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------------------------------------------------------------------------r2696 | schwicht | 2014-01-24 10:23:42 +0100 (Fri, 24 Jan 2014) | 1 line

Updated------------------------------------------------------------------------r2695 | schwicht | 2014-01-24 10:22:55 +0100 (Fri, 24 Jan 2014) | 1 line

Minor changes------------------------------------------------------------------------r2694 | schwicht | 2014-01-24 10:22:30 +0100 (Fri, 24 Jan 2014) | 2 lines

by-assume-minimal-with renamed into by-assume-minimal-wrt . Typoscorrected.------------------------------------------------------------------------r2693 | schwicht | 2014-01-24 10:21:20 +0100 (Fri, 24 Jan 2014) | 1 line

Display functions added. Minor corrections.------------------------------------------------------------------------r2692 | schwicht | 2014-01-24 10:20:17 +0100 (Fri, 24 Jan 2014) | 3 lines

In atr-rel-definite-proof atr-arb-definite-proof atr-irrel-goal-proofatr-arb-goal-proof impnc case added. min-excl-proof? replaced bymin-excl-formula?------------------------------------------------------------------------

r2691 | schwicht | 2014-01-24 10:19:47 +0100 (Fri, 24 Jan 2014) | 7 lines

Initial THEOREMS moved here because formula-substitute (used inmake-proof-in-aconst-form for AllncTotalIntro) needsformula-of-nulltype? truth-aconst redefined via the theorem Truth(with truth-proof). efq-atom-proof imp-to-atom-proofatom-to-imp-proof and-atom-to-left-proof and-atom-to-right-proofatoms-to-and-atom-proof dec-cases-proof moved here, because they needtruth-aconst .------------------------------------------------------------------------r2690 | schwicht | 2014-01-24 10:19:13 +0100 (Fri, 24 Jan 2014) | 3 lines

Initial THEOREMS moved to ets.scm because formula-substitute (used in

make-proof-in-aconst-form for AllncTotalIntro) needsformula-of-nulltype?------------------------------------------------------------------------r2689 | schwicht | 2014-01-24 10:18:43 +0100 (Fri, 24 Jan 2014) | 1 line

Typo corrected.------------------------------------------------------------------------r2688 | schwicht | 2014-01-24 10:18:17 +0100 (Fri, 24 Jan 2014) | 6 lines

typed-constr-name-to-step-formula corrected for multiary constructors,corresponding to constructor-type-to-step-type . This is necessary tofit the type of the recursion operator. Induction with partialvariables and stotality premise disallowed. Use elimination instead.

truth-aconst (with Truth-Axiom) removed. truth-aconst is redefined inets.scm via the theorem Truth (with truth-proof).------------------------------------------------------------------------r2687 | schwicht | 2014-01-24 10:17:46 +0100 (Fri, 24 Jan 2014) | 6 lines

In formula-substitute an active impnc becoming inactive aftersubstitution is changed to imp. In the fold-formula / unfold-formulamechanism only imp is used, not impnc (as before 2014-01-08).foldable-excl-form? and foldable-excu-form? changed accordingly.tensor-form-to-imp-impnc-formula and h-deg-respecting? then become

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superfluous and are removed.------------------------------------------------------------------------r2686 | schwicht | 2014-01-24 10:17:14 +0100 (Fri, 24 Jan 2014) | 3 lines

Change comment in constructor-type-to-step-type from Comment: nestedargtype: substitute alg times type to Comment: argtype tvar or nested(then substitute alg times type)------------------------------------------------------------------------r2685 | schwicht | 2014-01-08 12:38:41 +0100 (Wed, 08 Jan 2014) | 1 line

Initial commit------------------------------------------------------------------------r2684 | schwicht | 2014-01-08 11:13:04 +0100 (Wed, 08 Jan 2014) | 1 line

Updated------------------------------------------------------------------------r2683 | schwicht | 2014-01-08 11:11:56 +0100 (Wed, 08 Jan 2014) | 2 lines

Material in temp/nested.tex and in lectures/proofth/ss13/pt.tex included.Structural totality used as a convenient abbreviation only.------------------------------------------------------------------------r2682 | schwicht | 2014-01-08 11:11:09 +0100 (Wed, 08 Jan 2014) | 2 lines

Updated to the present terminology. For instance, Truth-Axiom

replaced by the theorem Truth. Minor corrections.------------------------------------------------------------------------r2681 | schwicht | 2014-01-08 11:10:19 +0100 (Wed, 08 Jan 2014) | 2 lines

Updated to the present terminology. For instance, Truth-Axiomreplaced by the theorem Truth. Minor corrections.------------------------------------------------------------------------r2680 | schwicht | 2014-01-08 11:07:36 +0100 (Wed, 08 Jan 2014) | 1 line

Extended and cleaned up.------------------------------------------------------------------------r2679 | schwicht | 2014-01-08 11:05:44 +0100 (Wed, 08 Jan 2014) | 2 lines

Theorem BooleEqTotal removed. It already is in ets.scm. Usage ofStab-Atom removed.------------------------------------------------------------------------r2678 | schwicht | 2014-01-08 11:04:13 +0100 (Wed, 08 Jan 2014) | 2 lines

Theorem BooleEqTotal removed. It already is in ets.scm. rtotalityfor list added.------------------------------------------------------------------------r2677 | schwicht | 2014-01-08 11:03:39 +0100 (Wed, 08 Jan 2014) | 1 line

AllPartial-All replaced by AllTotalIntro------------------------------------------------------------------------r2676 | schwicht | 2014-01-08 11:02:49 +0100 (Wed, 08 Jan 2014) | 5 lines

simpreal.scm loaded before real.scm. Constructor names L M R renaedin Lft Mid Rht. Simplified split lemmata. Removed an unnecessarylet. Inserted description of running the file cauchysds.hs generatedby terms-to-haskell-program . Extended experiments to include haskellcode.------------------------------------------------------------------------r2675 | schwicht | 2014-01-08 11:01:56 +0100 (Wed, 08 Jan 2014) | 3 lines

Added: (e, Total, RTotal) ~ (=, Equal, REqual). add-equality and

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add-requality to be defined. The predconst Equal_{\alpha} should havetype alpha. Example: CoREqualList, bisimilarity.------------------------------------------------------------------------r2674 | schwicht | 2014-01-08 11:00:51 +0100 (Wed, 08 Jan 2014) | 1 line

(map (lambda (x y) (list x y)) arg1 arg2) replaced by (map list arg1 arg2)------------------------------------------------------------------------r2673 | schwicht | 2014-01-08 11:00:19 +0100 (Wed, 08 Jan 2014) | 1 line

INITIAL- removed.------------------------------------------------------------------------r2672 | schwicht | 2014-01-08 10:59:10 +0100 (Wed, 08 Jan 2014) | 1 line

Reference to Vorobev 1964 added.------------------------------------------------------------------------r2671 | schwicht | 2014-01-08 10:58:40 +0100 (Wed, 08 Jan 2014) | 4 lines

atr-min-excl-proof-to-bot-reduced-proof atr-min-excl-proof-to-ex-proofatr-min-excl-proof-to-structured-extracted-term min-excl-proof?adapted to the fact that the premises in the final kernel ofwrong-formula (i.e., the goals) can be imp as well as impnc premises.------------------------------------------------------------------------r2670 | schwicht | 2014-01-08 10:57:57 +0100 (Wed, 08 Jan 2014) | 2 lines

impnc allowed. However, for the Dialectica interpretation there isno difference between imp and impnc.------------------------------------------------------------------------r2669 | schwicht | 2014-01-08 10:57:18 +0100 (Wed, 08 Jan 2014) | 15 lines

atom-true-proof rewritten and generalized to a partial variable. Itis moved here from pproof.scm since it uses EqD.idpredconst-to-et-type rewritten, to avoid that (exd boole T) getstype boole yprod unit. axiom-to-extracted-term corrected in case Elimof a uniform one-clause defined idpredconst (like EqD). Inglobal-assumption-to-extracted-term case EfqLog one needs an eterm offunction type, not inhab. all-formulas-to-et-rec-constall-formulas-to-mr-ind-proof now give an error message in case of a

nested algebra. number-and-idpredconst-to-et-constr-term corrected:simidpc-et-tvars instead of et-tvars needed. OrNc added. It isneeded for soundness proofs. boole-eq-total-proof and theoremBooleEqTotal added already here. axiom-to-soundness-proof extended bycases for Closure and Gfp. rtotality added for yprod ysum ysumuuysum. Efq-Log and Stab-Log renamed into EfqLog and StabLog. Ineqd-compat-proof and eqd-compat-rev-proof impnc replaced by imp.------------------------------------------------------------------------r2668 | schwicht | 2014-01-08 10:56:29 +0100 (Wed, 08 Jan 2014) | 15 lines

mk-imp-impnc-formula added. make-exc-intro-aconst split intomake-exca-intro-aconst and make-excl-intro-aconst. The latter takes alist nc-indicator of booleans and a positive integer n. The

implications after the Qs are determined by nc-indicator. Similarlyexc-formula-to-exc-intro-aconst is split intoexca-formula-to-exca-intro-aconst andexcl-formula-to-excl-intro-aconst. Both are used in exc-intro-intern.(make-exc-elim-aconst l-test m n) uses stability. In case the goal isa negation stability can be avoided. We then use(make-exca-elim-neg-aconst m n) (make-excl-elim-neg-aconstnc-indicator n). All these occur in(exca-formula-and-nega-concl-to-exca-elim-neg-aconst exca-formulanega-concl) (excl-formula-and-negl-concl-to-excl-elim-neg-aconst

