ABSTRACT We outline a series of exercises that relate propositional logic to various straightforw... more ABSTRACT We outline a series of exercises that relate propositional logic to various straightforward query languages as used by some popular programs. The exercises naturally motivate the use of boolean algebra to translate between equivalent formulas (including a practical application of converting a formula to conjunctive normal form). They also illustrate connections between topics student see in logic/discrete math, programming topics, and topics in design.
Many CS1 curricula introduce Java topics without giving a strong rationale of why they are needed... more Many CS1 curricula introduce Java topics without giving a strong rationale of why they are needed at that exact point. For example, most all Java texts introduce the keywords public and private long before the students write or see any program involving more than a single class; those keywords can have no demonstrable effect on their program. Such an approach
We report on experience implementing a functional image library designed for use in an introducto... more We report on experience implementing a functional image library designed for use in an introductory programming course. Designing the library revealed subtle aspects of image manipulation, and led to some interesting design decisions. Our new library improves on the earlier Racket library by adding rotation, mirroring, curves, new pen shapes, some new polygonal shapes, as well as having a significantly faster implementation of equal?.
Structural approximation theory seeks to provide a framework for expressing optimization problems... more Structural approximation theory seeks to provide a framework for expressing optimization problems, and isolating structural or syntactic conditions that explain the apparent difference in the approximation properties of different NP-optimization problems. In this paper, we initiate a study of structural approximation using integer programming (an optimization problem in its own right) as a general framework for expressing optimization problems. We isolate three classes of constant-approximable maximization problems, based on restricting appropriately the syntactic form of the integer programs expressing them. The first of these classes subsumes Max \Sigma 1 , which is the syntactic version of the well-studied class Max NP. Moreover, by allowing variables to take on not just 0/1 values but rather values in a polylogarithmic or polynomial range, we obtain syntactic maximization classes that are polylog-approximable and polyapproximable, respectively. The other two classes contain prob...
Computer science programs prepare students to construct systems. System construction requires rea... more Computer science programs prepare students to construct systems. System construction requires reasoning about the interactions, capabilities, and limitations of components. A good degree program should teach students the tools that assist in these tasks. Logic is the most fundamental such tool, as industry has begun to appreciate. Software developers analyze program behavior during design, debugging, and testing. Hardware designers perform minimization and equivalence checking on circuits. Operating system designers validate routing, scheduling, and synchronization protocols. Formal logic underlies all of these activities. A solid preparation in applied logic should therefore increase students’ abilities to reason about complex systems. Unfortunately, few undergraduate computer science curricula prepare students adequately in logic. The typical student sees a few weeks of truth tables and propositional logic in a discrete mathematics course. Such a cursory introduction does not illu...
We report on experience implementing a functional image library designed for use in an introducto... more We report on experience implementing a functional image library designed for use in an introductory programming course. Designing the library revealed subtle aspects of image manipulation, and led to some interesting design decisions. Our new library improves on the earlier Racket library by adding rotation, mirroring, curves, new pen shapes, some new polygonal shapes, as well as having a significantly faster implementation of equal?.
JavaTea is an on-line system being developed to help teach beginning programmers to write good un... more JavaTea is an on-line system being developed to help teach beginning programmers to write good unit test suites. JavaTea presents a problem specification, and then asks the student to enter a set of test-cases (using, for now, Java syntax for expressions). Then, JavaTea runs a battery of incorrect implementations against the student's test-cases. If any incorrect implementation passes all of the student's tests, JavaTea reports that their test cases are insufficient. (This can be viewed as a complement to sites like codingbat.org, where students write code and are then told whether it passes all tests. Indeed, in a classroom setting, JavaTea assignments would presumably be followed up with implementing the functions they just designed tests for.) The goal is to help students view test cases as helpful tools in (a) understanding a problem's specification, (b) thinking of corner cases in advance, and (c) giving confidence that an implementation really solves the entire pro...
