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Tagless Staged Interpreters for Typed Languages
 In the International Conference on Functional Programming (ICFP ’02
, 2002
"... Multistage programming languages provide a convenient notation for explicitly staging programs. Staging a definitional interpreter for a domain specific language is one way of deriving an implementation that is both readable and efficient. In an untyped setting, staging an interpreter "removes a co ..."
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Cited by 53 (11 self)
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Multistage programming languages provide a convenient notation for explicitly staging programs. Staging a definitional interpreter for a domain specific language is one way of deriving an implementation that is both readable and efficient. In an untyped setting, staging an interpreter "removes a complete layer of interpretive overhead", just like partial evaluation. In a typed setting however, HindleyMilner type systems do not allow us to exploit typing information in the language being interpreted. In practice, this can have a slowdown cost factor of three or more times.
Le Fun: Logic, equations, and Functions
 In Proc. 4th IEEE Internat. Symposium on Logic Programming
, 1987
"... Abstract † We introduce a new paradigm for the integration of functional and logic programming. Unlike most current research, our approach is not based on extending unification to generalpurpose equation solving. Rather, we propose a computation delaying mechanism called residuation. This allows a ..."
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Cited by 44 (1 self)
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Abstract † We introduce a new paradigm for the integration of functional and logic programming. Unlike most current research, our approach is not based on extending unification to generalpurpose equation solving. Rather, we propose a computation delaying mechanism called residuation. This allows a clear distinction between functional evaluation and logical deduction. The former is based on the λcalculus, and the latter on Horn clause resolution. In clear contrast with equationsolving approaches, our model supports higherorder function evaluation and efficient compilation of both functional and logic programming expressions, without being plagued by nondeterministic termrewriting. In addition, residuation lends itself naturally to process synchronization and constrained search. Besides unification (equations), other residuations may be any grounddecidable goal, such as mutual exclusion (inequations), and comparisons (inequalities). We describe an implementation of the residuation paradigm as a prototype language called Le Fun—Logic, equations, and Functions.
Constructing Recursion Operators in Intuitionistic Type Theory
 Journal of Symbolic Computation
, 1984
"... MartinLöf's Intuitionistic Theory of Types is becoming popular for formal reasoning about computer programs. To handle recursion schemes other than primitive recursion, a theory of wellfounded relations is presented. Using primitive recursion over higher types, induction and recursion are formally ..."
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Cited by 22 (5 self)
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MartinLöf's Intuitionistic Theory of Types is becoming popular for formal reasoning about computer programs. To handle recursion schemes other than primitive recursion, a theory of wellfounded relations is presented. Using primitive recursion over higher types, induction and recursion are formally derived for a large class of wellfounded relations. Included are < on natural numbers, and relations formed by inverse images, addition, multiplication, and exponentiation of other relations. The constructions are given in full detail to allow their use in theorem provers for Type Theory, such as Nuprl. The theory is compared with work in the field of ordinal recursion over higher types.
Decidability Extracted: Synthesizing ``CorrectbyConstruction'' Decision Procedures from Constructive Proofs
, 1998
"... The topic of this thesis is the extraction of efficient and readable programs from formal constructive proofs of decidability. The proof methods employed to generate the efficient code are new and result in clean and readable Nuprl extracts for two nontrivial programs. They are based on the use of ..."
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Cited by 3 (0 self)
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The topic of this thesis is the extraction of efficient and readable programs from formal constructive proofs of decidability. The proof methods employed to generate the efficient code are new and result in clean and readable Nuprl extracts for two nontrivial programs. They are based on the use of Nuprl's set type and techniques for extracting efficient programs from induction principles. The constructive formal theories required to express the decidability theorems are of independent interest. They formally circumscribe the mathematical knowledge needed to understand the derived algorithms. The formal theories express concepts that are taught at the senior college level. The decidability proofs themselves, depending on this material, are of interest and are presented in some detail. The proof of decidability of classical propositional logic is relative to a semantics based on Kleene's strong threevalued logic. The constructive proof of intuitionistic decidability presented here is the first machine formalization of this proof. The exposition reveals aspects of the Nuprl tactic collection relevant to the creation of readable proofs; clear extracts and efficient code are illustrated in the discussion of the proofs.
Extracting Propositional Decidability: A proof of propositional decidability in constructive type theory and its extracted program.
, 1997
"... This paper describes a formal constructive proof of the decidability of a sequent calculus presentation of classical propositional logic. The Nuprl theories and proofs reported on here are part of a larger program to safely incorporate formally justified decision procedures into theorem provers. ..."
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Cited by 1 (1 self)
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This paper describes a formal constructive proof of the decidability of a sequent calculus presentation of classical propositional logic. The Nuprl theories and proofs reported on here are part of a larger program to safely incorporate formally justified decision procedures into theorem provers. The proof is implemented in the Nuprl system and the resulting proof object yields a "correctbyconstruction" program for deciding propositional sequents. In the case the sequent is valid, the program reports that fact; in the case the sequent is falsifiable, the program returns a falsifying assignment. Also, the semantics of the propositional sequents is formulated here in Kleene's strong threevalued logic which both: agrees with the standard two valued semantics; and gives finer information in case the proposition is falsifiable. Contents 1 Introduction 2 1.1 Related Work : : : : : : : : : : : : : : : : : : : : : : : : : : : 3 1.2 Overview of the Approach : : : : : : : : : : : :...