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excl-formula negl-concl) (exc-formula-and-concl-to-exc-elim-aconstexc-formula concl). reset and INITIAL- removed.------------------------------------------------------------------------r2667 | schwicht | 2014-01-08 10:55:41 +0100 (Wed, 08 Jan 2014) | 25 lines

mk-proof-in-and-intro-form adapted to right-associative and.(mk-proof-in-cr-nc-intro-form x . rest) added. x is obtained from alist of premises and variables where each element is followed by anindicator for nc or cr (true means nc). When normalizing a proof vianbe in the elim case the associated rec constant has to accomodate thefree variables in inst-formula of the elim-aconst. The tvars in theirtypes may be affected by the tpsubst of the elim-aconst. When such atype clash occurs, we rename type variables implicitly bound by tsubstaway from tvars. In check-and-display-proof-aux it is checked that inc.r. parts every aconst has relevant pvars substituted by c.r. ctermsonly. Hand normalization of proofs redone, including beta conversionand idpredconst-elim-intro conversion. The latter uses for nestedidpredconstants formula-and-psubsts-to-mon-proof. An elim-intro redexoccurs when an elim aconst is applied to terms and the result ofapplying an intro-aconst to terms and an idpc-proof.proof-in-idpredconst-elim-intro-redex-form? andproof-to-one-step-idpredconst-elim-intro-reduct added.proof-to-one-step-beta-reduct replaced by proof-to-one-step-reduct.proof-to-beta-nf replaced by proof-to-normal-form

proof-in-beta-normal-form? replaced by proof-in-normal-form?proof-in-beta-normal-form-for-extraction? replaced byproof-in-normal-form-for-extraction? proof-in-beta-normal-form-aux?replaced by proof-in-normal-form-aux?formula-and-falsity-avar-to-efq-proof corrected and extended tocoinductively defined predicates (work of Kenji Miyamoto).------------------------------------------------------------------------r2666 | schwicht | 2014-01-08 10:55:06 +0100 (Wed, 08 Jan 2014) | 8 lines

Added Comp axioms corresponding to computation rules. In check-aconstopt-ignore-deco-flag (default: #t) introduced. If it is #f it ischecked that psubst for the relevant pvars has c.r. cterms only.all-formulas-to-ind-aconst and all-formula-to-cases-aconst now give an

error message in case of a nested algebra. Inimp-formulas-to-uninst-gfp-formulas-etc at the internally definedand-ex-fla-to-shortened-fla cases andu exl exu added.tpsubst-for-param-pvars renamed into tpsubst.------------------------------------------------------------------------r2665 | schwicht | 2014-01-08 10:54:29 +0100 (Wed, 08 Jan 2014) | 1 line

Token ornc added. make-injection corrected.------------------------------------------------------------------------r2664 | schwicht | 2014-01-08 10:53:47 +0100 (Wed, 08 Jan 2014) | 26 lines

formula-to-depth moved here from term.scm. formula-to-spos-pvarsmoved here from psym.scm. imp-impnc-all-allnc-form-to-vars added.

imp-impnc-all-allnc-form-to-vars-and-prems-with-nc-indicator added.tensor-form-to-imp-impnc-formula and h-deg-respecting? added.fold-formula and unfold-formula adapted to h-deg-respectingimplications. Reason: an excl-intro-aconst generated by(make-excl-intro-aconst nc-indicator n) when turned into a theoremshould have an extracted term whose type does not involve the unittype. This is generally needed in program extraction when the theoremis c.r. and contains general pvars some of whose are instantiated withn.c. cterms. Then cThm has a too general (i.e., not fitting) type,since unit types are simplified away. Therefore for the relevant

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pvars (i.e., those whose tvar appears in type of cThm, except bot anda final-val-type pvar) we say using nc-indicator which ones are are tobe specialized with n.c. cterms. make-andi corrected: make-andl wascalled with formula2 and formula1, i.e., in the wrong order. orncadded. make-bicon, bicon-form?, bicon-form-to-bicon,bicon-form-to-left, bicon-form-to-right or-form-to-disjunctsqf-to-term formula-to-token-tree all extended by an ornc case.formula-to-depth and formula-to-idpredconst-names added.negation-form? negation-form-to-kernel negation-log-form?negation-log-form-to-kernel added. totality-predicate? and(unfold-totality formula) added. In unfold-totalityterm-to-totality-formula replaced by term-to-unfolded-totality-formula .predicate-to-token-tree gets token-tree-tag idpredconst-op in casethere are cterms. cterm-to-token-tree added.------------------------------------------------------------------------r2663 | schwicht | 2014-01-08 10:53:10 +0100 (Wed, 08 Jan 2014) | 3 lines

token-tree-to-string and token-tree-to-pp-tree get new casesidpredconst-op and cterm. token-tree-tag-to-precedence andprime-token-tree? adapted.------------------------------------------------------------------------r2662 | schwicht | 2014-01-08 10:52:36 +0100 (Wed, 08 Jan 2014) | 9 lines

default-term-to-token-tree changed: if-terms for nested algebras do

not admit a case display. In match-aux A -> B and A --> B consideredequal if A is n.c. term-to-expr corrected: (i) in case GRecGuard iflanguage is scheme: then prevs rather than prevs-fix is used (ii) incase = if language is scheme: quotation inserted. (iii) parenthesesin var names are displayed with a semicolon. Example:\x28;nat=>nat=>nat@@nat\x29;. This confuses the parser who takes thesemicolon as a comment symbol. Cure: rename-parentheses . natrecnatgrecguard etc renamed into natRec natGrecGuard.------------------------------------------------------------------------r2661 | schwicht | 2014-01-08 10:51:52 +0100 (Wed, 08 Jan 2014) | 10 lines

PVAR-NAMES renamed into PREDICATE-VARIABLES . pvar-to-string changed.If a new arity has been assigned to a pvar name, pvar-to-string uses

the default display string, as var-to-string. idpredconst-to-stringchanged: new case for OrNc. term-to-unfolded-totality-formula added.It uses alg-name-to-rtotality-idpredconst-name in case alg hasparameters (needed when normalizing proofs with elim for totality).add-rftotality alg-name-to-rftotality-idpredconst-name andadd-rltotality alg-name-to-rftotality-idpredconst-name removed. Theycan be defined by rtotal where the other parameters are substituted bytotality. term-and-alist-to-totality-formula rewritten accordingly.------------------------------------------------------------------------r2660 | schwicht | 2014-01-08 10:51:13 +0100 (Wed, 08 Jan 2014) | 12 lines

rec-at partially rewritten. In the use of nbe-object-rec-compose theproper recobj is obtained by first applying the one obtained from

rel-simalg-names-to-recobjs-alist to free-objs.constr-name-to-rec-args-indicator now is obsolete.all-formulas-to-rec-const and all-formula-to-cases-const now give anerror message in case of a nested algebra. imp-formulas-to-rec-constchanged: free kept separate from recop-type, and unfold-totality isfirst applied to imp-formulas. destruct-at changed: it now usesinjection-or-f rather than injection. If there is no disjunction inthe result (eg ntree, yprod), injection-or-f is #f and theargument-product of the constructor is returned. In case of the unitalgebra, Dummy is returned.

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------------------------------------------------------------------------r2659 | schwicht | 2014-01-08 10:50:19 +0100 (Wed, 08 Jan 2014) | 1 line

VAR-NAMES renamed into VARIABLE-NAMES.------------------------------------------------------------------------r2658 | schwicht | 2014-01-08 10:49:43 +0100 (Wed, 08 Jan 2014) | 2 lines

remove-nulltype-argtypes nested-alg-name? added.type-to-alg-with-simalg-names added.------------------------------------------------------------------------r2657 | schwicht | 2014-01-08 10:48:56 +0100 (Wed, 08 Jan 2014) | 2 lines

init-segments nonnil-init-segments string-suffix?string-replace-substrings added. Examples for string functions added.------------------------------------------------------------------------r2656 | schwicht | 2013-09-27 14:44:43 +0200 (Fri, 27 Sep 2013) | 1 line

Updated------------------------------------------------------------------------r2655 | schwicht | 2013-09-27 14:43:15 +0200 (Fri, 27 Sep 2013) | 1 line

Updated------------------------------------------------------------------------r2654 | schwicht | 2013-09-16 10:03:37 +0200 (Mon, 16 Sep 2013) | 1 line

Updated------------------------------------------------------------------------r2653 | schwicht | 2013-09-16 10:02:36 +0200 (Mon, 16 Sep 2013) | 2 lines

NatLeast and NatLeastUp updated. Adapted the Example (introducinglet) in section 6.2 Normalization.------------------------------------------------------------------------r2652 | schwicht | 2013-09-16 10:02:07 +0200 (Mon, 16 Sep 2013) | 1 line

Symm, Tran replaced by Sym, Trans.------------------------------------------------------------------------r2651 | schwicht | 2013-09-16 09:41:37 +0200 (Mon, 16 Sep 2013) | 1 line

Symm, Tran replaced by Sym, Trans.------------------------------------------------------------------------r2650 | schwicht | 2013-09-16 09:40:12 +0200 (Mon, 16 Sep 2013) | 1 line

Updated------------------------------------------------------------------------r2649 | schwicht | 2013-09-16 09:39:44 +0200 (Mon, 16 Sep 2013) | 2 lines

Names for global assumptions unified. Equal replaced by Leibnizequality EqD.------------------------------------------------------------------------r2648 | schwicht | 2013-09-16 09:39:11 +0200 (Mon, 16 Sep 2013) | 9 lines

This file real.scm should be loaded after numbers.scm. Globalassumptions already proved in numbers.scm removed. Rules forRealTimes and proof of RealTimesTotal added. This requires much ofthis file, and in particular ord-field-simp-bwd from simpreal. Henceboth are covered only here. TotalReaPos TotalReadInt TotalReaRatadded. ApproxSplit and its corollaries, together with the used globalassumptions, moved here from cont.scm. We formulate ApproxSplit withoru rather than with ex boole. The latter version is calledApproxSplitBoole and proved from the present ApproxSplit in cont.scm.

