Construct a new record instances when the Record type has dependent binders in Coq
1
I intended to construct a new vector instance of Type Vector in the following code. However, initially, the Vector Record type has dependent ident binders. Like the second ident binder' or the second field -- 'proof' was dependent on the firstident binder' -- 'mpOf'. When I try to define the subtraction of two mass points, I find it impossible to pass the coq kernel.
Require Export Coq.Reals.Reals.
Open Scope R_scope.
Definition Point:= Type.
Record massPoint: Type := cons{number: R; point: Point}.
Definition isVector (v:massPoint) := exists A B : Point, v = add_MP(cons (-1) A)(cons 1 B).
Record Vector : Type := vecCons { mpOf : massPoint ; proof : isVector mpOf}.
Variable sub_MP: massPoint -> massPoint -> massPoint.
Definition point_sub (p1 p2: massPoint):Vector:=
vecCons (sub_MP p1 p2) proof (sub_MP p1 p2). (* errorsome definition*)
Anyone has any idea on how to define the point_sub?
record coq
edited Nov 25 '18 at 8:48
Robin Green
22.6k876156
asked Nov 25 '18 at 3:38
isPrimeisPrime
649
add a comment |
1
I intended to construct a new vector instance of Type Vector in the following code. However, initially, the Vector Record type has dependent ident binders. Like the second ident binder' or the second field -- 'proof' was dependent on the firstident binder' -- 'mpOf'. When I try to define the subtraction of two mass points, I find it impossible to pass the coq kernel.
Require Export Coq.Reals.Reals.
Open Scope R_scope.
Definition Point:= Type.
Record massPoint: Type := cons{number: R; point: Point}.
Definition isVector (v:massPoint) := exists A B : Point, v = add_MP(cons (-1) A)(cons 1 B).
Record Vector : Type := vecCons { mpOf : massPoint ; proof : isVector mpOf}.
Variable sub_MP: massPoint -> massPoint -> massPoint.
Definition point_sub (p1 p2: massPoint):Vector:=
vecCons (sub_MP p1 p2) proof (sub_MP p1 p2). (* errorsome definition*)
Anyone has any idea on how to define the point_sub?
record coq
edited Nov 25 '18 at 8:48
Robin Green
22.6k876156
asked Nov 25 '18 at 3:38
isPrimeisPrime
649
add a comment |
1
1
1
I intended to construct a new vector instance of Type Vector in the following code. However, initially, the Vector Record type has dependent ident binders. Like the second ident binder' or the second field -- 'proof' was dependent on the firstident binder' -- 'mpOf'. When I try to define the subtraction of two mass points, I find it impossible to pass the coq kernel.
Require Export Coq.Reals.Reals.
Open Scope R_scope.
Definition Point:= Type.
Record massPoint: Type := cons{number: R; point: Point}.
Definition isVector (v:massPoint) := exists A B : Point, v = add_MP(cons (-1) A)(cons 1 B).
Record Vector : Type := vecCons { mpOf : massPoint ; proof : isVector mpOf}.
Variable sub_MP: massPoint -> massPoint -> massPoint.
Definition point_sub (p1 p2: massPoint):Vector:=
vecCons (sub_MP p1 p2) proof (sub_MP p1 p2). (* errorsome definition*)
Anyone has any idea on how to define the point_sub?
record coq
edited Nov 25 '18 at 8:48
Robin Green
22.6k876156
asked Nov 25 '18 at 3:38
isPrimeisPrime
649
I intended to construct a new vector instance of Type Vector in the following code. However, initially, the Vector Record type has dependent ident binders. Like the second ident binder' or the second field -- 'proof' was dependent on the firstident binder' -- 'mpOf'. When I try to define the subtraction of two mass points, I find it impossible to pass the coq kernel.
Require Export Coq.Reals.Reals.
Open Scope R_scope.
Definition Point:= Type.
Record massPoint: Type := cons{number: R; point: Point}.
Definition isVector (v:massPoint) := exists A B : Point, v = add_MP(cons (-1) A)(cons 1 B).
Record Vector : Type := vecCons { mpOf : massPoint ; proof : isVector mpOf}.
Variable sub_MP: massPoint -> massPoint -> massPoint.