We outline a series of exercises that relate propositional logic to various straightforward query... more We outline a series of exercises that relate propositional logic to various straightforward query languages as used by some popular programs. The exercises naturally motivate the use of boolean algebra to translate between equivalent formulas (including a practical application of converting a formula to conjunctive normal form). They also illustrate connections between topics student see in logic/discrete math, programming topics, and topics in design.
JavaTea is an on-line system being developed to help teach beginning programmers to write good un... more JavaTea is an on-line system being developed to help teach beginning programmers to write good unit test suites. JavaTea presents a problem specification, and then asks the student to enter a set of test-cases (using, for now, Java syntax for expressions). Then, JavaTea runs a battery of incorrect implementations against the student's test-cases. If any incorrect implementation passes all of the student's tests, JavaTea reports that their test cases are insufficient. (This can be viewed as a complement to sites like codingbat.org, where students write code and are then told whether it passes all tests. Indeed, in a classroom setting, JavaTea assignments would presumably be followed up with implementing the functions they just designed tests for.) The goal is to help students view test cases as helpful tools in (a) understanding a problem's specification, (b) thinking of corner cases in advance, and (c) giving confidence that an implementation really solves the entire pro...
Typescript. Thesis (Ph. D.)--University of California, Santa Cruz, 1996. Includes bibliographical... more Typescript. Thesis (Ph. D.)--University of California, Santa Cruz, 1996. Includes bibliographical references (leaves 94-96).
We outline a series of exercises that relate propositional logic to various straightforward query... more We outline a series of exercises that relate propositional logic to various straightforward query languages as used by some popular programs. The exercises naturally motivate the use of boolean algebra to translate between equivalent formulas (including a practical application of converting a formula to conjunctive normal form). They also illustrate connections between topics student see in logic/discrete math, programming topics, and topics in design.
Structural approximation theory seeks to provide a framework for expressing optimization problems... more Structural approximation theory seeks to provide a framework for expressing optimization problems, and isolating structural or syntactic conditions that explain the apparent di erence in the approximation properties of di erent NP-optimization problems. In this paper, we initiate a study of structural approximation using integer programming (an optimization problem in its own right) as a general framework for expressing optimization problems. We isolate three classes of constant-approximable maximization problems, based on restricting appropriately the syntactic form of the integer programs expressing them. The rst of these classes subsumes Max 1, which is the syntactic version of the well-studied class Max NP. Moreover, by allowing variables to take on not just 0/1 values but rather values in a polylogarithmic or polynomial range, we obtain syntactic maximization classes that are polylog-approximable and polyapproximable, respectively. The other two classes contain problems, such as Max Matching, for which no previous structural explanation of approximability has been found. We also investigate structurally-de ned classes of integer programs for minimization problems, and show a di erence between their maximization counterparts.
Annual Joint Conference on Integrating Technology into Computer Science Education, 2000
Computer science programs prepare students to construct systems. System construction requires rea... more Computer science programs prepare students to construct systems. System construction requires reasoning about the interactions, capabilities, and limitations of components. A good degree program should teach students the tools that assist in these tasks. Logic is the most fundamental such tool, as industry has begun to appreciate. Software developers analyze program behavior during design, debugging, and testing. Hardware designers perform minimization and equivalence checking on circuits. Operating system designers ...
We report on experience implementing a functional image library designed for use in an introducto... more We report on experience implementing a functional image library designed for use in an introductory programming course. Designing the library revealed subtle aspects of image manipulation, and led to some interesting design decisions. Our new library improves on the earlier Racket library by adding rotation, mirroring, curves, new pen shapes, some new polygonal shapes, as well as having a significantly faster implementation of equal?.
