src/HOL/SMT.thy
author wenzelm
Sat, 07 Apr 2012 16:41:59 +0200
changeset 47389 e8552cba702d
parent 47152 446cfc760ccf
child 47701 157e6108a342
permissions -rw-r--r--
explicit checks stable_finished_theory/stable_command allow parallel asynchronous command transactions; tuned;
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
36898
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
     1
(*  Title:      HOL/SMT.thy
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
     2
    Author:     Sascha Boehme, TU Muenchen
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
     3
*)
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
     4
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
     5
header {* Bindings to Satisfiability Modulo Theories (SMT) solvers *}
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
     6
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
     7
theory SMT
41426
09615ed31f04 re-implemented support for datatypes (including records and typedefs);
boehmes
parents: 41328
diff changeset
     8
imports Record
46950
d0181abdbdac declare command keywords via theory header, including strict checking outside Pure;
wenzelm
parents: 45392
diff changeset
     9
keywords "smt_status" :: diag
36898
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
    10
uses
41124
1de17a2de5ad moved SMT classes and dictionary functions to SMT_Utils
boehmes
parents: 41121
diff changeset
    11
  "Tools/SMT/smt_utils.ML"
40424
7550b2cba1cb better modularization: moved SMT configuration options and diagnostics as well as SMT failure and exception into separate structures (both of which are loaded first and consequently are available to other SMT structures)
boehmes
parents: 40277
diff changeset
    12
  "Tools/SMT/smt_failure.ML"
7550b2cba1cb better modularization: moved SMT configuration options and diagnostics as well as SMT failure and exception into separate structures (both of which are loaded first and consequently are available to other SMT structures)
boehmes
parents: 40277
diff changeset
    13
  "Tools/SMT/smt_config.ML"
40277
4e3a3461c1a6 added crafted list of SMT built-in constants
boehmes
parents: 40274
diff changeset
    14
  ("Tools/SMT/smt_builtin.ML")
41426
09615ed31f04 re-implemented support for datatypes (including records and typedefs);
boehmes
parents: 41328
diff changeset
    15
  ("Tools/SMT/smt_datatypes.ML")
36898
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
    16
  ("Tools/SMT/smt_normalize.ML")
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
    17
  ("Tools/SMT/smt_translate.ML")
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
    18
  ("Tools/SMT/smt_solver.ML")
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
    19
  ("Tools/SMT/smtlib_interface.ML")
41328
6792a5c92a58 avoid ML structure aliases (especially single-letter abbreviations)
boehmes
parents: 41281
diff changeset
    20
  ("Tools/SMT/z3_interface.ML")
36898
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
    21
  ("Tools/SMT/z3_proof_parser.ML")
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
    22
  ("Tools/SMT/z3_proof_tools.ML")
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
    23
  ("Tools/SMT/z3_proof_literals.ML")
40662
798aad2229c0 added prove reconstruction for injective functions;
boehmes
parents: 40424
diff changeset
    24
  ("Tools/SMT/z3_proof_methods.ML")
36898
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
    25
  ("Tools/SMT/z3_proof_reconstruction.ML")
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
    26
  ("Tools/SMT/z3_model.ML")
40162
7f58a9a843c2 joined setup of SMT solvers in one place; turned Z3-specific options into SMT options (renamed configuration options from z3_* to smt_*); more detailed SMT exception; improved SMT filter interface
boehmes
parents: 39483
diff changeset
    27
  ("Tools/SMT/smt_setup_solvers.ML")
36898
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
    28
begin
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
    29
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
    30
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
    31
36902
c6bae4456741 use 'subsection' instead of 'section', to maintain 1 chapter per file in generated document
huffman
parents: 36899
diff changeset
    32
subsection {* Triggers for quantifier instantiation *}
36898
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
    33
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
    34
text {*
41125
4a9eec045f2a added option to enable trigger inference;
boehmes
parents: 41124
diff changeset
    35
Some SMT solvers support patterns as a quantifier instantiation
4a9eec045f2a added option to enable trigger inference;
boehmes
parents: 41124
diff changeset
    36
heuristics.  Patterns may either be positive terms (tagged by "pat")
4a9eec045f2a added option to enable trigger inference;
boehmes
parents: 41124
diff changeset
    37
triggering quantifier instantiations -- when the solver finds a
4a9eec045f2a added option to enable trigger inference;
boehmes
parents: 41124
diff changeset
    38
term matching a positive pattern, it instantiates the corresponding
4a9eec045f2a added option to enable trigger inference;
boehmes
parents: 41124
diff changeset
    39
quantifier accordingly -- or negative terms (tagged by "nopat")
4a9eec045f2a added option to enable trigger inference;
boehmes
parents: 41124
diff changeset
    40
inhibiting quantifier instantiations.  A list of patterns
4a9eec045f2a added option to enable trigger inference;
boehmes
parents: 41124
diff changeset
    41
of the same kind is called a multipattern, and all patterns in a
4a9eec045f2a added option to enable trigger inference;
boehmes
parents: 41124
diff changeset
    42
multipattern are considered conjunctively for quantifier instantiation.
4a9eec045f2a added option to enable trigger inference;
boehmes
parents: 41124
diff changeset
    43
A list of multipatterns is called a trigger, and their multipatterns
4a9eec045f2a added option to enable trigger inference;
boehmes
parents: 41124
diff changeset
    44
act disjunctively during quantifier instantiation.  Each multipattern
4a9eec045f2a added option to enable trigger inference;
boehmes
parents: 41124
diff changeset
    45
should mention at least all quantified variables of the preceding
4a9eec045f2a added option to enable trigger inference;
boehmes
parents: 41124
diff changeset
    46
quantifier block.
36898
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
    47
*}
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
    48
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
    49
datatype pattern = Pattern
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
    50
37124
fe22fc54b876 hide constants and types introduced by SMT,
boehmes
parents: 36902
diff changeset
    51
definition pat :: "'a \<Rightarrow> pattern" where "pat _ = Pattern"
fe22fc54b876 hide constants and types introduced by SMT,
boehmes
parents: 36902
diff changeset
    52
definition nopat :: "'a \<Rightarrow> pattern" where "nopat _ = Pattern"
36898
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
    53
37124
fe22fc54b876 hide constants and types introduced by SMT,
boehmes
parents: 36902
diff changeset
    54
definition trigger :: "pattern list list \<Rightarrow> bool \<Rightarrow> bool"
36898
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
    55
where "trigger _ P = P"
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
    56
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
    57
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
    58
40664
e023788a91a1 added support for quantifier weight annotations
boehmes
parents: 40662
diff changeset
    59
subsection {* Quantifier weights *}
e023788a91a1 added support for quantifier weight annotations
boehmes
parents: 40662
diff changeset
    60
e023788a91a1 added support for quantifier weight annotations
boehmes
parents: 40662
diff changeset
    61
text {*
e023788a91a1 added support for quantifier weight annotations
boehmes
parents: 40662
diff changeset
    62
Weight annotations to quantifiers influence the priority of quantifier
e023788a91a1 added support for quantifier weight annotations
boehmes
parents: 40662
diff changeset
    63
instantiations.  They should be handled with care for solvers, which support
e023788a91a1 added support for quantifier weight annotations
boehmes
parents: 40662
diff changeset
    64
them, because incorrect choices of weights might render a problem unsolvable.
