a postscript
... Note that what Goldstick rightly calls the "objectionable appropriation" is quite conscious. Black believes, wrongly, that the conclusion of any deductively valid argument with true premisses has been reached from its premisses by a reliable method. Note however that Black, unlike Copi seven years l ...
... Note that what Goldstick rightly calls the "objectionable appropriation" is quite conscious. Black believes, wrongly, that the conclusion of any deductively valid argument with true premisses has been reached from its premisses by a reliable method. Note however that Black, unlike Copi seven years l ...
Logic Design
... Example – see Example 9.4 in the course text The operation of the Exclusive OR gate can be stated as: “The output should be true if either of its inputs are true, but not if both inputs are true.” This can be rephrased as: ...
... Example – see Example 9.4 in the course text The operation of the Exclusive OR gate can be stated as: “The output should be true if either of its inputs are true, but not if both inputs are true.” This can be rephrased as: ...
Homework 8 and Sample Test
... 8. Which of the following is a formula of the predicate calculus? Part 1: Mulitiple Choice, 1/2 pt. each. Multiple Choice: (1 pt. each.) 1. (p → p) is a tautology because a. it is intuitively obvious. b. it is not necessarily false. c. every line of it’s truth table is true. d. most people would agr ...
... 8. Which of the following is a formula of the predicate calculus? Part 1: Mulitiple Choice, 1/2 pt. each. Multiple Choice: (1 pt. each.) 1. (p → p) is a tautology because a. it is intuitively obvious. b. it is not necessarily false. c. every line of it’s truth table is true. d. most people would agr ...
Computer Science 202a Homework #2, due in class
... Please turn in your homework in TWO SEPARATE PARTS: Part I is problems 1-3 and Part II is problems 4-6. Put your name on both parts. Please list (in Part I) any persons (including course staff) or resources (including online) you consulted with in connection with this assignment. Partial credit will ...
... Please turn in your homework in TWO SEPARATE PARTS: Part I is problems 1-3 and Part II is problems 4-6. Put your name on both parts. Please list (in Part I) any persons (including course staff) or resources (including online) you consulted with in connection with this assignment. Partial credit will ...
Computer Science 203 Programming Languages Bindings
... • There are many parameter-passing modes, such as: – By value: the formal is bound to a variable with an unused location, set to the actual’s value. – By name (in the ALGOL sense): the actual is not evaluated until the point of use. – By reference: the formal is bound to the variable designated ...
... • There are many parameter-passing modes, such as: – By value: the formal is bound to a variable with an unused location, set to the actual’s value. – By name (in the ALGOL sense): the actual is not evaluated until the point of use. – By reference: the formal is bound to the variable designated ...
Lambda Calculus
... Another form of abbreviations introduced by Church are schematic de nitions [Chu41]. Schematic de nitions de ne the form of expressions and allows a more readable form. As in the case of the nominal de nition the schema is on the left side of the arrow and the schematic de nition is on the right han ...
... Another form of abbreviations introduced by Church are schematic de nitions [Chu41]. Schematic de nitions de ne the form of expressions and allows a more readable form. As in the case of the nominal de nition the schema is on the left side of the arrow and the schematic de nition is on the right han ...