Many CS1 curricula introduce Java topics without giving a strong rationale of why they are needed... more Many CS1 curricula introduce Java topics without giving a strong rationale of why they are needed at that exact point. For example, most all Java texts introduce the keywords public and private long before the students write or see any program involving more than a single class; those keywords can have no demonstrable effect on their program. Such an approach
ABSTRACT We outline a series of exercises that relate propositional logic to various straightforw... more ABSTRACT We outline a series of exercises that relate propositional logic to various straightforward query languages as used by some popular programs. The exercises naturally motivate the use of boolean algebra to translate between equivalent formulas (including a practical application of converting a formula to conjunctive normal form). They also illustrate connections between topics student see in logic/discrete math, programming topics, and topics in design.
Many CS1 curricula introduce Java topics without giving a strong rationale of why they are needed... more Many CS1 curricula introduce Java topics without giving a strong rationale of why they are needed at that exact point. For example, most all Java texts introduce the keywords public and private long before the students write or see any program involving more than a single class; those keywords can have no demonstrable effect on their program. Such an approach
We report on experience implementing a functional image library designed for use in an introducto... more We report on experience implementing a functional image library designed for use in an introductory programming course. Designing the library revealed subtle aspects of image manipulation, and led to some interesting design decisions. Our new library improves on the earlier Racket library by adding rotation, mirroring, curves, new pen shapes, some new polygonal shapes, as well as having a significantly faster implementation of equal?.
Structural approximation theory seeks to provide a framework for expressing optimization problems... more Structural approximation theory seeks to provide a framework for expressing optimization problems, and isolating structural or syntactic conditions that explain the apparent difference in the approximation properties of different NP-optimization problems. In this paper, we initiate a study of structural approximation using integer programming (an optimization problem in its own right) as a general framework for expressing optimization problems. We isolate three classes of constant-approximable maximization problems, based on restricting appropriately the syntactic form of the integer programs expressing them. The first of these classes subsumes Max \Sigma 1 , which is the syntactic version of the well-studied class Max NP. Moreover, by allowing variables to take on not just 0/1 values but rather values in a polylogarithmic or polynomial range, we obtain syntactic maximization classes that are polylog-approximable and polyapproximable, respectively. The other two classes contain prob...
Computer science programs prepare students to construct systems. System construction requires rea... more Computer science programs prepare students to construct systems. System construction requires reasoning about the interactions, capabilities, and limitations of components. A good degree program should teach students the tools that assist in these tasks. Logic is the most fundamental such tool, as industry has begun to appreciate. Software developers analyze program behavior during design, debugging, and testing. Hardware designers perform minimization and equivalence checking on circuits. Operating system designers validate routing, scheduling, and synchronization protocols. Formal logic underlies all of these activities. A solid preparation in applied logic should therefore increase students’ abilities to reason about complex systems. Unfortunately, few undergraduate computer science curricula prepare students adequately in logic. The typical student sees a few weeks of truth tables and propositional logic in a discrete mathematics course. Such a cursory introduction does not illu...
We report on experience implementing a functional image library designed for use in an introducto... more We report on experience implementing a functional image library designed for use in an introductory programming course. Designing the library revealed subtle aspects of image manipulation, and led to some interesting design decisions. Our new library improves on the earlier Racket library by adding rotation, mirroring, curves, new pen shapes, some new polygonal shapes, as well as having a significantly faster implementation of equal?.
JavaTea is an on-line system being developed to help teach beginning programmers to write good un... more JavaTea is an on-line system being developed to help teach beginning programmers to write good unit test suites. JavaTea presents a problem specification, and then asks the student to enter a set of test-cases (using, for now, Java syntax for expressions). Then, JavaTea runs a battery of incorrect implementations against the student's test-cases. If any incorrect implementation passes all of the student's tests, JavaTea reports that their test cases are insufficient. (This can be viewed as a complement to sites like codingbat.org, where students write code and are then told whether it passes all tests. Indeed, in a classroom setting, JavaTea assignments would presumably be followed up with implementing the functions they just designed tests for.) The goal is to help students view test cases as helpful tools in (a) understanding a problem's specification, (b) thinking of corner cases in advance, and (c) giving confidence that an implementation really solves the entire pro...
