From cb093c7c2b6877f427f60a8621e3bface9825bb0 Mon Sep 17 00:00:00 2001 From: Lucas Pena Date: Thu, 12 Dec 2019 16:08:05 -0600 Subject: [PATCH 01/44] begin support for coq in ML --- prover/build | 7 +++- prover/drivers/coq-driver.md | 34 +++++++++++++++++ prover/lang/coq-lang.md | 71 ++++++++++++++++++++++++++++++++++++ prover/prover | 6 +++ prover/prover.md | 2 + prover/t/AndComm.v | 7 ++++ 6 files changed, 126 insertions(+), 1 deletion(-) create mode 100644 prover/drivers/coq-driver.md create mode 100644 prover/lang/coq-lang.md create mode 100644 prover/t/AndComm.v diff --git a/prover/build b/prover/build index 58551a797..fdf589fdf 100755 --- a/prover/build +++ b/prover/build @@ -18,9 +18,11 @@ proj = KProject() # Matching Logic Prover # ===================== -other_md_files = [ 'lang/smt-lang.md' +other_md_files = [ 'lang/coq-lang.md' + , 'lang/smt-lang.md' , 'lang/kore-lang.md' , 'drivers/base.md' + , 'drivers/coq-driver.md' , 'drivers/smt-driver.md' , 'drivers/kore-driver.md' , 'strategies/apply-equation.md' @@ -53,6 +55,7 @@ def prover(alias, flags = None): prover_kore = prover('prover-kore', '--main-module DRIVER-KORE --syntax-module DRIVER-KORE-SYNTAX') prover_smt = prover('prover-smt', '--main-module DRIVER-SMT --syntax-module DRIVER-SMT-SYNTAX' ) +prover_coq = prover('prover-coq', '--main-module DRIVER-COQ --syntax-module DRIVER-COQ-SYNTAX' ) # Functional tests # ---------------- @@ -60,6 +63,8 @@ prover_smt = prover('prover-smt', '--main-module DRIVER-SMT --syntax-module D # prover_kore.tests(inputs = glob('t/*.kore'), implicit_inputs = glob('t/definitions/*.kore'), flags = '-cCOMMANDLINE=.CommandLine') # prover_smt .tests(inputs = glob('t/*.smt2'), flags = '-cCOMMANDLINE=.CommandLine') +prover_coq .tests(inputs = glob('t/*.v'), flags = '-cCOMMANDLINE=.CommandLine') + def log_on_success(file, message): return proj.rule( 'log-to-success' , description = '$out: $message' diff --git a/prover/drivers/coq-driver.md b/prover/drivers/coq-driver.md new file mode 100644 index 000000000..74c34e95c --- /dev/null +++ b/prover/drivers/coq-driver.md @@ -0,0 +1,34 @@ +Coq Driver +========== + +This file is responsible for loading definitions in the Coq format. + +```k +module DRIVER-COQ-COMMON + imports COQ + imports STRATEGIES-EXPORTED-SYNTAX + syntax Pgm ::= CoqSentence +endmodule +``` + +```k +module DRIVER-COQ-SYNTAX + imports DRIVER-BASE-SYNTAX + imports DRIVER-COQ-COMMON + imports COQ-SYNTAX +endmodule +``` + +```k +module DRIVER-COQ + imports DRIVER-KORE + imports DRIVER-COQ-COMMON + imports KORE + imports PROVER-CONFIGURATION + imports PROVER-CORE-SYNTAX + imports STRATEGIES-EXPORTED-SYNTAX +``` + +```k +endmodule +``` diff --git a/prover/lang/coq-lang.md b/prover/lang/coq-lang.md new file mode 100644 index 000000000..93b164429 --- /dev/null +++ b/prover/lang/coq-lang.md @@ -0,0 +1,71 @@ +```k +module COQ-SYNTAX + imports TOKENS-SYNTAX + imports COQ +endmodule + +module COQ + imports INT-SYNTAX + imports BOOL-SYNTAX + imports STRING + imports KORE + +// Identifiers + syntax CoqIdent ::= LowerName + | UpperName + syntax CoqQualID ::= CoqIdent + syntax CoqName ::= CoqIdent + | "_" + syntax CoqNames ::= List{CoqName, ""} [klabel(CoqNames)] + +// Terms + syntax CoqTerm ::= "forall" CoqBinders "," CoqTerm + | "fun" CoqBinders "=>" CoqTerm + | "fix" CoqFixBodies + | "cofix" CoqCofixBodies + | "let" CoqIdent ":=" CoqTerm "in" CoqTerm + | "let" CoqIdent CoqBinders ":" CoqTerm ":=" CoqTerm "in" CoqTerm + | "match" CoqMatchItems "with" CoqEquations "end" + // TODO: more here + | Int + + syntax CoqBinder ::= CoqName + | "(" CoqNames ":" CoqTerm ")" + syntax CoqBinders ::= List{CoqBinder, ""} [klabel(CoqBinders)] + + syntax CoqFixBody ::= CoqIdent CoqBinders ":=" CoqTerm + syntax CoqFixBodyList ::= List{CoqFixBody, "with"} + syntax CoqFixBodies ::= CoqFixBody + | CoqFixBody CoqFixBodyList "for" CoqIdent + + syntax CoqCofixBody ::= CoqIdent CoqBinders ":=" CoqTerm + syntax CoqCofixBodyList ::= List{CoqCofixBody, "with"} + syntax CoqCofixBodies ::= CoqCofixBody + | CoqCofixBody CoqCofixBodyList "for" CoqIdent + + syntax CoqMatchItem ::= CoqTerm + syntax CoqMatchItems ::= List{CoqMatchItem, ","} [klabel(CoqMatchItems)] + + syntax CoqEquation ::= CoqMultPattern "=>" CoqTerm + syntax CoqEquations ::= List{CoqEquation, "|"} [klabel(CoqEquations)] + + syntax CoqPattern ::= CoqQualID CoqPatterns + | "@" CoqQualID CoqPatterns + | CoqPattern "as" CoqIdent + | CoqPattern "%" CoqIdent + | CoqQualID + | "_" + | Int + + syntax CoqMultPattern ::= List{CoqPattern, ","} [klabel(CoqMultPattern)] + syntax CoqPatterns ::= List{CoqPattern, ""} [klabel(CoqPatterns)] + +// Vernacular + syntax CoqSentence ::= CoqDefinition + + syntax CoqDefinition ::= "Definition" CoqIdent ":=" CoqTerm "." +``` + +```k +endmodule +``` diff --git a/prover/prover b/prover/prover index 4ba575218..031dd38e4 100755 --- a/prover/prover +++ b/prover/prover @@ -18,6 +18,12 @@ KDefinition( proj , directory = proj.builddir('defn/prover-smt') , krun_flags = '--interpret' ) +KDefinition( proj + , alias = 'prover-coq' + , backend = 'ocaml' + , directory = proj.builddir('defn/prover-coq') + , krun_flags = '--interpret' + ) KDefinition( proj , alias = 'test-driver' , backend = 'llvm' diff --git a/prover/prover.md b/prover/prover.md index 8b928190d..ef0f2605c 100644 --- a/prover/prover.md +++ b/prover/prover.md @@ -1,5 +1,7 @@ ```k requires "lang/kore-lang.k" +requires "lang/coq-lang.k" +requires "drivers/coq-driver.k" requires "drivers/smt-driver.k" requires "drivers/kore-driver.k" requires "drivers/base.k" diff --git a/prover/t/AndComm.v b/prover/t/AndComm.v new file mode 100644 index 000000000..3dd65757b --- /dev/null +++ b/prover/t/AndComm.v @@ -0,0 +1,7 @@ +Definition Four := 4 . + +// Definition AndComm := +// fun (A B : Prop) (H : A /\ B) => +// match H with +// | conj H0 H1 => conj H1 H0 +// end . From a721d74432c272bf85a366821f9f9549a8f80745 Mon Sep 17 00:00:00 2001 From: Lucas Pena Date: Fri, 13 Dec 2019 16:04:11 -0600 Subject: [PATCH 02/44] more support for coq in ML. inductive defs parse --- prover/drivers/coq-driver.md | 2 +- prover/lang/coq-lang.md | 28 ++++++++++++++++++++++++---- prover/t/And.v | 2 ++ prover/t/{AndComm.v => Four.v} | 0 prover/t/Logic.v | 12 ++++++++++++ prover/t/Or.v | 3 +++ 6 files changed, 42 insertions(+), 5 deletions(-) create mode 100644 prover/t/And.v rename prover/t/{AndComm.v => Four.v} (100%) create mode 100644 prover/t/Logic.v create mode 100644 prover/t/Or.v diff --git a/prover/drivers/coq-driver.md b/prover/drivers/coq-driver.md index 74c34e95c..a05f89a11 100644 --- a/prover/drivers/coq-driver.md +++ b/prover/drivers/coq-driver.md @@ -7,7 +7,7 @@ This file is responsible for loading definitions in the Coq format. module DRIVER-COQ-COMMON imports COQ imports STRATEGIES-EXPORTED-SYNTAX - syntax Pgm ::= CoqSentence + syntax Pgm ::= CoqSentences endmodule ``` diff --git a/prover/lang/coq-lang.md b/prover/lang/coq-lang.md index 93b164429..32c4dbb02 100644 --- a/prover/lang/coq-lang.md +++ b/prover/lang/coq-lang.md @@ -18,21 +18,35 @@ module COQ | "_" syntax CoqNames ::= List{CoqName, ""} [klabel(CoqNames)] +// Hardcoded Coq Sorts + syntax CoqSort ::= "SProp" + | "Prop" + | "Set" + | "Type" + // Terms - syntax CoqTerm ::= "forall" CoqBinders "," CoqTerm - | "fun" CoqBinders "=>" CoqTerm + syntax CoqTerm ::= "fun" CoqBinders "=>" CoqTerm | "fix" CoqFixBodies | "cofix" CoqCofixBodies | "let" CoqIdent ":=" CoqTerm "in" CoqTerm | "let" CoqIdent CoqBinders ":" CoqTerm ":=" CoqTerm "in" CoqTerm + | CoqTerm CoqArg [right] | "match" CoqMatchItems "with" CoqEquations "end" - // TODO: more here + | CoqQualID + | CoqSort | Int + | "_" + > "forall" CoqBinders "," CoqTerm syntax CoqBinder ::= CoqName | "(" CoqNames ":" CoqTerm ")" syntax CoqBinders ::= List{CoqBinder, ""} [klabel(CoqBinders)] + syntax CoqArg ::= CoqTerm + | "(" CoqIdent ":=" CoqTerm ")" + | CoqArg CoqArg + syntax CoqTerms ::= List{CoqTerm, ""} [klabel(CoqTerms)] + syntax CoqFixBody ::= CoqIdent CoqBinders ":=" CoqTerm syntax CoqFixBodyList ::= List{CoqFixBody, "with"} syntax CoqFixBodies ::= CoqFixBody @@ -62,8 +76,14 @@ module COQ // Vernacular syntax CoqSentence ::= CoqDefinition - + | CoqInductive + syntax CoqSentences ::= List{CoqSentence, ""} [klabel(CoqSentences)] syntax CoqDefinition ::= "Definition" CoqIdent ":=" CoqTerm "." + + syntax CoqInductive ::= "Inductive" CoqIndBody "." + syntax CoqIndBody ::= CoqIdent CoqBinders ":" CoqTerm ":=" CoqIndCases + syntax CoqIndCase ::= CoqIdent CoqBinders ":" CoqTerm + syntax CoqIndCases ::= List{CoqIndCase, "|"} ``` ```k diff --git a/prover/t/And.v b/prover/t/And.v new file mode 100644 index 000000000..0922f5013 --- /dev/null +++ b/prover/t/And.v @@ -0,0 +1,2 @@ +Inductive and (A B : Prop) : Prop := + conj : forall (x : A), forall (y : B), and A B . diff --git a/prover/t/AndComm.v b/prover/t/Four.v similarity index 100% rename from prover/t/AndComm.v rename to prover/t/Four.v diff --git a/prover/t/Logic.v b/prover/t/Logic.v new file mode 100644 index 000000000..c5e516a85 --- /dev/null +++ b/prover/t/Logic.v @@ -0,0 +1,12 @@ +Inductive and (A B : Prop) : Prop := + conj : forall (x : A), forall (y : B), and A B . + +Inductive or (A B : Prop) : Prop := + or_introl : forall (x : A), or A B + | or_intror : forall (y : A), or A B . + +// Definition AndComm := +// fun (A B : Prop) (H : A /\ B) => +// match H with +// | conj H0 H1 => conj H1 H0 +// end . diff --git a/prover/t/Or.v b/prover/t/Or.v new file mode 100644 index 000000000..52ab7940a --- /dev/null +++ b/prover/t/Or.v @@ -0,0 +1,3 @@ +Inductive or (A B : Prop) : Prop := + or_introl : forall (x : A), or A B + | or_intror : forall (y : A), or A B . From 7bb9ed50bdc12499c8616698359a86240aae8fc4 Mon Sep 17 00:00:00 2001 From: Nishant Rodrigues Date: Sat, 14 Dec 2019 06:31:42 +0530 Subject: [PATCH 03/44] coq: Fix parsing of underscores --- prover/lang/coq-lang.md | 6 +++--- prover/lang/kore-lang.md | 2 ++ 2 files changed, 5 insertions(+), 3 deletions(-) diff --git a/prover/lang/coq-lang.md b/prover/lang/coq-lang.md index 32c4dbb02..6936ceb43 100644 --- a/prover/lang/coq-lang.md +++ b/prover/lang/coq-lang.md @@ -15,7 +15,7 @@ module COQ | UpperName syntax CoqQualID ::= CoqIdent syntax CoqName ::= CoqIdent - | "_" + | Underscore syntax CoqNames ::= List{CoqName, ""} [klabel(CoqNames)] // Hardcoded Coq Sorts @@ -35,7 +35,7 @@ module COQ | CoqQualID | CoqSort | Int - | "_" + | Underscore > "forall" CoqBinders "," CoqTerm syntax CoqBinder ::= CoqName @@ -68,7 +68,7 @@ module COQ | CoqPattern "as" CoqIdent | CoqPattern "%" CoqIdent | CoqQualID - | "_" + | Underscore | Int syntax CoqMultPattern ::= List{CoqPattern, ","} [klabel(CoqMultPattern)] diff --git a/prover/lang/kore-lang.md b/prover/lang/kore-lang.md index 6bf8c1062..f6c3aee75 100644 --- a/prover/lang/kore-lang.md +++ b/prover/lang/kore-lang.md @@ -9,6 +9,7 @@ module TOKENS syntax ColonName syntax PipeQID syntax Decimal + syntax Underscore // Abstract syntax Symbol ::= UpperName | LowerName @@ -118,6 +119,7 @@ module TOKENS-SYNTAX syntax ColonName ::= r":[a-z][A-Za-z\\-0-9'\\#\\_]*" [token, autoReject] syntax Decimal ::= r"[0-9][0-9]*\\.[0-9][0-9]*" [token, autoreject] | "2.0" [token] + syntax Underscore ::= "_" [token] endmodule module KORE From 1a294ccf6a9cbb0eb045a395c7332d38e5a11b43 Mon Sep 17 00:00:00 2001 From: xc3 Date: Fri, 13 Dec 2019 19:44:50 -0600 Subject: [PATCH 04/44] add more parsing rules and Logic examples --- prover/lang/coq-lang.md | 4 ++++ prover/t/Logic.v | 24 ++++++++++++++++++++---- 2 files changed, 24 insertions(+), 4 deletions(-) diff --git a/prover/lang/coq-lang.md b/prover/lang/coq-lang.md index 6936ceb43..9213a31b9 100644 --- a/prover/lang/coq-lang.md +++ b/prover/lang/coq-lang.md @@ -37,6 +37,7 @@ module COQ | Int | Underscore > "forall" CoqBinders "," CoqTerm + > "(" CoqTerm ")" [bracket] syntax CoqBinder ::= CoqName | "(" CoqNames ":" CoqTerm ")" @@ -77,13 +78,16 @@ module COQ // Vernacular syntax CoqSentence ::= CoqDefinition | CoqInductive + // | CoqCoInductive syntax CoqSentences ::= List{CoqSentence, ""} [klabel(CoqSentences)] syntax CoqDefinition ::= "Definition" CoqIdent ":=" CoqTerm "." + | "Definition" CoqIdent CoqBinders ":" CoqTerm ":=" CoqTerm "." syntax CoqInductive ::= "Inductive" CoqIndBody "." syntax CoqIndBody ::= CoqIdent CoqBinders ":" CoqTerm ":=" CoqIndCases syntax CoqIndCase ::= CoqIdent CoqBinders ":" CoqTerm syntax CoqIndCases ::= List{CoqIndCase, "|"} + ``` ```k diff --git a/prover/t/Logic.v b/prover/t/Logic.v index c5e516a85..d2984dd61 100644 --- a/prover/t/Logic.v +++ b/prover/t/Logic.v @@ -1,3 +1,10 @@ +Inductive True : Prop := + I : True . + +Inductive False : Prop := . + +Definition not (A : Prop) : Prop := forall (x : A), False . + Inductive and (A B : Prop) : Prop := conj : forall (x : A), forall (y : B), and A B . @@ -5,8 +12,17 @@ Inductive or (A B : Prop) : Prop := or_introl : forall (x : A), or A B | or_intror : forall (y : A), or A B . +Definition iff (A B : Prop) : Prop := + (and (forall (x : A), B)) (forall (y : B), A) . + +Definition IF_then_else (P Q R : Prop) : Prop := + (or (and P Q)) (and (not P) R) . + +// Inductive ex (A : Type) (P : forall (x : A), Prop) : Prop := +// ex_intro : forall x : A, forall y : (P x), ex (A:=A) P. + // Definition AndComm := -// fun (A B : Prop) (H : A /\ B) => -// match H with -// | conj H0 H1 => conj H1 H0 -// end . +// fun (A B : Prop) (H : A /\ B) => +// match H with +// | conj H0 H1 => conj H1 H0 +// end . From e9245c321c1bf7a133db14c4bc7f30b4b1f85d1e Mon Sep 17 00:00:00 2001 From: xc3 Date: Fri, 13 Dec 2019 20:08:37 -0600 Subject: [PATCH 05/44] minor --- prover/t/Logic.v | 9 +++++++++ 1 file changed, 9 insertions(+) diff --git a/prover/t/Logic.v b/prover/t/Logic.v index d2984dd61..0e46323cc 100644 --- a/prover/t/Logic.v +++ b/prover/t/Logic.v @@ -18,6 +18,15 @@ Definition iff (A B : Prop) : Prop := Definition IF_then_else (P Q R : Prop) : Prop := (or (and P Q)) (and (not P) R) . +// Syntax in https://github.com/coq/coq/blob/master/theories/Init/Logic +// that we cannot parse for now. + +// All Theorems (Are we going to support those?) + +// Inductive ex (A:Type) (P:A -> Prop) : Prop := +// ex_intro : forall x:A, P x -> ex (A:=A) P. +// + // Inductive ex (A : Type) (P : forall (x : A), Prop) : Prop := // ex_intro : forall x : A, forall y : (P x), ex (A:=A) P. From 13c1df5ea530473e339d5a5a3063942aebd078c0 Mon Sep 17 00:00:00 2001 From: Lucas Pena Date: Mon, 16 Dec 2019 14:44:22 -0600 Subject: [PATCH 06/44] coq-lang: parsing more logic, can parse exists and AndComm --- prover/lang/coq-lang.md | 8 +++++--- prover/t/Logic.v | 29 +++++++++++++++++------------ 2 files changed, 22 