e023788a91a1 added support for quantifier weight annotations
boehmes
parents: 40662
diff changeset
    65
*}
e023788a91a1 added support for quantifier weight annotations
boehmes
parents: 40662
diff changeset
    66
e023788a91a1 added support for quantifier weight annotations
boehmes
parents: 40662
diff changeset
    67
definition weight :: "int \<Rightarrow> bool \<Rightarrow> bool" where "weight _ P = P"
e023788a91a1 added support for quantifier weight annotations
boehmes
parents: 40662
diff changeset
    68
e023788a91a1 added support for quantifier weight annotations
boehmes
parents: 40662
diff changeset
    69
text {*
e023788a91a1 added support for quantifier weight annotations
boehmes
parents: 40662
diff changeset
    70
Weights must be non-negative.  The value @{text 0} is equivalent to providing
e023788a91a1 added support for quantifier weight annotations
boehmes
parents: 40662
diff changeset
    71
no weight at all.
e023788a91a1 added support for quantifier weight annotations
boehmes
parents: 40662
diff changeset
    72
e023788a91a1 added support for quantifier weight annotations
boehmes
parents: 40662
diff changeset
    73
Weights should only be used at quantifiers and only inside triggers (if the
e023788a91a1 added support for quantifier weight annotations
boehmes
parents: 40662
diff changeset
    74
quantifier has triggers).  Valid usages of weights are as follows:
e023788a91a1 added support for quantifier weight annotations
boehmes
parents: 40662
diff changeset
    75
e023788a91a1 added support for quantifier weight annotations
boehmes
parents: 40662
diff changeset
    76
\begin{itemize}
e023788a91a1 added support for quantifier weight annotations
boehmes
parents: 40662
diff changeset
    77
\item
e023788a91a1 added support for quantifier weight annotations
boehmes
parents: 40662
diff changeset
    78
@{term "\<forall>x. trigger [[pat (P x)]] (weight 2 (P x))"}
e023788a91a1 added support for quantifier weight annotations
boehmes
parents: 40662
diff changeset
    79
\item
e023788a91a1 added support for quantifier weight annotations
boehmes
parents: 40662
diff changeset
    80
@{term "\<forall>x. weight 3 (P x)"}
e023788a91a1 added support for quantifier weight annotations
boehmes
parents: 40662
diff changeset
    81
\end{itemize}
e023788a91a1 added support for quantifier weight annotations
boehmes
parents: 40662
diff changeset
    82
*}
e023788a91a1 added support for quantifier weight annotations
boehmes
parents: 40662
diff changeset
    83
e023788a91a1 added support for quantifier weight annotations
boehmes
parents: 40662
diff changeset
    84
e023788a91a1 added support for quantifier weight annotations
boehmes
parents: 40662
diff changeset
    85
36902
c6bae4456741 use 'subsection' instead of 'section', to maintain 1 chapter per file in generated document
huffman
parents: 36899
diff changeset
    86
subsection {* Higher-order encoding *}
36898
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
    87
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
    88
text {*
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
    89
Application is made explicit for constants occurring with varying
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
    90
numbers of arguments.  This is achieved by the introduction of the
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
    91
following constant.
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
    92
*}
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
    93
41127
2ea84c8535c6 re-implemented eta-expansion, lambda-lifting, and explicit application on terms (exploiting the control over the term structure);
boehmes
parents: 41126
diff changeset
    94
definition fun_app where "fun_app f = f"
36898
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
    95
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
    96
text {*
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
    97
Some solvers support a theory of arrays which can be used to encode
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
    98
higher-order functions.  The following set of lemmas specifies the
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
    99
properties of such (extensional) arrays.
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   100
*}
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   101
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   102
lemmas array_rules = ext fun_upd_apply fun_upd_same fun_upd_other
37157
86872cbae9e9 added function update examples and set examples
boehmes
parents: 37153
diff changeset
   103
  fun_upd_upd fun_app_def
36898
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   104
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   105
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   106
36902
c6bae4456741 use 'subsection' instead of 'section', to maintain 1 chapter per file in generated document
huffman
parents: 36899
diff changeset
   107
subsection {* First-order logic *}
36898
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   108
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   109
text {*
41059
d2b1fc1b8e19 centralized handling of built-in types and constants;
boehmes
parents: 40806
diff changeset
   110
Some SMT solvers only accept problems in first-order logic, i.e.,
d2b1fc1b8e19 centralized handling of built-in types and constants;
boehmes
parents: 40806
diff changeset
   111
where formulas and terms are syntactically separated. When
d2b1fc1b8e19 centralized handling of built-in types and constants;
boehmes
parents: 40806
diff changeset
   112
translating higher-order into first-order problems, all
d2b1fc1b8e19 centralized handling of built-in types and constants;
boehmes
parents: 40806
diff changeset
   113
uninterpreted constants (those not built-in in the target solver)
36898
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   114
are treated as function symbols in the first-order sense.  Their
41059
d2b1fc1b8e19 centralized handling of built-in types and constants;
boehmes
parents: 40806
diff changeset
   115
occurrences as head symbols in atoms (i.e., as predicate symbols) are
41281
679118e35378 removed odd decoration of built-in symbols as Vars (instead provide built-in desctructor functions along with their inverse functions);
boehmes
parents: 41280
diff changeset
   116
turned into terms by logically equating such atoms with @{term True}.
679118e35378 removed odd decoration of built-in symbols as Vars (instead provide built-in desctructor functions along with their inverse functions);
boehmes
parents: 41280
diff changeset
   117
For technical reasons, @{term True} and @{term False} occurring inside
679118e35378 removed odd decoration of built-in symbols as Vars (instead provide built-in desctructor functions along with their inverse functions);
boehmes
parents: 41280
diff changeset
   118
terms are replaced by the following constants.