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------------------------------------------------------------------------r2647 | schwicht | 2013-09-16 09:38:37 +0200 (Mon, 16 Sep 2013) | 3 lines

Algebra real renamed into rea. This avoids a clash with data Real =RealConstr .. in average.hs produced by terms-to-haskell-program .Comment syntax with hash symbol removed.------------------------------------------------------------------------r2646 | schwicht | 2013-09-16 09:37:41 +0200 (Mon, 16 Sep 2013) | 21 lines

TranslationPosAsInt added. nat.scm always loaded if not already done.Algebra real renamed in to rea. This avoids a clash with data Real =RealConstr .. in average.hs produced by terms-to-haskell-program .Added PosTotalVar PosEqToEqD PosIfTotal PosRecTotal . Similarly forthe algebras int rat rea cpx. Computation rule for RealLt corrected.PosExpOne added, and also the rewrite rule 1**n -> 1. To transferproperties proved for nat to pos is seems best to have an inverseNatToPos to PosToNat . This requires introduction of NatEvenNatDouble and NatHalf . PosToNat redefined using NatDoubleNatToPosToNatId and PosToNatToPosId added, proving the identities.PosToNatPlus PosToNatTimes PosToNatLe PosToNatLt added, proving thatPosToNat is an isomorphism w.r.t. + *

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equality EqD and ExR are available. From them Truth := atom(True) (apreferred alternative to Truth-Axiom) is proved and added to THEOREMS.Then EqDCompat EqDCompatRev EqDSymm EqDTrans EqDCompatApp EFEqD areproven and added to THEOREMS. Also InhabTotal (needed to express thatan arbitrary type given by a type variable is inhabited) andInhabTotalMR (needed for its realizability interpretation) are provedfrom the corresponding axioms and added (in ets.scm) to THEOREMS.INITIAL-THEOREMS updated accordingly. In resetINCREASING-ALGEBRAS-TO-COERCION-ALIST commented out. simp-with-interncorrected: when testing whether the substitution of lhs by varterm haschanged the formula, the comparison should be done *without*normalization. Use formula=? rather than classical-formula=? Furtherchange in simp-with-intern : all non-normalized cases are checkedfirst, to avoid unwanted normalizations. Names in simp-withcorrected: opt-dir -> opt-dir-or-x and rest -> x-and-xs-or-xs. A goalhas ncvars as a separate field. This is a sublist of its context,containing all object and assumption variables used later forallnc-intro or impnc-intro. Obsolete: goal-to-cvars. New:context-and-ncvars-and-formula-to-formula which replacescontext-and-cvars-and-formula-to-formula . In inst-with-intern testfor nc-violations corrected. It is now done as in use-with-intern,via nc-violations of final-proof. symm replaced by sym.------------------------------------------------------------------------r2642 | schwicht | 2013-09-16 09:34:45 +0200 (Mon, 16 Sep 2013) | 7 lines

alltotal-aconst and alltotal-rev-aconst marked as obsolete (not used).alltotal-intro-aconst added (for allpartial-all-aconst ).alltotal-elim-aconst added (for all-allpartial-aconst ).allnctotal-intro-aconst and allnctotal-elim-aconst added. Inaconst-to-computed-repro-data occurence of make-stotal removed, andtypo for the Cases aconst eliminated. In check-aconst newlyintroduced assumption constants inserted. symm replaced by sym.------------------------------------------------------------------------r2641 | schwicht | 2013-09-16 09:34:01 +0200 (Mon, 16 Sep 2013) | 1 line

Display strings des and desyprod changed into Des and DesYprod.------------------------------------------------------------------------

r2640 | schwicht | 2013-09-16 09:33:25 +0200 (Mon, 16 Sep 2013) | 17 lines

default-term-to-token-tree corrected: if an alternative in an if-termdoes not have sufficiently many abstracted variables, then they aregenerated via term-to-simple-outer-eta-expansion .term-to-simple-outer-eta-expansion introduced. It takes an optionalargument l for the number of argument types to be abstracted. Incontrast to term-to-outer-eta-expansion it does not expand newlyintroduced variables. Moreover new abstracted variables are onlygenerated when necessary. Changes made by Fredrik Nordvall Forsberg(Haskell translation): (i) The list of pconst names mapped to Haskellfunctions was outdated. (ii) We sometimes added more functiondefinitions than needed, e.g. IntPred is defined in terms of PosPred,

but IntPred is translated to a builtin function, so there is no needto pull in the definition of PosPred anymore. (iii) Take the type ofconstants, not only their names, into account when deciding if theyare numeric terms. (iv) Star-types now considered in the translationof canonical inhabitants. (v) Bug repaired in the version of thetranslation which removes the measure from general recursion.------------------------------------------------------------------------r2639 | schwicht | 2013-09-16 09:32:38 +0200 (Mon, 16 Sep 2013) | 2 lines

In add-ids enforced-et-alg-names removed. One can use arbitrary

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algebra names.------------------------------------------------------------------------r2638 | schwicht | 2013-09-16 09:32:03 +0200 (Mon, 16 Sep 2013) | 1 line

RESERVED-NAMES extended, and made into a simple list.------------------------------------------------------------------------r2637 | schwicht | 2013-09-16 09:31:28 +0200 (Mon, 16 Sep 2013) | 1 line

remove-nth added.------------------------------------------------------------------------r2636 | miyamoto | 2013-06-17 13:16:06 +0200 (Mon, 17 Jun 2013) | 10 lines

Contribution by Fredrik Nordvall Forsberg.The Haskell translation treats the numerator of rational numbersin computation rules correctly.Example:(add-program-constant "TestOne" (py "rat=>int=>rat") t-deg-zero)(add-computation-rules"TestOne (IntP pos1#pos2) (IntN pos3)" "0#pos1")(terms-to-haskell-program "testone.hs"

(list (list (pt "TestOne") "testone")))

------------------------------------------------------------------------r2635 | miyamoto | 2013-06-04 12:58:50 +0200 (Tue, 04 Jun 2013) | 2 lines

The bibtex file name fixed.

------------------------------------------------------------------------r2634 | schwicht | 2013-06-02 19:04:06 +0200 (Sun, 02 Jun 2013) | 1 line

Updated------------------------------------------------------------------------r2633 | schwicht | 2013-06-02 19:00:26 +0200 (Sun, 02 Jun 2013) | 1 line

Minor changes------------------------------------------------------------------------r2632 | schwicht | 2013-06-02 18:57:23 +0200 (Sun, 02 Jun 2013) | 1 line

Minor changes------------------------------------------------------------------------r2631 | schwicht | 2013-06-02 18:56:48 +0200 (Sun, 02 Jun 2013) | 26 lines

Example (introducing let) added in section 6.2 Normalization.Example (introducing abbreviations) added in the by-assume section.Section on nat.scm added.

New names of abbreviating axioms:

AllTotalIntro (was AllPartial-All or AllTotalRev)AllTotalElim (was All-AllPartial or AllTotal)

AllncTotalIntro (was AllncPartial-Allnc or AllncTotalRev)AllncTotalElim (was Allnc-AllncPartial or AllncTotal)

For the inductively defined existential quantifiers

ExDTotalIntro (was ExDTotalRev)ExLTotalIntro (was ExLTotalRev)ExRTotalIntro (was ExRTotalRev)ExUTotalIntro (was ExUTotalRev)ExDTotalElim (was ExDTotal)

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ExLTotalElim (was ExLTotal)ExRTotalElim (was ExRTotal)ExUTotalElim (was ExUTotal)

For the primitive existential quantifier (possibly useful for efficiency)

ExTotalIntro (was ExPartial-Ex or ExTotalRev)ExTotalElim (was Ex-ExPartial or ExTotal)------------------------------------------------------------------------r2630 | schwicht | 2013-06-02 18:55:43 +0200 (Sun, 02 Jun 2013) | 3 lines

Definition of PosMinus and of RatExp corrected. Totality proofs added,also for PosMax PosMin IntAbs IntMax IntMin IntEqTotal RatEqTotalRatAbsTotal RealAbsTotal. Rewrite rule PosPred(PosS pos) -> pos added.------------------------------------------------------------------------r2629 | schwicht | 2013-06-02 18:55:08 +0200 (Sun, 02 Jun 2013) | 3 lines

LeastNat added, with theorems LeastNatTotal LeastNatBoundLeastNatLtIntro LeastNatLtElim1 LeastNatLtElim2 LeastNatEqIntroLeastNatEqElim . LeastNat supersedes AllBNat. NatMaxLUB added.------------------------------------------------------------------------r2628 | schwicht | 2013-06-02 18:54:10 +0200 (Sun, 02 Jun 2013) | 1 line

formula-with-total-extract? removed.