insertions(+), 15 deletions(-) diff --git a/prover/lang/coq-lang.md b/prover/lang/coq-lang.md index 9213a31b9..5c1107466 100644 --- a/prover/lang/coq-lang.md +++ b/prover/lang/coq-lang.md @@ -30,8 +30,9 @@ module COQ | "cofix" CoqCofixBodies | "let" CoqIdent ":=" CoqTerm "in" CoqTerm | "let" CoqIdent CoqBinders ":" CoqTerm ":=" CoqTerm "in" CoqTerm - | CoqTerm CoqArg [right] + | "@" CoqQualID CoqTerm | "match" CoqMatchItems "with" CoqEquations "end" + > CoqTerm CoqArg [right] | CoqQualID | CoqSort | Int @@ -64,8 +65,9 @@ module COQ syntax CoqEquation ::= CoqMultPattern "=>" CoqTerm syntax CoqEquations ::= List{CoqEquation, "|"} [klabel(CoqEquations)] - syntax CoqPattern ::= CoqQualID CoqPatterns - | "@" CoqQualID CoqPatterns + syntax CoqPattern ::= CoqQualID CoqPattern + | "@" CoqQualID CoqPattern + | CoqPattern CoqPattern | CoqPattern "as" CoqIdent | CoqPattern "%" CoqIdent | CoqQualID diff --git a/prover/t/Logic.v b/prover/t/Logic.v index 0e46323cc..96c94a51e 100644 --- a/prover/t/Logic.v +++ b/prover/t/Logic.v @@ -23,15 +23,20 @@ Definition IF_then_else (P Q R : Prop) : Prop := // All Theorems (Are we going to support those?) -// Inductive ex (A:Type) (P:A -> Prop) : Prop := -// ex_intro : forall x:A, P x -> ex (A:=A) P. -// - -// Inductive ex (A : Type) (P : forall (x : A), Prop) : Prop := -// ex_intro : forall x : A, forall y : (P x), ex (A:=A) P. - -// Definition AndComm := -// fun (A B : Prop) (H : A /\ B) => -// match H with -// | conj H0 H1 => conj H1 H0 -// end . +Inductive ex1 (A : Type) (P : forall (x : A), Prop) : Prop := + ex_intro1 : forall (x : A), forall (y : (P x)), ex1 A P . + +Inductive ex2 (A : Type) (P : forall (x : A), Prop) : Prop := + ex_intro2 : forall (x : A), forall (y : (P x)), ex2 P . + +Inductive ex3 (A : Type) (P : forall (x : A), Prop) : Prop := + ex_intro3 : forall (x : A), forall (y : (P x)), ex3 (A:=A) P . + +Inductive ex4 (A : Type) (P : forall (x : A), Prop) : Prop := + ex_intro4 : forall (x : A), forall (y : (P x)), @ ex4 A P . + +Definition AndComm := + fun (A B : Prop) (H : and A B) => + match H with + conj H0 H1 => conj H1 H0 + end . From 7155865003aebf7c25d3bcc3d4c12eb6247a56af Mon Sep 17 00:00:00 2001 From: Lucas Pena Date: Mon, 16 Dec 2019 14:44:35 -0600 Subject: [PATCH 07/44] coq-lang: format sentences (newline) --- prover/lang/coq-lang.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/prover/lang/coq-lang.md b/prover/lang/coq-lang.md index 5c1107466..eb650f88e 100644 --- a/prover/lang/coq-lang.md +++ b/prover/lang/coq-lang.md @@ -81,7 +81,7 @@ module COQ syntax CoqSentence ::= CoqDefinition | CoqInductive // | CoqCoInductive - syntax CoqSentences ::= List{CoqSentence, ""} [klabel(CoqSentences)] + syntax CoqSentences ::= List{CoqSentence, ""} [klabel(CoqSentences), format(%1%n%2 %3)] syntax CoqDefinition ::= "Definition" CoqIdent ":=" CoqTerm "." | "Definition" CoqIdent CoqBinders ":" CoqTerm ":=" CoqTerm "." From 24139683810ee8013e0d48c434aaa53fa0b3a958 Mon Sep 17 00:00:00 2001 From: Lucas Pena Date: Tue, 17 Dec 2019 10:57:21 -0600 Subject: [PATCH 08/44] t/Logic.v: added eq inductive type --- prover/t/Logic.v | 8 +++----- 1 file changed, 3 insertions(+), 5 deletions(-) diff --git a/prover/t/Logic.v b/prover/t/Logic.v index 96c94a51e..b46e46b4f 100644 --- a/prover/t/Logic.v +++ b/prover/t/Logic.v @@ -18,11 +18,6 @@ Definition iff (A B : Prop) : Prop := Definition IF_then_else (P Q R : Prop) : Prop := (or (and P Q)) (and (not P) R) . -// Syntax in https://github.com/coq/coq/blob/master/theories/Init/Logic -// that we cannot parse for now. - -// All Theorems (Are we going to support those?) - Inductive ex1 (A : Type) (P : forall (x : A), Prop) : Prop := ex_intro1 : forall (x : A), forall (y : (P x)), ex1 A P . @@ -40,3 +35,6 @@ Definition AndComm := match H with conj H0 H1 => conj H1 H0 end . + +Inductive eq (A:Type) (x:A) : forall (_:A), Prop := + eq_refl : @ eq A x x . From 2d5da277e31c2499b23a8f251a99db7144b529fd Mon Sep 17 00:00:00 2001 From: Lucas Pena Date: Tue, 17 Dec 2019 20:00:48 -0600 Subject: [PATCH 09/44] coq-driver: begin translating inductive defs to ml --- prover/drivers/coq-driver.md | 24 ++++++++++++++++++++++++ prover/lang/coq-lang.md | 14 ++++++++++++-- prover/t/Logic.v | 8 ++++---- 3 files changed, 40 insertions(+), 6 deletions(-) diff --git a/prover/drivers/coq-driver.md b/prover/drivers/coq-driver.md index a05f89a11..be1ab8989 100644 --- a/prover/drivers/coq-driver.md +++ b/prover/drivers/coq-driver.md @@ -27,6 +27,30 @@ module DRIVER-COQ imports PROVER-CONFIGURATION imports PROVER-CORE-SYNTAX imports STRATEGIES-EXPORTED-SYNTAX + + rule CS:CoqSentence CSs:CoqSentences => CS ~> CSs ... + + rule Inductive ID BINDERs : TERM := .CoqIndCases . + => .K + ... + + ( .Bag + => sort CoqTermToSort(ID) + ) ... + + + rule Inductive ID BINDERs : TERM := (IDC BINDERCs : TERMC) | CASEs . + => Inductive ID BINDERs : TERM := CASEs . + ... + + ( .Bag + => symbol CoqIdentToSymbol(IDC)(CoqBindersToSorts(BINDERCs)) : CoqTermToSort(ID) + ) ... + + + syntax Sorts ::= CoqBindersToSorts(CoqBinders) [function] + rule CoqBindersToSorts(.CoqBinders) => .Sorts + rule CoqBindersToSorts((_ : SORT) BINDERs) => CoqTermToSort(SORT), CoqBindersToSorts(BINDERs) ``` ```k diff --git a/prover/lang/coq-lang.md b/prover/lang/coq-lang.md index eb650f88e..168f2c321 100644 --- a/prover/lang/coq-lang.md +++ b/prover/lang/coq-lang.md @@ -18,12 +18,22 @@ module COQ | Underscore syntax CoqNames ::= List{CoqName, ""} [klabel(CoqNames)] -// Hardcoded Coq Sorts +// Sorts syntax CoqSort ::= "SProp" | "Prop" | "Set" | "Type" +// Converting between Sorts: + syntax Sort ::= CoqTermToSort(CoqTerm) [function] + rule CoqTermToSort(SORT:UpperName) => SORT + rule CoqTermToSort(SORT:LowerName) => SORT + + syntax Symbol ::= CoqIdentToSymbol(CoqIdent) [function] + rule CoqIdentToSymbol(IDENT:UpperName) => IDENT + rule CoqIdentToSymbol(IDENT:LowerName) => IDENT + + // Terms syntax CoqTerm ::= "fun" CoqBinders "=>" CoqTerm | "fix" CoqFixBodies @@ -88,7 +98,7 @@ module COQ syntax CoqInductive ::= "Inductive" CoqIndBody "." syntax CoqIndBody ::= CoqIdent CoqBinders ":" CoqTerm ":=" CoqIndCases syntax CoqIndCase ::= CoqIdent CoqBinders ":" CoqTerm - syntax CoqIndCases ::= List{CoqIndCase, "|"} + syntax CoqIndCases ::= List{CoqIndCase, "|"} [klabel(CoqIndCases)] ``` diff --git a/prover/t/Logic.v b/prover/t/Logic.v index b46e46b4f..0db457935 100644 --- a/prover/t/Logic.v +++ b/prover/t/Logic.v @@ -3,8 +3,6 @@ Inductive True : Prop := Inductive False : Prop := . -Definition not (A : Prop) : Prop := forall (x : A), False . - Inductive and (A B : Prop) : Prop := conj : forall (x : A), forall (y : B), and A B . @@ -12,6 +10,8 @@ Inductive or (A B : Prop) : Prop := or_introl : forall (x : A), or A B | or_intror : forall (y : A), or A B . +Definition not (A : Prop) : Prop := forall (x : A), False . + Definition iff (A B : Prop) : Prop := (and (forall (x : A), B)) (forall (y : B), A) . @@ -31,9 +31,9 @@ Inductive ex4 (A : Type) (P : forall (x : A), Prop) : Prop := ex_intro4 : forall (x : A), forall (y : (P x)), @ ex4 A P . Definition AndComm := - fun (A B : Prop) (H : and A B) => + fun (A B : Prop) (H : and A B) ==> match H with - conj H0 H1 => conj H1 H0 + conj H0 H1 ==> conj H1 H0 end . Inductive eq (A:Type) (x:A) : forall (_:A), Prop := From 40317e2e86d78894151f0832b8a53031accc9335 Mon Sep 17 00:00:00 2001 From: Lucas Pena Date: Thu, 19 Dec 2019 10:02:03 -0600 Subject: [PATCH 10/44] coq-driver: begin translating Definitions --- prover/drivers/coq-driver.md | 16 +++++++++++++++- prover/lang/coq-lang.md | 6 +++--- prover/lang/kore-lang.md | 1 + 3 files changed, 19 insertions(+), 4 deletions(-) diff --git a/prover/drivers/coq-driver.md b/prover/drivers/coq-driver.md index be1ab8989..3ac20ba5a 100644 --- a/prover/drivers/coq-driver.md +++ b/prover/drivers/coq-driver.md @@ -50,7 +50,21 @@ module DRIVER-COQ syntax Sorts ::= CoqBindersToSorts(CoqBinders) [function] rule CoqBindersToSorts(.CoqBinders) => .Sorts - rule CoqBindersToSorts((_ : SORT) BINDERs) => CoqTermToSort(SORT), CoqBindersToSorts(BINDERs) + rule CoqBindersToSorts(NAME:CoqName BINDERs) => StringToSort("Term"), CoqBindersToSorts(BINDERs) + rule CoqBindersToSorts((NAMES : TYPE) BINDERs) => CoqNamesToSorts(NAMES) ++Sorts CoqBindersToSorts(BINDERs) + + syntax Sorts ::= CoqNamesToSorts(CoqNames) [function] + rule CoqNamesToSorts(.CoqNames) => .Sorts + rule CoqNamesToSorts(NAME:CoqName NAMEs) => StringToSort("Term"), CoqNamesToSorts(NAMEs) + + rule Definition ID BINDERs : TYPE := TERM . + => .K + ... + + ( .Bag + => symbol CoqIdentToSymbol(ID)(CoqBindersToSorts(BINDERs)) : CoqTermToSort(ID) + ) ... + ``` ```k diff --git a/prover/lang/coq-lang.md b/prover/lang/coq-lang.md index 168f2c321..fc4e2e23c 100644 --- a/prover/lang/coq-lang.md +++ b/prover/lang/coq-lang.md @@ -8,7 +8,7 @@ module COQ imports INT-SYNTAX imports BOOL-SYNTAX imports STRING - imports KORE + imports KORE-HELPERS // Identifiers syntax CoqIdent ::= LowerName @@ -26,8 +26,8 @@ module COQ // Converting between Sorts: syntax Sort ::= CoqTermToSort(CoqTerm) [function] - rule CoqTermToSort(SORT:UpperName) => SORT - rule CoqTermToSort(SORT:LowerName) => SORT + rule CoqTermToSort(SORT:UpperName) => StringToSort("Term") + rule CoqTermToSort(SORT:LowerName) => StringToSort("Term") syntax Symbol ::= CoqIdentToSymbol(CoqIdent) [function] rule CoqIdentToSymbol(IDENT:UpperName) => IDENT diff --git a/prover/lang/kore-lang.md b/prover/lang/kore-lang.md index f6c3aee75..1fcdd4050 100644 --- a/prover/lang/kore-lang.md +++ b/prover/lang/kore-lang.md @@ -209,6 +209,7 @@ module KORE-HELPERS syntax String ::= SortToString(Sort) [function, functional, hook(STRING.token2string)] syntax String ::= SymbolToString(Symbol) [function, functional, hook(STRING.token2string)] syntax LowerName ::= StringToSymbol(String) [function, functional, hook(STRING.string2token)] + syntax UpperName ::= StringToSort(String) [function, functional, hook(STRING.string2token)] syntax Symbol ::= parameterizedSymbol(Symbol, Sort) [function] rule parameterizedSymbol(SYMBOL, SORT) => StringToSymbol(SymbolToString(SYMBOL) +String "_" +String SortToString(SORT)) From 2dd0facebee6b5fd4d5556561dd365a910b385fd Mon Sep 17 00:00:00 2001 From: Lucas Pena Date: Thu, 19 Dec 2019 15:28:44 -0600 Subject: [PATCH 11/44] coq-driver: translating some definitions/terms --- prover/drivers/coq-driver.md | 40 ++++++++++++++++++++++++++++-------- prover/lang/coq-lang.md | 5 +++++ prover/lang/kore-lang.md | 6 ++++++ prover/lang/smt-lang.md | 2 +- prover/t/Logic.v | 29 ++++++++++++++------------ 5 files changed, 60 insertions(+), 22 deletions(-) diff --git a/prover/drivers/coq-driver.md b/prover/drivers/coq-driver.md index 3ac20ba5a..ae4154dc5 100644 --- a/prover/drivers/coq-driver.md +++ b/prover/drivers/coq-driver.md @@ -30,6 +30,24 @@ module DRIVER-COQ rule CS:CoqSentence CSs:CoqSentences => CS ~> CSs ... + rule Definition ID BINDERs : TYPE := TERM . + => .K + ... + + ( .Bag + => symbol CoqIdentToSymbol(ID)(CoqBindersToSorts(BINDERs)) : CoqTermToSort(ID) + ) ... + + + rule Definition ID := TERM . + => .K + ... + + ( .Bag + => axiom \equals(CoqIdentToSymbol(ID), CoqTermToPattern(TERM)) + ) ... + + rule Inductive ID BINDERs : TERM := .CoqIndCases . => .K ... @@ -57,14 +75,20 @@ module DRIVER-COQ rule CoqNamesToSorts(.CoqNames) => .Sorts rule CoqNamesToSorts(NAME:CoqName NAMEs) => StringToSort("Term"), CoqNamesToSorts(NAMEs) - rule Definition ID BINDERs : TYPE := TERM . - => .K - ... - - ( .Bag - => symbol CoqIdentToSymbol(ID)(CoqBindersToSorts(BINDERs)) : CoqTermToSort(ID) - ) ... - + syntax Pattern ::= CoqTermToPattern(CoqTerm) [function] + rule CoqTermToPattern(fun BINDERs => TERM) => \lambda { CoqBindersToPatterns(BINDERs) } CoqTermToPattern(TERM) + rule CoqTermToPattern(forall BINDERs, TERM) => \forall { CoqBindersToPatterns(BINDERs) } CoqTermToPattern(TERM) + rule CoqTermToPattern(_:CoqTerm) => \bottom() + + syntax Patterns ::= CoqBindersToPatterns(CoqBinders) [function] + rule CoqBindersToPatterns(.CoqBinders) => .Patterns + rule CoqBindersToPatterns(BINDER BINDERs:CoqBinders) => + CoqBinderToPatterns(BINDER) ++Patterns CoqBindersToPatterns(BINDERs) + + syntax Patterns ::= CoqBinderToPatterns(CoqBinder) [function] + rule CoqBinderToPatterns(NAME:CoqName) => CoqNameToVariableName(NAME) { StringToSort("Term") } + rule CoqBinderToPatterns((.CoqNames : TYPE:CoqTerm)) => .Patterns + rule CoqBinderToPatterns(((NAME:CoqName NAMES:CoqNames) : TYPE:CoqTerm)) => CoqNameToVariableName(NAME) { StringToSort("Term") }, CoqBinderToPatterns((NAMES : TYPE)) ``` ```k diff --git a/prover/lang/coq-lang.md b/prover/lang/coq-lang.md index fc4e2e23c..c1c47045f 100644 --- a/prover/lang/coq-lang.md +++ b/prover/lang/coq-lang.md @@ -24,6 +24,9 @@ module COQ | "Set" | "Type" +// Seralize to String: + syntax String ::= CoqNameToString(CoqName) [function, functional, hook(STRING.token2string)] + // Converting between Sorts: syntax Sort ::= CoqTermToSort(CoqTerm) [function] rule CoqTermToSort(SORT:UpperName) => StringToSort("Term") @@ -33,6 +36,8 @@ module COQ rule CoqIdentToSymbol(IDENT:UpperName) => IDENT rule CoqIdentToSymbol(IDENT:LowerName) => IDENT + syntax VariableName ::= CoqNameToVariableName(CoqName) [function] + rule CoqNameToVariableName(NAME) => StringToVariableName(CoqNameToString(NAME)) // Terms syntax CoqTerm ::= "fun" CoqBinders "=>" CoqTerm diff --git a/prover/lang/kore-lang.md b/prover/lang/kore-lang.md index 1fcdd4050..9f7700a9e 100644 --- a/prover/lang/kore-lang.md +++ b/prover/lang/kore-lang.md @@ -164,6 +164,10 @@ only in this scenario*. | "heap" "(" Sort "," Sort ")" // Location, Data | "\\hole" "(" ")" [klabel(Phole)] + // for Coq translation + | "\\lambda" "{" Patterns "}" Pattern [klabel(lambda)] + | "\\pi" "{" Patterns "}" Pattern [klabel(pi)] + rule \top() => \and(.Patterns) [anywhere] rule \bottom() => \or(.Patterns) [anywhere] @@ -211,6 +215,8 @@ module KORE-HELPERS syntax LowerName ::= StringToSymbol(String) [function, functional, hook(STRING.string2token)] syntax UpperName ::= StringToSort(String) [function, functional, hook(STRING.string2token)] + syntax VariableName ::= StringToVariableName(String) [function, functional, hook(STRING.string2token)] + syntax Symbol ::= parameterizedSymbol(Symbol, Sort) [function] rule parameterizedSymbol(SYMBOL, SORT) => StringToSymbol(SymbolToString(SYMBOL) +String "_" +String SortToString(SORT)) diff --git a/prover/lang/smt-lang.md b/prover/lang/smt-lang.md index e1a092d2a..f999a7d4a 100644 --- a/prover/lang/smt-lang.md +++ b/prover/lang/smt-lang.md @@ -103,6 +103,7 @@ module SMTLIB2-HELPERS imports K-IO imports SMTLIB2 imports PROVER-CORE-SYNTAX + imports