T. Coquand. A constructive topological proof of Van der Waerden's theorem, Journal of Pure and Applied Algebra 105(3), pp. 251259, 1995. Home/Search Document Details and Download
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A Pointfree approach to Constructive Analysis in Type Theory - Cederquist (1997) (8 citations) (Correct)
....constructive only uses inductive denitions) and, following Coquand s idea, Negri and Valentini [NV97] gave a proof in the framework of formal topologies. Johnstone gives a few more examples of constructive proofs of theorems formulated in a pointfree way in [Joh83] and for further examples see [Coq92a, Coq95]. 4 Implementations of type theory ALF (Another Logical Framework) ALF [Mag95] is an implementation of Martin L#f s monomorphic type theory [NPS90] extended with pattern matching [Coq92c] In the type theory used in ALF there are two basic levels: sets and types. Sets are formed by induction. ....
T. Coquand. A constructive topological proof of Van der Waerden's theorem, Journal of Pure and Applied Algebra 105(3), pp. 251259, 1995.
A proof of Higman's Lemma by open induction - Geser (1996) (Correct)
....Moreover by (4) Noetherian induction is a special case. Open induction appears appropriate for proofs where Noetherian induction does not apply because the underlying order is not wellfounded. Coquand has used open induction to give proofs to Higman s Lemma [Coq94a] and van der Waerden s Theorem [Coq94b]. Below we give another proof of Higman s Lemma. 3 Basic Notions Let us briefly review some standard results. Rather than speaking about ascending chains, Noetherian, least upper bounds, etc. we will speak about descending chains, wellfoundedness, greatest lower bounds, etc. we think it better ....
Thierry Coquand. A constructive topological proof of van der Waerden's Theorem. Technical report, Chalmers University, 1994. Revised version.
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