------------------------------------------------------------------------r2627 | schwicht | 2013-06-02 18:53:39 +0200 (Sun, 02 Jun 2013) | 3 lines

In add-theorem for lemma L degree of totality of the pconst cL changedto (term-to-t-deg (proof-to-extracted-term proof)). Usage offormula-with-total-extract? removed.------------------------------------------------------------------------r2626 | schwicht | 2013-06-02 18:52:51 +0200 (Sun, 02 Jun 2013) | 1 line

Discarded code (with add-param-alg) removed.------------------------------------------------------------------------r2625 | schwicht | 2013-05-16 21:32:16 +0200 (Thu, 16 May 2013) | 1 line

Minor update------------------------------------------------------------------------r2624 | schwicht | 2013-05-16 21:31:24 +0200 (Thu, 16 May 2013) | 1 line

Adapted to right-associative and. Dot notation removed. Definition of application notation f x simplified.------------------------------------------------------------------------r2623 | schwicht | 2013-05-16 21:29:48 +0200 (Thu, 16 May 2013) | 1 line

term-to-numerator-and-denominator rewritten, to work with general application terms------------------------------------------------------------------------r2622 | schwicht | 2013-05-16 21:27:39 +0200 (Thu, 16 May 2013) | 1 line

Updated------------------------------------------------------------------------r2621 | schwicht | 2013-05-16 21:26:50 +0200 (Thu, 16 May 2013) | 1 line

Minor changes. Mainly removal of obsolete material------------------------------------------------------------------------r2620 | schwicht | 2013-05-16 21:26:10 +0200 (Thu, 16 May 2013) | 1 line

Minor changes. Mainly removal of obsolete material

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------------------------------------------------------------------------r2619 | schwicht | 2013-05-06 13:23:21 +0200 (Mon, 06 May 2013) | 1 line

Order of arguments repaired in totality proof for RatDiv------------------------------------------------------------------------r2618 | schwicht | 2013-05-06 13:09:27 +0200 (Mon, 06 May 2013) | 1 line

Totality proofs added for RatDiv, RealPlus and RealMinus------------------------------------------------------------------------r2617 | schwicht | 2013-05-06 13:08:08 +0200 (Mon, 06 May 2013) | 3 lines

In term-to-external-expr with language scheme quotation at binaryprogram constants removed, and typo (missing parentheses) in the ifcase corrected.------------------------------------------------------------------------r2616 | schwicht | 2013-05-06 13:06:39 +0200 (Mon, 06 May 2013) | 1 line

change-t-deg-to-one typo corrected: lc -> lr------------------------------------------------------------------------r2615 | miyamoto | 2013-04-10 23:41:46 +0200 (Wed, 10 Apr 2013) | 2 lines

Minor modification in order not to get a warning message by petite.

------------------------------------------------------------------------

r2614 | miyamoto | 2013-04-03 22:19:57 +0200 (Wed, 03 Apr 2013) | 2 lines

*.save files changed. It works with petite chez scheme v8.

------------------------------------------------------------------------r2613 | miyamoto | 2013-03-20 18:27:36 +0100 (Wed, 20 Mar 2013) | 7 lines

Improvements by Fredrik Nordvall Forsberg.The definition of the constant "TranslationNatMinusPosDiff"is moved from lib/numbers.scm to lib/nat.scm.Haskell translator capitalizes the initial letter of constructor names.Programmable constant names without computation rules start with a small letter.It declares Nat and Pos as a synonym of Interger in Haskell code.

------------------------------------------------------------------------r2612 | miyamoto | 2013-02-14 11:08:23 +0100 (Thu, 14 Feb 2013) | 2 lines

Proofs was fixed to adopt the change of idpc formulas.

------------------------------------------------------------------------r2611 | miyamoto | 2013-02-12 21:55:28 +0100 (Tue, 12 Feb 2013) | 3 lines

Rounding up results.readwrite.scm is excluded from testing, since it takes long.

------------------------------------------------------------------------

r2610 | miyamoto | 2013-02-12 17:56:18 +0100 (Tue, 12 Feb 2013) | 3 lines

In examples/analysis/cauchysds.scm, Haskell translation added.examples/analysis/cauchysds.scm updated.

------------------------------------------------------------------------r2609 | miyamoto | 2013-02-08 17:24:42 +0100 (Fri, 08 Feb 2013) | 2 lines

Haskell translation (work by Fredrik Nordvall Forsberg) added.

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------------------------------------------------------------------------r2608 | miyamoto | 2013-01-30 19:03:10 +0100 (Wed, 30 Jan 2013) | 4 lines

In number-and-idpredconst-to-et-constr-term type variables to substituteare taken from algebra definitions instead of standard indexed tvars.A test case is added for this change.

------------------------------------------------------------------------r2607 | miyamoto | 2013-01-11 15:13:01 +0100 (Fri, 11 Jan 2013) | 2 lines

examples/analysis/readwrite.scm used for testing.


initial version of examples/analysis/integration.scm


Some lines are commented out, eg. time procedure which doesn'twork in some scheme interpreters.

------------------------------------------------------------------------

r2604 | miyamoto | 2013-01-04 11:19:17 +0100 (Fri, 04 Jan 2013) | 2 lines

initial version of examples/analysis/readwrite.scm.

------------------------------------------------------------------------r2603 | miyamoto | 2013-01-03 19:25:17 +0100 (Thu, 03 Jan 2013) | 2 lines

examples/analysis/cauchysds.scm added to a part of the testing.


examples/analysis/cauchysds.scm added.


*.save files in examples (other than in examples/test) updated.


Minor modification to examples/test/*.scm, mainly about comments.*.save files updated.

------------------------------------------------------------------------

r2599 | miyamoto | 2013-01-03 17:58:27 +0100 (Thu, 03 Jan 2013) | 15 lines

According to the change of the order of premises in elimination axioms,some proofs are fixed.add-theorem requires for theorems with name suffix "Sound" to have theextracted term as the realizer in the statement. Until finding a solutionto allow arbitrary realizer in the statement, suffix of some theorem namesare changed to "Real".The following theorems are the case.In lib/list.scm

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ListAppendTotalReal, ListAppdTotalReal, ListLengthTotalReal, ListProjTotalRealIn lib/numbers.scmPosEqTotalReal, PosSTotalReal, PosPredTotalReal, PosPlusTotalReal,PosMinusTotalReal, PosTimesTotalReal, PosLtTotalReal, PosLeTotalReal,BooleIfTotalReal, IntPlusTotalReal, IntMinusTotalReal, IntTimesTotalReal,RatPlusTotalReal, RatMinusTotalReal, RatTimesTotalReal.


impnc added


token-tree-tag-to-precedence corrected: alg-typeop has one less thanthe maximal precedence


idpredconst-name-to-spos-param-pvars idpredconst-to-spos-pvarsformula-to-spos-pvars added. add-ids adapted to nested clauses.idpc-clause? removed. For simplicity it is required that nullary

clauses come first in the listing of clauses. This makesclauses-with-idpc-pvars-to-nullary-clauses superfluous. Minorcleanup in add-mr-ids . formula-to-et-type-for-mr-clauses adaptedto nestedness by referring to a newidpredconst-to-et-type-for-mr-clauses . In the imp/impnc case ofreal-and-idpc-clause-to-mr-idpc-clause allnc, impnc replaced by all,imp. This modifies the IMR clauses which allows in the IMR case toconstruct the correct formula inimp-formulas-to-uninst-elim-formulas-etc .real-and-idpc-clause-to-mr-idpc-clause is similar toreal-and-formula-to-mr-formula-aux . The difference is in the usageof the local pvar-to-mr-pvar (with special results for idpc-pvars)and formula-to-et-type-for-mr-clauses. add-co extended to nested

clauses.


Introduction of application notation simplified: add-applicationtakes an application operator as argument.


make-map-const type-etc-to-map-const map-at and map-at-intern added.In alg-name-etc-to-rec-const rec-at nbe-object-rec-compose usage of

apply made more readable (no cons needed for initial arguments).Recursion and corec-const-and-bound-to-bcorec-term adapted to nestedalgebras. corec-const-to-uninst-alg-or-arrow-types corrected.


imp-formulas-to-mr-elim-proof corrected in case (car imp-formulas)is c.i.: then the lists gs are all empty (cf. [SW12, p.344]). Inimp-formulas-to-mr-elim-proof pvar-to-tvar replaced by PVAR-TO-TVAR

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idpredconst-to-mr-idpredconst adapted to nested algebras. AndLadded. imp-formulas-to-et-rec-const adapted to nested algebras.


andl included. formula-to-efq-proof simplified.unfold-total-variables fold-total-variables fold-to-unfoldunfold-to-fold fold-imp-unfold-proof added.constructor-eqd-proof-to-args-eqd-proof corrected (arg-type -> alg)


check-aconst adapted to ElimMR.mr-elim-aconst-to-computed-repro-formulas added.non-computational-invariant? adapted to andl.

alltotal-aconst alltotal-rev-aconstallnctotal-aconst allnctotal-rev-aconst exdtotal-aconstexltotal-aconst exrtotal-aconst exutotal-aconst exdtotal-rev-aconstexltotal-rev-aconst exrtotal-rev-aconst exutotal-rev-aconstextotal-aconst extotal-rev-aconst total-pair-aconsttotal-pair-rev-aconst added. In add-theorem error identification

corrected for soundness theorems.

imp-formulas-to-uninst-elim-formulas-etc adapted to nested idpcs.imp-formulas-to-elim-aconst returns ElimMR aconst in IMR case.formula-to-prem-modified-formula added.imp-form-to-param-premises-and-rec-prems-imp-final-conclrec-premise-of-idpc-clause? (appeared twice)idpc-clause-to-rec-premisesimp-form-to-param-premises-imp-rec-prems-imp-final-concl removed.strictly-positive? removed. It is superseded by type-to-spos-tvarsand formula-to-spos-pvars .


unfold-simplified-simrec-appterm and simplify-simrec-apptermadapted. first-match rewritten to accomodate inductive predicates.pattern-and-instance-to-tsubst-aux extended to deal with Total x^and TotalNat n^ (as in match-aux).


andl included


casedist added (was forgotten). andl included. elim-intern adaptedto the fact that the uninst-formula of an elim-aconst for IMR startswith all x. In inversion-intern, simplified-inversion-intern andcases-intern the obsolete make-eq replaced by make-eqd. Inx-and-x-list-to-proof-and-new-num-goals-and-maxgoal partialarguments for and-const and imp-const allowed.

