number-theory

Index185#-contraction 4of typed terms 69Q-conversion 5Church-Rosser theorem for 5decidable in TAx 28of typed terms 69rule (Eqf) in TA,t+p 52with strong type-invariance 158fl-equality (see fl-conversion)ii-Postponement theorem 8n-redex 7typed 69n-reduction 7Church-Rosser theorem for 8Commuting lemma with fl 8A-abstract 1A-calculus, definition 1#-expansion 5 basic facts 1-11sometimes preserves types 24A-model 57fl-nf (see #-normal forms)extensional 58fl-nf (set of all fl-normal forms) 6structural characterization 7#-normal forms 6 Al-PT 94structure of 7typed 69structure of 110A-term (see term)Al-calculus, Al-terms 10AK-calculus, AK-terms 10AK-PT 94long typed 110structure of long typed 115 0 (Church numeral zero) 4fl-redex 4 principal type of 50typed 69 1-property 96fl-redex-occurrence 1441 (Church numeral 1) 4argument-part 144principal type of 50function-part 144newly-created 1472-length of a position 129residuals of 145fl-reduction 4oo (possible length of a reduction) 5Church-Rosser theorem for 5ao (possible no. of inhabitants) 109leftmost red. 6length of a red. 5#( ) (cardinality of a set of terms) 109non-cancelling red. 11non-duplicating red. 11(-+E), -* -elimination rulepreserves types (Subject-reduction thm.) 24 in TAx 16red. with strong type-invariance 158in propositional logics 76, 89typed red. 69(-I), - -introduction rulefln-contraction 8in TAx 16fin-conversion 8Church-Rosser theorem for 8in propositional logics 76rule (Egp,t) in TAx+Rn 52discharging assumptions 76-9Pry-equality (see Bn-conversion)(-'I)main, (-'I)vac 16fln-nf (see Bn-normal forms)fin-nf (set of all fln-normal forms) 9* (for concatenation) 130fln-normal forms 9(symbol in a position) 140, 153seeking 10 . (meaning #-normal form of) 6typed 69 (meaning fln-normal form of) 9fln-redex 8.n (meaning n-normal form of) 9#n-reduction 8Church-Rosser theorem for 8Commuting lemma for 8(identity of terms etc.) 1n-Postponement theorem for 8 - (a-convertibility) 3r (for arbitrary type-contexts) 14r-x 1sr )M 15AL (see Curry-Howard mapping)A2 (logic-to-lambda mapping) 82n-contraction, conversion 7typed 69n-family 8typed 112n-nf (see n-normal forms)n-normal forms 9typed 69(isomorphism of components) 115, 143= (identity of nos., sets, etc.) 1=ext 35(see #-conversion)=fin (see fln-conversion)=9[n] (used for both =p, =pq) 53=n (see n-conversion)rt9 (fl-contracts to, see fl-contraction)r-p (/f-reduces to, see #-reduction)t>f,, (flu-reduces to, see flu-reduction)E>n (n-reduces to, see n-reduction)