Definition point_sub (p1 p2: massPoint):Vector:=
vecCons (sub_MP p1 p2) proof (sub_MP p1 p2). (* errorsome definition*)
Anyone has any idea on how to define the point_sub?
record coq
record coq
edited Nov 25 '18 at 8:48
Robin Green
22.6k876156
asked Nov 25 '18 at 3:38
isPrimeisPrime
649
edited Nov 25 '18 at 8:48
Robin Green
22.6k876156
asked Nov 25 '18 at 3:38
isPrimeisPrime
649
edited Nov 25 '18 at 8:48
Robin Green
22.6k876156
edited Nov 25 '18 at 8:48
Robin Green
22.6k876156
edited Nov 25 '18 at 8:48
Robin Green
22.6k876156
22.6k876156
asked Nov 25 '18 at 3:38
isPrimeisPrime
649
asked Nov 25 '18 at 3:38
isPrimeisPrime
649
asked Nov 25 '18 at 3:38
isPrimeisPrime
649
649
add a comment |
add a comment |
1 Answer
1
active
oldest
votes
2
You are having basic instantiation problems with regards on what a proof is. See for example this code and try to understand what you are missing:
Require Import Coq.Reals.Reals.
Open Scope R_scope.
Definition Point := Type.
Record massPoint: Type := cons { number: R; point: Point}.
Variable add_MP: massPoint -> massPoint -> massPoint.
Variable sub_MP: massPoint -> massPoint -> massPoint.
Definition isVector (v : massPoint) :=
exists A B : Point, v = add_MP (cons (-1) A) (cons 1 B).
Record Vector : Type := vecCons { mpOf : massPoint; proof : isVector mpOf }.
Definition point_sub (p1 p2: massPoint) : Vector.
Proof.
refine (vecCons (sub_MP p1 p2) _).
repeat eexists.
answered Nov 25 '18 at 3:59
ejgallegoejgallego
5,4691926
It looks like Coq cannot find the supporting mass point A and B. So I think it should beDefinition point_sub (p1 p2: massPoint) : Vector := vecCons (sub_MP p1 p2) add_MP (cons (-1) (point p1))(cons 1 (point p2)).But coq kernel is still complainingwhile it is expected to have type "isVector (sub_MP p1 p2)".I feel like I don't have enough commands in my proof repertoire to tackle it. Or I didn't understand your hint well enough. If possible, could you please elaborate a bit? Much appreciate your way of giving hints.
– isPrime
Nov 25 '18 at 4:46
You need to find ?A ?B such that ` sub_MP p1 p2 = add_MP {| number := -1; point := ?A |} {| number := 1; point := ?B |}` The way you write the above term doesn't make sense to the Coq typer, you are expected to write a term with the above type.
– ejgallego
Nov 25 '18 at 5:20
Honestly, the syntax is exactly the help I need. I can’t figure out how to write it in a way that Coq understands. I still lack the knowledge of it. If you decide to write it out, would you please also explain why the syntax is written that way? I want to understand the connections.
– isPrime
Nov 25 '18 at 15:31
You need to proveLemma my_proof : exists A B, sub_MP p1 p2 = add_MP {| number := -1; point := A |} {| number := 1; point := B |}, then you can usemy_proofin the construction of your record. But I'd say you need to take a course in Coq first, so you learn the basic syntax and typing rules first.
– ejgallego
Nov 25 '18 at 16:31
1
Thanks for the further hint. I'm able to construct that new record using the following syntaxDefinition mp_sub (p1 p2: massPoint) : Vector:= vecCons (sub_MP p1 p2) (mp_proof p1 p2).
– isPrime
Nov 25 '18 at 17:48
add a comment |
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You are having basic instantiation problems with regards on what a proof is. See for example this code and try to understand what you are missing:
Require Import Coq.Reals.Reals.
Open Scope R_scope.
Definition Point := Type.
Record massPoint: Type := cons { number: R; point: Point}.
Variable add_MP: massPoint -> massPoint -> massPoint.
Variable sub_MP: massPoint -> massPoint -> massPoint.
Definition isVector (v : massPoint) :=
exists A B : Point, v = add_MP (cons (-1) A) (cons 1 B).
Record Vector : Type := vecCons { mpOf : massPoint; proof : isVector mpOf }.
Definition point_sub (p1 p2: massPoint) : Vector.