36898
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   119
*}
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   120
41281
679118e35378 removed odd decoration of built-in symbols as Vars (instead provide built-in desctructor functions along with their inverse functions);
boehmes
parents: 41280
diff changeset
   121
definition term_true where "term_true = True"
679118e35378 removed odd decoration of built-in symbols as Vars (instead provide built-in desctructor functions along with their inverse functions);
boehmes
parents: 41280
diff changeset
   122
definition term_false where "term_false = False"
679118e35378 removed odd decoration of built-in symbols as Vars (instead provide built-in desctructor functions along with their inverse functions);
boehmes
parents: 41280
diff changeset
   123
36898
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   124
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   125
37151
3e9e8dfb3c98 use Z3's builtin support for div and mod
boehmes
parents: 37124
diff changeset
   126
subsection {* Integer division and modulo for Z3 *}
3e9e8dfb3c98 use Z3's builtin support for div and mod
boehmes
parents: 37124
diff changeset
   127
3e9e8dfb3c98 use Z3's builtin support for div and mod
boehmes
parents: 37124
diff changeset
   128
definition z3div :: "int \<Rightarrow> int \<Rightarrow> int" where
3e9e8dfb3c98 use Z3's builtin support for div and mod
boehmes
parents: 37124
diff changeset
   129
  "z3div k l = (if 0 \<le> l then k div l else -(k div (-l)))"
3e9e8dfb3c98 use Z3's builtin support for div and mod
boehmes
parents: 37124
diff changeset
   130
3e9e8dfb3c98 use Z3's builtin support for div and mod
boehmes
parents: 37124
diff changeset
   131
definition z3mod :: "int \<Rightarrow> int \<Rightarrow> int" where
3e9e8dfb3c98 use Z3's builtin support for div and mod
boehmes
parents: 37124
diff changeset
   132
  "z3mod k l = (if 0 \<le> l then k mod l else k mod (-l))"
3e9e8dfb3c98 use Z3's builtin support for div and mod
boehmes
parents: 37124
diff changeset
   133
3e9e8dfb3c98 use Z3's builtin support for div and mod
boehmes
parents: 37124
diff changeset
   134
3e9e8dfb3c98 use Z3's builtin support for div and mod
boehmes
parents: 37124
diff changeset
   135
36902
c6bae4456741 use 'subsection' instead of 'section', to maintain 1 chapter per file in generated document
huffman
parents: 36899
diff changeset
   136
subsection {* Setup *}
36898
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   137
40277
4e3a3461c1a6 added crafted list of SMT built-in constants
boehmes
parents: 40274
diff changeset
   138
use "Tools/SMT/smt_builtin.ML"
41426
09615ed31f04 re-implemented support for datatypes (including records and typedefs);
boehmes
parents: 41328
diff changeset
   139
use "Tools/SMT/smt_datatypes.ML"
36898
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   140
use "Tools/SMT/smt_normalize.ML"
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   141
use "Tools/SMT/smt_translate.ML"
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   142
use "Tools/SMT/smt_solver.ML"
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   143
use "Tools/SMT/smtlib_interface.ML"
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   144
use "Tools/SMT/z3_interface.ML"
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   145
use "Tools/SMT/z3_proof_parser.ML"
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   146
use "Tools/SMT/z3_proof_tools.ML"
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   147
use "Tools/SMT/z3_proof_literals.ML"
40662
798aad2229c0 added prove reconstruction for injective functions;
boehmes
parents: 40424
diff changeset
   148
use "Tools/SMT/z3_proof_methods.ML"
36898
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   149
use "Tools/SMT/z3_proof_reconstruction.ML"
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   150
use "Tools/SMT/z3_model.ML"
40162
7f58a9a843c2 joined setup of SMT solvers in one place; turned Z3-specific options into SMT options (renamed configuration options from z3_* to smt_*); more detailed SMT exception; improved SMT filter interface
boehmes
parents: 39483
diff changeset
   151
use "Tools/SMT/smt_setup_solvers.ML"
36898
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   152
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   153
setup {*
40424
7550b2cba1cb better modularization: moved SMT configuration options and diagnostics as well as SMT failure and exception into separate structures (both of which are loaded first and consequently are available to other SMT structures)
boehmes
parents: 40277
diff changeset
   154
  SMT_Config.setup #>
41059
d2b1fc1b8e19 centralized handling of built-in types and constants;
boehmes
parents: 40806
diff changeset
   155
  SMT_Normalize.setup #>
36898
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   156
  SMT_Solver.setup #>
41059
d2b1fc1b8e19 centralized handling of built-in types and constants;
boehmes
parents: 40806
diff changeset
   157
  SMTLIB_Interface.setup #>
d2b1fc1b8e19 centralized handling of built-in types and constants;
boehmes
parents: 40806
diff changeset
   158
  Z3_Interface.setup #>
36898
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   159
  Z3_Proof_Reconstruction.setup #>
40162
7f58a9a843c2 joined setup of SMT solvers in one place; turned Z3-specific options into SMT options (renamed configuration options from z3_* to smt_*); more detailed SMT exception; improved SMT filter interface
boehmes
parents: 39483
diff changeset
   160
  SMT_Setup_Solvers.setup
36898
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   161
*}
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   162
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   163
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   164
36902
c6bae4456741 use 'subsection' instead of 'section', to maintain 1 chapter per file in generated document
huffman
parents: 36899
diff changeset
   165
subsection {* Configuration *}
36898
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   166
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   167
text {*
36899
bcd6fce5bf06 layered SMT setup, adapted SMT clients, added further tests, made Z3 proof abstraction configurable
boehmes
parents: 36898
diff changeset
   168
The current configuration can be printed by the command
bcd6fce5bf06 layered SMT setup, adapted SMT clients, added further tests, made Z3 proof abstraction configurable
boehmes
parents: 36898
diff changeset
   169
@{text smt_status}, which shows the values of most options.
36898
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   170
*}
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   171
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   172
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   173
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   174
subsection {* General configuration options *}
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   175
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   176
text {*
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   177
The option @{text smt_solver} can be used to change the target SMT
41432
3214c39777ab differentiate between local and remote SMT solvers (e.g., "z3" vs. "remote_z3");
boehmes
parents: 41426
diff changeset
   178
solver.  The possible values can be obtained from the @{text smt_status}
3214c39777ab differentiate between local and remote SMT solvers (e.g., "z3" vs. "remote_z3");
boehmes
parents: 41426
diff changeset
   179
command.
41459
f0db8f40d656 added hints about licensing restrictions and how to enable Z3
boehmes
parents: 41432
diff changeset
   180
f0db8f40d656 added hints about licensing restrictions and how to enable Z3
boehmes
parents: 41432
diff changeset
   181
Due to licensing restrictions, Yices and Z3 are not installed/enabled
f0db8f40d656 added hints about licensing restrictions and how to enable Z3
boehmes
parents: 41432
diff changeset
   182
by default.  Z3 is free for non-commercial applications and can be enabled
41462
5f4939d46b63 tuned text
boehmes
parents: 41459
diff changeset
   183
by simply setting the environment variable @{text Z3_NON_COMMERCIAL} to
5f4939d46b63 tuned text
boehmes
parents: 41459
diff changeset
   184
@{text yes}.
36898
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   185
*}
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   186
41601
fda8511006f9 made Z3 the default SMT solver again
boehmes
parents: 41462
diff changeset
   187
declare [[ smt_solver = z3 ]]
36898
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   188
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   189
text {*
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   190
Since SMT solvers are potentially non-terminating, there is a timeout
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   191
(given in seconds) to restrict their runtime.  A value greater than
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   192
120 (seconds) is in most cases not advisable.
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   193
*}
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   194
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   195
declare [[ smt_timeout = 20 ]]
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   196
40162
7f58a9a843c2 joined setup of SMT solvers in one place; turned Z3-specific options into SMT options (renamed configuration options from z3_* to smt_*); more detailed SMT exception; improved SMT filter interface
boehmes
parents: 39483
diff changeset
   197
text {*
41121
5c5d05963f93 added option to modify the random seed of SMT solvers
boehmes
parents: 41059
diff changeset
   198
SMT solvers apply randomized heuristics.  In case a problem is not
5c5d05963f93 added option to modify the random seed of SMT solvers
boehmes
parents: 41059
diff changeset
   199
solvable by an SMT solver, changing the following option might help.