We outline a series of exercises that relate propositional logic to various straightforward query... more We outline a series of exercises that relate propositional logic to various straightforward query languages as used by some popular programs. The exercises naturally motivate the use of boolean algebra to translate between equivalent formulas (including a practical application of converting a formula to conjunctive normal form). They also illustrate connections between topics student see in logic/discrete math, programming topics, and topics in design.
JavaTea is an on-line system being developed to help teach beginning programmers to write good un... more JavaTea is an on-line system being developed to help teach beginning programmers to write good unit test suites. JavaTea presents a problem specification, and then asks the student to enter a set of test-cases (using, for now, Java syntax for expressions). Then, JavaTea runs a battery of incorrect implementations against the student's test-cases. If any incorrect implementation passes all of the student's tests, JavaTea reports that their test cases are insufficient. (This can be viewed as a complement to sites like codingbat.org, where students write code and are then told whether it passes all tests. Indeed, in a classroom setting, JavaTea assignments would presumably be followed up with implementing the functions they just designed tests for.) The goal is to help students view test cases as helpful tools in (a) understanding a problem's specification, (b) thinking of corner cases in advance, and (c) giving confidence that an implementation really solves the entire pro...
Typescript. Thesis (Ph. D.)--University of California, Santa Cruz, 1996. Includes bibliographical... more Typescript. Thesis (Ph. D.)--University of California, Santa Cruz, 1996. Includes bibliographical references (leaves 94-96).
We outline a series of exercises that relate propositional logic to various straightforward query... more We outline a series of exercises that relate propositional logic to various straightforward query languages as used by some popular programs. The exercises naturally motivate the use of boolean algebra to translate between equivalent formulas (including a practical application of converting a formula to conjunctive normal form). They also illustrate connections between topics student see in logic/discrete math, programming topics, and topics in design.
Structural approximation theory seeks to provide a framework for expressing optimization problems... more Structural approximation theory seeks to provide a framework for expressing optimization problems, and isolating structural or syntactic conditions that explain the apparent di erence in the approximation properties of di erent NP-optimization problems. In this paper, we initiate a study of structural approximation using integer programming (an optimization problem in its own right) as a general framework for expressing optimization problems. We isolate three classes of constant-approximable maximization problems, based on restricting appropriately the syntactic form of the integer programs expressing them. The rst of these classes subsumes Max 1, which is the syntactic version of the well-studied class Max NP. Moreover, by allowing variables to take on not just 0/1 values but rather values in a polylogarithmic or polynomial range, we obtain syntactic maximization classes that are polylog-approximable and polyapproximable, respectively. The other two classes contain problems, such as Max Matching, for which no previous structural explanation of approximability has been found. We also investigate structurally-de ned classes of integer programs for minimization problems, and show a di erence between their maximization counterparts.
Annual Joint Conference on Integrating Technology into Computer Science Education, 2000
Computer science programs prepare students to construct systems. System construction requires rea... more Computer science programs prepare students to construct systems. System construction requires reasoning about the interactions, capabilities, and limitations of components. A good degree program should teach students the tools that assist in these tasks. Logic is the most fundamental such tool, as industry has begun to appreciate. Software developers analyze program behavior during design, debugging, and testing. Hardware designers perform minimization and equivalence checking on circuits. Operating system designers ...
We report on experience implementing a functional image library designed for use in an introducto... more We report on experience implementing a functional image library designed for use in an introductory programming course. Designing the library revealed subtle aspects of image manipulation, and led to some interesting design decisions. Our new library improves on the earlier Racket library by adding rotation, mirroring, curves, new pen shapes, some new polygonal shapes, as well as having a significantly faster implementation of equal?.
Many CS1 curricula introduce Java topics without giving a strong rationale of why they are needed... more Many CS1 curricula introduce Java topics without giving a strong rationale of why they are needed at that exact point. For example, most all Java texts introduce the keywords public and private long before the students write or see any program involving more than a single class; those keywords can have no demonstrable effect on their program. Such an approach
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