Proof.
refine (vecCons (sub_MP p1 p2) _).
repeat eexists.
answered Nov 25 '18 at 3:59
ejgallegoejgallego
5,4691926
It looks like Coq cannot find the supporting mass point A and B. So I think it should beDefinition point_sub (p1 p2: massPoint) : Vector := vecCons (sub_MP p1 p2) add_MP (cons (-1) (point p1))(cons 1 (point p2)).But coq kernel is still complainingwhile it is expected to have type "isVector (sub_MP p1 p2)".I feel like I don't have enough commands in my proof repertoire to tackle it. Or I didn't understand your hint well enough. If possible, could you please elaborate a bit? Much appreciate your way of giving hints.
– isPrime
Nov 25 '18 at 4:46
You need to find ?A ?B such that ` sub_MP p1 p2 = add_MP {| number := -1; point := ?A |} {| number := 1; point := ?B |}` The way you write the above term doesn't make sense to the Coq typer, you are expected to write a term with the above type.
– ejgallego
Nov 25 '18 at 5:20
Honestly, the syntax is exactly the help I need. I can’t figure out how to write it in a way that Coq understands. I still lack the knowledge of it. If you decide to write it out, would you please also explain why the syntax is written that way? I want to understand the connections.
– isPrime
Nov 25 '18 at 15:31
You need to proveLemma my_proof : exists A B, sub_MP p1 p2 = add_MP {| number := -1; point := A |} {| number := 1; point := B |}, then you can usemy_proofin the construction of your record. But I'd say you need to take a course in Coq first, so you learn the basic syntax and typing rules first.
– ejgallego
Nov 25 '18 at 16:31
1
Thanks for the further hint. I'm able to construct that new record using the following syntaxDefinition mp_sub (p1 p2: massPoint) : Vector:= vecCons (sub_MP p1 p2) (mp_proof p1 p2).
– isPrime
Nov 25 '18 at 17:48
add a comment |
2
You are having basic instantiation problems with regards on what a proof is. See for example this code and try to understand what you are missing:
Require Import Coq.Reals.Reals.
Open Scope R_scope.
Definition Point := Type.
Record massPoint: Type := cons { number: R; point: Point}.
Variable add_MP: massPoint -> massPoint -> massPoint.
Variable sub_MP: massPoint -> massPoint -> massPoint.
Definition isVector (v : massPoint) :=
exists A B : Point, v = add_MP (cons (-1) A) (cons 1 B).
Record Vector : Type := vecCons { mpOf : massPoint; proof : isVector mpOf }.
Definition point_sub (p1 p2: massPoint) : Vector.
Proof.
refine (vecCons (sub_MP p1 p2) _).
repeat eexists.
answered Nov 25 '18 at 3:59
ejgallegoejgallego
5,4691926
It looks like Coq cannot find the supporting mass point A and B. So I think it should beDefinition point_sub (p1 p2: massPoint) : Vector := vecCons (sub_MP p1 p2) add_MP (cons (-1) (point p1))(cons 1 (point p2)).But coq kernel is still complainingwhile it is expected to have type "isVector (sub_MP p1 p2)".I feel like I don't have enough commands in my proof repertoire to tackle it. Or I didn't understand your hint well enough. If possible, could you please elaborate a bit? Much appreciate your way of giving hints.
– isPrime
Nov 25 '18 at 4:46
You need to find ?A ?B such that ` sub_MP p1 p2 = add_MP {| number := -1; point := ?A |} {| number := 1; point := ?B |}` The way you write the above term doesn't make sense to the Coq typer, you are expected to write a term with the above type.
– ejgallego
Nov 25 '18 at 5:20
Honestly, the syntax is exactly the help I need. I can’t figure out how to write it in a way that Coq understands. I still lack the knowledge of it. If you decide to write it out, would you please also explain why the syntax is written that way? I want to understand the connections.
– isPrime
Nov 25 '18 at 15:31
You need to proveLemma my_proof : exists A B, sub_MP p1 p2 = add_MP {| number := -1; point := A |} {| number := 1; point := B |}, then you can usemy_proofin the construction of your record. But I'd say you need to take a course in Coq first, so you learn the basic syntax and typing rules first.
– ejgallego
Nov 25 '18 at 16:31
1
Thanks for the further hint. I'm able to construct that new record using the following syntaxDefinition mp_sub (p1 p2: massPoint) : Vector:= vecCons (sub_MP p1 p2) (mp_proof p1 p2).
– isPrime
Nov 25 '18 at 17:48
add a comment |
2
2
2
You are having basic instantiation problems with regards on what a proof is. See for example this code and try to understand what you are missing:
Require Import Coq.Reals.Reals.