5c5d05963f93 added option to modify the random seed of SMT solvers
boehmes
parents: 41059
diff changeset
   200
*}
5c5d05963f93 added option to modify the random seed of SMT solvers
boehmes
parents: 41059
diff changeset
   201
5c5d05963f93 added option to modify the random seed of SMT solvers
boehmes
parents: 41059
diff changeset
   202
declare [[ smt_random_seed = 1 ]]
5c5d05963f93 added option to modify the random seed of SMT solvers
boehmes
parents: 41059
diff changeset
   203
5c5d05963f93 added option to modify the random seed of SMT solvers
boehmes
parents: 41059
diff changeset
   204
text {*
40162
7f58a9a843c2 joined setup of SMT solvers in one place; turned Z3-specific options into SMT options (renamed configuration options from z3_* to smt_*); more detailed SMT exception; improved SMT filter interface
boehmes
parents: 39483
diff changeset
   205
In general, the binding to SMT solvers runs as an oracle, i.e, the SMT
7f58a9a843c2 joined setup of SMT solvers in one place; turned Z3-specific options into SMT options (renamed configuration options from z3_* to smt_*); more detailed SMT exception; improved SMT filter interface
boehmes
parents: 39483
diff changeset
   206
solvers are fully trusted without additional checks.  The following
7f58a9a843c2 joined setup of SMT solvers in one place; turned Z3-specific options into SMT options (renamed configuration options from z3_* to smt_*); more detailed SMT exception; improved SMT filter interface
boehmes
parents: 39483
diff changeset
   207
option can cause the SMT solver to run in proof-producing mode, giving
7f58a9a843c2 joined setup of SMT solvers in one place; turned Z3-specific options into SMT options (renamed configuration options from z3_* to smt_*); more detailed SMT exception; improved SMT filter interface
boehmes
parents: 39483
diff changeset
   208
a checkable certificate.  This is currently only implemented for Z3.
7f58a9a843c2 joined setup of SMT solvers in one place; turned Z3-specific options into SMT options (renamed configuration options from z3_* to smt_*); more detailed SMT exception; improved SMT filter interface
boehmes
parents: 39483
diff changeset
   209
*}
7f58a9a843c2 joined setup of SMT solvers in one place; turned Z3-specific options into SMT options (renamed configuration options from z3_* to smt_*); more detailed SMT exception; improved SMT filter interface
boehmes
parents: 39483
diff changeset
   210
7f58a9a843c2 joined setup of SMT solvers in one place; turned Z3-specific options into SMT options (renamed configuration options from z3_* to smt_*); more detailed SMT exception; improved SMT filter interface
boehmes
parents: 39483
diff changeset
   211
declare [[ smt_oracle = false ]]
7f58a9a843c2 joined setup of SMT solvers in one place; turned Z3-specific options into SMT options (renamed configuration options from z3_* to smt_*); more detailed SMT exception; improved SMT filter interface
boehmes
parents: 39483
diff changeset
   212
7f58a9a843c2 joined setup of SMT solvers in one place; turned Z3-specific options into SMT options (renamed configuration options from z3_* to smt_*); more detailed SMT exception; improved SMT filter interface
boehmes
parents: 39483
diff changeset
   213
text {*
7f58a9a843c2 joined setup of SMT solvers in one place; turned Z3-specific options into SMT options (renamed configuration options from z3_* to smt_*); more detailed SMT exception; improved SMT filter interface
boehmes
parents: 39483
diff changeset
   214
Each SMT solver provides several commandline options to tweak its
7f58a9a843c2 joined setup of SMT solvers in one place; turned Z3-specific options into SMT options (renamed configuration options from z3_* to smt_*); more detailed SMT exception; improved SMT filter interface
boehmes
parents: 39483
diff changeset
   215
behaviour.  They can be passed to the solver by setting the following
7f58a9a843c2 joined setup of SMT solvers in one place; turned Z3-specific options into SMT options (renamed configuration options from z3_* to smt_*); more detailed SMT exception; improved SMT filter interface
boehmes
parents: 39483
diff changeset
   216
options.
7f58a9a843c2 joined setup of SMT solvers in one place; turned Z3-specific options into SMT options (renamed configuration options from z3_* to smt_*); more detailed SMT exception; improved SMT filter interface
boehmes
parents: 39483
diff changeset
   217
*}
7f58a9a843c2 joined setup of SMT solvers in one place; turned Z3-specific options into SMT options (renamed configuration options from z3_* to smt_*); more detailed SMT exception; improved SMT filter interface
boehmes
parents: 39483
diff changeset
   218
41432
3214c39777ab differentiate between local and remote SMT solvers (e.g., "z3" vs. "remote_z3");
boehmes
parents: 41426
diff changeset
   219
declare [[ cvc3_options = "", remote_cvc3_options = "" ]]
3214c39777ab differentiate between local and remote SMT solvers (e.g., "z3" vs. "remote_z3");
boehmes
parents: 41426
diff changeset
   220
declare [[ yices_options = "" ]]
3214c39777ab differentiate between local and remote SMT solvers (e.g., "z3" vs. "remote_z3");
boehmes
parents: 41426
diff changeset
   221
declare [[ z3_options = "", remote_z3_options = "" ]]
40162
7f58a9a843c2 joined setup of SMT solvers in one place; turned Z3-specific options into SMT options (renamed configuration options from z3_* to smt_*); more detailed SMT exception; improved SMT filter interface
boehmes
parents: 39483
diff changeset
   222
7f58a9a843c2 joined setup of SMT solvers in one place; turned Z3-specific options into SMT options (renamed configuration options from z3_* to smt_*); more detailed SMT exception; improved SMT filter interface
boehmes
parents: 39483
diff changeset
   223
text {*
7f58a9a843c2 joined setup of SMT solvers in one place; turned Z3-specific options into SMT options (renamed configuration options from z3_* to smt_*); more detailed SMT exception; improved SMT filter interface
boehmes
parents: 39483
diff changeset
   224
Enable the following option to use built-in support for datatypes and
7f58a9a843c2 joined setup of SMT solvers in one place; turned Z3-specific options into SMT options (renamed configuration options from z3_* to smt_*); more detailed SMT exception; improved SMT filter interface
boehmes
parents: 39483
diff changeset
   225
records.  Currently, this is only implemented for Z3 running in oracle
7f58a9a843c2 joined setup of SMT solvers in one place; turned Z3-specific options into SMT options (renamed configuration options from z3_* to smt_*); more detailed SMT exception; improved SMT filter interface
boehmes
parents: 39483
diff changeset
   226
mode.