KORE-HELPERS syntax SMTLIB2AttributeValue ::= CheckSATResult syntax CheckSATResult ::= "error" "(" K ")" @@ -116,7 +117,6 @@ module SMTLIB2-HELPERS // Converting between Sorts: - syntax VariableName ::= StringToVariableName(String) [function, functional, hook(STRING.string2token)] syntax VariableName ::= SMTLIB2SimpleSymbolToVariableName(SMTLIB2SimpleSymbol) [function] rule SMTLIB2SimpleSymbolToVariableName(SYMBOL) => StringToVariableName("V" +String SMTLIB2SimpleSymbolToString(SYMBOL)) diff --git a/prover/t/Logic.v b/prover/t/Logic.v index 0db457935..a4114e30f 100644 --- a/prover/t/Logic.v +++ b/prover/t/Logic.v @@ -1,14 +1,4 @@ -Inductive True : Prop := - I : True . - -Inductive False : Prop := . - -Inductive and (A B : Prop) : Prop := - conj : forall (x : A), forall (y : B), and A B . - -Inductive or (A B : Prop) : Prop := - or_introl : forall (x : A), or A B - | or_intror : forall (y : A), or A B . +Definition not := fun (A: Prop) => (forall (x : A), False) . Definition not (A : Prop) : Prop := forall (x : A), False . @@ -31,10 +21,23 @@ Inductive ex4 (A : Type) (P : forall (x : A), Prop) : Prop := ex_intro4 : forall (x : A), forall (y : (P x)), @ ex4 A P . Definition AndComm := - fun (A B : Prop) (H : and A B) ==> + fun (A B : Prop) (H : and A B) => match H with - conj H0 H1 ==> conj H1 H0 + conj H0 H1 => conj H1 H0 end . + +Inductive True : Prop := + I : True . + +Inductive False : Prop := . + +Inductive and (A B : Prop) : Prop := + conj : forall (x : A), forall (y : B), and A B . + +Inductive or (A B : Prop) : Prop := + or_introl : forall (x : A), or A B + | or_intror : forall (y : A), or A B . + Inductive eq (A:Type) (x:A) : forall (_:A), Prop := eq_refl : @ eq A x x . From 8e88b50d372f1a7d037c142b5aac30670f6a731b Mon Sep 17 00:00:00 2001 From: Lucas Pena Date: Fri, 10 Jan 2020 13:17:24 -0600 Subject: [PATCH 12/44] coq-driver: more translating coq term to pattern. AndComm mostly translated --- prover/drivers/coq-driver.md | 42 +++++++++++++++++++++++++++++++++++- prover/lang/coq-lang.md | 7 ++++-- prover/t/AndComm.v | 10 +++++++++ prover/t/Logic.v | 17 +++++++++------ 4 files changed, 66 insertions(+), 10 deletions(-) create mode 100644 prover/t/AndComm.v diff --git a/prover/drivers/coq-driver.md b/prover/drivers/coq-driver.md index ae4154dc5..e422181b7 100644 --- a/prover/drivers/coq-driver.md +++ b/prover/drivers/coq-driver.md @@ -76,9 +76,49 @@ module DRIVER-COQ rule CoqNamesToSorts(NAME:CoqName NAMEs) => StringToSort("Term"), CoqNamesToSorts(NAMEs) syntax Pattern ::= CoqTermToPattern(CoqTerm) [function] + rule CoqTermToPattern(H:UpperName) => CoqIdentToSymbol(H) rule CoqTermToPattern(fun BINDERs => TERM) => \lambda { CoqBindersToPatterns(BINDERs) } CoqTermToPattern(TERM) rule CoqTermToPattern(forall BINDERs, TERM) => \forall { CoqBindersToPatterns(BINDERs) } CoqTermToPattern(TERM) - rule CoqTermToPattern(_:CoqTerm) => \bottom() + rule CoqTermToPattern(match Ts with .CoqEquations end) => \bottom() + rule CoqTermToPattern(match Ts with (MP:CoqMultPattern => TM:CoqTerm) | EQs end) => + \or( #flattenOrs( + \or( \exists { .Patterns } + \and( #equals(CoqMatchItemsToPatterns(Ts), CoqMultPatternToPatterns(MP)) + ++Patterns + CoqTermToPattern(TM) + ) + ++Patterns + CoqTermToPattern(match Ts with EQs end) + ), .Patterns)) + // TODO: if TM is not a QualID, still need to translate. ex: (fun x => x) 3 + rule CoqTermToPattern(TM:CoqQualID ARG) => CoqIdentToSymbol(TM)(CoqArgToPatterns(ARG)) + + syntax Patterns ::= CoqArgToPatterns(CoqArg) [function] + rule CoqArgToPatterns(ARG1 ARG2) => CoqArgToPatterns(ARG1) ++Patterns CoqArgToPatterns(ARG2) + rule CoqArgToPatterns(TM:CoqTerm) => CoqTermToPattern(TM), .Patterns + [owise] + + syntax Patterns ::= CoqMatchItemsToPatterns(CoqMatchItems) [function] + syntax Pattern ::= CoqMatchItemToPattern(CoqMatchItem) [function] + rule CoqMatchItemsToPatterns(.CoqMatchItems) => .Patterns + rule CoqMatchItemsToPatterns(MI:CoqMatchItem, MIs) => CoqMatchItemToPattern(MI), .Patterns + + rule CoqMatchItemToPattern(MI:CoqTerm) => CoqTermToPattern(MI) + + syntax Patterns ::= #equals(Patterns, Patterns) [function] + rule #equals(.Patterns, .Patterns) => .Patterns + rule #equals((P1, Ps1), (P2, Ps2)) => \equals(P1, P2), #equals(Ps1, Ps2) + + syntax Pattern ::= CoqPatternToPattern(CoqPattern) [function] + syntax Patterns ::= CoqPatternToPatterns(CoqPattern) [function] + syntax Patterns ::= CoqMultPatternToPatterns(CoqMultPattern) [function] + rule CoqMultPatternToPatterns(.CoqMultPattern) => .Patterns + rule CoqMultPatternToPatterns(MP, MPs) => CoqPatternToPattern(MP), CoqMultPatternToPatterns(MPs) + + rule CoqPatternToPattern(ID:CoqQualID) => CoqIdentToSymbol(ID) + rule CoqPatternToPattern(ID:CoqQualID P:CoqPattern) => CoqIdentToSymbol(ID)(CoqPatternToPatterns(P)) + rule CoqPatternToPatterns(ID:CoqQualID) => CoqIdentToSymbol(ID), .Patterns + rule CoqPatternToPatterns(P1:CoqPattern P2:CoqPattern) => CoqPatternToPatterns(P1) ++Patterns CoqPatternToPatterns(P2) syntax Patterns ::= CoqBindersToPatterns(CoqBinders) [function] rule CoqBindersToPatterns(.CoqBinders) => .Patterns diff --git a/prover/lang/coq-lang.md b/prover/lang/coq-lang.md index c1c47045f..b767411da 100644 --- a/prover/lang/coq-lang.md +++ b/prover/lang/coq-lang.md @@ -36,6 +36,9 @@ module COQ rule CoqIdentToSymbol(IDENT:UpperName) => IDENT rule CoqIdentToSymbol(IDENT:LowerName) => IDENT + syntax Symbol ::= CoqQualIDToSymbol(CoqQualID) [function] + rule CoqQualIDToSymbol(ID:CoqIdent) => CoqIdentToSymbol(ID) + syntax VariableName ::= CoqNameToVariableName(CoqName) [function] rule CoqNameToVariableName(NAME) => StringToVariableName(CoqNameToString(NAME)) @@ -59,9 +62,9 @@ module COQ | "(" CoqNames ":" CoqTerm ")" syntax CoqBinders ::= List{CoqBinder, ""} [klabel(CoqBinders)] - syntax CoqArg ::= CoqTerm + syntax CoqArg ::= CoqArg CoqArg | "(" CoqIdent ":=" CoqTerm ")" - | CoqArg CoqArg + > CoqTerm syntax CoqTerms ::= List{CoqTerm, ""} [klabel(CoqTerms)] syntax CoqFixBody ::= CoqIdent CoqBinders ":=" CoqTerm diff --git a/prover/t/AndComm.v b/prover/t/AndComm.v new file mode 100644 index 000000000..f2037a45b --- /dev/null +++ b/prover/t/AndComm.v @@ -0,0 +1,10 @@ +Definition AndComm := + fun (A B : Prop) (H : and A B) => + match H with + conj H0 H1 => conj H1 H0 + end . + +// exists H0, H1. H = conj(H0, H1) /\ conj(H1, H0) + + +// desugarMatch(H, (conj(H0, H1), conj(H1, H0)), ... ) diff --git a/prover/t/Logic.v b/prover/t/Logic.v index a4114e30f..6111d86bd 100644 --- a/prover/t/Logic.v +++ b/prover/t/Logic.v @@ -1,6 +1,15 @@ +Inductive True : Prop := + I : True . + +Inductive False : Prop := . + +Inductive nat : Prop := + Z : nat + | S : nat -> nat . + Definition not := fun (A: Prop) => (forall (x : A), False) . -Definition not (A : Prop) : Prop := forall (x : A), False . +// Definition not (A : Prop) : Prop := forall (x : A), False . Definition iff (A B : Prop) : Prop := (and (forall (x : A), B)) (forall (y : B), A) . @@ -26,12 +35,6 @@ Definition AndComm := conj H0 H1 => conj H1 H0 end . - -Inductive True : Prop := - I : True . - -Inductive False : Prop := . - Inductive and (A B : Prop) : Prop := conj : forall (x : A), forall (y : B), and A B . From 93bb94e988e6dd6c7300c4b1f6b113f316746d39 Mon Sep 17 00:00:00 2001 From: Lucas Pena Date: Mon, 13 Jan 2020 11:36:03 -0600 Subject: [PATCH 13/44] add mu, translating fix --- prover/drivers/coq-driver.md | 5 ++++- prover/lang/coq-lang.md | 1 + prover/lang/kore-lang.md | 7 ++++++- prover/t/False_ind.v | 3 +++ prover/t/nat_ind.v | 8 ++++++++ 5 files changed, 22 insertions(+), 2 deletions(-) create mode 100644 prover/t/False_ind.v create mode 100644 prover/t/nat_ind.v diff --git a/prover/drivers/coq-driver.md b/prover/drivers/coq-driver.md index e422181b7..cd3aaf901 100644 --- a/prover/drivers/coq-driver.md +++ b/prover/drivers/coq-driver.md @@ -76,7 +76,8 @@ module DRIVER-COQ rule CoqNamesToSorts(NAME:CoqName NAMEs) => StringToSort("Term"), CoqNamesToSorts(NAMEs) syntax Pattern ::= CoqTermToPattern(CoqTerm) [function] - rule CoqTermToPattern(H:UpperName) => CoqIdentToSymbol(H) + rule CoqTermToPattern(UN:UpperName) => CoqIdentToSymbol(UN) + rule CoqTermToPattern(LN:LowerName) => CoqIdentToSymbol(LN) rule CoqTermToPattern(fun BINDERs => TERM) => \lambda { CoqBindersToPatterns(BINDERs) } CoqTermToPattern(TERM) rule CoqTermToPattern(forall BINDERs, TERM) => \forall { CoqBindersToPatterns(BINDERs) } CoqTermToPattern(TERM) rule CoqTermToPattern(match Ts with .CoqEquations end) => \bottom() @@ -93,6 +94,8 @@ module DRIVER-COQ // TODO: if TM is not a QualID, still need to translate. ex: (fun x => x) 3 rule CoqTermToPattern(TM:CoqQualID ARG) => CoqIdentToSymbol(TM)(CoqArgToPatterns(ARG)) + rule CoqTermToPattern(fix ID BINDERs := TM) => \mu { CoqNameToVariableName(ID) {{ StringToSort("Term") }} } CoqTermToPattern(fun BINDERs => TM) + syntax Patterns ::= CoqArgToPatterns(CoqArg) [function] rule CoqArgToPatterns(ARG1 ARG2) => CoqArgToPatterns(ARG1) ++Patterns CoqArgToPatterns(ARG2) rule CoqArgToPatterns(TM:CoqTerm) => CoqTermToPattern(TM), .Patterns diff --git a/prover/lang/coq-lang.md b/prover/lang/coq-lang.md index b767411da..0e27d4716 100644 --- a/prover/lang/coq-lang.md +++ b/prover/lang/coq-lang.md @@ -68,6 +68,7 @@ module COQ syntax CoqTerms ::= List{CoqTerm, ""} [klabel(CoqTerms)] syntax CoqFixBody ::= CoqIdent CoqBinders ":=" CoqTerm + | CoqIdent CoqBinders ":" CoqTerm ":=" CoqTerm syntax CoqFixBodyList ::= List{CoqFixBody, "with"} syntax CoqFixBodies ::= CoqFixBody | CoqFixBody CoqFixBodyList "for" CoqIdent diff --git a/prover/lang/kore-lang.md b/prover/lang/kore-lang.md index 9f7700a9e..b98299b42 100644 --- a/prover/lang/kore-lang.md +++ b/prover/lang/kore-lang.md @@ -137,9 +137,11 @@ is to be used for generating fresh variables. *The second variety must be used only in this scenario*. ```k - syntax Variable ::= VariableName "{" Sort "}" [klabel(sortedVariable)] + syntax Variable ::= VariableName "{" Sort "}" [klabel(sortedVariable)] + syntax SetVariable ::= VariableName "{{" Sort "}}" [klabel(sortedSetVariable)] syntax Pattern ::= Int | Variable + | SetVariable | Symbol | Symbol "(" Patterns ")" [klabel(apply)] @@ -155,6 +157,9 @@ only in this scenario*. | "\\exists" "{" Patterns "}" Pattern [klabel(exists)] | "\\forall" "{" Patterns "}" Pattern [klabel(forall)] + | "\\mu" "{" Patterns "}" Pattern [klabel(mu)] + | "\\nu" "{" Patterns "}" Pattern [klabel(nu)] + /* Sugar for \iff, \mu and application */ | "\\iff-lfp" "(" Pattern "," Pattern ")" [klabel(ifflfp)] diff --git a/prover/t/False_ind.v b/prover/t/False_ind.v new file mode 100644 index 000000000..e10e975d3 --- /dev/null +++ b/prover/t/False_ind.v @@ -0,0 +1,3 @@ +Definition False_ind := +fun (P : Prop) (f : False) => match f return P with + end . diff --git a/prover/t/nat_ind.v b/prover/t/nat_ind.v new file mode 100644 index 000000000..3fba7716b --- /dev/null +++ b/prover/t/nat_ind.v @@ -0,0 +1,8 @@ +Definition nat_ind := +fun (P : nat -> Prop) (f : P 0) (f0 : forall (n : nat), P n -> P (S n)) => +fix F (n : nat) := match n with + Z => f + | S n0 => f0 n0 (F n0) + end . + +// tr(fun ... ) \mu { F {{ Term }} } tr( fun n => match ) ... ) \ No newline at end of file From ba950175d77244aae20e48553f7d3e8de4dbfcd4 Mon Sep 17 00:00:00 2001 From: Lucas Pena Date: Mon, 13 Jan 2020 14:47:25 -0600 Subject: [PATCH 14/44] coq-driver: translate binders from match clauses --- prover/drivers/coq-driver.md | 12 ++++++++++-- prover/lang/coq-lang.md | 4 ++-- 2 files changed, 12 insertions(+), 4 deletions(-) diff --git a/prover/drivers/coq-driver.md b/prover/drivers/coq-driver.md index cd3aaf901..fb7694c17 100644 --- a/prover/drivers/coq-driver.md +++ b/prover/drivers/coq-driver.md @@ -83,7 +83,7 @@ module DRIVER-COQ rule CoqTermToPattern(match Ts with .CoqEquations end) => \bottom() rule CoqTermToPattern(match Ts with (MP:CoqMultPattern => TM:CoqTerm) | EQs end) => \or( #flattenOrs( - \or( \exists { .Patterns } + \or( \exists { CoqMultPatternToBinders(MP) } \and( #equals(CoqMatchItemsToPatterns(Ts), CoqMultPatternToPatterns(MP)) ++Patterns CoqTermToPattern(TM) @@ -121,7 +121,15 @@ module DRIVER-COQ rule CoqPatternToPattern(ID:CoqQualID) => CoqIdentToSymbol(ID) rule CoqPatternToPattern(ID:CoqQualID P:CoqPattern) => CoqIdentToSymbol(ID)(CoqPatternToPatterns(P)) rule CoqPatternToPatterns(ID:CoqQualID) => CoqIdentToSymbol(ID), .Patterns - rule CoqPatternToPatterns(P1:CoqPattern P2:CoqPattern) => CoqPatternToPatterns(P1) ++Patterns CoqPatternToPatterns(P2) + rule CoqPatternToPatterns(ID:CoqQualID P:CoqPattern) => CoqIdentToSymbol(ID) ++Patterns CoqPatternToPatterns(P) + + // Get binders from MultPattern + syntax Patterns ::= CoqMultPatternToBinders(CoqMultPattern) [function] + syntax Patterns ::= CoqPatternToBinders(CoqMultPattern) [function] + rule CoqMultPatternToBinders(ID:CoqQualID) => .Patterns + rule CoqMultPatternToBinders(ID:CoqQualID P:CoqPattern) => CoqPatternToBinders(P) + rule CoqPatternToBinders(ID:CoqQualID) => CoqIdentToSymbol(ID), .Patterns + rule CoqPatternToBinders(ID:CoqQualID P:CoqPattern) => CoqIdentToSymbol(ID), CoqPatternToBinders(P) syntax Patterns ::= CoqBindersToPatterns(CoqBinders) [function] rule CoqBindersToPatterns(.CoqBinders) => .Patterns diff --git a/prover/lang/coq-lang.md b/prover/lang/coq-lang.md index 0e27d4716..8ad049bcb 100644 --- a/prover/lang/coq-lang.md +++ b/prover/lang/coq-lang.md @@ -86,7 +86,7 @@ module COQ syntax CoqPattern ::= CoqQualID CoqPattern | "@" CoqQualID CoqPattern - | CoqPattern CoqPattern + // | CoqPattern CoqPattern | CoqPattern "as" CoqIdent | CoqPattern "%" CoqIdent | CoqQualID @@ -94,7 +94,7 @@ module COQ | Int syntax CoqMultPattern ::= List{CoqPattern, ","} [klabel(CoqMultPattern)] - syntax CoqPatterns ::= List{CoqPattern, ""} [klabel(CoqPatterns)] + syntax CoqPatterns ::= NeList{CoqPattern, ""} [klabel(CoqPatterns)] // Vernacular syntax CoqSentence ::= CoqDefinition From 54749f9cc7fc7c81abdfcee5edabff5f5c5e5477 Mon Sep 17 00:00:00 2001 From: Lucas Pena Date: Wed, 15 Jan 2020 15:41:54 -0600 Subject: [PATCH 15/44] translating ind defs --- prover/drivers/coq-driver.md | 4 ++-- prover/lang/kore-lang.md | 1 + prover/t/nat_ind.v | 10 +++++++++- 3 files changed, 12 insertions(+), 3 deletions(-) diff --git a/prover/drivers/coq-driver.md b/prover/drivers/coq-driver.md index fb7694c17..307e8117b 100644 --- a/prover/drivers/coq-driver.md +++ b/prover/drivers/coq-driver.md @@ -29,7 +29,6 @@ module DRIVER-COQ imports STRATEGIES-EXPORTED-SYNTAX rule CS:CoqSentence CSs:CoqSentences => CS ~> CSs ... - rule Definition ID BINDERs : TYPE := TERM . => .K ... @@ -53,7 +52,7 @@ module DRIVER-COQ ... ( .Bag - => sort CoqTermToSort(ID) + => symbol