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minima and choices added.


type-to-free renamed into type-to-tvars . In make-substitution-wrterror message improved. (type-gen-substitute type gen-tsubst)substitutes simultaneously the left hand sides of the alistgen-tsubst by the corresponding right hand sides. gen-subst is analist associating types to types. alg-name-to-spos-tvarsalg-to-spos-tvars type-to-spos-tvars added. finalg? adapted tonested algebras. add-algebras-with-parameters extended to nestedalgebras. To add algebras use add-algs. Example:

(add-algs (list "list") 'prefix-typeop '("list" "Nil") '("alpha=>list=>list" "Cons"))

Parallel to add-ids, the constructor names are optional and hencewritten after the type-string. However, since by convention algebranames start with a lower case character and constructor names with

an upper case character we can also use the opposite order (asbefore). We require that the constructor types are given in a fixedorder, where nullary constructor types come first.type-to-canonical-inhabitant adapted (should be renamed intotype-to-total-inhabitant ).

constr-types-with-names-and-rest-names-to-inhabcritstype-to-inhabcrits alg-name-to-constr-types-with-names added.


COMMENT-STRING changed.


Token andL added. make-ysumu and make-uysum added.

------------------------------------------------------------------------r2583 | miyamoto | 2013-01-01 16:53:10 +0100 (Tue, 01 Jan 2013) | 2 lines

examples/test.scm and examples/test.save removed.

------------------------------------------------------------------------r2582 | miyamoto | 2013-01-01 16:49:56 +0100 (Tue, 01 Jan 2013) | 2 lines

test.scm is split into sections and placed in examples/test.

------------------------------------------------------------------------r2581 | miyamoto | 2012-12-27 03:01:15 +0100 (Thu, 27 Dec 2012) | 2 lines

converting comments in "#| ... |#" to ";; ".


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converting comments in "#| ... |#" to ";; ".


all test files work in the COQ goal display.


Adopting COQ-GOAL-DISPLAY to be #t for testing.


Fixing existing examples for testing.

------------------------------------------------------------------------r2576 | schwicht | 2012-10-24 15:32:14 +0200 (Wed, 24 Oct 2012) | 1 line

Bibtex reference to minlog.bib------------------------------------------------------------------------r2575 | schwicht | 2012-10-22 11:47:03 +0200 (Mon, 22 Oct 2012) | 1 line

Bibtex reference updated------------------------------------------------------------------------r2574 | schwicht | 2012-10-18 17:08:14 +0200 (Thu, 18 Oct 2012) | 1 line

Updated------------------------------------------------------------------------r2573 | schwicht | 2012-10-18 17:04:30 +0200 (Thu, 18 Oct 2012) | 2 lines

COQ-GOAL-DISPLAY set to false. by-assume-with replaced by by-assume.display-constructors replaced by display-alg.------------------------------------------------------------------------r2572 | schwicht | 2012-10-18 16:58:11 +0200 (Thu, 18 Oct 2012) | 1 line

makeindex added for tutor.------------------------------------------------------------------------r2571 | schwicht | 2012-10-18 16:57:22 +0200 (Thu, 18 Oct 2012) | 2 lines

by-assume-with replaced by by-assume. display-constructors replacedby display-alg. Index added.------------------------------------------------------------------------r2570 | schwicht | 2012-10-18 16:56:32 +0200 (Thu, 18 Oct 2012) | 2 lines

Updated and extended. New subsection on Basic proof constructionsadded.------------------------------------------------------------------------

r2569 | schwicht | 2012-10-18 16:55:48 +0200 (Thu, 18 Oct 2012) | 1 line

Updated minlogman and SchwichtenbergWainer------------------------------------------------------------------------r2568 | schwicht | 2012-10-18 16:53:54 +0200 (Thu, 18 Oct 2012) | 2 lines

ListNatEqToEqD added (for use in compat-at, to avoid Equal).ListNatEqTotal BooleEqTotal ListBooleEqToEqD ListBooleEqTotal added.------------------------------------------------------------------------r2567 | schwicht | 2012-10-18 16:53:17 +0200 (Thu, 18 Oct 2012) | 2 lines

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Theorem BooleEqToEqD added (for use in NatMinusPlusEq when simp isapplied to NatMinusPlus).------------------------------------------------------------------------r2566 | schwicht | 2012-10-18 16:51:53 +0200 (Thu, 18 Oct 2012) | 1 line

Removed ../doc/ref.tex ../doc/tutor.tex from TAGS------------------------------------------------------------------------r2565 | schwicht | 2012-10-18 16:50:57 +0200 (Thu, 18 Oct 2012) | 1 line

check-formula should check predicates------------------------------------------------------------------------r2564 | schwicht | 2012-10-18 16:48:52 +0200 (Thu, 18 Oct 2012) | 1 line

Typo corrected------------------------------------------------------------------------r2563 | schwicht | 2012-10-18 16:47:48 +0200 (Thu, 18 Oct 2012) | 1 line

Very minor simplification------------------------------------------------------------------------r2562 | schwicht | 2012-10-18 16:45:55 +0200 (Thu, 18 Oct 2012) | 1 line

Discarded code removed------------------------------------------------------------------------

r2561 | schwicht | 2012-10-18 16:44:21 +0200 (Thu, 18 Oct 2012) | 1 line

Typos corrected------------------------------------------------------------------------r2560 | schwicht | 2012-10-18 16:42:21 +0200 (Thu, 18 Oct 2012) | 7 lines

inhabtotal-aconst and inhabtotalmr-aconst moved here from axiom.scm.Theorems InhabTotal and InhabTotalMR added. imp-const-total-proofor-const-total-proof neg-const-total-proof pair-one-total-proofpair-two-total-proof added. Theorems ImpConstTotal OrConstTotalNegConstTotal PairOneTotal PairTwoTotal added.constructors-overlap-imp-falsity-proof moved to proof.scm from here.truth-proof and theorem Truth added.

------------------------------------------------------------------------r2559 | schwicht | 2012-10-18 16:41:09 +0200 (Thu, 18 Oct 2012) | 4 lines

InhabTotal and InhabTotalMR removed from INITIAL-THEOREMS . They willbe proved from the respective axioms in ets.scm and added to THEOREMS. formula-to-efq-proof renamed into formula-to-efq-proof-or-f , since itis used as a test in inversion and simplified-inversion , and occursonly there. strip-intern adapted to inductively defined connectives.------------------------------------------------------------------------r2558 | schwicht | 2012-10-18 16:39:36 +0200 (Thu, 18 Oct 2012) | 15 lines

formula-to-efq-proof renamed into formula-to-efq-proof-or-f , since itis used as a test in inversion and simplified-inversion , and occurs

only there. A new section 10-8 Basic proof constructions has beenadded. There a proper formula-to-efq-proof is provided, which returnsa proof of F --> A . make-proof-in-iterated-imp-elim-form andeqd-proofs-and-predicate-proof-to-proof added. To generate proofs ofthe injectivity of constructorsconstructor-eqd-proof-to-args-eqd-proof added. It expects aneqd-proof of C rs eqd C ss with the same constructor C and C rs ofground type, and an optional index (with default value 0). The resultis a proof of ri eqd si. constructor-eqd-imp-args-eqd-proof issimilar, but expects an eqd-formula rather than an eqd-proof, and

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proves the implication C rs eqd C ss --> ri eqd si.constructors-overlap-imp-falsity-proof moved from ets.scm to here. Itis used for formula-to-efq-proof and this in turn for inversion.------------------------------------------------------------------------r2557 | schwicht | 2012-10-18 16:38:50 +0200 (Thu, 18 Oct 2012) | 3 lines

Degrees of totality changed to t-deg-zero for pconsts Inhab AndConstImpConst OrConst NegConst PairOne PairTwo. Duplicated falsity-log(commented out) removed.------------------------------------------------------------------------r2556 | schwicht | 2012-10-18 16:38:02 +0200 (Thu, 18 Oct 2012) | 2 lines

In add-theorem special treatment of Inhab removed. inhabtotal-aconstand inhabtotalmr-aconst moved from here to axiom.scm.------------------------------------------------------------------------r2555 | schwicht | 2012-10-18 16:37:03 +0200 (Thu, 18 Oct 2012) | 5 lines

