Version 4.5.0 provides a major update to the invariant generation and proving techniques for differential equations in its automated ODE tactic.
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[New] Pegasus invariant generator for differential equations
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[New] ODE automation tactics for axiomatic proofs from differential ghost and differential refinement axioms, proofs of barrier certificates, and proofs of invariance properties that involve Darboux polynomials
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[Preview] Invariant generation for loops based on fixpoint-search over invariants for differential equations
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[Tactics] Liveness: loop convergence with user-definable convergence variable, improved <:=> assignment tactics
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[Tactics] Extended proof search automation in the context of universal/existential quantifiers
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[Tools] C code generator for structured monitors with sub-routines and error message printing
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[New] Tactic
barrierproves barrier certificates of ODEs (automatically used inODEtactic)
For example, provex>=0 |- [{x'=100*x^4+y*x^3-x^2+x+c, c'=x+y+z & c>x}]x>=0
with tacticbarrier(1)or tacticODE(1) -
[New] Tactic
dbxproves ODEs using Darboux polynomials (automatically used inODEtactic)
For example, provex+z<0 |- [{x'=x^2, z'=z*x+y & y=-x^2}]x+z<0
with tacticdbx({x},1)or tacticODE(1) -
[New] Model documentation and proof hints with
@invariantannotations for ODEs
For example, provide a list of two differential invariants:
[{x'=2,y'=-1} @invariant(x>=old(x), /* x increases */ y<=old(y)) /* y descreases */ ]p() -
[New] Conditional differential invariant annotations
For example, provide a list of two differential invariants, one for each branch:
[{a:=2; ++ a:=-1;} ; {x'=a} @invariant( (x'=2 -> x>=old(x)), /* x increases */ (x'=-1 -> x<=old(x))) /* x decreases */ ]p() -
[UI] Performance improvements
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[Tactics] Tactic
dWnow keeps all initial conditions -
[Tactics] Configurable timeouts for tactics
QEandODE(configuration file keymaerax.conf) -
[Tactics] Combinator
s > truns tacticsfirst and then tactictregardless of the result ofs
- [UI] New web UI axiom and proof step browser
- [UI] Hint display and tactic popover fixes
- [Performance] Significant performance improvements by disabling logging by default
- [Tactics] New loop induction with abstraction
throughout(inv,pos)for loopsinit -> [{a;b}*]safe
proves loop from subgoals
base case:init -> inv
use case:inv -> safe
induction steps:inv -> [a]invandinv -> [b]inv
- Backend tool and tactic stability improvements
- [New] Store and use lemma entries in .kyx archives:
Store: Lemma "My lemma". ... End. to store the given lemma under the identified name "My lemma".
Use:
useLemma({`My lemma`},{`prop`})to close goal by lemma, use propositional reasoning to adapt shape
useLemmaAt({`My lemma`},{`1`},2)to match lemma expression at sub-position 1 with formula at sequent position 2 - [New] Convert proof terms to Isabelle dL proof checker
- [New] Configuration is now stored in a text file: ~/.keymaerax/keymaerax.conf
- [New] Transform hybrid programs to C control code
KeYmaera X version 4.4
- [Core] New: N-ary formula and function definitions.
For example,
define a binary function 'sum' as: sum(R,R) = ( ._0 + ._1).
define predicate 'sumgt' as: sumgt(R,R,R) <-> ( sum(._0,._1) > ._2 ). - [Parser] New: Program definitions.
For example, HP increment ::= { x:=x+1; }. - [Tactics] New: use finished proofs as lemmas, for example useLemma({
Name of proved model}) when the open goal matches the lemma literally, useLemma({Name of proved model}, {prop}) to apply the lemma with propositional reasoning. - [Tools] New: proof statistics after checking archives with -check
- [Tools] New: C control code synthesis (feature preview)
- [Tools] Improved: C monitor code synthesis (feature preview)
- Stability improvements: archive checking, ODE solution ordering
Version 4.3.16 of the KeYmaera X Theorem Prover
- [Tactics] Three new tactics for automatic approximation of
{e'=e}and{s'=c, c'=-s}
out tonterms in the series expansion.circularApproximate(s,c,n,pos): For circular dynamics{s'=c, c'=-s}.expApproximate(e,n,pos): for{e'=e}.autoApproximate(n,pos): Tries to find{e'=c}then tries to find.
{s'=c,c'=-s}and applies the relevant approximation tactic.
- [UI] The startup sequence is improved.
- The status indicator now actually indicates status.
- We no longer automatically open a browser window on Linux, since this
caused hanging on some machines.
- [UI] Formula editing
- Expand functions min/max/abs, e.g., expand(abs(0)) >= 0
- Abbreviate terms, e.g., x+abbrv(2+3,five) >= 0
- [UI] Search and apply lemmas
- Auto-completion search box in the formula dialog
- Click lemma subformulas to adjust the direction in which lemmas are applied
- [Parser] Bug fix in how numbers are pretty-printed.
- [Tactics] Various improvements to the tactics framework and standard library.
Version 4.3.15 of the KeYmaera X theorem prover
- UI: Improvements to presentation and /show mode
- UI: Render nullary function symbols without parentheses
- Updates Z3 to 4.5.0, improved QE support for machines without Mathematica.
- Improved update code for Windows.
Version 4.3.14 of the KeYmaera X theorem prover.
- Fix: ODE solve tactic printing
Version 4.3.13 of the KeYmaera X theorem prover.
- New: model editing
- New: proof step justification with rule/axiom in proof browsing
- Feature preview: exercise models with placeholders
- Web UI and backend fixes
Version 4.3.12 of the KeYmaera X theorem prover
- New: step-by-step proof browsing
- New: tactic tooltips on proof step in sequent proofs
- Improved proof step highlighting
- User interface and backend stability improvements