Open Scope R_scope.
Definition Point := Type.
Record massPoint: Type := cons { number: R; point: Point}.
Variable add_MP: massPoint -> massPoint -> massPoint.
Variable sub_MP: massPoint -> massPoint -> massPoint.
Definition isVector (v : massPoint) :=
exists A B : Point, v = add_MP (cons (-1) A) (cons 1 B).
Record Vector : Type := vecCons { mpOf : massPoint; proof : isVector mpOf }.
Definition point_sub (p1 p2: massPoint) : Vector.
Proof.
refine (vecCons (sub_MP p1 p2) _).
repeat eexists.
answered Nov 25 '18 at 3:59
ejgallegoejgallego
5,4691926
You are having basic instantiation problems with regards on what a proof is. See for example this code and try to understand what you are missing:
Require Import Coq.Reals.Reals.
Open Scope R_scope.
Definition Point := Type.
Record massPoint: Type := cons { number: R; point: Point}.
Variable add_MP: massPoint -> massPoint -> massPoint.
Variable sub_MP: massPoint -> massPoint -> massPoint.
Definition isVector (v : massPoint) :=
exists A B : Point, v = add_MP (cons (-1) A) (cons 1 B).
Record Vector : Type := vecCons { mpOf : massPoint; proof : isVector mpOf }.
Definition point_sub (p1 p2: massPoint) : Vector.
Proof.
refine (vecCons (sub_MP p1 p2) _).
repeat eexists.
answered Nov 25 '18 at 3:59
ejgallegoejgallego
5,4691926
answered Nov 25 '18 at 3:59
ejgallegoejgallego
5,4691926
answered Nov 25 '18 at 3:59
ejgallegoejgallego
5,4691926
answered Nov 25 '18 at 3:59
ejgallegoejgallego
5,4691926
5,4691926
It looks like Coq cannot find the supporting mass point A and B. So I think it should beDefinition point_sub (p1 p2: massPoint) : Vector := vecCons (sub_MP p1 p2) add_MP (cons (-1) (point p1))(cons 1 (point p2)).But coq kernel is still complainingwhile it is expected to have type "isVector (sub_MP p1 p2)".I feel like I don't have enough commands in my proof repertoire to tackle it. Or I didn't understand your hint well enough. If possible, could you please elaborate a bit? Much appreciate your way of giving hints.
– isPrime
Nov 25 '18 at 4:46
You need to find ?A ?B such that ` sub_MP p1 p2 = add_MP {| number := -1; point := ?A |} {| number := 1; point := ?B |}` The way you write the above term doesn't make sense to the Coq typer, you are expected to write a term with the above type.
– ejgallego
Nov 25 '18 at 5:20
Honestly, the syntax is exactly the help I need. I can’t figure out how to write it in a way that Coq understands. I still lack the knowledge of it. If you decide to write it out, would you please also explain why the syntax is written that way? I want to understand the connections.
– isPrime
Nov 25 '18 at 15:31
You need to proveLemma my_proof : exists A B, sub_MP p1 p2 = add_MP {| number := -1; point := A |} {| number := 1; point := B |}, then you can usemy_proofin the construction of your record. But I'd say you need to take a course in Coq first, so you learn the basic syntax and typing rules first.
– ejgallego
Nov 25 '18 at 16:31
1
Thanks for the further hint. I'm able to construct that new record using the following syntaxDefinition mp_sub (p1 p2: massPoint) : Vector:= vecCons (sub_MP p1 p2) (mp_proof p1 p2).
– isPrime
Nov 25 '18 at 17:48
add a comment |
It looks like Coq cannot find the supporting mass point A and B. So I think it should beDefinition point_sub (p1 p2: massPoint) : Vector := vecCons (sub_MP p1 p2) add_MP (cons (-1) (point p1))(cons 1 (point p2)).But coq kernel is still complainingwhile it is expected to have type "isVector (sub_MP p1 p2)".I feel like I don't have enough commands in my proof repertoire to tackle it. Or I didn't understand your hint well enough. If possible, could you please elaborate a bit? Much appreciate your way of giving hints.
– isPrime
Nov 25 '18 at 4:46
You need to find ?A ?B such that ` sub_MP p1 p2 = add_MP {| number := -1; point := ?A |} {| number := 1; point := ?B |}` The way you write the above term doesn't make sense to the Coq typer, you are expected to write a term with the above type.