7f58a9a843c2 joined setup of SMT solvers in one place; turned Z3-specific options into SMT options (renamed configuration options from z3_* to smt_*); more detailed SMT exception; improved SMT filter interface
boehmes
parents: 39483
diff changeset
   227
*}
7f58a9a843c2 joined setup of SMT solvers in one place; turned Z3-specific options into SMT options (renamed configuration options from z3_* to smt_*); more detailed SMT exception; improved SMT filter interface
boehmes
parents: 39483
diff changeset
   228
7f58a9a843c2 joined setup of SMT solvers in one place; turned Z3-specific options into SMT options (renamed configuration options from z3_* to smt_*); more detailed SMT exception; improved SMT filter interface
boehmes
parents: 39483
diff changeset
   229
declare [[ smt_datatypes = false ]]
7f58a9a843c2 joined setup of SMT solvers in one place; turned Z3-specific options into SMT options (renamed configuration options from z3_* to smt_*); more detailed SMT exception; improved SMT filter interface
boehmes
parents: 39483
diff changeset
   230
41125
4a9eec045f2a added option to enable trigger inference;
boehmes
parents: 41124
diff changeset
   231
text {*
4a9eec045f2a added option to enable trigger inference;
boehmes
parents: 41124
diff changeset
   232
The SMT method provides an inference mechanism to detect simple triggers
4a9eec045f2a added option to enable trigger inference;
boehmes
parents: 41124
diff changeset
   233
in quantified formulas, which might increase the number of problems
4a9eec045f2a added option to enable trigger inference;
boehmes
parents: 41124
diff changeset
   234
solvable by SMT solvers (note: triggers guide quantifier instantiations
4a9eec045f2a added option to enable trigger inference;
boehmes
parents: 41124
diff changeset
   235
in the SMT solver).  To turn it on, set the following option.
4a9eec045f2a added option to enable trigger inference;
boehmes
parents: 41124
diff changeset
   236
*}
4a9eec045f2a added option to enable trigger inference;
boehmes
parents: 41124
diff changeset
   237
4a9eec045f2a added option to enable trigger inference;
boehmes
parents: 41124
diff changeset
   238
declare [[ smt_infer_triggers = false ]]
4a9eec045f2a added option to enable trigger inference;
boehmes
parents: 41124
diff changeset
   239
4a9eec045f2a added option to enable trigger inference;
boehmes
parents: 41124
diff changeset
   240
text {*
4a9eec045f2a added option to enable trigger inference;
boehmes
parents: 41124
diff changeset
   241
The SMT method monomorphizes the given facts, that is, it tries to
4a9eec045f2a added option to enable trigger inference;
boehmes
parents: 41124
diff changeset
   242
instantiate all schematic type variables with fixed types occurring
4a9eec045f2a added option to enable trigger inference;
boehmes
parents: 41124
diff changeset
   243
in the problem.  This is a (possibly nonterminating) fixed-point
4a9eec045f2a added option to enable trigger inference;
boehmes
parents: 41124
diff changeset
   244
construction whose cycles are limited by the following option.
4a9eec045f2a added option to enable trigger inference;
boehmes
parents: 41124
diff changeset
   245
*}
4a9eec045f2a added option to enable trigger inference;
boehmes
parents: 41124
diff changeset
   246
43230
dabf6e311213 clarified meaning of monomorphization configuration option by renaming it
boehmes
parents: 41762
diff changeset
   247
declare [[ monomorph_max_rounds = 5 ]]
41125
4a9eec045f2a added option to enable trigger inference;
boehmes
parents: 41124
diff changeset
   248
41762
00060198de12 limit the number of generated SMT monomorphization instances (in addition to the existing monomorphization limit which does not prevent seemingly infinite loops);
boehmes
parents: 41601
diff changeset
   249
text {*
00060198de12 limit the number of generated SMT monomorphization instances (in addition to the existing monomorphization limit which does not prevent seemingly infinite loops);
boehmes
parents: 41601
diff changeset
   250
In addition, the number of generated monomorphic instances is limited
00060198de12 limit the number of generated SMT monomorphization instances (in addition to the existing monomorphization limit which does not prevent seemingly infinite loops);
boehmes
parents: 41601
diff changeset
   251
by the following option.
00060198de12 limit the number of generated SMT monomorphization instances (in addition to the existing monomorphization limit which does not prevent seemingly infinite loops);
boehmes
parents: 41601
diff changeset
   252
*}
00060198de12 limit the number of generated SMT monomorphization instances (in addition to the existing monomorphization limit which does not prevent seemingly infinite loops);
boehmes
parents: 41601
diff changeset
   253
43230
dabf6e311213 clarified meaning of monomorphization configuration option by renaming it
boehmes
parents: 41762
diff changeset
   254
declare [[ monomorph_max_new_instances = 500 ]]
41762
00060198de12 limit the number of generated SMT monomorphization instances (in addition to the existing monomorphization limit which does not prevent seemingly infinite loops);
boehmes
parents: 41601
diff changeset
   255
36898
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   256
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   257
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   258
subsection {* Certificates *}
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   259
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   260
text {*
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   261
By setting the option @{text smt_certificates} to the name of a file,
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   262
all following applications of an SMT solver a cached in that file.
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   263
Any further application of the same SMT solver (using the very same
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   264
configuration) re-uses the cached certificate instead of invoking the
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   265
solver.  An empty string disables caching certificates.
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   266
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   267
The filename should be given as an explicit path.  It is good
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   268
practice to use the name of the current theory (with ending
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   269
@{text ".certs"} instead of @{text ".thy"}) as the certificates file.
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   270
*}
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   271
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   272
declare [[ smt_certificates = "" ]]
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   273
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   274
text {*
47152
446cfc760ccf renamed "smt_fixed" to "smt_read_only_certificates"
blanchet
parents: 46950
diff changeset
   275
The option @{text smt_read_only_certificates} controls whether only
446cfc760ccf renamed "smt_fixed" to "smt_read_only_certificates"
blanchet
parents: 46950
diff changeset
   276
stored certificates are should be used or invocation of an SMT solver
446cfc760ccf renamed "smt_fixed" to "smt_read_only_certificates"
blanchet
parents: 46950
diff changeset
   277
is allowed.  When set to @{text true}, no SMT solver will ever be
36898
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   278
invoked and only the existing certificates found in the configured
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   279
cache are used;  when set to @{text false} and there is no cached
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   280
certificate for some proposition, then the configured SMT solver is
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   281
invoked.
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   282
*}
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   283
47152
446cfc760ccf renamed "smt_fixed" to "smt_read_only_certificates"
blanchet
parents: 46950
diff changeset
   284
declare [[ smt_read_only_certificates = false ]]
36898
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   285
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   286
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   287
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   288
subsection {* Tracing *}
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   289
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   290
text {*
40424
7550b2cba1cb better modularization: moved SMT configuration options and diagnostics as well as SMT failure and exception into separate structures (both of which are loaded first and consequently are available to other SMT structures)
boehmes
parents: 40277
diff changeset
   291
The SMT method, when applied, traces important information.  To
7550b2cba1cb better modularization: moved SMT configuration options and diagnostics as well as SMT failure and exception into separate structures (both of which are loaded first and consequently are available to other SMT structures)
boehmes
parents: 40277
diff changeset
   292
make it entirely silent, set the following option to @{text false}.
