Justus Diller. Zur Berechenbarkeit primitiv-rekursiver Funktionale endlicher Typen. In Kurt Schutte, editor, Contributions to Mathematical Logic, pages 109-120. North{Holland, Amsterdam, 1968.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....far as syntactically possible. The simultaneous substitution of terms s for x in r is de ned as usual and written either r x [ s ] or r[ x : s ] Terms which di er only in names of bound variables are identi ed, i.e. equal terms are equal. Other approaches can be found for instance in [Dil68], How80] and [Sch93] Nipkow veri ed lemmata 3.3, 3.4 and 4 with the theorem prover Isabelle and gave worthwhile hints for improvement. 1.2. Inductive characterization and normal forms. The set of terms is inductively characterized by the following grammar 3 r; s : x r j xr j ....

....recursion in nite types over the calculus presents additional diculties in normalization proofs: reduction might substitute variables in the recursion arguments, giving rise to new recursion steps. This mixing of and recursion steps can be avoided by adapting a special reduction strategy [Dil68, How80] or restricting recursion arguments to numerals only. In this section we show strong normalization for the general form of a calculus enriched by number and recursion constructors as well as recursion reductions. In order to keep the presentation short we directly proceed to the typed ....

Justus Diller. Zur Berechenbarkeit primitiv-rekursiver Funktionale endlicher Typen. In Kurt Schutte, editor, Contributions to Mathematical Logic, pages 109-120. North{Holland, Amsterdam, 1968.

....di er only in names of bound variables are identi ed, i.e. equal terms are equal. 1.2. Inductive characterization and normal forms. The set of terms is inductively characterized by the following grammar 3 r; s : x r j xr j ( xr)s s; Other approaches can be found for instance in [Dil68], How80] and [Sch93] Nipkow veri ed lemmata 3.3, 3.4 and 4 with the theorem prover Isabelle and gave worthwhile hints for improvement. where the last form captures non normal terms; we will see later that this presentation exhibits the leftmost outermost reducible expression (redex) ....

....recursion in nite types over the calculus presents additional diculties in normalization proofs: reduction might substitute variables in the recursion arguments, giving rise to new recursion steps. This mixing of and recursion steps can be avoided by adapting a special reduction strategy [Dil68, How80] or restricting recursion arguments to numerals only. In this section we show strong normalization for the general form of a calculus enriched by number and recursion constructors as well as recursion reductions. In order to keep the presentation short we directly proceed to the typed ....

Justus Diller. Zur Berechenbarkeit primitiv-rekursiver Funktionale endlicher Typen. In Kurt Schutte, editor, Contributions to Mathematical Logic, pages 109-120. North{Holland, Amsterdam, 1968.

....which di er only in names of bound variables are identi ed, i.e. equal terms are equal. 1.2. Inductive characterization and normal forms. The set of terms is inductively characterized by the following grammar 3 r; s : x r j xr j ( xr)s s; 7 Other approaches can be found for instance in [Dil68], How80] and [Sch93] 8 Nipkow veri ed lemmata 3.3, 3.4 and 4 with the theorem prover Isabelle and gave worthwhile hints for improvement. 3 where the last form captures non normal terms; we will see later that this presentation exhibits the leftmost outermost reducible expression (redex) ....

....recursion in nite types over the calculus presents additional diculties in normalization proofs: reduction might substitute variables in the recursion arguments, giving rise to new recursion steps. This mixing of and recursion steps can be avoided by adapting a special reduction strategy [Dil68, How80] or restricting recursion arguments to numerals only. 34 In this section we show strong normalization for the general form of a calculus enriched by number and recursion constructors as well as recursion reductions. In order to keep the presentation short we directly proceed to the typed ....

Justus Diller. Zur Berechenbarkeit primitiv-rekursiver Funktionale endlicher Typen. In Kurt Schutte, editor, Contributions to Mathematical Logic, pages 109-120. North{Holland, Amsterdam, 1968.

....for numerous encouraging meetings and stimulating advice. Wilfried Buchholz 6 The type of any subterm of r : ae is subtype of either the type of a free variable or of ae. See, e.g. Sch94] for a good exposition. 7 Other approaches, building on Sanchis work, can be found for instance in [Dil68], How80] and [Sch93] provided invaluable insight into inductive definitions. For repeated discussions and helpful remarks we are grateful to Ulrich Berger, Healfdene Goguen, Tobias Nipkow 8 , Ren e David, Henk Barendregt and Anne Troelstra. 1 calculus 1.1. Terms. Raw) terms r; s; t 2 are ....

....in finite types over the calculus presents additional difficulties in normalization proofs: fi reduction might substitute variables in the recursion arguments, giving rise to new recursion steps. This mixing of fi and recursion steps can be avoided by adapting a special reduction strategy [Dil68, How80] or restricting recursion arguments to numerals only. 26 In this section we show strong normalization for the general form of a calculus enriched by number and recursion constructors as well as recursion reductions. In order to keep the presentation short we directly proceed to the typed ....

Justus Diller. Zur Berechenbarkeit primitiv-rekursiver Funktionale endlicher Typen. In Kurt Schutte, editor, Contributions to Mathematical Logic, pages 109--120. North--Holland, Amsterdam, 1968.

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