Duplicated term-to-totality-formula (commented out) removed. Inadd-ids it is checked that taking the initial clause of each idpcproduces clauses without recursive calls which are terminating. Inclauses-with-idpc-pvars-to-nullary-clauses imp-form-to-premisesreplaced by imp-impnc-form-to-premises.------------------------------------------------------------------------r2554 | schwicht | 2012-10-18 16:36:18 +0200 (Thu, 18 Oct 2012) | 3 lines

In change-t-deg-to-one new-rhs and new-lhs generated by term-gen-substfor pconst and new-pconst, rather than by first producing a displaystring and then parsing this string.------------------------------------------------------------------------r2553 | schwicht | 2012-10-18 16:35:00 +0200 (Thu, 18 Oct 2012) | 1 line

list-tabulate and find-tail added.------------------------------------------------------------------------r2552 | schwicht | 2012-03-16 08:58:36 +0100 (Fri, 16 Mar 2012) | 1 line

Updated------------------------------------------------------------------------

r2551 | schwicht | 2012-03-16 08:57:50 +0100 (Fri, 16 Mar 2012) | 2 lines

permutative-aconst-proof-to-eta-expansion-aux corrected:proof-to-formula replaced by aconst-to-inst-formula------------------------------------------------------------------------r2550 | schwicht | 2012-03-15 21:57:19 +0100 (Thu, 15 Mar 2012) | 1 line

Updated------------------------------------------------------------------------r2549 | schwicht | 2012-03-15 21:56:19 +0100 (Thu, 15 Mar 2012) | 2 lines

Removed add-totality for pos and int. They are already innumbers.scm.

------------------------------------------------------------------------r2548 | schwicht | 2012-03-15 21:55:36 +0100 (Thu, 15 Mar 2012) | 1 line

Removed add-mr-ids for TotalNat. It is already in lib/nat.scm.------------------------------------------------------------------------r2547 | schwicht | 2012-03-13 23:38:36 +0100 (Tue, 13 Mar 2012) | 1 line

Updated------------------------------------------------------------------------r2546 | schwicht | 2012-03-13 23:26:31 +0100 (Tue, 13 Mar 2012) | 1 line

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RatEq replaced by RatEqv------------------------------------------------------------------------r2545 | schwicht | 2012-03-13 23:25:46 +0100 (Tue, 13 Mar 2012) | 4 lines

In ord-field-simp-bwd the newly generated global assumptionex k RealLt 0(abs x)k -> ... 0 ... -> atom -> simp-atomnow is formulated (as it should) with an integer k, not a pos.RatEq replaced by RatEqv------------------------------------------------------------------------r2544 | schwicht | 2012-03-13 23:25:03 +0100 (Tue, 13 Mar 2012) | 1 line

Updated------------------------------------------------------------------------r2543 | schwicht | 2012-03-13 23:21:30 +0100 (Tue, 13 Mar 2012) | 1 line

Updated------------------------------------------------------------------------r2542 | schwicht | 2012-03-13 23:20:56 +0100 (Tue, 13 Mar 2012) | 8 lines

Added totality proofs. The successor S for pos renamed in PosS, toavoind conflict with the reserved name STotal. CpxMax CpxMin removed.SOne pos1--SZero pos2 mapsto SZero pos1--(SZero pos2--1) replaced bymapsto SOne(pos1--pos2). ALGEBRA-EDGE-TO-EMBED-TERM-ALIST needs to be

updated once PosToNat and NatToInt have been proved to be total.replace-item-in-algebra-edge-to-embed-term-alist provided for this.Postponed: some rewrite rules, and totality proofs of PosMax PosMin.RatEq renamed into RatEqv to avoid clash with ordinary equality.------------------------------------------------------------------------r2541 | schwicht | 2012-03-13 23:20:22 +0100 (Tue, 13 Mar 2012) | 4 lines

TotalListMR and STotalListMR added. ListAppendTotalSoundListAppendSTotalSound ListAppendNilPartialSound ListAppdTotalSoundListAppdSTotalSound ListAppdNilPartialSound ListLengthTotalSoundListLengthSTotalSound ListProjTotal ListProjTotalSound added.------------------------------------------------------------------------r2540 | schwicht | 2012-03-13 23:19:53 +0100 (Tue, 13 Mar 2012) | 29 lines

TotalNatMR added. Inductively defined predicate TotalBoole moved toboole.scm. (add-theorem AndConstTotal and-const-total-proof) movedto ets.scm. NatIfTotal NatEqTotal NatLtToLe and NatLeGeToEq added.NatLtToLePred and NatLtMonPred added. NatEqToEqD added. NatIfTotalNatEqTotal NatLtToLe and NatLeGeToEq added. NatLtToLePred andNatLtMonPred added. Monotonicity properties NatLeMonPlus,NatLeMonTimes, NatLeMonPred, NatLeMonMinus added. NatPlusMinusNatMinusPlus NatMinusPlusEq NatMinusMinus added. Further rewriterules added:

nat1*Pred nat2 => nat1*nat2--nat1Pred nat2*nat1 => nat2*nat1--nat1

nat1*(nat2--nat3) => nat1*nat2--nat1*nat3(nat2--nat3)*nat1 => nat2*nat1--nat3*nat1

nat1+nat2 Falsenat1+nat2 False

nat1 TruePred nat Truenat1--nat2 True

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0--nat => 0nat1+nat2--nat2 => nat1nat2+nat1--nat2 => nat1nat1--nat2--nat3 => nat1--(nat2+nat3)

Renamed Nat=Trans into NatEqTrans, etc. Generally: = -> Eq. ForLeibniz equality use EqD------------------------------------------------------------------------r2539 | schwicht | 2012-03-13 23:10:49 +0100 (Tue, 13 Mar 2012) | 33 lines

In formula-to-et-type treatment of preconst TotalMR included.formula-of-nulltype? and formula-of-nulltype-under-extension? in thepreconst case Total corrected (the result then must be #f).proof-to-extracted-term-aux corrected for an ExR elim aconst withc.i. kernel. proof-to-extracted-term and theorem-to-extracted-termget an unfold-let-flag as optional argument. If it is present andtrue, than cId's will be unfolded. axiom-to-extracted-termtheorem-to-extracted-term and global-assumption-to-extracted-termadded. imp-formulas-to-et-rec-const adapted to c.r. Total predconsts.efeqd-proof added. This allows to put EFEqD into THEOREMS whenloading init. It is done here, since the proof uses EqDCompat.constructors-overlap-imp-falsity-proof added. This can be used forformula-to-efq-proof and this in turn for inversion. Added (beforethe internal proof of soundness): and-const-total-proof

boole-if-total-proof . Theorem BooleIfTotal added.idpredconst-to-mr-idpredconst corrected. Inreal-and-formula-to-mr-formula-aux c.r. idpcs with identity instead ofan alg name (i.e., ExL, ExR, ExLT, ExRT, AndR) are treated separately.In the predconst case the predconst Total (which is c.r.) gets aspecial treatment. Local variable pvar-to-mr-pvar replaced byreference to a newly introduced global variable PVAR-TO-MR-PVAR, whichrefers to and updates PVAR-TO-MR-PVAR-ALIST.proof-to-soundness-proof-aux extended to Intro and Elim axioms forinductively defined predicates. Auxiliary functionsnumber-and-idpredconst-to-intro-mr-proof imp-formulas-to-mr-elim-proofproof-to-allnc-impnc-proofreal-mr-clause-proof-and-clause-to-clause-proof

allnc-impnc-to-exu-imp-proof added. exl-formula-to-exl-intro-mr-proofexr-formula-to-exr-intro-mr-proof exu-formula-to-exu-intro-mr-proofandr-formula-to-andr-intro-mr-proofeqd-elim-aconst-to-eqd-mr-elim-proof added. axiom-to-soundness-prooftheorem-to-soundness-proof and global-assumption-to-soundness-proofadded. proof-to-soundness-formula added.------------------------------------------------------------------------r2538 | schwicht | 2012-03-13 23:10:08 +0100 (Tue, 13 Mar 2012) | 2 lines

elem-form? redefined, to make formulas built with (inductivelydefined) binary connectives (ord, andd etc) elementary.------------------------------------------------------------------------r2537 | schwicht | 2012-03-13 23:09:24 +0100 (Tue, 13 Mar 2012) | 20 lines

set-goal displays the goal with the originally chosen variable names:it uses display-num-goal with fold-formula only. This overrides thedefault display function (with rename-variables) in display-num-goal .Error message introduced for sg . INITIAL-THEOREMS updated,InhabTotalMR included. INITIAL-COQ-GOAL-DISPLAY set to true.display-num-goal uses rename-variables (default case). If renaming ofvariables in a goal is not desired, usedisplay-current-goal-with-original-variables abbreviated dcgo .assert and cut both accept a string as argument, which is parsed into

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a formula. drop-except added. In (drop-except . x-list), x-list is alist of numbers or strings identifying hypotheses from the context. Anew goal is created, which differs from the previous one only indisplay aspects: all hypotheses except the listed ones are hidden (butstill present). split extended to inductively defined conjunctionsandd andr andu. msplit adapted to right-associative and. ex-introaccepts a string as argument, which is parsed into a term. compat-atand compat-rev-at rewritten, using Leibniz equality EqD rather thanEqual. This makes Equal obsolete. Auxiliary functionsfinalg-to-string and finalg-to-=-to-eqd-aconst added.simphyp-with-intern corrected. simp-with-to removed.------------------------------------------------------------------------r2536 | schwicht | 2012-03-13 23:08:15 +0100 (Tue, 13 Mar 2012) | 14 lines