– ejgallego
Nov 25 '18 at 5:20
Honestly, the syntax is exactly the help I need. I can’t figure out how to write it in a way that Coq understands. I still lack the knowledge of it. If you decide to write it out, would you please also explain why the syntax is written that way? I want to understand the connections.
– isPrime
Nov 25 '18 at 15:31
You need to proveLemma my_proof : exists A B, sub_MP p1 p2 = add_MP {| number := -1; point := A |} {| number := 1; point := B |}, then you can usemy_proofin the construction of your record. But I'd say you need to take a course in Coq first, so you learn the basic syntax and typing rules first.
– ejgallego
Nov 25 '18 at 16:31
1
Thanks for the further hint. I'm able to construct that new record using the following syntaxDefinition mp_sub (p1 p2: massPoint) : Vector:= vecCons (sub_MP p1 p2) (mp_proof p1 p2).
– isPrime
Nov 25 '18 at 17:48
It looks like Coq cannot find the supporting mass point A and B. So I think it should be
Definition point_sub (p1 p2: massPoint) : Vector := vecCons (sub_MP p1 p2) add_MP (cons (-1) (point p1))(cons 1 (point p2)). But coq kernel is still complaining while it is expected to have type "isVector (sub_MP p1 p2)". I feel like I don't have enough commands in my proof repertoire to tackle it. Or I didn't understand your hint well enough. If possible, could you please elaborate a bit? Much appreciate your way of giving hints.– isPrime
Nov 25 '18 at 4:46
It looks like Coq cannot find the supporting mass point A and B. So I think it should be
Definition point_sub (p1 p2: massPoint) : Vector := vecCons (sub_MP p1 p2) add_MP (cons (-1) (point p1))(cons 1 (point p2)). But coq kernel is still complaining while it is expected to have type "isVector (sub_MP p1 p2)". I feel like I don't have enough commands in my proof repertoire to tackle it. Or I didn't understand your hint well enough. If possible, could you please elaborate a bit? Much appreciate your way of giving hints.– isPrime
Nov 25 '18 at 4:46
You need to find ?A ?B such that ` sub_MP p1 p2 = add_MP {| number := -1; point := ?A |} {| number := 1; point := ?B |}` The way you write the above term doesn't make sense to the Coq typer, you are expected to write a term with the above type.
– ejgallego
Nov 25 '18 at 5:20
You need to find ?A ?B such that ` sub_MP p1 p2 = add_MP {| number := -1; point := ?A |} {| number := 1; point := ?B |}` The way you write the above term doesn't make sense to the Coq typer, you are expected to write a term with the above type.
– ejgallego
Nov 25 '18 at 5:20
Honestly, the syntax is exactly the help I need. I can’t figure out how to write it in a way that Coq understands. I still lack the knowledge of it. If you decide to write it out, would you please also explain why the syntax is written that way? I want to understand the connections.
– isPrime
Nov 25 '18 at 15:31
Honestly, the syntax is exactly the help I need. I can’t figure out how to write it in a way that Coq understands. I still lack the knowledge of it. If you decide to write it out, would you please also explain why the syntax is written that way? I want to understand the connections.
– isPrime
Nov 25 '18 at 15:31
You need to prove
Lemma my_proof : exists A B, sub_MP p1 p2 = add_MP {| number := -1; point := A |} {| number := 1; point := B |}, then you can use my_proof in the construction of your record. But I'd say you need to take a course in Coq first, so you learn the basic syntax and typing rules first.– ejgallego
Nov 25 '18 at 16:31
You need to prove
Lemma my_proof : exists A B, sub_MP p1 p2 = add_MP {| number := -1; point := A |} {| number := 1; point := B |}, then you can use my_proof in the construction of your record. But I'd say you need to take a course in Coq first, so you learn the basic syntax and typing rules first.– ejgallego
Nov 25 '18 at 16:31
1
1
Thanks for the further hint. I'm able to construct that new record using the following syntax
Definition mp_sub (p1 p2: massPoint) : Vector:= vecCons (sub_MP p1 p2) (mp_proof p1 p2).– isPrime
Nov 25 '18 at 17:48
Thanks for the further hint. I'm able to construct that new record using the following syntax
Definition mp_sub (p1 p2: massPoint) : Vector:= vecCons (sub_MP p1 p2) (mp_proof p1 p2).– isPrime
Nov 25 '18 at 17:48
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