CoqIdentToSymbol(ID)(CoqBindersToSorts(BINDERs)) : CoqTermToSort(ID) ) ... @@ -63,6 +62,7 @@ module DRIVER-COQ ( .Bag => symbol CoqIdentToSymbol(IDC)(CoqBindersToSorts(BINDERCs)) : CoqTermToSort(ID) + axiom \type(CoqIdentToSymbol(IDC)(.Patterns), CoqTermToPattern(TERMC)) ) ... diff --git a/prover/lang/kore-lang.md b/prover/lang/kore-lang.md index b98299b42..aac0c625d 100644 --- a/prover/lang/kore-lang.md +++ b/prover/lang/kore-lang.md @@ -172,6 +172,7 @@ only in this scenario*. // for Coq translation | "\\lambda" "{" Patterns "}" Pattern [klabel(lambda)] | "\\pi" "{" Patterns "}" Pattern [klabel(pi)] + | "\\type" "(" Pattern "," Pattern ")" [klabel(type)] rule \top() => \and(.Patterns) [anywhere] rule \bottom() => \or(.Patterns) [anywhere] diff --git a/prover/t/nat_ind.v b/prover/t/nat_ind.v index 3fba7716b..b127282e6 100644 --- a/prover/t/nat_ind.v +++ b/prover/t/nat_ind.v @@ -1,3 +1,11 @@ +Inductive nat : Type := Z : nat | S : forall (x : nat), nat . + +// symbol nat() : Term +// symbol Z() : Term +// symbol S() : Term + +// axiom \type(Z(), nat()) + Definition nat_ind := fun (P : nat -> Prop) (f : P 0) (f0 : forall (n : nat), P n -> P (S n)) => fix F (n : nat) := match n with @@ -5,4 +13,4 @@ fix F (n : nat) := match n with | S n0 => f0 n0 (F n0) end . -// tr(fun ... ) \mu { F {{ Term }} } tr( fun n => match ) ... ) \ No newline at end of file +// tr(fun ... ) \mu { F {{ Term }} } tr( fun n => match ) ... ) From 12b53bc1b5c78479716abc9dd3ede89e40fcbfdc Mon Sep 17 00:00:00 2001 From: Lucas Pena Date: Mon, 27 Jan 2020 09:38:07 -0600 Subject: [PATCH 16/44] parsing Logic.v --- prover/drivers/coq-driver.md | 5 +++++ prover/t/Logic.v | 8 ++++---- 2 files changed, 9 insertions(+), 4 deletions(-) diff --git a/prover/drivers/coq-driver.md b/prover/drivers/coq-driver.md index 307e8117b..fc0430239 100644 --- a/prover/drivers/coq-driver.md +++ b/prover/drivers/coq-driver.md @@ -29,6 +29,11 @@ module DRIVER-COQ imports STRATEGIES-EXPORTED-SYNTAX rule CS:CoqSentence CSs:CoqSentences => CS ~> CSs ... + ( .Bag + => sort StringToSort("Term") + ) ... + + rule Definition ID BINDERs : TYPE := TERM . => .K ... diff --git a/prover/t/Logic.v b/prover/t/Logic.v index 6111d86bd..7f886c87d 100644 --- a/prover/t/Logic.v +++ b/prover/t/Logic.v @@ -23,8 +23,8 @@ Inductive ex1 (A : Type) (P : forall (x : A), Prop) : Prop := Inductive ex2 (A : Type) (P : forall (x : A), Prop) : Prop := ex_intro2 : forall (x : A), forall (y : (P x)), ex2 P . -Inductive ex3 (A : Type) (P : forall (x : A), Prop) : Prop := - ex_intro3 : forall (x : A), forall (y : (P x)), ex3 (A:=A) P . +// Inductive ex3 (A : Type) (P : forall (x : A), Prop) : Prop := +// ex_intro3 : forall (x : A), forall (y : (P x)), ex3 (A:=A) P . Inductive ex4 (A : Type) (P : forall (x : A), Prop) : Prop := ex_intro4 : forall (x : A), forall (y : (P x)), @ ex4 A P . @@ -42,5 +42,5 @@ Inductive or (A B : Prop) : Prop := or_introl : forall (x : A), or A B | or_intror : forall (y : A), or A B . -Inductive eq (A:Type) (x:A) : forall (_:A), Prop := - eq_refl : @ eq A x x . +// Inductive eq (A:Type) (x:A) : forall (_:A), Prop := +// eq_refl : @ eq A x x . From 0c607458849e3b99d790b34eb99d3414be975fdf Mon Sep 17 00:00:00 2001 From: Lucas Pena Date: Mon, 27 Jan 2020 11:47:56 -0600 Subject: [PATCH 17/44] kore-lang: for aml: application is Pattern(Patterns) --- prover/drivers/coq-driver.md | 5 ++--- prover/lang/kore-lang.md | 2 +- 2 files changed, 3 insertions(+), 4 deletions(-) diff --git a/prover/drivers/coq-driver.md b/prover/drivers/coq-driver.md index fc0430239..bb57f7c2e 100644 --- a/prover/drivers/coq-driver.md +++ b/prover/drivers/coq-driver.md @@ -96,10 +96,9 @@ module DRIVER-COQ ++Patterns CoqTermToPattern(match Ts with EQs end) ), .Patterns)) - // TODO: if TM is not a QualID, still need to translate. ex: (fun x => x) 3 - rule CoqTermToPattern(TM:CoqQualID ARG) => CoqIdentToSymbol(TM)(CoqArgToPatterns(ARG)) - + rule CoqTermToPattern(TM:CoqTerm ARG) => CoqTermToPattern(TM)(CoqArgToPatterns(ARG)) rule CoqTermToPattern(fix ID BINDERs := TM) => \mu { CoqNameToVariableName(ID) {{ StringToSort("Term") }} } CoqTermToPattern(fun BINDERs => TM) + rule CoqTermToPattern(@ QID:CoqQualID TM:CoqTerm) => CoqIdentToSymbol(QID)(CoqTermToPattern(TM)) syntax Patterns ::= CoqArgToPatterns(CoqArg) [function] rule CoqArgToPatterns(ARG1 ARG2) => CoqArgToPatterns(ARG1) ++Patterns CoqArgToPatterns(ARG2) diff --git a/prover/lang/kore-lang.md b/prover/lang/kore-lang.md index aac0c625d..cf13f2b36 100644 --- a/prover/lang/kore-lang.md +++ b/prover/lang/kore-lang.md @@ -143,7 +143,7 @@ only in this scenario*. | Variable | SetVariable | Symbol - | Symbol "(" Patterns ")" [klabel(apply)] + | Pattern "(" Patterns ")" [klabel(apply)] | "\\top" "(" ")" [klabel(top)] | "\\bottom" "(" ")" [klabel(bottom)] From 46b712b005f1c7d7c92c75bdddff8ee40702248c Mon Sep 17 00:00:00 2001 From: Lucas Pena Date: Wed, 5 Feb 2020 11:23:08 -0600 Subject: [PATCH 18/44] cleanup --- prover/drivers/coq-driver.md | 32 ++++++++++---------------------- prover/lang/coq-lang.md | 15 ++++++++++----- 2 files changed, 20 insertions(+), 27 deletions(-) diff --git a/prover/drivers/coq-driver.md b/prover/drivers/coq-driver.md index bb57f7c2e..13a19fa01 100644 --- a/prover/drivers/coq-driver.md +++ b/prover/drivers/coq-driver.md @@ -28,36 +28,32 @@ module DRIVER-COQ imports PROVER-CORE-SYNTAX imports STRATEGIES-EXPORTED-SYNTAX +// Add sort "Term" to declarations rule CS:CoqSentence CSs:CoqSentences => CS ~> CSs ... ( .Bag => sort StringToSort("Term") ) ... - rule Definition ID BINDERs : TYPE := TERM . - => .K - ... - - ( .Bag - => symbol CoqIdentToSymbol(ID)(CoqBindersToSorts(BINDERs)) : CoqTermToSort(ID) - ) ... - - +// Add symbol (of sort Term) and equality axiom corresponding to each definition + rule Definition ID BINDERs : TYPE := TERM . => Definition ID := TERM . rule Definition ID := TERM . => .K ... ( .Bag - => axiom \equals(CoqIdentToSymbol(ID), CoqTermToPattern(TERM)) + => symbol CoqIdentToSymbol(ID)(.Sorts) : StringToSort("Term") + axiom \equals(CoqIdentToSymbol(ID), CoqTermToPattern(TERM)) ) ... +// Translate inductive cases rule Inductive ID BINDERs : TERM := .CoqIndCases . => .K ... ( .Bag - => symbol CoqIdentToSymbol(ID)(CoqBindersToSorts(BINDERs)) : CoqTermToSort(ID) + => symbol CoqIdentToSymbol(ID)(.Sorts) : StringToSort("Term") ) ... @@ -66,20 +62,12 @@ module DRIVER-COQ ... ( .Bag - => symbol CoqIdentToSymbol(IDC)(CoqBindersToSorts(BINDERCs)) : CoqTermToSort(ID) + => symbol CoqIdentToSymbol(IDC)(.Sorts) : StringToSort("Term") axiom \type(CoqIdentToSymbol(IDC)(.Patterns), CoqTermToPattern(TERMC)) ) ... - syntax Sorts ::= CoqBindersToSorts(CoqBinders) [function] - rule CoqBindersToSorts(.CoqBinders) => .Sorts - rule CoqBindersToSorts(NAME:CoqName BINDERs) => StringToSort("Term"), CoqBindersToSorts(BINDERs) - rule CoqBindersToSorts((NAMES : TYPE) BINDERs) => CoqNamesToSorts(NAMES) ++Sorts CoqBindersToSorts(BINDERs) - - syntax Sorts ::= CoqNamesToSorts(CoqNames) [function] - rule CoqNamesToSorts(.CoqNames) => .Sorts - rule CoqNamesToSorts(NAME:CoqName NAMEs) => StringToSort("Term"), CoqNamesToSorts(NAMEs) - +// Converting Term to Pattern syntax Pattern ::= CoqTermToPattern(CoqTerm) [function] rule CoqTermToPattern(UN:UpperName) => CoqIdentToSymbol(UN) rule CoqTermToPattern(LN:LowerName) => CoqIdentToSymbol(LN) @@ -127,7 +115,7 @@ module DRIVER-COQ rule CoqPatternToPatterns(ID:CoqQualID) => CoqIdentToSymbol(ID), .Patterns rule CoqPatternToPatterns(ID:CoqQualID P:CoqPattern) => CoqIdentToSymbol(ID) ++Patterns CoqPatternToPatterns(P) - // Get binders from MultPattern +// Get binders from MultPattern syntax Patterns ::= CoqMultPatternToBinders(CoqMultPattern) [function] syntax Patterns ::= CoqPatternToBinders(CoqMultPattern) [function] rule CoqMultPatternToBinders(ID:CoqQualID) => .Patterns diff --git a/prover/lang/coq-lang.md b/prover/lang/coq-lang.md index 8ad049bcb..ba92ca165 100644 --- a/prover/lang/coq-lang.md +++ b/prover/lang/coq-lang.md @@ -27,11 +27,7 @@ module COQ // Seralize to String: syntax String ::= CoqNameToString(CoqName) [function, functional, hook(STRING.token2string)] -// Converting between Sorts: - syntax Sort ::= CoqTermToSort(CoqTerm) [function] - rule CoqTermToSort(SORT:UpperName) => StringToSort("Term") - rule CoqTermToSort(SORT:LowerName) => StringToSort("Term") - +// Sort conversions syntax Symbol ::= CoqIdentToSymbol(CoqIdent) [function] rule CoqIdentToSymbol(IDENT:UpperName) => IDENT rule CoqIdentToSymbol(IDENT:LowerName) => IDENT @@ -42,6 +38,15 @@ module COQ syntax VariableName ::= CoqNameToVariableName(CoqName) [function] rule CoqNameToVariableName(NAME) => StringToVariableName(CoqNameToString(NAME)) + syntax Sorts ::= CoqBindersToSorts(CoqBinders) [function] + rule CoqBindersToSorts(.CoqBinders) => .Sorts + rule CoqBindersToSorts(NAME:CoqName BINDERs) => StringToSort("Term"), CoqBindersToSorts(BINDERs) + rule CoqBindersToSorts((NAMES : TYPE) BINDERs) => CoqNamesToSorts(NAMES) ++Sorts CoqBindersToSorts(BINDERs) + + syntax Sorts ::= CoqNamesToSorts(CoqNames) [function] + rule CoqNamesToSorts(.CoqNames) => .Sorts + rule CoqNamesToSorts(NAME:CoqName NAMEs) => StringToSort("Term"), CoqNamesToSorts(NAMEs) + // Terms syntax CoqTerm ::= "fun" CoqBinders "=>" CoqTerm | "fix" CoqFixBodies From b802ed306e02f3298e8095418e29f3eb3bf64ceb Mon Sep 17 00:00:00 2001 From: Lucas Pena Date: Wed, 5 Feb 2020 12:32:13 -0600 Subject: [PATCH 19/44] remove coq tests besides Logic and nat_ind, add expeted output for those --- prover/t/And.v | 2 - prover/t/AndComm.v | 10 ----- prover/t/False_ind.v | 3 -- prover/t/Four.v | 7 ---- prover/t/Logic.v.expected | 84 +++++++++++++++++++++++++++++++++++++ prover/t/Or.v | 3 -- prover/t/nat_ind.v.expected | 30 +++++++++++++ 7 files changed, 114 insertions(+), 25 deletions(-) delete mode 100644 prover/t/And.v delete mode 100644 prover/t/AndComm.v delete mode 100644 prover/t/False_ind.v delete mode 100644 prover/t/Four.v create mode 100644 prover/t/Logic.v.expected delete mode 100644 prover/t/Or.v create mode 100644 prover/t/nat_ind.v.expected diff --git a/prover/t/And.v b/prover/t/And.v deleted file mode 100644 index 0922f5013..000000000 --- a/prover/t/And.v +++ /dev/null @@ -1,2 +0,0 @@ -Inductive and (A B : Prop) : Prop := - conj : forall (x : A), forall (y : B), and A B . diff --git a/prover/t/AndComm.v b/prover/t/AndComm.v deleted file mode 100644 index f2037a45b..000000000 --- a/prover/t/AndComm.v +++ /dev/null @@ -1,10 +0,0 @@ -Definition AndComm := - fun (A B : Prop) (H : and A B) => - match H with - conj H0 H1 => conj H1 H0 - end . - -// exists H0, H1. H = conj(H0, H1) /\ conj(H1, H0) - - -// desugarMatch(H, (conj(H0, H1), conj(H1, H0)), ... ) diff --git a/prover/t/False_ind.v b/prover/t/False_ind.v deleted file mode 100644 index e10e975d3..000000000 --- a/prover/t/False_ind.v +++ /dev/null @@ -1,3 +0,0 @@ -Definition False_ind := -fun (P : Prop) (f : False) => match f return P with - end . diff --git a/prover/t/Four.v b/prover/t/Four.v deleted file mode 100644 index 3dd65757b..000000000 --- a/prover/t/Four.v +++ /dev/null @@ -1,7 +0,0 @@ -Definition Four := 4 . - -// Definition AndComm := -// fun (A B : Prop) (H : A /\ B) => -// match H with -// | conj H0 H1 => conj H1 H0 -// end . diff --git a/prover/t/Logic.v.expected b/prover/t/Logic.v.expected new file mode 100644 index 000000000..e70bbc419 --- /dev/null +++ b/prover/t/Logic.v.expected @@ -0,0 +1,84 @@ + + + .CoqSentences + + + 1 + + + .GoalCellSet + + + + axiom \equals ( AndComm , \lambda { A { Term } , B { Term } , H { Term } , .Patterns } \or ( \exists { H0 , H1 , .Patterns } \and ( \equals ( H , conj ( H0 , H1 , .Patterns ) ) , conj ( H1 , H0 , .Patterns ) , .Patterns ) , .Patterns ) ) + + axiom \equals ( IF_then_else , or ( and , P , Q , .Patterns ) ( and , not , P , R , .Patterns ) ) + + axiom \equals ( iff , and ( \forall { x { Term } , .Patterns } B , .Patterns ) ( \forall { y { Term } , .Patterns } A , .Patterns ) ) + + axiom \equals ( not , \lambda { A { Term } , .Patterns } \forall { x { Term } , .Patterns } False ) + + axiom \type ( I ( .Patterns ) , True ) + + axiom \type ( S ( .Patterns ) , nat ( - , > , nat , .Patterns ) ) + + axiom \type ( Z ( .Patterns ) , nat ) + + axiom \type ( conj ( .Patterns ) , \forall { x { Term } , .Patterns } \forall { y { Term } , .Patterns } ( and ( A , B , .Patterns ) ) ) + + axiom \type ( ex_intro1 ( .Patterns ) , \forall { x { Term } , .Patterns } \forall { y { Term } , .Patterns } ( ex1 ( A , P , .Patterns ) ) ) + + axiom \type ( ex_intro2 ( .Patterns ) , \forall { x { Term } , .Patterns } \forall { y { Term } , .Patterns } ( ex2 ( P , .Patterns ) ) ) + + axiom \type ( ex_intro4 ( .Patterns ) , \forall { x { Term } , .Patterns } \forall { y { Term } , .Patterns } ( ex4 ( A , .Patterns ) ( P , .Patterns ) ) ) + + axiom \type ( or_introl ( .Patterns ) , \forall { x { Term } , .Patterns } ( or ( A , B , .Patterns ) ) ) + + axiom \type ( or_intror ( .Patterns ) , \forall { y { Term } , .Patterns } ( or ( A , B , .Patterns ) ) ) + + sort Term + + symbol AndComm ( .Sorts ) : Term + + symbol False ( .Sorts ) : Term + + symbol I ( .Sorts ) : Term + + symbol IF_then_else ( .Sorts ) : Term + + symbol S ( .Sorts ) : Term + + symbol True ( .Sorts ) : Term + + symbol Z ( .Sorts ) : Term + + symbol and ( .Sorts ) : Term + + symbol conj ( .Sorts ) : Term + + symbol ex1 ( .Sorts ) : Term + + symbol ex2 ( .Sorts ) : Term + + symbol ex4 ( .Sorts ) : Term + + symbol ex_intro1 ( .Sorts ) : Term + + symbol ex_intro2 ( .Sorts ) : Term + + symbol ex_intro4 ( .Sorts ) : Term + + symbol iff ( .Sorts ) : Term + + symbol nat ( .Sorts ) : Term + + symbol not ( .Sorts ) : Term + + symbol or ( .Sorts ) : Term + + symbol or_introl ( .Sorts ) : Term + + symbol or_intror ( .Sorts ) : Term + + + diff --git a/prover/t/Or.v b/prover/t/Or.v deleted file mode 100644 index 52ab7940a..000000000 --- a/prover/t/Or.v +++ /dev/null @@ -1,3 +0,0 @@ -Inductive or (A B : Prop) : Prop := - or_introl : forall (x : A), or A B - | or_intror : forall (y : A), or A B . diff --git a/prover/t/nat_ind.v.expected b/prover/t/nat_ind.v.expected new file mode 100644 index 000000000..d64c4c59b --- /dev/null +++ b/prover/t/nat_ind.v.expected @@ -0,0 +1,30 @@ + + + .CoqSentences + + + 1 + + + .GoalCellSet + + + + axiom \equals ( nat_ind , \lambda { P { Term } , f { Term } , f0 { Term } , .Patterns } \mu { F {{ Term }} , .Patterns } \lambda { n { Term } , .Patterns } \or ( \exists { .Patterns } \and ( \equals ( n , Z ) , f , .Patterns ) , \exists { n0 , .Patterns } \and ( \equals ( n , S ( n0 , .Patterns ) ) , f0 ( n0 , F , n0 , .Patterns ) , .Patterns ) , .Patterns ) ) + + axiom \type ( S ( .Patterns ) , \forall { x { Term } , .Patterns } nat ) + + axiom \type ( Z ( .Patterns ) , nat ) + + sort Term + + symbol S ( .Sorts ) : Term + + symbol Z ( .Sorts ) : Term + + symbol nat ( .Sorts ) : Term + + symbol nat_ind ( .Sorts ) : Term + + + From 8585a5d9d808882467446b7f7d1cd7f1ff5f51f9 Mon Sep 17 00:00:00 2001 From: Lucas Pena Date: Tue, 11 Feb 2020 14:42:20 -0600 Subject: [PATCH 20/44] coq tests in own directory --- prover/build | 2 +- prover/t/{ => coq-tests}/Logic.v | 0 prover/t/{ => coq-tests}/Logic.v.expected | 0 prover/t/{ => coq-tests}/nat_ind.v | 0 prover/t/{ => coq-tests}/nat_ind.v.expected | 0 5 files changed, 1 insertion(+), 1 deletion(-) rename prover/t/{ => coq-tests}/Logic.v (100%) rename prover/t/{ => coq-tests}/Logic.v.expected (100%) rename prover/t/{ => coq-tests}/nat_ind.v (100%) rename prover/t/{ => coq-tests}/nat_ind.v.expected (100%) diff --git a/prover/build b/prover/build index fdf589fdf..5ca7e6530 100755 --- a/prover/build +++ b/prover/build @@ -63,7 +63,7 @@ prover_coq = prover('prover-coq', '--main-module DRIVER-COQ --syntax-module D # prover_kore.tests(inputs = glob('t/*.kore'), implicit_inputs = glob('t/definitions/*.kore'), flags = '-cCOMMANDLINE=.CommandLine') # prover_smt .tests(inputs = glob('t/*.smt2'), flags = '-cCOMMANDLINE=.CommandLine') -prover_coq .tests(inputs = glob('t/*.v'), flags = '-cCOMMANDLINE=.CommandLine') +prover_coq .tests(inputs = glob('t/coq-tests/*.v'), flags = '-cCOMMANDLINE=.CommandLine') def log_on_success(file, message): return proj.rule( 'log-to-success' diff --git a/prover/t/Logic.v b/prover/t/coq-tests/Logic.v similarity index 100% rename from prover/t/Logic.v rename to prover/t/coq-tests/Logic.v diff --git a/prover/t/Logic.v.expected b/prover/t/coq-tests/Logic.v.expected similarity index 100% rename from prover/t/Logic.v.expected rename to prover/t/coq-tests/Logic.v.expected diff --git a/prover/t/nat_ind.v b/prover/t/coq-tests/nat_ind.v similarity index 100% rename from prover/t/nat_ind.v rename to prover/t/coq-tests/nat_ind.v diff --git a/prover/t/nat_ind.v.expected b/prover/t/coq-tests/nat_ind.v.expected similarity index 100% rename from prover/t/nat_ind.v.expected rename to prover/t/coq-tests/nat_ind.v.expected From 74f3c0bc27420a99bafd2736793014e7a2b6facb Mon Sep 17 00:00:00 2001 From: Lucas Pena Date: Tue, 11 Feb 2020 15:03:56 -0600 Subject: [PATCH 21/44] use named axioms --- prover/drivers/coq-driver.md | 6 +++--- prover/lang/coq-lang.md | 5 ----- prover/t/coq-tests/Logic.v | 2 +- prover/t/coq-tests/nat_ind.v | 2 +- 4 files changed, 5 insertions(+), 10 deletions(-) diff --git a/prover/drivers/coq-driver.md b/prover/drivers/coq-driver.md index 13a19fa01..ffba1500f 100644 --- a/prover/drivers/coq-driver.md +++ b/prover/drivers/coq-driver.md @@ -43,9 +43,9 @@ module DRIVER-COQ ( .Bag => symbol CoqIdentToSymbol(ID)(.Sorts) : StringToSort("Term") - axiom \equals(CoqIdentToSymbol(ID), CoqTermToPattern(TERM)) + axiom getFreshGlobalAxiomName() : \equals(CoqIdentToSymbol(ID), CoqTermToPattern(TERM)) ) ... - + // Translate inductive cases rule Inductive ID BINDERs : TERM := .CoqIndCases . @@ -63,7 +63,7 @@ module DRIVER-COQ ( .Bag => symbol CoqIdentToSymbol(IDC)(.Sorts) : StringToSort("Term") - axiom \type(CoqIdentToSymbol(IDC)(.Patterns), CoqTermToPattern(TERMC)) + axiom getFreshGlobalAxiomName() : \type(CoqIdentToSymbol(IDC)(.Patterns), CoqTermToPattern(TERMC)) ) ... diff --git a/prover/lang/coq-lang.md b/prover/lang/coq-lang.md index ba92ca165..f9eeaeb79 100644 --- a/prover/lang/coq-lang.md +++ b/prover/lang/coq-lang.md @@ -38,11 +38,6 @@ module COQ syntax VariableName ::= CoqNameToVariableName(CoqName) [function] rule CoqNameToVariableName(NAME) => StringToVariableName(CoqNameToString(NAME)) - syntax Sorts ::= CoqBindersToSorts(CoqBinders) [function] - rule CoqBindersToSorts(.CoqBinders) => .Sorts - rule CoqBindersToSorts(NAME:CoqName BINDERs) => StringToSort("Term"), CoqBindersToSorts(BINDERs) - rule CoqBindersToSorts((NAMES : TYPE) BINDERs) => CoqNamesToSorts(NAMES) ++Sorts CoqBindersToSorts(BINDERs) - syntax Sorts ::= CoqNamesToSorts(CoqNames) [function] rule CoqNamesToSorts(.CoqNames) => .Sorts rule CoqNamesToSorts(NAME:CoqName NAMEs) => StringToSort("Term"), CoqNamesToSorts(NAMEs) diff --git a/prover/t/coq-tests/Logic.v b/prover/t/coq-tests/Logic.v index 7f886c87d..8a18dcdbe 100644 --- a/prover/t/coq-tests/Logic.v +++ b/prover/t/coq-tests/Logic.v @@ -5,7 +5,7 @@ Inductive False : Prop := . Inductive nat : Prop := Z : nat - | S : nat -> nat . + | S : (forall (x : nat), nat) . Definition not := fun (A: Prop) => (forall (x : A), False) . diff --git a/prover/t/coq-tests/nat_ind.v b/prover/t/coq-tests/nat_ind.v index b127282e6..03111631f 100644 --- a/prover/t/coq-tests/nat_ind.v +++ b/prover/t/coq-tests/nat_ind.v @@ -7,7 +7,7 @@ Inductive nat : Type := Z : nat | S : forall (x : nat), nat . // axiom \type(Z(), nat()) Definition nat_ind := -fun (P : nat -> Prop) (f : P 0) (f0 : forall (n : nat), P n -> P (S n)) => +fun (P : (forall (n : nat), Prop)) (f : P 0) (f0 : forall (n : nat), (forall (x : P n), P (S n))) => fix F (n : nat) := match n with Z => f | S n0 => f0 n0 (F n0) From 968a224f499e60be7805b172536812e8c33fa202 Mon Sep 17 00:00:00 2001 From: Lucas Pena Date: Tue, 11 Feb 2020 15:11:01 -0600 Subject: [PATCH 22/44] set variables no longer sorted --- prover/drivers/coq-driver.md | 2 +- prover/lang/kore-lang.md | 2 +- 2 files changed, 2 insertions(+), 2 deletions(-) diff --git a/prover/drivers/coq-driver.md b/prover/drivers/coq-driver.md index ffba1500f..4ebf9121c 100644 --- a/prover/drivers/coq-driver.md +++ b/prover/drivers/coq-driver.md @@ -85,7 +85,7 @@ module DRIVER-COQ CoqTermToPattern(match Ts with EQs end) ), .Patterns)) rule CoqTermToPattern(TM:CoqTerm ARG) => CoqTermToPattern(TM)(CoqArgToPatterns(ARG)) - rule CoqTermToPattern(fix ID BINDERs := TM) => \mu { CoqNameToVariableName(ID) {{ StringToSort("Term") }} } CoqTermToPattern(fun BINDERs => TM) + rule CoqTermToPattern(fix ID BINDERs := TM) => \mu { # CoqNameToVariableName(ID) } CoqTermToPattern(fun BINDERs => TM) rule CoqTermToPattern(@ QID:CoqQualID TM:CoqTerm) => CoqIdentToSymbol(QID)(CoqTermToPattern(TM)) syntax Patterns ::= CoqArgToPatterns(CoqArg) [function] diff --git a/prover/lang/kore-lang.md b/prover/lang/kore-lang.md index cf13f2b36..845b5f15f 100644 --- a/prover/lang/kore-lang.md +++ b/prover/lang/kore-lang.md @@ -138,7 +138,7 @@ only in this scenario*. ```k syntax Variable ::= VariableName "{" Sort "}" [klabel(sortedVariable)] - syntax SetVariable ::= VariableName "{{" Sort "}}" [klabel(sortedSetVariable)] + syntax SetVariable ::= "#" VariableName [klabel(setVariable)] syntax Pattern ::= Int | Variable | SetVariable From 5c2e2cee66129aaad7ab8244f6434becb10a01af Mon Sep 17 00:00:00 2001 From: Lucas Pena Date: Wed, 12 Feb 2020 16:43:10 -0600 Subject: [PATCH 23/44] create goals for typing coq defs. add result type to definitions --- prover/drivers/coq-driver.md | 21 +++++++++++++++++++-- prover/lang/coq-lang.md | 12 ++++++------ prover/prover.md | 1 + prover/t/coq-tests/Logic.v | 35 +++++++++++++++++------------------ prover/t/coq-tests/nat_ind.v | 5 ++++- 5 files changed, 47 insertions(+), 27 deletions(-) diff --git a/prover/drivers/coq-driver.md b/prover/drivers/coq-driver.md index 4ebf9121c..dc3df016d 100644 --- a/prover/drivers/coq-driver.md +++ b/prover/drivers/coq-driver.md @@ -36,8 +36,8 @@ module DRIVER-COQ // Add symbol (of sort Term) and equality axiom corresponding to each definition - rule Definition ID BINDERs : TYPE := TERM . => Definition ID := TERM . - rule Definition ID := TERM . + rule Definition ID BINDERs : TYPE1 := TERM hasType TYPE2 . => Definition ID := TERM hasType TYPE2 . + rule Definition ID := TERM hasType TYPE . => .K ... @@ -46,6 +46,22 @@ module DRIVER-COQ axiom getFreshGlobalAxiomName() : \equals(CoqIdentToSymbol(ID), CoqTermToPattern(TERM)) ) ... + + ( .Bag => + + !N:ClaimName + true:Bool + .K + \type(CoqIdentToSymbol(ID), CoqTermToPattern(TYPE)) + type-check + success + .Bag + .K + + ) + ... + + // Translate inductive cases rule Inductive ID BINDERs : TERM := .CoqIndCases . @@ -71,6 +87,7 @@ module DRIVER-COQ syntax Pattern ::= CoqTermToPattern(CoqTerm) [function] rule CoqTermToPattern(UN:UpperName) => CoqIdentToSymbol(UN) rule CoqTermToPattern(LN:LowerName) => CoqIdentToSymbol(LN) + rule CoqTermToPattern(#token("Prop", "CoqSort")) => StringToSort("Term") rule CoqTermToPattern(fun BINDERs => TERM) => \lambda { CoqBindersToPatterns(BINDERs) } CoqTermToPattern(TERM) rule CoqTermToPattern(forall BINDERs, TERM) => \forall { CoqBindersToPatterns(BINDERs) } CoqTermToPattern(TERM) rule CoqTermToPattern(match Ts with .CoqEquations end) => \bottom() diff --git a/prover/lang/coq-lang.md b/prover/lang/coq-lang.md index f9eeaeb79..3364ea9d3 100644 --- a/prover/lang/coq-lang.md +++ b/prover/lang/coq-lang.md @@ -19,10 +19,10 @@ module COQ syntax CoqNames ::= List{CoqName, ""} [klabel(CoqNames)] // Sorts - syntax CoqSort ::= "SProp" - | "Prop" - | "Set" - | "Type" + syntax CoqSort ::= "SProp" [token] + | "Prop" [token] + | "Set" [token] + | "Type" [token] // Seralize to String: syntax String ::= CoqNameToString(CoqName) [function, functional, hook(STRING.token2string)] @@ -101,8 +101,8 @@ module COQ | CoqInductive // | CoqCoInductive syntax CoqSentences ::= List{CoqSentence, ""} [klabel(CoqSentences), format(%1%n%2 %3)] - syntax CoqDefinition ::= "Definition" CoqIdent ":=" CoqTerm "." - | "Definition" CoqIdent CoqBinders ":" CoqTerm ":=" CoqTerm "." + syntax CoqDefinition ::= "Definition" CoqIdent ":=" CoqTerm "hasType" CoqTerm "." + | "Definition" CoqIdent CoqBinders ":" CoqTerm ":=" CoqTerm "hasType" CoqTerm "." syntax CoqInductive ::= "Inductive" CoqIndBody "." syntax CoqIndBody ::= CoqIdent CoqBinders ":" CoqTerm ":=" CoqIndCases diff --git a/prover/prover.md b/prover/prover.md index ef0f2605c..85d5c99d4 100644 --- a/prover/prover.md +++ b/prover/prover.md @@ -70,6 +70,7 @@ module STRATEGIES-EXPORTED-SYNTAX "in:" AxiomName "," "vars:" VariableNames "," "with:" Patterns ")" + | "type-check" syntax RewriteDirection ::= "->" | "<-" diff --git a/prover/t/coq-tests/Logic.v b/prover/t/coq-tests/Logic.v index 8a18dcdbe..6a756f7b1 100644 --- a/prover/t/coq-tests/Logic.v +++ b/prover/t/coq-tests/Logic.v @@ -7,19 +7,17 @@ Inductive nat : Prop := Z : nat | S : (forall (x : nat), nat) . -Definition not := fun (A: Prop) => (forall (x : A), False) . - -// Definition not (A : Prop) : Prop := forall (x : A), False . +Definition not := fun (A: Prop) => (forall (x : A), False) hasType (forall (x : Prop), Prop) . Definition iff (A B : Prop) : Prop := - (and (forall (x : A), B)) (forall (y : B), A) . + (and (forall (x : A), B)) (forall (y : B), A) hasType (forall (x : Prop), (forall (y : Prop), Prop)) . Definition IF_then_else (P Q R : Prop) : Prop := - (or (and P Q)) (and (not P) R) . + (or (and P Q)) (and (not P) R) hasType (forall (x : Prop), (forall (y : Prop), (forall (z : Prop), Prop))) . Inductive ex1 (A : Type) (P : forall (x : A), Prop) : Prop := ex_intro1 : forall (x : A), forall (y : (P x)), ex1 A P . - + Inductive ex2 (A : Type) (P : forall (x : A), Prop) : Prop := ex_intro2 : forall (x : A), forall (y : (P x)), ex2 P . @@ -30,17 +28,18 @@ Inductive ex4 (A : Type) (P : forall (x : A), Prop) : Prop := ex_intro4 : forall (x : A), forall (y : (P x)), @ ex4 A P . Definition AndComm := - fun (A B : Prop) (H : and A B) => - match H with - conj H0 H1 => conj H1 H0 - end . - -Inductive and (A B : Prop) : Prop := - conj : forall (x : A), forall (y : B), and A B . - -Inductive or (A B : Prop) : Prop := - or_introl : forall (x : A), or A B - | or_intror : forall (y : A), or A B . - + fun (A B : Prop) (H : and A B) => + match H with + conj H0 H1 => conj H1 H0 + end + hasType (forall (A B : Prop), (forall (c : and A B), and B A)) . + +// Inductive and (A B : Prop) : Prop := +// conj : forall (x : A), forall (y : B), and A B . +// +// Inductive or (A B : Prop) : Prop := +// or_introl : forall (x : A), or A B +// | or_intror : forall (y : A), or A B . +// // Inductive eq (A:Type) (x:A) : forall (_:A), Prop := // eq_refl : @ eq A x x . diff --git a/prover/t/coq-tests/nat_ind.v b/prover/t/coq-tests/nat_ind.v index 03111631f..236cad436 100644 --- a/prover/t/coq-tests/nat_ind.v +++ b/prover/t/coq-tests/nat_ind.v @@ -11,6 +11,9 @@ fun (P : (forall (n : nat), Prop)) (f : P 0) (f0 : forall (n : nat), (forall (x fix F (n : nat) := match n with Z => f | S n0 => f0 n0 (F n0) - end . + end +hasType (forall (P : (forall (x : nat), Prop)), + (forall (y : P 0), (forall (l : (forall (n : nat), (forall (y : P n), P (S n)))), (forall (n : nat), P n)))) . +// forall P : nat -> Prop, P 0 -> (forall n : nat, P n -> P (S n)) -> forall n : nat, P n // tr(fun ... ) \mu { F {{ Term }} } tr( fun n => match ) ... ) From b2bd250a41e8679fe39552e9a4af199df1780f2e Mon Sep 17 00:00:00 2001 From: Lucas Pena Date: Fri, 14 Feb 2020 09:23:15 -0600 Subject: [PATCH 24/44] change format for terms having type in v files --- prover/drivers/coq-driver.md | 4 ++-- prover/lang/coq-lang.md | 4 ++-- prover/t/coq-tests/Logic.v | 8 ++++---- prover/t/coq-tests/nat_ind.v | 5 ++++- 4 files changed, 12 insertions(+), 9 deletions(-) diff --git a/prover/drivers/coq-driver.md b/prover/drivers/coq-driver.md index dc3df016d..81b08c906 100644 --- a/prover/drivers/coq-driver.md +++ b/prover/drivers/coq-driver.md @@ -36,8 +36,8 @@ module DRIVER-COQ // Add symbol (of sort Term) and equality axiom corresponding to each definition - rule Definition ID BINDERs : TYPE1 := TERM hasType TYPE2 . => Definition ID := TERM hasType TYPE2 . - rule Definition ID := TERM hasType TYPE . + rule Definition ID BINDERs : TYPE1 := TERM (* hasType TYPE2 *) . => Definition ID := TERM (* hasType TYPE2 *) . + rule Definition ID := TERM (* hasType TYPE *) . => .K ... diff --git a/prover/lang/coq-lang.md b/prover/lang/coq-lang.md index 3364ea9d3..24f9db557 100644 --- a/prover/lang/coq-lang.md +++ b/prover/lang/coq-lang.md @@ -101,8 +101,8 @@ module COQ | CoqInductive // | CoqCoInductive syntax CoqSentences ::= List{CoqSentence, ""} [klabel(CoqSentences), format(%1%n%2 %3)] - syntax CoqDefinition ::= "Definition" CoqIdent ":=" CoqTerm "hasType" CoqTerm "." - | "Definition" CoqIdent CoqBinders ":" CoqTerm ":=" CoqTerm "hasType" CoqTerm "." + syntax CoqDefinition ::= "Definition" CoqIdent ":=" CoqTerm "(*" "hasType" CoqTerm "*)" "." + | "Definition" CoqIdent CoqBinders ":" CoqTerm ":=" CoqTerm "(*" "hasType" CoqTerm "*)" "." syntax CoqInductive ::= "Inductive" CoqIndBody "." syntax CoqIndBody ::= CoqIdent CoqBinders ":" CoqTerm ":=" CoqIndCases diff --git a/prover/t/coq-tests/Logic.v b/prover/t/coq-tests/Logic.v index 