Corrected (free variables were forgotten):make-proof-in-andd-elim-left-form make-proof-in-andd-elim-right-formmake-proof-in-andr-elim-left-form make-proof-in-andr-elim-right-formmake-proof-in-andu-elim-left-form make-proof-in-andu-elim-right-fordisplay-proof display-normalized-proof proof-to-expr andproof-to-expr-with-formulas now have opt-proof-or-thm-name asargument. opt-proof-or-thm-name-and-ignore-deco-flag now hasopt-proof-or-thm-name-and-ignore-deco-flag as argument. Adapted toadmissible substitutions: proof-to-goedel-gentzen-translation-auxspreading-formula-to-proof spreading-formula-to-proof-aux

wiping-formula-to-proof wiping-formula-to-proof-auxisolating-formula-to-proof isolating-formula-to-proof-aux Suffix Real(for realize) changed to MR. In reset TotalMR included. Typocorrected: myerreor -> myerror.------------------------------------------------------------------------r2535 | schwicht | 2012-03-13 23:07:37 +0100 (Tue, 13 Mar 2012) | 30 lines

aconst=? gives #f in case one argument is not of aconst form.check-aconst corrected for Elim and Gfp aconsts. total-aconstremoved. It is obsolete because Total f unfolds via unfold-formulainto allnc x^(Total x^ -> Total(f x^)). STotal make-stotalstotal-aconst and the initial theorem Stotal removed. Reason:stotality does not make sense abstractly, but only for an algebra.

There it can be defined inductively. Example: STotalList.constr-name-to-constr-total-aconst removed: this is just what theclauses of TotalNat say.constr-name-and-index-to-constr-total-args-aconst removed. Reason:TotalNat(Succ n^) -> TotalNat n^ can be proved by inversion (cftest.scm for the idpc Even). total-pair-aconst and total-proj-aconstremoved, because for instance Total(x^ @y^) unfolds via unfold-formulainto Total x^ & Total y^ . Moreover one should use the inductivelydefined TotalYprod(x^ pair y^) instead. finalg-to-eq-to-=-1-aconstand finalg-to-eq-to-=-2-aconst and finalg-to-=-to-eq-aconst areobsolete because Equal is. TotalInhab renamed into InhabTotal.inhabtotalmr-aconst added. sfinalg-to-se-to-stotal-aconst andsfinalg-to-stotal-to-se-aconst removed since they contain the obsolete

predconct STotal. allnc-allncpartial-aconst and its converseallncpartial-allnc-aconst and also ex-expartial-aconstexpartial-ex-aconst exnc-exncpartial-aconst exncpartial-exnc-aconstconflict with Total being c.r. and are discarded.idpc-clause-to-rec-premises added. non-computational-invariant?extended to inductively defined connectives.theorem-or-global-assumption-name-to-pconst-name changed:RatTimesTotal maps to RatTimes, not cRatTimesTotal. add-theoremadapted to the case where the theorem name ends with Total.add-global-assumption accepts a string as argument, which is parsed

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into a formula. Suffix Real (for realize) changed to MR.------------------------------------------------------------------------r2534 | schwicht | 2012-03-13 23:03:25 +0100 (Tue, 13 Mar 2012) | 1 line

STotal removed and TotalMR added predconst-names.------------------------------------------------------------------------r2533 | schwicht | 2012-03-13 23:02:47 +0100 (Tue, 13 Mar 2012) | 5 lines

make-totalmr added. formula-substitute extended to predconst TotalMR.make-stotal removed. unfold-formula now unfolds (Total r) viaterm-to-totality-formula and (TotalMR r0 r) viaterms-to-mr-totality-formula. rename-variables-aux simplified foridentity substitutions. formula-subst-and-beta0-nf added.------------------------------------------------------------------------r2532 | schwicht | 2012-03-13 23:02:17 +0100 (Tue, 13 Mar 2012) | 27 lines

Suffix Real (for realize) changed to MR. terms-to-mr-totality-formulaalg-to-mr-totality-idpredconst andalg-name-to-mr-totality-idpredconst-name added.string-and-arity-to-predconst-parse-function rewritten withformula-substitute, to parse Total and (arity nat) into TotalNat.check-idpredconst added, as test function for idpredconsts. If theargument is not an idpredconst, an error is returned.idpredconst-name-to-tvars corrected for mr-idpcs. We must distinguish

whether we have an original idpc or an mr-idpc. In the former casetake orig-idpredconst-name-to-tvars, i.e., the tvars in the originalclauses. In the latter case from et-types take all tvars associatedto param-pvars. These mr-tvars are appended in front of orig-tvars.add-ids-aux adapted: param-tvars and param-pvars are only computedafter idpc-names are added to IDS. This enables the newidpredconst-name-to-tvars (which distinguishes original idpc-names andmr-idpc-names) to produce correct results. add-mr-ids corrected.cr-param-pvars and ci-param-pvars treated differently. Its auxiliaryfunctions formula-to-et-type-for-mr-clauses andreal-and-idpc-clause-to-mr-idpc-clause both need additional argumentsmr-et-tvars and idpc-pvars. Notice that the generalreal-and-formula-to-mr-formula-aux does not need these additional

arguments mr-et-tvars and idpc-pvars: in the pvar case the h-deg ofthe pvar suffices. term-to-totality-formula andterm-to-stotality-formula corrected for terms with type in star form.In real-and-idpc-clause-to-mr-idpc-clause andformula-to-et-type-for-mr-clauses in the predconst case the predconstTotal (which is c.r.) gets a special treatment.------------------------------------------------------------------------r2531 | schwicht | 2012-03-13 23:01:38 +0100 (Tue, 13 Mar 2012) | 4 lines

token-tree-to-string extended to tokens case-op and caseitem-op.Auxiliary function token-tree-tag-to-precedence added.token-tree-to-pp-tree added. pretty-print-with-case-display(abbreviated ppc) added.

------------------------------------------------------------------------r2530 | schwicht | 2012-03-13 23:00:14 +0100 (Tue, 13 Mar 2012) | 14 lines

app-term-with-low-original-types? added. It is used interm-to-token-tree, to display coercions where the strategy of doingarthmetical operations at the lowest possible level has not beenobserved. Example: (IntPlus pos n) has this display, not (pos+n).The pconst RealPos does not appear, since it has no special display.formula-to-token-tree need not be changed, since a prime formula iseither given by a boolean term or else has no special display

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(examples: RealEq RealNNeg RealLe). default-term-to-token-tree incase term-in-if-form and a newly introduced global variableCASE-DISPLAY is true returns a token tree with case-op, which includestoken trees with case-item. In term-to-expr NatMax and NatMin etcallowed. term-in-rec-normal-form? corrected. term-to-rec-nf added.match-aux extended to match Total xs with TotalList ns.huet-unifiers-rigid-rigid extended similarly.------------------------------------------------------------------------r2529 | schwicht | 2012-03-13 22:59:46 +0100 (Tue, 13 Mar 2012) | 7 lines

display-pconst corrected for external code. In add-rewrite-rulereference (via make-eq) to the obsolete predicate constant Equalremoved. In change-t-deg-to-one usage of (term-to-string lhs)replaced by (token-tree-to-string (default-term-to-token-tree lhs)).This avoids disappearance of coercion functions like NatToInt, whichcan lead to type errors in subsequent parsing. In destruct-at wrongparenthesis moved to the right place.------------------------------------------------------------------------r2528 | schwicht | 2012-03-13 22:59:08 +0100 (Tue, 13 Mar 2012) | 5 lines

TotalMR added as reserved name. check-admissible-tpsubst added, astest function for tpsubsts. If the argument is not an admissibletpsubst, an error is returned. type-match-modulo-coercion-auxcorrected. For the rigid components of the type type-le? had to be

used in the ~other direction.------------------------------------------------------------------------r2527 | schwicht | 2012-03-13 22:58:09 +0100 (Tue, 13 Mar 2012) | 1 line

list-and-test-to-head-up-to-last added.------------------------------------------------------------------------r2526 | schwicht | 2012-03-13 22:57:16 +0100 (Tue, 13 Mar 2012) | 1 line

Theory of spreading, wiping and isolating formulas included.------------------------------------------------------------------------r2525 | miyamoto | 2011-10-10 20:10:43 +0200 (Mon, 10 Oct 2011) | 3 lines

The latest minitab.scm from the latest grammar.scm.

In pconst.scm, a bug in destruct-at fixed.