7550b2cba1cb better modularization: moved SMT configuration options and diagnostics as well as SMT failure and exception into separate structures (both of which are loaded first and consequently are available to other SMT structures)
boehmes
parents: 40277
diff changeset
   293
*}
7550b2cba1cb better modularization: moved SMT configuration options and diagnostics as well as SMT failure and exception into separate structures (both of which are loaded first and consequently are available to other SMT structures)
boehmes
parents: 40277
diff changeset
   294
7550b2cba1cb better modularization: moved SMT configuration options and diagnostics as well as SMT failure and exception into separate structures (both of which are loaded first and consequently are available to other SMT structures)
boehmes
parents: 40277
diff changeset
   295
declare [[ smt_verbose = true ]]
7550b2cba1cb better modularization: moved SMT configuration options and diagnostics as well as SMT failure and exception into separate structures (both of which are loaded first and consequently are available to other SMT structures)
boehmes
parents: 40277
diff changeset
   296
7550b2cba1cb better modularization: moved SMT configuration options and diagnostics as well as SMT failure and exception into separate structures (both of which are loaded first and consequently are available to other SMT structures)
boehmes
parents: 40277
diff changeset
   297
text {*
36898
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   298
For tracing the generated problem file given to the SMT solver as
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   299
well as the returned result of the solver, the option
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   300
@{text smt_trace} should be set to @{text true}.
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   301
*}
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   302
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   303
declare [[ smt_trace = false ]]
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   304
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   305
text {*
40162
7f58a9a843c2 joined setup of SMT solvers in one place; turned Z3-specific options into SMT options (renamed configuration options from z3_* to smt_*); more detailed SMT exception; improved SMT filter interface
boehmes
parents: 39483
diff changeset
   306
From the set of assumptions given to the SMT solver, those assumptions
7f58a9a843c2 joined setup of SMT solvers in one place; turned Z3-specific options into SMT options (renamed configuration options from z3_* to smt_*); more detailed SMT exception; improved SMT filter interface
boehmes
parents: 39483
diff changeset
   307
used in the proof are traced when the following option is set to
7f58a9a843c2 joined setup of SMT solvers in one place; turned Z3-specific options into SMT options (renamed configuration options from z3_* to smt_*); more detailed SMT exception; improved SMT filter interface
boehmes
parents: 39483
diff changeset
   308
@{term true}.  This only works for Z3 when it runs in non-oracle mode
7f58a9a843c2 joined setup of SMT solvers in one place; turned Z3-specific options into SMT options (renamed configuration options from z3_* to smt_*); more detailed SMT exception; improved SMT filter interface
boehmes
parents: 39483
diff changeset
   309
(see options @{text smt_solver} and @{text smt_oracle} above).
36898
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   310
*}
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   311
40162
7f58a9a843c2 joined setup of SMT solvers in one place; turned Z3-specific options into SMT options (renamed configuration options from z3_* to smt_*); more detailed SMT exception; improved SMT filter interface
boehmes
parents: 39483
diff changeset
   312
declare [[ smt_trace_used_facts = false ]]
39298
5aefb5bc8a93 added preliminary support for SMT datatypes (for now restricted to tuples and lists); only the Z3 interface (in oracle mode) makes use of it, there is especially no Z3 proof reconstruction support for datatypes yet
boehmes
parents: 37818
diff changeset
   313
36898
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   314
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   315
36902
c6bae4456741 use 'subsection' instead of 'section', to maintain 1 chapter per file in generated document
huffman
parents: 36899
diff changeset
   316
subsection {* Schematic rules for Z3 proof reconstruction *}
36898
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   317
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   318
text {*
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   319
Several prof rules of Z3 are not very well documented.  There are two
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   320
lemma groups which can turn failing Z3 proof reconstruction attempts
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   321
into succeeding ones: the facts in @{text z3_rule} are tried prior to
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   322
any implemented reconstruction procedure for all uncertain Z3 proof
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   323
rules;  the facts in @{text z3_simp} are only fed to invocations of
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   324
the simplifier when reconstructing theory-specific proof steps.
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   325
*}
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   326
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   327
lemmas [z3_rule] =
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   328
  refl eq_commute conj_commute disj_commute simp_thms nnf_simps
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   329
  ring_distribs field_simps times_divide_eq_right times_divide_eq_left
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   330
  if_True if_False not_not
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   331
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   332
lemma [z3_rule]:
44488
587bf61a00a1 improved completeness and efficiency of Z3 proof reconstruction, especially by an improved handling of Skolemization
boehmes
parents: 44087
diff changeset
   333
  "(P \<and> Q) = (\<not>(\<not>P \<or> \<not>Q))"
587bf61a00a1 improved completeness and efficiency of Z3 proof reconstruction, especially by an improved handling of Skolemization
boehmes
parents: 44087
diff changeset
   334
  "(P \<and> Q) = (\<not>(\<not>Q \<or> \<not>P))"
587bf61a00a1 improved completeness and efficiency of Z3 proof reconstruction, especially by an improved handling of Skolemization
boehmes
parents: 44087
diff changeset
   335
  "(\<not>P \<and> Q) = (\<not>(P \<or> \<not>Q))"
587bf61a00a1 improved completeness and efficiency of Z3 proof reconstruction, especially by an improved handling of Skolemization
boehmes
parents: 44087
diff changeset
   336
  "(\<not>P \<and> Q) = (\<not>(\<not>Q \<or> P))"
587bf61a00a1 improved completeness and efficiency of Z3 proof reconstruction, especially by an improved handling of Skolemization
boehmes
parents: 44087
diff changeset
   337
  "(P \<and> \<not>Q) = (\<not>(\<not>P \<or> Q))"
587bf61a00a1 improved completeness and efficiency of Z3 proof reconstruction, especially by an improved handling of Skolemization
boehmes
parents: 44087
diff changeset
   338
  "(P \<and> \<not>Q) = (\<not>(Q \<or> \<not>P))"
587bf61a00a1 improved completeness and efficiency of Z3 proof reconstruction, especially by an improved handling of Skolemization
boehmes
parents: 44087
diff changeset
   339
  "(\<not>P \<and> \<not>Q) = (\<not>(P \<or> Q))"
587bf61a00a1 improved completeness and efficiency of Z3 proof reconstruction, especially by an improved handling of Skolemization
boehmes
parents: 44087
diff changeset
   340
  "(\<not>P \<and> \<not>Q) = (\<not>(Q \<or> P))"
587bf61a00a1 improved completeness and efficiency of Z3 proof reconstruction, especially by an improved handling of Skolemization
boehmes
parents: 44087
diff changeset
   341
  by auto
587bf61a00a1 improved completeness and efficiency of Z3 proof reconstruction, especially by an improved handling of Skolemization