6a756f7b1..1d2cc2373 100644 --- a/prover/t/coq-tests/Logic.v +++ b/prover/t/coq-tests/Logic.v @@ -7,13 +7,13 @@ Inductive nat : Prop := Z : nat | S : (forall (x : nat), nat) . -Definition not := fun (A: Prop) => (forall (x : A), False) hasType (forall (x : Prop), Prop) . +Definition not := fun (A: Prop) => (forall (x : A), False) (* hasType (forall (x : Prop), Prop) *) . Definition iff (A B : Prop) : Prop := - (and (forall (x : A), B)) (forall (y : B), A) hasType (forall (x : Prop), (forall (y : Prop), Prop)) . + (and (forall (x : A), B)) (forall (y : B), A) (* hasType (forall (x : Prop), (forall (y : Prop), Prop)) *) . Definition IF_then_else (P Q R : Prop) : Prop := - (or (and P Q)) (and (not P) R) hasType (forall (x : Prop), (forall (y : Prop), (forall (z : Prop), Prop))) . + (or (and P Q)) (and (not P) R) (* hasType (forall (x : Prop), (forall (y : Prop), (forall (z : Prop), Prop))) *) . Inductive ex1 (A : Type) (P : forall (x : A), Prop) : Prop := ex_intro1 : forall (x : A), forall (y : (P x)), ex1 A P . @@ -32,7 +32,7 @@ Definition AndComm := match H with conj H0 H1 => conj H1 H0 end - hasType (forall (A B : Prop), (forall (c : and A B), and B A)) . + (* hasType (forall (A B : Prop), (forall (c : and A B), and B A)) *) . // Inductive and (A B : Prop) : Prop := // conj : forall (x : A), forall (y : B), and A B . diff --git a/prover/t/coq-tests/nat_ind.v b/prover/t/coq-tests/nat_ind.v index 236cad436..827426134 100644 --- a/prover/t/coq-tests/nat_ind.v +++ b/prover/t/coq-tests/nat_ind.v @@ -12,8 +12,11 @@ fix F (n : nat) := match n with Z => f | S n0 => f0 n0 (F n0) end +(* hasType (forall (P : (forall (x : nat), Prop)), - (forall (y : P 0), (forall (l : (forall (n : nat), (forall (y : P n), P (S n)))), (forall (n : nat), P n)))) . + (forall (y : P 0), (forall (l : (forall (n : nat), (forall (y : P n), P (S n)))), (forall (n : nat), P n)))) +*) +. // forall P : nat -> Prop, P 0 -> (forall n : nat, P n -> P (S n)) -> forall n : nat, P n // tr(fun ... ) \mu { F {{ Term }} } tr( fun n => match ) ... ) From 3090652feef18117cc61497317a780a5a239e63d Mon Sep 17 00:00:00 2001 From: Lucas Pena Date: Mon, 17 Feb 2020 14:42:25 -0600 Subject: [PATCH 25/44] coq-driver: translate forall to pi --- prover/drivers/coq-driver.md | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/prover/drivers/coq-driver.md b/prover/drivers/coq-driver.md index 81b08c906..488757b3d 100644 --- a/prover/drivers/coq-driver.md +++ b/prover/drivers/coq-driver.md @@ -52,8 +52,8 @@ module DRIVER-COQ !N:ClaimName true:Bool .K - \type(CoqIdentToSymbol(ID), CoqTermToPattern(TYPE)) type-check + \type(CoqIdentToSymbol(ID), CoqTermToPattern(TYPE)) success .Bag .K @@ -89,7 +89,7 @@ module DRIVER-COQ rule CoqTermToPattern(LN:LowerName) => CoqIdentToSymbol(LN) rule CoqTermToPattern(#token("Prop", "CoqSort")) => StringToSort("Term") rule CoqTermToPattern(fun BINDERs => TERM) => \lambda { CoqBindersToPatterns(BINDERs) } CoqTermToPattern(TERM) - rule CoqTermToPattern(forall BINDERs, TERM) => \forall { CoqBindersToPatterns(BINDERs) } CoqTermToPattern(TERM) + rule CoqTermToPattern(forall BINDERs, TERM) => \pi { CoqBindersToPatterns(BINDERs) } CoqTermToPattern(TERM) rule CoqTermToPattern(match Ts with .CoqEquations end) => \bottom() rule CoqTermToPattern(match Ts with (MP:CoqMultPattern => TM:CoqTerm) | EQs end) => \or( #flattenOrs( From 61881a274e05d163c1d8edd21136e021164a0b81 Mon Sep 17 00:00:00 2001 From: Lucas Pena Date: Mon, 17 Feb 2020 14:42:54 -0600 Subject: [PATCH 26/44] change type-check to typecheck --- prover/drivers/coq-driver.md | 2 +- prover/prover.md | 2 +- 2 files changed, 2 insertions(+), 2 deletions(-) diff --git a/prover/drivers/coq-driver.md b/prover/drivers/coq-driver.md index 488757b3d..fc0a77173 100644 --- a/prover/drivers/coq-driver.md +++ b/prover/drivers/coq-driver.md @@ -52,8 +52,8 @@ module DRIVER-COQ !N:ClaimName true:Bool .K - type-check \type(CoqIdentToSymbol(ID), CoqTermToPattern(TYPE)) + typecheck success .Bag .K diff --git a/prover/prover.md b/prover/prover.md index 85d5c99d4..61851f147 100644 --- a/prover/prover.md +++ b/prover/prover.md @@ -70,7 +70,7 @@ module STRATEGIES-EXPORTED-SYNTAX "in:" AxiomName "," "vars:" VariableNames "," "with:" Patterns ")" - | "type-check" + | "typecheck" syntax RewriteDirection ::= "->" | "<-" From 85e82292f123d81eb2e67619640b3b3b0baf43d9 Mon Sep 17 00:00:00 2001 From: Lucas Pena Date: Mon, 17 Feb 2020 14:43:35 -0600 Subject: [PATCH 27/44] placeholder for typecheck strategy --- prover/build | 1 + prover/drivers/base.md | 1 + prover/prover.md | 1 + prover/strategies/typecheck.md | 12 ++++++++++++ 4 files changed, 15 insertions(+) create mode 100644 prover/strategies/typecheck.md diff --git a/prover/build b/prover/build index 5ca7e6530..34e6ec78f 100755 --- a/prover/build +++ b/prover/build @@ -36,6 +36,7 @@ other_md_files = [ 'lang/coq-lang.md' , 'strategies/replace-evar-with-func-constant.md' , 'strategies/simplification.md' , 'strategies/search-bound.md' + , 'strategies/typecheck.md' , 'strategies/smt.md' , 'strategies/unfolding.md' , 'utils/load-named.md' diff --git a/prover/drivers/base.md b/prover/drivers/base.md index 9ec7a5afb..d13fa8c8c 100644 --- a/prover/drivers/base.md +++ b/prover/drivers/base.md @@ -79,6 +79,7 @@ module DRIVER-BASE imports STRATEGY-UNFOLDING imports STRATEGY-KNASTER-TARSKI imports STRATEGY-REPLACE-EVAR-WITH-FUNC-CONSTANT + imports STRATEGY-TYPECHECK imports SYNTACTIC-MATCH-RULES imports VISITOR imports PATTERN-LENGTH diff --git a/prover/prover.md b/prover/prover.md index 61851f147..834c3b44e 100644 --- a/prover/prover.md +++ b/prover/prover.md @@ -13,6 +13,7 @@ requires "strategies/intros.k" requires "strategies/knaster-tarski.k" requires "strategies/matching.k" requires "strategies/search-bound.k" +requires "strategies/typecheck.k" requires "strategies/simplification.k" requires "strategies/smt.k" requires "strategies/reflexivity.k" diff --git a/prover/strategies/typecheck.md b/prover/strategies/typecheck.md new file mode 100644 index 000000000..73ce96215 --- /dev/null +++ b/prover/strategies/typecheck.md @@ -0,0 +1,12 @@ +# typecheck - for Coq terms + +```k +module STRATEGY-TYPECHECK + imports PROVER-CORE + imports STRATEGIES-EXPORTED-SYNTAX + + rule typecheck => noop ... + + +endmodule +``` From 33e7f103bf7a6d68e4adf6b230eb8b6f6c58286c Mon Sep 17 00:00:00 2001 From: Lucas Pena Date: Mon, 24 Feb 2020 10:59:19 -0600 Subject: [PATCH 28/44] encode output type in coq syntax rather than comment --- prover/drivers/coq-driver.md | 3 +-- prover/lang/coq-lang.md | 4 ++-- prover/t/coq-tests/Logic.v | 15 ++++++++------- prover/t/coq-tests/nat_ind.v | 10 +++++----- 4 files changed, 16 insertions(+), 16 deletions(-) diff --git a/prover/drivers/coq-driver.md b/prover/drivers/coq-driver.md index fc0a77173..50ba7843b 100644 --- a/prover/drivers/coq-driver.md +++ b/prover/drivers/coq-driver.md @@ -36,8 +36,7 @@ module DRIVER-COQ // Add symbol (of sort Term) and equality axiom corresponding to each definition - rule Definition ID BINDERs : TYPE1 := TERM (* hasType TYPE2 *) . => Definition ID := TERM (* hasType TYPE2 *) . - rule Definition ID := TERM (* hasType TYPE *) . + rule Definition ID : TYPE := TERM . => .K ... diff --git a/prover/lang/coq-lang.md b/prover/lang/coq-lang.md index 24f9db557..1d82f0613 100644 --- a/prover/lang/coq-lang.md +++ b/prover/lang/coq-lang.md @@ -101,8 +101,8 @@ module COQ | CoqInductive // | CoqCoInductive syntax CoqSentences ::= List{CoqSentence, ""} [klabel(CoqSentences), format(%1%n%2 %3)] - syntax CoqDefinition ::= "Definition" CoqIdent ":=" CoqTerm "(*" "hasType" CoqTerm "*)" "." - | "Definition" CoqIdent CoqBinders ":" CoqTerm ":=" CoqTerm "(*" "hasType" CoqTerm "*)" "." + syntax CoqDefinition ::= "Definition" CoqIdent ":" CoqTerm ":=" CoqTerm "." +// | "Definition" CoqIdent CoqBinders ":" CoqTerm ":=" CoqTerm "." syntax CoqInductive ::= "Inductive" CoqIndBody "." syntax CoqIndBody ::= CoqIdent CoqBinders ":" CoqTerm ":=" CoqIndCases diff --git a/prover/t/coq-tests/Logic.v b/prover/t/coq-tests/Logic.v index 1d2cc2373..bb31c87d3 100644 --- a/prover/t/coq-tests/Logic.v +++ b/prover/t/coq-tests/Logic.v @@ -7,13 +7,14 @@ Inductive nat : Prop := Z : nat | S : (forall (x : nat), nat) . -Definition not := fun (A: Prop) => (forall (x : A), False) (* hasType (forall (x : Prop), Prop) *) . +Definition not : (forall (x : Prop), Prop) b := + fun (A: Prop) => (forall (x : A), False) . -Definition iff (A B : Prop) : Prop := - (and (forall (x : A), B)) (forall (y : B), A) (* hasType (forall (x : Prop), (forall (y : Prop), Prop)) *) . +Definition iff : (forall (x : Prop), (forall (y : Prop), Prop)) := + (and (forall (x : A), B)) (forall (y : B), A) . -Definition IF_then_else (P Q R : Prop) : Prop := - (or (and P Q)) (and (not P) R) (* hasType (forall (x : Prop), (forall (y : Prop), (forall (z : Prop), Prop))) *) . +Definition IF_then_else : (forall (x : Prop), (forall (y : Prop), (forall (z : Prop), Prop))) := + (or (and P Q)) (and (not P) R) . Inductive ex1 (A : Type) (P : forall (x : A), Prop) : Prop := ex_intro1 : forall (x : A), forall (y : (P x)), ex1 A P . @@ -27,12 +28,12 @@ Inductive ex2 (A : Type) (P : forall (x : A), Prop) : Prop := Inductive ex4 (A : Type) (P : forall (x : A), Prop) : Prop := ex_intro4 : forall (x : A), forall (y : (P x)), @ ex4 A P . -Definition AndComm := +Definition AndComm : (forall (A B : Prop), (forall (c : and A B), and B A)) := fun (A B : Prop) (H : and A B) => match H with conj H0 H1 => conj H1 H0 end - (* hasType (forall (A B : Prop), (forall (c : and A B), and B A)) *) . + . // Inductive and (A B : Prop) : Prop := // conj : forall (x : A), forall (y : B), and A B . diff --git a/prover/t/coq-tests/nat_ind.v b/prover/t/coq-tests/nat_ind.v index 827426134..f3c9036b3 100644 --- a/prover/t/coq-tests/nat_ind.v +++ b/prover/t/coq-tests/nat_ind.v @@ -6,16 +6,16 @@ Inductive nat : Type := Z : nat | S : forall (x : nat), nat . // axiom \type(Z(), nat()) -Definition nat_ind := +Definition nat_ind : (forall (P : (forall (x : nat), Prop)), + (forall (y : P 0), + (forall (l : (forall (n : nat), + (forall (y : P n), P (S n)))), + (forall (n : nat), P n)))) := fun (P : (forall (n : nat), Prop)) (f : P 0) (f0 : forall (n : nat), (forall (x : P n), P (S n))) => fix F (n : nat) := match n with Z => f | S n0 => f0 n0 (F n0) end -(* -hasType (forall (P : (forall (x : nat), Prop)), - (forall (y : P 0), (forall (l : (forall (n : nat), (forall (y : P n), P (S n)))), (forall (n : nat), P n)))) -*) . // forall P : nat -> Prop, P 0 -> (forall n : nat, P n -> P (S n)) -> forall n : nat, P n From 2eb94c10dd4bcafd7bc19bdc0882ee3f5e9ccdc6 Mon Sep 17 00:00:00 2001 From: Lucas Pena Date: Mon, 24 Feb 2020 16:42:04 -0600 Subject: [PATCH 29/44] begin typecheck strategy --- prover/strategies/typecheck.md | 20 ++++++++- prover/t/coq-tests/Logic.v | 74 +++++++++++++++++----------------- 2 files changed, 55 insertions(+), 39 deletions(-) diff --git a/prover/strategies/typecheck.md b/prover/strategies/typecheck.md index 73ce96215..9f142821e 100644 --- a/prover/strategies/typecheck.md +++ b/prover/strategies/typecheck.md @@ -5,8 +5,24 @@ module STRATEGY-TYPECHECK imports PROVER-CORE imports STRATEGIES-EXPORTED-SYNTAX - rule typecheck => noop ... - + rule + \type(ID:Symbol, TYPE) => \type(TERM, TYPE) + typecheck ... + axiom AXID : \equals(ID, TERM) + + rule + \type(TYPE, TYPE) + typecheck => success ... + + // lambda + rule + \type(\lambda { VARs } TERM, \pi { VARs } TYPE) => \type(TERM, TYPE) + typecheck ... + + // application + rule + \type(TERM1 ( TERM2 ), TYPE) => \type(TERM1, \pi { !X:VariableName { StringToSort("Term") } } TYPE) + typecheck ... endmodule ``` diff --git a/prover/t/coq-tests/Logic.v b/prover/t/coq-tests/Logic.v index bb31c87d3..7709a6a76 100644 --- a/prover/t/coq-tests/Logic.v +++ b/prover/t/coq-tests/Logic.v @@ -1,46 +1,46 @@ -Inductive True : Prop := - I : True . +// Inductive True : Prop := +// I : True . -Inductive False : Prop := . +// Inductive False : Prop := . -Inductive nat : Prop := - Z : nat - | S : (forall (x : nat), nat) . +// Inductive nat : Prop := +// Z : nat +// | S : (forall (x : nat), nat) . Definition not : (forall (x : Prop), Prop) b := fun (A: Prop) => (forall (x : A), False) . -Definition iff : (forall (x : Prop), (forall (y : Prop), Prop)) := - (and (forall (x : A), B)) (forall (y : B), A) . +// Definition iff : (forall (x : Prop), (forall (y : Prop), Prop)) := +// (and (forall (x : A), B)) (forall (y : B), A) . -Definition IF_then_else : (forall (x : Prop), (forall (y : Prop), (forall (z : Prop), Prop))) := - (or (and P Q)) (and (not P) R) . +// Definition IF_then_else : (forall (x : Prop), (forall (y : Prop), (forall (z : Prop), Prop))) := +// (or (and P Q)) (and (not P) R) . -Inductive ex1 (A : Type) (P : forall (x : A), Prop) : Prop := - ex_intro1 : forall (x : A), forall (y : (P x)), ex1 A P . +// Inductive ex1 (A : Type) (P : forall (x : A), Prop) : Prop := +// ex_intro1 : forall (x : A), forall (y : (P x)), ex1 A P . -Inductive ex2 (A : Type) (P : forall (x : A), Prop) : Prop := - ex_intro2 : forall (x : A), forall (y : (P x)), ex2 P . - -// Inductive ex3 (A : Type) (P : forall (x : A), Prop) : Prop := -// ex_intro3 : forall (x : A), forall (y : (P x)), ex3 (A:=A) P . - -Inductive ex4 (A : Type) (P : forall (x : A), Prop) : Prop := - ex_intro4 : forall (x : A), forall (y : (P x)), @ ex4 A P . - -Definition AndComm : (forall (A B : Prop), (forall (c : and A B), and B A)) := - fun (A B : Prop) (H : and A B) => - match H with - conj H0 H1 => conj H1 H0 - end - . - -// Inductive and (A B : Prop) : Prop := -// conj : forall (x : A), forall (y : B), and A B . -// -// Inductive or (A B : Prop) : Prop := -// or_introl : forall (x : A), or A B -// | or_intror : forall (y : A), or A B . -// -// Inductive eq (A:Type) (x:A) : forall (_:A), Prop := -// eq_refl : @ eq A x x . +// Inductive ex2 (A : Type) (P : forall (x : A), Prop) : Prop := +// ex_intro2 : forall (x : A), forall (y : (P x)), ex2 P . + +// // Inductive ex3 (A : Type) (P : forall (x : A), Prop) : Prop := +// // ex_intro3 : forall (x : A), forall (y : (P x)), ex3 (A:=A) P . + +// Inductive ex4 (A : Type) (P : forall (x : A), Prop) : Prop := +// ex_intro4 : forall (x : A), forall (y : (P x)), @ ex4 A P . + +// Definition AndComm : (forall (A B : Prop), (forall (c : and A B), and B A)) := +// fun (A B : Prop) (H : and A B) => +// match H with +// conj H0 H1 => conj H1 H0 +// end +// . + +// // Inductive and (A B : Prop) : Prop := +// // conj : forall (x : A), forall (y : B), and A B . +// // +// // Inductive or (A B : Prop) : Prop := +// // or_introl : forall (x : A), or A B +// // | or_intror : forall (y : A), or A B . +// // +// // Inductive eq (A:Type) (x:A) : forall (_:A), Prop := +// // eq_refl : @ eq A x x . From 974aac4431a6190f34d7584d67b0281283916d69 Mon Sep 17 00:00:00 2001 From: Lucas Pena Date: Thu, 27 Feb 2020 09:34:50 -0600 Subject: [PATCH 30/44] typecheck works for simple examples --- prover/drivers/coq-driver.md | 14 +++++++------- prover/strategies/typecheck.md | 9 +++++++-- prover/t/coq-tests/Logic.v | 22 +++++++++++----------- 3 files changed, 25 insertions(+), 20 deletions(-) diff --git a/prover/drivers/coq-driver.md b/prover/drivers/coq-driver.md index 50ba7843b..11a569af5 100644 --- a/prover/drivers/coq-driver.md +++ b/prover/drivers/coq-driver.md @@ -31,7 +31,7 @@ module DRIVER-COQ // Add sort "Term" to declarations rule CS:CoqSentence CSs:CoqSentences => CS ~> CSs ... ( .Bag - => sort StringToSort("Term") + => sort #token("Term", "UpperName") ) ... @@ -41,7 +41,7 @@ module DRIVER-COQ ... ( .Bag - => symbol CoqIdentToSymbol(ID)(.Sorts) : StringToSort("Term") + => symbol CoqIdentToSymbol(ID)(.Sorts) : #token("Term", "UpperName") axiom getFreshGlobalAxiomName() : \equals(CoqIdentToSymbol(ID), CoqTermToPattern(TERM)) ) ... @@ -68,7 +68,7 @@ module DRIVER-COQ ... ( .Bag - => symbol CoqIdentToSymbol(ID)(.Sorts) : StringToSort("Term") + => symbol CoqIdentToSymbol(ID)(.Sorts) : #token("Term", "UpperName") ) ... @@ -77,7 +77,7 @@ module DRIVER-COQ ... ( .Bag - => symbol CoqIdentToSymbol(IDC)(.Sorts) : StringToSort("Term") + => symbol CoqIdentToSymbol(IDC)(.Sorts) : #token("Term", "UpperName") axiom getFreshGlobalAxiomName() : \type(CoqIdentToSymbol(IDC)(.Patterns), CoqTermToPattern(TERMC)) ) ... @@ -86,7 +86,7 @@ module DRIVER-COQ syntax Pattern ::= CoqTermToPattern(CoqTerm) [function] rule CoqTermToPattern(UN:UpperName) => CoqIdentToSymbol(UN) rule CoqTermToPattern(LN:LowerName) => CoqIdentToSymbol(LN) - rule CoqTermToPattern(#token("Prop", "CoqSort")) => StringToSort("Term") + rule CoqTermToPattern(#token("Prop", "CoqSort")) => #token("Term", "UpperName") rule CoqTermToPattern(fun BINDERs => TERM) => \lambda { CoqBindersToPatterns(BINDERs) } CoqTermToPattern(TERM) rule CoqTermToPattern(forall BINDERs, TERM) => \pi { CoqBindersToPatterns(BINDERs) } CoqTermToPattern(TERM) rule CoqTermToPattern(match Ts with .CoqEquations end) => \bottom() @@ -145,9 +145,9 @@ module DRIVER-COQ CoqBinderToPatterns(BINDER) ++Patterns CoqBindersToPatterns(BINDERs) syntax Patterns ::= CoqBinderToPatterns(CoqBinder) [function] - rule CoqBinderToPatterns(NAME:CoqName) => CoqNameToVariableName(NAME) { StringToSort("Term") } + rule CoqBinderToPatterns(NAME:CoqName) => CoqNameToVariableName(NAME) { #token("Term", "UpperName") } rule CoqBinderToPatterns((.CoqNames : TYPE:CoqTerm)) => .Patterns - rule CoqBinderToPatterns(((NAME:CoqName NAMES:CoqNames) : TYPE:CoqTerm)) => CoqNameToVariableName(NAME) { StringToSort("Term") }, CoqBinderToPatterns((NAMES : TYPE)) + rule CoqBinderToPatterns(((NAME:CoqName NAMES:CoqNames) : TYPE:CoqTerm)) => CoqNameToVariableName(NAME) { #token("Term", "UpperName") }, CoqBinderToPatterns((NAMES : TYPE)) ``` ```k diff --git a/prover/strategies/typecheck.md b/prover/strategies/typecheck.md index 9f142821e..72e1a4118 100644 --- a/prover/strategies/typecheck.md +++ b/prover/strategies/typecheck.md @@ -14,14 +14,19 @@ module STRATEGY-TYPECHECK \type(TYPE, TYPE) typecheck => success ... + // axiom: (Term, Term, Term) + rule + \type(\pi { VARs } TYPE, #token("Term", "UpperName")) + typecheck => success ... + // lambda rule - \type(\lambda { VARs } TERM, \pi { VARs } TYPE) => \type(TERM, TYPE) + \type(\lambda { VARs1 } TERM, \pi { VARs2 } TYPE) => \type(TERM, TYPE) typecheck ... // application rule - \type(TERM1 ( TERM2 ), TYPE) => \type(TERM1, \pi { !X:VariableName { StringToSort("Term") } } TYPE) + \type(TERM1 ( TERM2 ), TYPE) => \type(TERM1, \pi { !X:VariableName { #token("Term", "UpperName") } } TYPE) typecheck ... endmodule diff --git a/prover/t/coq-tests/Logic.v b/prover/t/coq-tests/Logic.v index 7709a6a76..42c98d955 100644 --- a/prover/t/coq-tests/Logic.v +++ b/prover/t/coq-tests/Logic.v @@ -7,14 +7,14 @@ // Z : nat // | S : (forall (x : nat), nat) . -Definition not : (forall (x : Prop), Prop) b := +Definition not : (forall (x : Prop), Prop) := fun (A: Prop) => (forall (x : A), False) . -// Definition iff : (forall (x : Prop), (forall (y : Prop), Prop)) := -// (and (forall (x : A), B)) (forall (y : B), A) . +Definition iff : (forall (x : Prop), (forall (y : Prop), Prop)) := + (and (forall (x : A), B)) (forall (y : B), A) . -// Definition IF_then_else : (forall (x : Prop), (forall (y : Prop), (forall (z : Prop), Prop))) := -// (or (and P Q)) (and (not P) R) . +Definition IF_then_else : (forall (x : Prop), (forall (y : Prop), (forall (z : Prop), Prop))) := + (or (and P Q)) (and (not P) R) . // Inductive ex1 (A : Type) (P : forall (x : A), Prop) : Prop := // ex_intro1 : forall (x : A), forall (y : (P x)), ex1 A P . @@ -28,12 +28,12 @@ Definition not : (forall (x : Prop), Prop) b := // Inductive ex4 (A : Type) (P : forall (x : A), Prop) : Prop := // ex_intro4 : forall (x : A), forall (y : (P x)), @ ex4 A P . -// Definition AndComm : (forall (A B : Prop), (forall (c : and A B), and B A)) := -// fun (A B : Prop) (H : and A B) => -// match H with -// conj H0 H1 => conj H1 H0 -// end -// . +Definition AndComm : (forall (A B : Prop), (forall (c : and A B), and B A)) := + fun (A B : Prop) (H : and A B) => + match H with + conj H0 H1 => conj H1 H0 + end + . // // Inductive and (A B : Prop) : Prop := // // conj : forall (x : A), forall (y : B), and A B . From 182db6bd8abaf7eff25d0d4f602ba8abefeecec4 Mon Sep 17 00:00:00 2001 From: Lucas Pena Date: Thu, 5 Mar 2020 09:42:17 -0600 Subject: [PATCH 31/44] typecheck: minor change --- prover/strategies/typecheck.md | 1 + 1 file changed, 1 insertion(+) diff --git a/prover/strategies/typecheck.md b/prover/strategies/typecheck.md index 72e1a4118..73604058d 100644 --- a/prover/strategies/typecheck.md +++ b/prover/strategies/typecheck.md @@ -15,6 +15,7 @@ module STRATEGY-TYPECHECK typecheck => success ... // axiom: (Term, Term, Term) + // TODO: use Term as constant rule \type(\pi { VARs } TYPE, #token("Term", "UpperName")) typecheck => success ... From 5b13db3451911ac4862cbf449931f136c22b98c1 Mon Sep 17 00:00:00 2001 From: Xiaohong Chen Date: Tue, 10 Mar 2020 12:37:36 -0500 Subject: [PATCH 32/44] add coq rules --- prover/coq_rules/coq_rules.pdf | Bin 0 -> 147637 bytes prover/coq_rules/coq_rules.tex | 110 +++++++++++++++++++++++++++++++ prover/coq_rules/newcommands.tex | 27 ++++++++ 3 files changed, 137 insertions(+) create mode 100644 prover/coq_rules/coq_rules.pdf create mode 100644 prover/coq_rules/coq_rules.tex create mode 100644 prover/coq_rules/newcommands.tex diff --git a/prover/coq_rules/coq_rules.pdf b/prover/coq_rules/coq_rules.pdf new file mode 100644 index 0000000000000000000000000000000000000000..4c159324c110a2d112063a2acfde474efbc0cd25 GIT binary patch literal 147637 zcma&MQ;;qI*IxOyt<$z`+qP}nK5g5!ZQHhOp0>?=$xM<;{ZlpBS9{++SI?@wNEJlH zXc_5Pp-JbLN7kVk83-5%?2W9Td3d1dWlZhNT`UNgSveUA{>MPmi&@&Zm^u;Ai`f{u zn2MMh+nbm|^YKADyEvH|+CqD5u4qd;AGad)eyX2IsMZj4<2$|Y+gwqV{TWM1$x+$h zQ(#_(S1!WLIKHa=x?FGpPtNh$+#Mj4*W_4FmK 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b/prover/coq_rules/coq_rules.tex index 3fcdef4f2..b865a6f3d 100644 --- a/prover/coq_rules/coq_rules.tex +++ b/prover/coq_rules/coq_rules.tex @@ -3,7 +3,10 @@ \usepackage{amsmath,amssymb,amsthm} \usepackage{fullpage} \usepackage{hyperref} +\usepackage{longtable} \usepackage{mathtools} +\usepackage{prftree} +\usepackage[dvipsnames]{xcolor} \usepackage{xspace} \input{newcommands} @@ -33,7 +36,7 @@ \section{Syntax} conditions: \begin{enumerate} \item $\SProp,\Prop,\Set \in \CoqTerm$; $\Type(i) \in \CoqTerm$ for every $i -\in \NN$. +\in \NNp$. \item $\V \subseteq \CoqTerm$. \item $\C \subseteq \CoqTerm$. \item If $x \in \V$ and $T,U \in \CoqTerm$, @@ -73,7 +76,7 @@ \section{Syntax} We use $\Gamma$, possibly with subscripts, to denote local contexts. \end{definition} -\begin{notation} +\begin{notation}\label{not:ldcl} We use the notation $[\lasm{x}{T} \scln \ldef{y}{u}{U} \scln \lasm{z}{V}]$ to denote the local context that consists of the local assumption $\lasm{x}{T}$, @@ -102,13 +105,15 @@ \section{Syntax} \end{notation} \begin{definition} -A \emph{global assumption} is written $(\gasm{x}{T})$, where $c \in \C$ and $T \in +A \emph{global assumption} is written $(\gasm{c}{T})$, +with the parentheses, where $c \in \C$ and $T \in \CoqTerm$. A \emph{global definition} is written $\gldef{c}{u}{T}$, where $c \in \C$ and $u,T \in \CoqTerm$. In both cases, we call $c$ the \emph{declared constant}. A \emph{global environment} is an ordered list of global assumptions and global -definitions. +definitions, and also \emph{declarations of inductive objects}, which are +defined later. We use $E$, possibly with subscripts, to denote global environments. \end{definition} @@ -134,18 +139,171 @@ \section{Syntax} \end{notation} \begin{notation} -We write $E[\Gamma] \proves \lasm{u}{T}$ to mean that $u$ is well-typed with -type $T$ in global environment $E$ and local environment $\Gamma$. -We write $\wf(E)[\Gamma]$ to mean that the global environment $E$ is well-formed -and $\Gamma$ is a valid local context in $E$. +We write $E[\Gamma] \proves \lasm{u}{T}$ to mean that $u$ is \emph{well-typed} +with type $T$ in global environment $E$ and local environment $\Gamma$. +We write $\wf(E)[\Gamma]$ to mean that the global environment $E$ is +\emph{well-formed} +and $\Gamma$ is a \emph{valid local context} in $E$. \end{notation} \begin{definition} A term $u$ is \emph{well-typed} in a global environment $E$ if there is a -local environment $\Gamma$ and type $T$ such that +local context $\Gamma$ and type $T$ such that $E[\Gamma] \proves \lasm{u}{T}$ is derivable with the rules below. \end{definition} -\section{Coq Typing Rules} +\section{Coq Rules} + +In this section we list all Coq rules. +A \emph{rule} consists of a set of \emph{premises} and one \emph{conclusion}, +separated by a horizontal bar. +For readability, we put \emph{side conditions} alongside the premises. +Side conditions are typed in $\sd{\text{green}}$, to distinguish +from the premises. + + +\subsection{Basic Typing Rules} + +There are 18 basic typing rules, as shown below. + + +\begin{center} +\bgroup +\def\arraystretch{4} +\begin{longtable}{llp{5cm}} +\textbf{Names} & \textbf{Rules} & \textbf{Comments} \\\hline +\prule{W-Empty}& +$\prftree{\cdot}{\wf([])[]}$ & +The empty global environment is well-formed, and the empty local context is a +valid local context in the empty global environment.\\ +\prule{W-Local-Assum}& +$\prftree{E[\Gamma]\vdash T \cln s} +{\sd{s \in S}} +{\sd{x \not\in \Gamma}} +{\wf(E)[\Gamma \dcln (x \cln T)]}$& +The side condition $x \not\in \Gamma$ needs not to be specified because +it is implicitly +implied +by the notation $\Gamma \dcln (x \cln T)$; see Notation~\ref{not:ldcl}.\\ +\prule{W-Local-Def}& +$\prftree{E[\Gamma]\vdash t \cln T} +{\sd{x \not\in \Gamma}} +{\wf(E)[\Gamma \dcln (\ldef{x}{t}{T})]}$& +The side condition $x \not\in \Gamma$ needs not to be specified because +it is implicitly implied +by the notation $\Gamma \dcln (\ldef{x}{t}{T})$; see Notation~\ref{not:ldcl}.\\ +\prule{W-Global-Assum}& +$ +\prftree +{E[]\vdash T \cln s} +{\sd{s \in S}} +{\sd{c \not\in E}} +{\wf(E ; c \cln T)[]} +$ & \\ +\prule{W-Global-Def} & +$ +\prftree +{E[]\vdash t \cln T} +{\sd{c \not\in E}} +{\wf(E ; \gldef{c}{t}{T})[]} +$ & \\ +\prule{Ax-SProp} & +$ +\prftree{\wf(E)[\Gamma]} +{E[\Gamma] \vdash \SProp \cln \Type(1)} +$ &\\ +\prule{Ax-Prop} & +$ +\prftree{\wf(E)[\Gamma]} +{E[\Gamma] \vdash \Prop \cln \Type(1)} +$ &\\ +\prule{Ax-Set} & +$ +\prftree{\wf(E)[\Gamma]} +{E[\Gamma] \vdash \Set \cln \Type(1)} +$ &\\ +\prule{Ax-Type} & +$ +\prftree{\wf(E)[\Gamma]} +{E[\Gamma] \vdash \Type(i) \cln \Type(i+1)} +$ & Here, $i \in \NNp$ is any positive natural number. \\ +\prule{Var} & +\multicolumn{2}{l}{ +$ +\prftree{\wf(E)[\Gamma]} +{\sd{\text{$(\lasm{x}{T} \in \Gamma)$, or $(\ldef{x}{t}{T}) \in \Gamma$ for +some $t \in \CoqTerm$}}} +{E[\Gamma] \vdash x \cln T} +$} \\ +\prule{Const} & +\multicolumn{2}{l}{ +$ +\prftree{\wf(E)[\Gamma]} +{\sd{\text{$(\lasm{c}{T} \in E)$, or $(\ldef{c}{t}{T}) \in E$ for +some $t \in \CoqTerm$}}} +{E[\Gamma] \vdash c \cln T} +$} \\ +\prule{Prod-SProp} & +$ +\prftree +{E[\Gamma] \vdash T \cln s} +{\sd{s \in S}} +{E[\Gamma \dcln (x \cln T)] \vdash U \cln \SProp} +{E[\Gamma]\vdash \cfa{x}{T}{U} \cln \SProp} +$ &\\ +\prule{Prod-Prop} & +$ +\prftree +{E[\Gamma] \vdash T \cln s} +{\sd{s \in S}} +{E[\Gamma \dcln (x \cln T)] \vdash U \cln \Prop} +{E[\Gamma]\vdash \cfa{x}{T}{U} \cln \Prop} +$ &\\ +\prule{Prod-Set} & +\multicolumn{2}{l}{ +$ +\prftree +{E[\Gamma] \vdash T \cln s} +{\sd{s \in \{\SProp,\Prop,\Set\}}} +{E[\Gamma \dcln (x \cln T)] \vdash U \cln \Set} +{E[\Gamma]\vdash \cfa{x}{T}{U} \cln \Set} +$ +} \\ +\prule{Prod-Type} & +\multicolumn{2}{l}{ +$ +\prftree +{E[\Gamma] \vdash T \cln s} +{\sd{s \in \{\SProp,\Type(i)\}}} +{E[\Gamma \dcln (x \cln T)] \vdash U \cln \Type(i)} +{E[\Gamma]\vdash \cfa{x}{T}{U} \cln \Type(i)} +$ +} \\ +\prule{Lam} & +$ +\prftree +{E[\Gamma] \vdash \cfa{x}{T}{U} \cln s} +{\sd{s \in S}} +{E[\Gamma \dcln (x \cln T)] \vdash t \cln U} +{E[\Gamma] \vdash \clm{x}{T}{t} \cln \cfa{x}{T}{U}} +$ &\\ +\prule{App} & +$ +\prftree +{E[\Gamma] \vdash t \cln \cfa{x}{U}{T}} +{E[\Gamma] \vdash u \cln U} +{E[\Gamma] \vdash (t \, u) \cln T[u/x]} +$ &\\ +\prule{Let} & +$\prftree +{E[\Gamma] \vdash t \cln T} +{E[\Gamma \dcln (\ldef{x}{t}{T})] \vdash u \cln U} +{E[\Gamma] \vdash \clt{x}{t}{T}{u} \cln U[t/x]} +$ +\end{longtable} +\egroup +\end{center} + +\subsection{Conversion Rules} \end{document} diff --git a/prover/coq_rules/newcommands.tex b/prover/coq_rules/newcommands.tex index df701c63d..09d1fede8 100644 --- a/prover/coq_rules/newcommands.tex +++ b/prover/coq_rules/newcommands.tex @@ -10,6 +10,7 @@ \newcommand{\Set}{\mathsf{Set}} \newcommand{\Type}{\mathsf{Type}} \newcommand{\NN}{\mathbb{N}} +\newcommand{\NNp}{{\NN_{\ge 1}}} \newcommand{\V}{V} \newcommand{\C}{C} \newcommand{\cln}{{\,:\,}} @@ -29,4 +30,6 @@ \newcommand{\gldef}[3]{#1 \coloneqq #2 \cln #3} \newcommand{\proves}{\vdash} -\newcommand{\wf}{\mathcal{WF}} +\newcommand{\wf}{\mathcal{W\!F}} +\newcommand{\prule}[1]{\textsc{(#1)}} +\newcommand{\sd}[1]{{{\color{JungleGreen} #1}}} From 477dde5b770fcbc36560bf65f9dcebcc71aba896 Mon Sep 17 00:00:00 2001 From: Xiaohong Chen Date: Wed, 25 Mar 2020 22:55:21 -0500 Subject: [PATCH 35/44] add authors --- prover/coq_rules/coq_rules.pdf | Bin 180838 -> 181663 bytes prover/coq_rules/coq_rules.tex | 2 +- 2 files changed, 1 insertion(+), 1 deletion(-) diff --git a/prover/coq_rules/coq_rules.pdf b/prover/coq_rules/coq_rules.pdf index a1cc747a6761482a31587fc37573daf911f9e663..096a434f89dfa22986e429f6acf727e3daaf80a5 100644 GIT binary patch delta 20236 zcmV)AK*Yc1gbSaG3lSwyL`E$!E;R}z(A34)3NkX05fqo+bpa}oPZxhq*^Vn(JE@X< z;LdP0OwG=$NsguUA-_G12T70wIVh z{1v%nfj0?