------------------------------------------------------------------------r2524 | schwicht | 2011-08-27 16:52:09 +0200 (Sat, 27 Aug 2011) | 1 line

Updated------------------------------------------------------------------------r2523 | schwicht | 2011-08-27 16:50:59 +0200 (Sat, 27 Aug 2011) | 2 lines

Proof of totality of Test updated. Totality predicate for the algebrapar added.------------------------------------------------------------------------r2522 | schwicht | 2011-08-27 16:49:53 +0200 (Sat, 27 Aug 2011) | 4 lines

Adapted to the the new convention in psym.scm: in add-idset-constr-names written with capital C followed by the clause name(like CInitEv) to avoid clash with program constants for theclause-theorems. Hence we need CGenQ rather than cGenQ.------------------------------------------------------------------------r2521 | schwicht | 2011-08-14 15:32:47 +0200 (Sun, 14 Aug 2011) | 1 line

Initial commit------------------------------------------------------------------------

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r2520 | schwicht | 2011-08-14 14:52:24 +0200 (Sun, 14 Aug 2011) | 1 line

Updated------------------------------------------------------------------------r2519 | schwicht | 2011-08-14 14:51:41 +0200 (Sun, 14 Aug 2011) | 1 line

Extended.------------------------------------------------------------------------r2518 | schwicht | 2011-08-14 14:50:33 +0200 (Sun, 14 Aug 2011) | 1 line

Major extension, and adaption to the present state.------------------------------------------------------------------------r2517 | schwicht | 2011-08-14 14:49:12 +0200 (Sun, 14 Aug 2011) | 1 line

For tutor.tex second call to pdflatex and dependencies added.------------------------------------------------------------------------r2516 | schwicht | 2011-08-14 14:48:26 +0200 (Sun, 14 Aug 2011) | 1 line

Updated, and sychronized with examples/tutor.scm.------------------------------------------------------------------------r2515 | schwicht | 2011-08-14 14:47:03 +0200 (Sun, 14 Aug 2011) | 1 line

Adapted to list.scm (not listrev.scm which should be removed).------------------------------------------------------------------------

r2514 | schwicht | 2011-08-14 14:46:29 +0200 (Sun, 14 Aug 2011) | 1 line

Adapted to list.scm (not listrev.scm which should be removed).------------------------------------------------------------------------r2513 | schwicht | 2011-08-14 14:45:21 +0200 (Sun, 14 Aug 2011) | 1 line

Major cleanup and extension.------------------------------------------------------------------------r2512 | schwicht | 2011-08-14 14:44:38 +0200 (Sun, 14 Aug 2011) | 6 lines

atom-to-eqd-true-aconst and eqd-true-to-atom-aconst added.formula-to-et-type for the predicate constant Total_rho returns rho.idpredconst-to-et-type corrected: et-types must use all clauses. In

number-and-idpredconst-to-et-constr-term et-constr-names written withcapital C followed by the clause name (like CInitEv) to avoid clashwith program constants for the clause-theorems.------------------------------------------------------------------------r2511 | schwicht | 2011-08-14 14:44:09 +0200 (Sun, 14 Aug 2011) | 8 lines

by-assume and by-assume-intern extended to the inductively definedexistential quantifiers exd, exr, exl, exu. exnc marked as obsolete.It can be replaced by exr. Display function for display-num-goal nowhas as default case (lambda (fla) (rename-variables (fold-formulafla))). STotal as a premise in ind and simind and cases and casedistwith a partial variable removed: one should use elim instead.dec-stotal-cases-proof removed. coind-intern corrected in the

simultaneous case.------------------------------------------------------------------------r2510 | schwicht | 2011-08-14 14:43:41 +0200 (Sun, 14 Aug 2011) | 2 lines

proof-substitute changed to avoid superfluous renaming (work of AntonFreund).------------------------------------------------------------------------r2509 | schwicht | 2011-08-14 14:43:14 +0200 (Sun, 14 Aug 2011) | 14 lines

check-aconst adapted to atom-to-eqd-true-aconst and

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eqd-true-to-atom-aconst. Both all-allpartial-aconst andallpartial-all-aconst written with allnc alpha^(Total alpha^ -> (Pvaralpha)alpha^) rather than with all alpha^(Total alpha^ -> (Pvaralpha)alpha^). This is necessary since the predicate constant Totalis c.r. In all-formulas-to-uninst-imp-formulas-and-tpsubst onlyall-formulas with total variables are allowed. stotal-imp-formula?stotal-or-se-imp-formula? stotal-or-se-or-e-imp-formula?all-partial-stotal-imp-formula? marked as obsolete.imp-formulas-to-uninst-gfp-formulas-etc corrected in the simultaneouscase: all clauses are needed, and the original ordering of the idpcsneeds to be introduced at various places (corrections due to KenjiMiyamoto). In add-theorem totality-flag is used to indicate that noproof of totality is needed.------------------------------------------------------------------------r2508 | schwicht | 2011-08-14 14:42:45 +0200 (Sun, 14 Aug 2011) | 3 lines

Token and display for desyprod (destructor w.r.t. yprod) added.term-to-components rewritten. It now works for the primitive product(via make-star) as well as for the defined product (via make-yprod).------------------------------------------------------------------------r2507 | schwicht | 2011-08-14 14:41:53 +0200 (Sun, 14 Aug 2011) | 3 lines

make-eq marked as obsolete. mk-and rewritten. make-and-without-truthadded. In formula-substitute the predicate form Total r now uses

term-to-totality-formula for the substituted term r.------------------------------------------------------------------------r2506 | schwicht | 2011-08-14 14:41:21 +0200 (Sun, 14 Aug 2011) | 2 lines

pretty-print-string uses rename-variables for names of theorems orglobal-assumptions.------------------------------------------------------------------------r2505 | schwicht | 2011-08-14 14:40:55 +0200 (Sun, 14 Aug 2011) | 3 lines

nbe-mk-prod-obj added. rec-op-and-args-to-if-term rewritten.simplify-simrec-appterm corrected: alg-names-with-val-tvars shouldremain in the order given by the recursion operator.------------------------------------------------------------------------

r2504 | schwicht | 2011-08-14 14:40:06 +0200 (Sun, 14 Aug 2011) | 22 lines

clauses-with-idpc-pvars-to-nullary-clauses added. It is used inadd-ids to check that nullary clauses are present (and might be usedin formula-to-efq-proof to construct such a proof for an idpc). Inadd-ids-aux total program constants for the clause-theorems added. Inadd-ids et-constr-names written with capital C followed by the clausename (like CInitEv) to avoid clash with program constants for theclause-theorems. term-to-totality-formula extended to terms of typein star form. add-stotality and its auxiliary functionalg-name-to-stotality-clauses-and-pvars removed. Instead one shoulduse add-ids with the proper clauses for e.g. STotalList. Then one canprovide a known alg name (nat in this case).

term-to-stotality-formula rewritten. For an sfinalg it uses STotalAlgrather than TotalAlg, assuming STotalAlg exists (otherwise: error) Inalg-name-to-totality-clauses-and-pvars pvar name totality-idpc-namereplaced by the empty string. In add-totality double occurrence ofconstr-names-list removed. display-idpc added. remove-idpc-namecorrected (more was to be removed). add-co takes an optional argumentopt-prim-prod-flag. If this is not present or true, the clause isformed with mk-ex, mk-and (generating extracted terms with theprimitive product make-star). If this is present and #f, the clauseis formed with mk-exi, mk-andu, mk-andd (generating extracted terms

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with the defined product yprod)------------------------------------------------------------------------r2503 | schwicht | 2011-08-14 14:39:33 +0200 (Sun, 14 Aug 2011) | 17 lines

In add-program-constant an optional totality-flag can indicate that noproof of totality is needed. display-pconst added. It replacesdisplay-program-constants and display-program-constant. Terminologyin arrow-types-to-uninst-recop-types-and-tsubst clarified.alg-or-arrow-types-to-uninst-corecop-types-and-tsubst corrected in thesimultaneous case: the uninst-step-types need to be taken in theiroriginal order (correction due to Kenji Miyamoto). Incorec-const-and-bound-to-bcorec-term again in the simultaneous casethe resulting application term of product type (with a recursionconstant as operator) is replaced by an appropriate component. Thismakes both bcorec-term-and-alg-name-to-component andbcorec-term-and-alg-name-to-component-aux (which were originallyintended for this purpose) superfluous. They are discarded.display-constructors renamed into display-alg and moved to typ.scm.undelay-delayed-corec corrected: terms in lcomp and rcomp formincluded. alg-to-uninst-destr-type-and-tsubst alg-to-destr-const anddestruct-at all take opt-prim-prod-flag as an optional argument.------------------------------------------------------------------------r2502 | schwicht | 2011-08-14 14:38:49 +0200 (Sun, 14 Aug 2011) | 6 lines

mk-star added. In compose-substitutionscompose-substitutions-and-beta-nf compose-substitutions-and-beta0-nfit is now checked that the second substitution is admissible for thevalues of the first substitution (work of Anton Freund).display-constructors renamed into display-alg and moved frompconst.scm to typ.scm.------------------------------------------------------------------------r2501 | schwicht | 2011-08-14 14:38:08 +0200 (Sun, 14 Aug 2011) | 3 lines

Inductively defined predicate TotalList added. Arguments of Consnswitched: the parameter argument now comes first. Usage offinalg-to-e-to-total-aconst removed from proofs totality theorems.------------------------------------------------------------------------

r2500 | schwicht | 2011-08-14 14:37:32 +0200 (Sun, 14 Aug 2011) | 3 lines

Inductively defined predicate TotalNat and TotalBoole added. Usageof finalg-to-e-to-total-aconst removed from the proof ofNatPlusTotal and other totality theorems.------------------------------------------------------------------------r2499 | schwicht | 2011-08-14 14:34:26 +0200 (Sun, 14 Aug 2011) | 1 line

Renamed. Was tutorial.scm------------------------------------------------------------------------r2498 | schwicht | 2011-06-18 16:56:23 +0200 (Sat, 18 Jun 2011) | 1 line

Updated

------------------------------------------------------------------------r2497 | schwicht | 2011-06-18 16:55:11 +0200 (Sat, 18 Jun 2011) | 2 lines

arrow-types-to-corec-const replaced byalg-or-arrow-types-to-corec-const------------------------------------------------------------------------

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