boehmes
parents: 44087
diff changeset
   342
587bf61a00a1 improved completeness and efficiency of Z3 proof reconstruction, especially by an improved handling of Skolemization
boehmes
parents: 44087
diff changeset
   343
lemma [z3_rule]:
36898
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   344
  "(P \<longrightarrow> Q) = (Q \<or> \<not>P)"
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   345
  "(\<not>P \<longrightarrow> Q) = (P \<or> Q)"
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   346
  "(\<not>P \<longrightarrow> Q) = (Q \<or> P)"
44488
587bf61a00a1 improved completeness and efficiency of Z3 proof reconstruction, especially by an improved handling of Skolemization
boehmes
parents: 44087
diff changeset
   347
  "(True \<longrightarrow> P) = P"
587bf61a00a1 improved completeness and efficiency of Z3 proof reconstruction, especially by an improved handling of Skolemization
boehmes
parents: 44087
diff changeset
   348
  "(P \<longrightarrow> True) = True"
587bf61a00a1 improved completeness and efficiency of Z3 proof reconstruction, especially by an improved handling of Skolemization
boehmes
parents: 44087
diff changeset
   349
  "(False \<longrightarrow> P) = True"
587bf61a00a1 improved completeness and efficiency of Z3 proof reconstruction, especially by an improved handling of Skolemization
boehmes
parents: 44087
diff changeset
   350
  "(P \<longrightarrow> P) = True"
36898
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   351
  by auto
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   352
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   353
lemma [z3_rule]:
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   354
  "((P = Q) \<longrightarrow> R) = (R | (Q = (\<not>P)))"
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   355
  by auto
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   356
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   357
lemma [z3_rule]:
44488
587bf61a00a1 improved completeness and efficiency of Z3 proof reconstruction, especially by an improved handling of Skolemization
boehmes
parents: 44087
diff changeset
   358
  "(\<not>True) = False"
587bf61a00a1 improved completeness and efficiency of Z3 proof reconstruction, especially by an improved handling of Skolemization
boehmes
parents: 44087
diff changeset
   359
  "(\<not>False) = True"
587bf61a00a1 improved completeness and efficiency of Z3 proof reconstruction, especially by an improved handling of Skolemization
boehmes
parents: 44087
diff changeset
   360
  "(x = x) = True"
587bf61a00a1 improved completeness and efficiency of Z3 proof reconstruction, especially by an improved handling of Skolemization
boehmes
parents: 44087
diff changeset
   361
  "(P = True) = P"
587bf61a00a1 improved completeness and efficiency of Z3 proof reconstruction, especially by an improved handling of Skolemization
boehmes
parents: 44087
diff changeset
   362
  "(True = P) = P"
587bf61a00a1 improved completeness and efficiency of Z3 proof reconstruction, especially by an improved handling of Skolemization
boehmes
parents: 44087
diff changeset
   363
  "(P = False) = (\<not>P)"
587bf61a00a1 improved completeness and efficiency of Z3 proof reconstruction, especially by an improved handling of Skolemization
boehmes
parents: 44087
diff changeset
   364
  "(False = P) = (\<not>P)"
36898
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   365
  "((\<not>P) = P) = False"
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   366
  "(P = (\<not>P)) = False"
44488
587bf61a00a1 improved completeness and efficiency of Z3 proof reconstruction, especially by an improved handling of Skolemization
boehmes
parents: 44087
diff changeset
   367
  "((\<not>P) = (\<not>Q)) = (P = Q)"
587bf61a00a1 improved completeness and efficiency of Z3 proof reconstruction, especially by an improved handling of Skolemization
boehmes
parents: 44087
diff changeset
   368
  "\<not>(P = (\<not>Q)) = (P = Q)"
587bf61a00a1 improved completeness and efficiency of Z3 proof reconstruction, especially by an improved handling of Skolemization
boehmes
parents: 44087
diff changeset
   369
  "\<not>((\<not>P) = Q) = (P = Q)"
36898
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   370
  "(P \<noteq> Q) = (Q = (\<not>P))"
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   371
  "(P = Q) = ((\<not>P \<or> Q) \<and> (P \<or> \<not>Q))"
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   372
  "(P \<noteq> Q) = ((\<not>P \<or> \<not>Q) \<and> (P \<or> Q))"
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   373
  by auto
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   374
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   375
lemma [z3_rule]:
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   376
  "(if P then P else \<not>P) = True"
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   377
  "(if \<not>P then \<not>P else P) = True"
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   378
  "(if P then True else False) = P"
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   379
  "(if P then False else True) = (\<not>P)"
44488
587bf61a00a1 improved completeness and efficiency of Z3 proof reconstruction, especially by an improved handling of Skolemization
boehmes
parents: 44087
diff changeset
   380
  "(if P then Q else True) = ((\<not>P) \<or> Q)"
587bf61a00a1 improved completeness and efficiency of Z3 proof reconstruction, especially by an improved handling of Skolemization
boehmes
parents: 44087
diff changeset
   381
  "(if P then Q else True) = (Q \<or> (\<not>P))"
587bf61a00a1 improved completeness and efficiency of Z3 proof reconstruction, especially by an improved handling of Skolemization
boehmes
parents: 44087
diff changeset
   382
  "(if P then Q else \<not>Q) = (P = Q)"
587bf61a00a1 improved completeness and efficiency of Z3 proof reconstruction, especially by an improved handling of Skolemization
boehmes
parents: 44087
diff changeset
   383
  "(if P then Q else \<not>Q) = (Q = P)"
587bf61a00a1 improved completeness and efficiency of Z3 proof reconstruction, especially by an improved handling of Skolemization
boehmes
parents: 44087
diff changeset
   384
  "(if P then \<not>Q else Q) = (P = (\<not>Q))"
587bf61a00a1 improved completeness and efficiency of Z3 proof reconstruction, especially by an improved handling of Skolemization
boehmes
parents: 44087
diff changeset
   385
  "(if P then \<not>Q else Q) = ((\<not>Q) = P)"
36898
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   386
  "(if \<not>P then x else y) = (if P then y else x)"
44488
587bf61a00a1 improved completeness and efficiency of Z3 proof reconstruction, especially by an improved handling of Skolemization
boehmes
parents: 44087
diff changeset
   387
  "(if P then (if Q then x else y) else x) = (if P \<and> (\<not>Q) then y else x)"
587bf61a00a1 improved completeness and efficiency of Z3 proof reconstruction, especially by an improved handling of Skolemization
boehmes
parents: 44087
diff changeset
   388
  "(if P then (if Q then x else y) else x) = (if (\<not>Q) \<and> P then y else x)"
587bf61a00a1 improved completeness and efficiency of Z3 proof reconstruction, especially by an improved handling of Skolemization
boehmes
parents: 44087
diff changeset
   389
  "(if P then (if Q then x else y) else y) = (if P \<and> Q then x else y)"
587bf61a00a1 improved completeness and efficiency of Z3 proof reconstruction, especially by an improved handling of Skolemization
boehmes
parents: 44087
diff changeset
   390
  "(if P then (if Q then x else y) else y) = (if Q \<and> P then x else y)"
587bf61a00a1 improved completeness and efficiency of Z3 proof reconstruction, especially by an improved handling of Skolemization
boehmes
parents: 44087
diff changeset
   391
  "(if P then x else if P then y else z) = (if P then x else z)"
587bf61a00a1 improved completeness and efficiency of Z3 proof reconstruction, especially by an improved handling of Skolemization
boehmes
parents: 44087
diff changeset
   392
  "(if P then x else if Q then x else y) = (if P \<or> Q then x else y)"
