Leen Helmink. Goal directed proof construction in type theory. In Procs. of the first Workshop on Logical Frameworks. Cambridge University Press, 1991. Home/Search Document Not in Database Summary Related Articles Check |
This paper is cited in the following contexts:
Pure Type Systems with Definitions - Paula Severi Erik (1993) (37 citations) (Correct)
....of PTS s is that they do not provide the possibility to introduce definitions, i.e. abbreviations for larger expressions that are used several times. A definition mechanism is essential for practical use, and indeed implementations of PTS s such as Coq [Dea91] Lego [LP92] or Constructor [Hel91] do provide such a facility, even though the formal definitions of the systems they implement do not. In this paper, we introduce an extension of PTS s with definitions. Definitions will be of the form x = a : A. A definition x = a : A introduces x as an abbreviation of the term a of type A. ....
Leen Helmink. Goal directed proof construction in type theory. In Procs. of the first Workshop on Logical Frameworks. Cambridge University Press, 1991.
TPS: A Theorem-Proving System for Classical Type Theory - Andrews, Bishop, Issar.. (1996) (43 citations) (Correct)
....and [17] also find proofs automatically by using techniques that have essential relevance to higher order logic. TPS is far from comprehensive, and the systems mentioned above have many other features that are not available in TPS. Perhaps closest in spirit to TPS is the work by Helmink and Ahn [30], who have also proven significant theorems in type theory (such as Cantor s theorem) completely automatically. 2. An Overview of TPS Our experience has shown that even if one is primarily interested in the problem of proving theorems automatically, one needs good interactive tools in order to ....
Helmink, L. and Ahn, R.: Goal directed proof construction in type theory, in G. Huet and G. Plotkin (eds), Logical Frameworks, Cambridge University Press, 1991, pp. 120--148.
Typechecking in Pure Type Systems - Pollack, Poll (1992) (3 citations) (Correct)
....implementations of formal systems that are either PTS or closely related to PTS. For example, LEGO [LP92] implements the Pure Calculus of Constructions [CH88] PCC) the Extended Calculus of Constructions [Luo90] and the Edinburgh Logical Framework [HHP87] ELF [Pfe89] implements LF; CONSTRUCTOR [Hel91] implements arbitrary PTS with finite set of sorts. Are these implementations actually correct It is not difficult to find a natural efficient algorithm that is provably sound (Section 3) but completeness is more difficult. In fact Jutting has shown typechecking is decidable for all normalizing ....
Leen Helmink. Goal directed proof construction in type theory. In Logical Frameworks. Cambridge University Press, 1991.
Logic Programming in the LF Logical Framework - Pfenning (1991) (138 citations) (Correct)
....that the algorithm will not enumerate unifiers, but simply reduce the original problem to a satisfiable set of constraints (so called flex flex pairs) whose unifiers are difficult to enumerate. While this unification algorithm has proven quite useful in the context of automated theorem proving [1, 13], as the basis for a a logic programming language it has some drawbacks. In particular, the potentially high branching factor and the possibility of non termination make it difficult to exploit the full power of Huet s algorithm in a safe and predictable way. Observing the actual practice of ....
Leen Helmink and Ren'e Ahn. Goal directed proof construction in type theory. In G'erard Huet and Gordon D. Plotkin, editors, Logical Frameworks. Cambridge University Press, 1991. To appear.
Pure Type Systems with Definitions - Severi, Poll (1993) (37 citations) (Correct)
....not provide the possibility to introduce a definition, i.e. an abbreviation (name) for a larger term which can be used several times in a program or proof. A definition mechanism is essential for practical use, and indeed implementantions of PTS s such as Coq [ea91] Lego [LP92] or Constructor [Hel91] do provide such facility, even though the formal definition of the systems they implement do not. In this chapter, we introduce an extension of the PTS with (non recursive) definitions. The extension of a PTS with definitions looks very harmless and this may not seem a topic worthy of ....
Leen Helmink. Goal directed proof construction in type theory. In Procs. of the first Workshop on Logical Frameworks. Cambridge University Press, 1991.
Checking Algorithms for Pure Type Systems - Jutting, McKinna, Pollack (1992) (10 citations) (Correct)
....of formal systems that are either PTS or closely related to PTS. For example, LEGO [LP92] implements the Pure Calculus of Constructions (PCC) CH88] the Extended Calculus of Constructions [Luo90] and the Edinburgh Logical Framework (LF) HHP87] ELF [Pfe89] implements LF; CONSTRUCTOR [Hel91] implements arbitrary PTS with finite set of sorts. Are these implementations actually correct Of course, we may enumerate all derivations of a given PTS, and Jutting [vBJ93] has shown that a large class of normalizing PTS have decidable typechecking by computing the normal forms of types, but ....
Leen Helmink. Goal directed proof construction in type theory. In Logical Frameworks. Cambridge University Press, 1991.
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