~29$pYcrqd=u{=~|j&7>UEsS54*O!}9RTYQkvMO$F^TXvnKfFEVZ;Q)K zxk0<;b|1bRE0;2iq)_dbk?$e^V;nIq9mdvF2qd7tT|!2~*U8125Gt})_lFBcvL=7; 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+++ b/prover/coq_rules/coq_rules.tex @@ -12,7 +12,7 @@ \input{newcommands} \title{All Coq Rules in One Place} -\author{Xiaohong Chen} +\author{Xiaohong Chen \and Lucas Pe{\~{n}}a} \begin{document} From 895d236b5c024b134915b0fced585e451106b9e7 Mon Sep 17 00:00:00 2001 From: Lucas Pena Date: Thu, 26 Mar 2020 14:54:00 -0500 Subject: [PATCH 36/44] wording of comment in W-Local-Assum --- prover/coq_rules/coq_rules.tex | 5 ++--- 1 file changed, 2 insertions(+), 3 deletions(-) diff --git a/prover/coq_rules/coq_rules.tex b/prover/coq_rules/coq_rules.tex index 769eebd45..987a7f2d7 100644 --- a/prover/coq_rules/coq_rules.tex +++ b/prover/coq_rules/coq_rules.tex @@ -182,9 +182,8 @@ \subsection{Basic Typing Rules} {\sd{x \not\in \Gamma}} {\wf(E)[\Gamma \dcln (x \cln T)]}$& The side condition $x \not\in \Gamma$ needs not to be specified because -it is implicitly -implied -by the notation $\Gamma \dcln (x \cln T)$; see Notation~\ref{not:ldcl}.\\ +it is implicit +in the notation $\Gamma \dcln (x \cln T)$; see Notation~\ref{not:ldcl}.\\ \prule{W-Local-Def}& $\prftree{E[\Gamma]\vdash t \cln T} {\sd{x \not\in \Gamma}} From 1de18209946733b8a14e06b8deffd1abc5531769 Mon Sep 17 00:00:00 2001 From: Lucas Pena Date: Mon, 30 Mar 2020 12:37:01 -0500 Subject: [PATCH 37/44] parsing more terms in coq translation --- prover/drivers/coq-driver.md | 4 ++++ prover/lang/coq-lang.md | 2 ++ 2 files changed, 6 insertions(+) diff --git a/prover/drivers/coq-driver.md b/prover/drivers/coq-driver.md index 11a569af5..6d5b7adf7 100644 --- a/prover/drivers/coq-driver.md +++ b/prover/drivers/coq-driver.md @@ -103,6 +103,10 @@ module DRIVER-COQ rule CoqTermToPattern(TM:CoqTerm ARG) => CoqTermToPattern(TM)(CoqArgToPatterns(ARG)) rule CoqTermToPattern(fix ID BINDERs := TM) => \mu { # CoqNameToVariableName(ID) } CoqTermToPattern(fun BINDERs => TM) rule CoqTermToPattern(@ QID:CoqQualID TM:CoqTerm) => CoqIdentToSymbol(QID)(CoqTermToPattern(TM)) + // TODO: incorporate qualfied name + rule CoqTermToPattern(QID:CoqQualID . ID:CoqIdent) => CoqIdentToSymbol(ID) + // TODO: do we need to do anything with the type here? + rule CoqTermToPattern((TM:CoqTerm : TY:CoqType):CoqTerm) => CoqTermToPattern(TM) syntax Patterns ::= CoqArgToPatterns(CoqArg) [function] rule CoqArgToPatterns(ARG1 ARG2) => CoqArgToPatterns(ARG1) ++Patterns CoqArgToPatterns(ARG2) diff --git a/prover/lang/coq-lang.md b/prover/lang/coq-lang.md index 1d82f0613..c3558438d 100644 --- a/prover/lang/coq-lang.md +++ b/prover/lang/coq-lang.md @@ -14,6 +14,7 @@ module COQ syntax CoqIdent ::= LowerName | UpperName syntax CoqQualID ::= CoqIdent + | CoqQualID "." CoqIdent syntax CoqName ::= CoqIdent | Underscore syntax CoqNames ::= List{CoqName, ""} [klabel(CoqNames)] @@ -50,6 +51,7 @@ module COQ | "let" CoqIdent CoqBinders ":" CoqTerm ":=" CoqTerm "in" CoqTerm | "@" CoqQualID CoqTerm | "match" CoqMatchItems "with" CoqEquations "end" + | CoqTerm ":" CoqTerm > CoqTerm CoqArg [right] | CoqQualID | CoqSort From 07675a4699656ca0463d0dabdb1d189f8a8e8680 Mon Sep 17 00:00:00 2001 From: Lucas Pena Date: Mon, 13 Apr 2020 11:37:54 -0500 Subject: [PATCH 38/44] coq-lang, coq-driver: handling more constructs for generated verbose defs --- prover/drivers/coq-driver.md | 8 ++- prover/lang/coq-lang.md | 14 ++++-- prover/lang/kore-lang.md | 4 ++ prover/t/coq-tests/ml_coq_verbose.v | 75 +++++++++++++++++++++++++++++ 4 files changed, 97 insertions(+), 4 deletions(-) create mode 100644 prover/t/coq-tests/ml_coq_verbose.v diff --git a/prover/drivers/coq-driver.md b/prover/drivers/coq-driver.md index 6d5b7adf7..0753a5bf5 100644 --- a/prover/drivers/coq-driver.md +++ b/prover/drivers/coq-driver.md @@ -89,7 +89,10 @@ module DRIVER-COQ rule CoqTermToPattern(#token("Prop", "CoqSort")) => #token("Term", "UpperName") rule CoqTermToPattern(fun BINDERs => TERM) => \lambda { CoqBindersToPatterns(BINDERs) } CoqTermToPattern(TERM) rule CoqTermToPattern(forall BINDERs, TERM) => \pi { CoqBindersToPatterns(BINDERs) } CoqTermToPattern(TERM) + rule CoqTermToPattern(match Ts return P with EQs end) => CoqTermToPattern(match Ts with EQs end) rule CoqTermToPattern(match Ts with .CoqEquations end) => \bottom() + rule CoqTermToPattern(match Ts with (| MP:CoqMultPattern => TM:CoqTerm) | EQs end) + => CoqTermToPattern(match Ts with (MP:CoqMultPattern => TM:CoqTerm) | EQs end) rule CoqTermToPattern(match Ts with (MP:CoqMultPattern => TM:CoqTerm) | EQs end) => \or( #flattenOrs( \or( \exists { CoqMultPatternToBinders(MP) } @@ -106,7 +109,7 @@ module DRIVER-COQ // TODO: incorporate qualfied name rule CoqTermToPattern(QID:CoqQualID . ID:CoqIdent) => CoqIdentToSymbol(ID) // TODO: do we need to do anything with the type here? - rule CoqTermToPattern((TM:CoqTerm : TY:CoqType):CoqTerm) => CoqTermToPattern(TM) + rule CoqTermToPattern((TM:CoqTerm : TY:CoqTerm):CoqTerm) => CoqTermToPattern(TM) syntax Patterns ::= CoqArgToPatterns(CoqArg) [function] rule CoqArgToPatterns(ARG1 ARG2) => CoqArgToPatterns(ARG1) ++Patterns CoqArgToPatterns(ARG2) @@ -131,9 +134,11 @@ module DRIVER-COQ rule CoqMultPatternToPatterns(MP, MPs) => CoqPatternToPattern(MP), CoqMultPatternToPatterns(MPs) rule CoqPatternToPattern(ID:CoqQualID) => CoqIdentToSymbol(ID) + syntax Symbol ::= #stuck() [function] rule CoqPatternToPattern(ID:CoqQualID P:CoqPattern) => CoqIdentToSymbol(ID)(CoqPatternToPatterns(P)) rule CoqPatternToPatterns(ID:CoqQualID) => CoqIdentToSymbol(ID), .Patterns rule CoqPatternToPatterns(ID:CoqQualID P:CoqPattern) => CoqIdentToSymbol(ID) ++Patterns CoqPatternToPatterns(P) + rule CoqPatternToPatterns(U:Underscore P:CoqPattern) => !S:Symbol ++Patterns CoqPatternToPatterns(P) // Get binders from MultPattern syntax Patterns ::= CoqMultPatternToBinders(CoqMultPattern) [function] @@ -142,6 +147,7 @@ module DRIVER-COQ rule CoqMultPatternToBinders(ID:CoqQualID P:CoqPattern) => CoqPatternToBinders(P) rule CoqPatternToBinders(ID:CoqQualID) => CoqIdentToSymbol(ID), .Patterns rule CoqPatternToBinders(ID:CoqQualID P:CoqPattern) => CoqIdentToSymbol(ID), CoqPatternToBinders(P) + rule CoqPatternToBinders(U:Underscore P:CoqPattern) => !S:Symbol, CoqPatternToBinders(P) syntax Patterns ::= CoqBindersToPatterns(CoqBinders) [function] rule CoqBindersToPatterns(.CoqBinders) => .Patterns diff --git a/prover/lang/coq-lang.md b/prover/lang/coq-lang.md index c3558438d..693dc6432 100644 --- a/prover/lang/coq-lang.md +++ b/prover/lang/coq-lang.md @@ -15,6 +15,7 @@ module COQ | UpperName syntax CoqQualID ::= CoqIdent | CoqQualID "." CoqIdent + | Underscore syntax CoqName ::= CoqIdent | Underscore syntax CoqNames ::= List{CoqName, ""} [klabel(CoqNames)] @@ -22,7 +23,7 @@ module COQ // Sorts syntax CoqSort ::= "SProp" [token] | "Prop" [token] - | "Set" [token] + // | "Set" [token] | "Type" [token] // Seralize to String: @@ -51,6 +52,7 @@ module COQ | "let" CoqIdent CoqBinders ":" CoqTerm ":=" CoqTerm "in" CoqTerm | "@" CoqQualID CoqTerm | "match" CoqMatchItems "with" CoqEquations "end" + | "match" CoqMatchItems CoqReturnType "with" CoqEquations "end" | CoqTerm ":" CoqTerm > CoqTerm CoqArg [right] | CoqQualID @@ -71,19 +73,25 @@ module COQ syntax CoqFixBody ::= CoqIdent CoqBinders ":=" CoqTerm | CoqIdent CoqBinders ":" CoqTerm ":=" CoqTerm + | CoqIdent CoqBinders CoqAnnotation ":" CoqTerm ":=" CoqTerm syntax CoqFixBodyList ::= List{CoqFixBody, "with"} syntax CoqFixBodies ::= CoqFixBody | CoqFixBody CoqFixBodyList "for" CoqIdent + syntax CoqAnnotation ::= "{" "struct" CoqIdent "}" - syntax CoqCofixBody ::= CoqIdent CoqBinders ":=" CoqTerm + syntax CoqCofixBody ::= CoqIdent CoqBinders ":" CoqTerm ":=" CoqTerm syntax CoqCofixBodyList ::= List{CoqCofixBody, "with"} syntax CoqCofixBodies ::= CoqCofixBody | CoqCofixBody CoqCofixBodyList "for" CoqIdent syntax CoqMatchItem ::= CoqTerm + | CoqTerm "as" CoqName syntax CoqMatchItems ::= List{CoqMatchItem, ","} [klabel(CoqMatchItems)] + syntax CoqReturnType ::= "return" CoqTerm + syntax CoqEquation ::= CoqMultPattern "=>" CoqTerm + | "|" CoqMultPattern "=>" CoqTerm syntax CoqEquations ::= List{CoqEquation, "|"} [klabel(CoqEquations)] syntax CoqPattern ::= CoqQualID CoqPattern @@ -92,7 +100,7 @@ module COQ | CoqPattern "as" CoqIdent | CoqPattern "%" CoqIdent | CoqQualID - | Underscore + | Underscore [prefer] | Int syntax CoqMultPattern ::= List{CoqPattern, ","} [klabel(CoqMultPattern)] diff --git a/prover/lang/kore-lang.md b/prover/lang/kore-lang.md index 845b5f15f..43aae4bd6 100644 --- a/prover/lang/kore-lang.md +++ b/prover/lang/kore-lang.md @@ -449,6 +449,10 @@ and values, passed to K's substitute. syntax Patterns ::= makeFreshVariables(Patterns) [function] rule makeFreshVariables(P, REST) => !V1:VariableName { getReturnSort(P) }, makeFreshVariables(REST) rule makeFreshVariables(.Patterns) => .Patterns + + syntax Symbol ::= String2Symbol(String) [function, functional, hook(STRING.string2token)] + syntax Symbol ::= freshSymbol(Int) [freshGenerator, function, functional] + rule freshSymbol(I:Int) => String2Symbol("F" +String Int2String(I)) ``` ```k diff --git a/prover/t/coq-tests/ml_coq_verbose.v b/prover/t/coq-tests/ml_coq_verbose.v new file mode 100644 index 000000000..875648b29 --- /dev/null +++ b/prover/t/coq-tests/ml_coq_verbose.v @@ -0,0 +1,75 @@ +Inductive and' (A B : Prop) : Prop := + conj' : forall (_ : A) (_ : B), and' A B . + +Definition and'_ind_verbose : forall (A B P : Prop) (_ : forall (_ : A) (_ : B), P)(_ : and' A B), P := +fun (A B P : Prop) (f : forall (_ : A) (_ : B), P) (a : and' A B) => +match a return P with +| conj' _ _ x x0 => f x x0 +end . + +Definition and'_rec_verbose : forall (A B : Prop) (P : Set) (_ : forall (_ : A) (_ : B), P)(_ : and' A B), P := +fun (A B : Prop) (P : Set) => and'_rect A B P . + +Definition and'_rect_verbose : forall (A B : Prop) (P : Type) (_ : forall (_ : A) (_ : B), P)(_ : and' A B), P := +fun (A B : Prop) (P : Type) (f : forall (_ : A) (_ : B), P) + (a : and' A B) => +match a return P with +| conj' _ _ x x0 => f x x0 +end . + +Inductive ex1 (A : Type) (P : forall (_ : A), Prop) : Prop := + ex_intro1 : forall (x : A) (_ : P x), ex1 A P . + +Definition ex1_ind_verbose : forall (A : Type) (P : forall (_ : A), Prop)(P0 : Prop) (_ : forall (x : A) (_ : P x), P0)(_ : ex1 A P), P0 := +fun (A : Type) (P : forall (_ : A), Prop) (P0 : Prop) + (f : forall (x : A) (_ : P x), P0) (e : ex1 A P) => +match e return P0 with +| ex_intro1 _ _ x x0 => f x x0 +end . + +Definition False_ind : forall (P : Prop) (_ : False), P := +fun (P : Prop) (f : False) => match f return P with + end . + +Definition add_ind' : forall (_ : nat) (_ : nat), nat := +fix add (n m : nat) {struct n} : nat := + match n return nat with + | O => m + | S p => S (add p m) + end . + +Definition nat_ind' : forall (P : forall (_ : nat), Prop) (_ : P O)(_ : forall (n : nat) (_ : P n), P (S n))(n : nat), P n := +fun (P : forall (_ : nat), Prop) (f : P O) + (f0 : forall (n : nat) (_ : P n), P (S n)) => +fix F (n : nat) : P n := + match n as n0 return (P n0) with + | O => f + | S n0 => f0 n0 (F n0) + end . + +Definition AddZero : forall (n : nat), @eq nat (Nat.add n O) n := +fun (n : nat) => +nat_ind (fun (n0 : nat) => @eq nat (Nat.add n0 O) n0) + (@eq_refl nat O : @eq nat (Nat.add O O) O) + (fun (n0 : nat) (IHn : @eq nat (Nat.add n0 O) n0) => + @eq_ind_r nat n0 (fun (n1 : nat) => @eq nat (S n1) (S n0)) + (@eq_refl nat (S n0)) (Nat.add n0 O) IHn + : + @eq nat (Nat.add (S n0) O) (S n0)) n . + +Definition AndComm : forall (A B : Prop) (_ : and A B), and B A := +fun (A B : Prop) (H : and A B) => +match H return (and B A) with +| conj H0 H1 => @conj B A H1 H0 +end . + +Definition AndComm' : forall (A B : Prop) (_ : and A B), and B A := +fun (A B : Prop) (H : and A B) => +match H return (and B A) with +| conj H0 H1 => @conj B A H1 H0 +end . + +Definition AndComm'' : forall (A B : Prop) (_ : and A B), and B A := +AndComm' . + +Definition test : forall (_ : Prop), Prop := fun (_ : Prop) => True . From 3deae833210650619146b6e1684e6610abce54a0 Mon Sep 17 00:00:00 2001 From: Lucas Pena Date: Sun, 19 Apr 2020 13:38:56 -0500 Subject: [PATCH 39/44] more parsing --- prover/drivers/coq-driver.md | 5 ++++- prover/lang/coq-lang.md | 3 +-- 2 files changed, 5 insertions(+), 3 deletions(-) diff --git a/prover/drivers/coq-driver.md b/prover/drivers/coq-driver.md index 0753a5bf5..06fe7b0bb 100644 --- a/prover/drivers/coq-driver.md +++ b/prover/drivers/coq-driver.md @@ -104,7 +104,8 @@ module DRIVER-COQ CoqTermToPattern(match Ts with EQs end) ), .Patterns)) rule CoqTermToPattern(TM:CoqTerm ARG) => CoqTermToPattern(TM)(CoqArgToPatterns(ARG)) - rule CoqTermToPattern(fix ID BINDERs := TM) => \mu { # CoqNameToVariableName(ID) } CoqTermToPattern(fun BINDERs => TM) + rule CoqTermToPattern(fix ID BINDERs ANN:CoqAnnotation : TY := TM) => CoqTermToPattern(fix ID BINDERs : TY := TM) + rule CoqTermToPattern(fix ID BINDERs : TY := TM) => \mu { # CoqNameToVariableName(ID) } CoqTermToPattern(fun BINDERs => TM) rule CoqTermToPattern(@ QID:CoqQualID TM:CoqTerm) => CoqIdentToSymbol(QID)(CoqTermToPattern(TM)) // TODO: incorporate qualfied name rule CoqTermToPattern(QID:CoqQualID . ID:CoqIdent) => CoqIdentToSymbol(ID) @@ -122,6 +123,8 @@ module DRIVER-COQ rule CoqMatchItemsToPatterns(MI:CoqMatchItem, MIs) => CoqMatchItemToPattern(MI), .Patterns rule CoqMatchItemToPattern(MI:CoqTerm) => CoqTermToPattern(MI) + // TODO: is this right? + rule CoqMatchItemToPattern(MI:CoqTerm as N:CoqName) => CoqTermToPattern(MI) syntax Patterns ::= #equals(Patterns, Patterns) [function] rule #equals(.Patterns, .Patterns) => .Patterns diff --git a/prover/lang/coq-lang.md b/prover/lang/coq-lang.md index 693dc6432..275688611 100644 --- a/prover/lang/coq-lang.md +++ b/prover/lang/coq-lang.md @@ -71,8 +71,7 @@ module COQ > CoqTerm syntax CoqTerms ::= List{CoqTerm, ""} [klabel(CoqTerms)] - syntax CoqFixBody ::= CoqIdent CoqBinders ":=" CoqTerm - | CoqIdent CoqBinders ":" CoqTerm ":=" CoqTerm + syntax CoqFixBody ::= CoqIdent CoqBinders ":" CoqTerm ":=" CoqTerm | CoqIdent CoqBinders CoqAnnotation ":" CoqTerm ":=" CoqTerm syntax CoqFixBodyList ::= List{CoqFixBody, "with"} syntax CoqFixBodies 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