587bf61a00a1 improved completeness and efficiency of Z3 proof reconstruction, especially by an improved handling of Skolemization
boehmes
parents: 44087
diff changeset
   393
  "(if P then x else if Q then x else y) = (if Q \<or> P then x else y)"
587bf61a00a1 improved completeness and efficiency of Z3 proof reconstruction, especially by an improved handling of Skolemization
boehmes
parents: 44087
diff changeset
   394
  "(if P then x = y else x = z) = (x = (if P then y else z))"
587bf61a00a1 improved completeness and efficiency of Z3 proof reconstruction, especially by an improved handling of Skolemization
boehmes
parents: 44087
diff changeset
   395
  "(if P then x = y else y = z) = (y = (if P then x else z))"
587bf61a00a1 improved completeness and efficiency of Z3 proof reconstruction, especially by an improved handling of Skolemization
boehmes
parents: 44087
diff changeset
   396
  "(if P then x = y else z = y) = (y = (if P then x else z))"
36898
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   397
  by auto
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   398
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   399
lemma [z3_rule]:
44488
587bf61a00a1 improved completeness and efficiency of Z3 proof reconstruction, especially by an improved handling of Skolemization
boehmes
parents: 44087
diff changeset
   400
  "0 + (x::int) = x"
587bf61a00a1 improved completeness and efficiency of Z3 proof reconstruction, especially by an improved handling of Skolemization
boehmes
parents: 44087
diff changeset
   401
  "x + 0 = x"
587bf61a00a1 improved completeness and efficiency of Z3 proof reconstruction, especially by an improved handling of Skolemization
boehmes
parents: 44087
diff changeset
   402
  "x + x = 2 * x"
587bf61a00a1 improved completeness and efficiency of Z3 proof reconstruction, especially by an improved handling of Skolemization
boehmes
parents: 44087
diff changeset
   403
  "0 * x = 0"
587bf61a00a1 improved completeness and efficiency of Z3 proof reconstruction, especially by an improved handling of Skolemization
boehmes
parents: 44087
diff changeset
   404
  "1 * x = x"
587bf61a00a1 improved completeness and efficiency of Z3 proof reconstruction, especially by an improved handling of Skolemization
boehmes
parents: 44087
diff changeset
   405
  "x + y = y + x"
587bf61a00a1 improved completeness and efficiency of Z3 proof reconstruction, especially by an improved handling of Skolemization
boehmes
parents: 44087
diff changeset
   406
  by auto
587bf61a00a1 improved completeness and efficiency of Z3 proof reconstruction, especially by an improved handling of Skolemization
boehmes
parents: 44087
diff changeset
   407
587bf61a00a1 improved completeness and efficiency of Z3 proof reconstruction, especially by an improved handling of Skolemization
boehmes
parents: 44087
diff changeset
   408
lemma [z3_rule]:  (* for def-axiom *)
36898
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   409
  "P = Q \<or> P \<or> Q"
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   410
  "P = Q \<or> \<not>P \<or> \<not>Q"
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   411
  "(\<not>P) = Q \<or> \<not>P \<or> Q"
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   412
  "(\<not>P) = Q \<or> P \<or> \<not>Q"
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   413
  "P = (\<not>Q) \<or> \<not>P \<or> Q"
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   414
  "P = (\<not>Q) \<or> P \<or> \<not>Q"
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   415
  "P \<noteq> Q \<or> P \<or> \<not>Q"
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   416
  "P \<noteq> Q \<or> \<not>P \<or> Q"
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   417
  "P \<noteq> (\<not>Q) \<or> P \<or> Q"
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   418
  "(\<not>P) \<noteq> Q \<or> P \<or> Q"
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   419
  "P \<or> Q \<or> P \<noteq> (\<not>Q)"
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   420
  "P \<or> Q \<or> (\<not>P) \<noteq> Q"
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   421
  "P \<or> \<not>Q \<or> P \<noteq> Q"
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   422
  "\<not>P \<or> Q \<or> P \<noteq> Q"
44488
587bf61a00a1 improved completeness and efficiency of Z3 proof reconstruction, especially by an improved handling of Skolemization
boehmes
parents: 44087
diff changeset
   423
  "P \<or> y = (if P then x else y)"
587bf61a00a1 improved completeness and efficiency of Z3 proof reconstruction, especially by an improved handling of Skolemization
boehmes
parents: 44087
diff changeset
   424
  "P \<or> (if P then x else y) = y"
587bf61a00a1 improved completeness and efficiency of Z3 proof reconstruction, especially by an improved handling of Skolemization
boehmes
parents: 44087
diff changeset
   425
  "\<not>P \<or> x = (if P then x else y)"
587bf61a00a1 improved completeness and efficiency of Z3 proof reconstruction, especially by an improved handling of Skolemization
boehmes
parents: 44087
diff changeset
   426
  "\<not>P \<or>  (if P then x else y) = x"
587bf61a00a1 improved completeness and efficiency of Z3 proof reconstruction, especially by an improved handling of Skolemization
boehmes
parents: 44087
diff changeset
   427
  "P \<or> R \<or> \<not>(if P then Q else R)"
587bf61a00a1 improved completeness and efficiency of Z3 proof reconstruction, especially by an improved handling of Skolemization
boehmes
parents: 44087
diff changeset
   428
  "\<not>P \<or> Q \<or> \<not>(if P then Q else R)"
587bf61a00a1 improved completeness and efficiency of Z3 proof reconstruction, especially by an improved handling of Skolemization
boehmes
parents: 44087
diff changeset
   429
  "\<not>(if P then Q else R) \<or> \<not>P \<or> Q"
587bf61a00a1 improved completeness and efficiency of Z3 proof reconstruction, especially by an improved handling of Skolemization
boehmes
parents: 44087
diff changeset
   430
  "\<not>(if P then Q else R) \<or> P \<or> R"
587bf61a00a1 improved completeness and efficiency of Z3 proof reconstruction, especially by an improved handling of Skolemization
boehmes
parents: 44087
diff changeset
   431
  "(if P then Q else R) \<or> \<not>P \<or> \<not>Q"
587bf61a00a1 improved completeness and efficiency of Z3 proof reconstruction, especially by an improved handling of Skolemization
boehmes
parents: 44087
diff changeset
   432
  "(if P then Q else R) \<or> P \<or> \<not>R"
587bf61a00a1 improved completeness and efficiency of Z3 proof reconstruction, especially by an improved handling of Skolemization
boehmes
parents: 44087
diff changeset
   433
  "(if P then \<not>Q else R) \<or> \<not>P \<or> Q"
587bf61a00a1 improved completeness and efficiency of Z3 proof reconstruction, especially by an improved handling of Skolemization
boehmes
parents: 44087
diff changeset
   434
  "(if P then Q else \<not>R) \<or> P \<or> R"
36898
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   435
  by auto
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   436
37124
fe22fc54b876 hide constants and types introduced by SMT,
boehmes
parents: 36902
diff changeset
   437
fe22fc54b876 hide constants and types introduced by SMT,
boehmes
parents: 36902
diff changeset
   438
fe22fc54b876 hide constants and types introduced by SMT,
boehmes
parents: 36902
diff changeset
   439
hide_type (open) pattern
41281
679118e35378 removed odd decoration of built-in symbols as Vars (instead provide built-in desctructor functions along with their inverse functions);
boehmes
parents: 41280
diff changeset
   440
hide_const Pattern fun_app term_true term_false z3div z3mod
41280
a7de9d36f4f2 only linear occurrences of multiplication are treated as built-in (SMT solvers only support linear arithmetic in general);
boehmes
parents: 41174
diff changeset
   441
hide_const (open) trigger pat nopat weight
37124
fe22fc54b876 hide constants and types introduced by SMT,
boehmes
parents: 36902
diff changeset
   442
36898
8e55aa1306c5 integrated SMT into the HOL image
boehmes
parents:
diff changeset
   443
end